Sea ice thickness product data evaluation and fusion method based on finite true value

Abstract

The invention discloses a method for evaluating and fusing sea ice thickness product data based on a finite true value. The method comprises the following steps: carrying out precondition inspection of a TC algorithm on to-be-evaluated and fused product data, and establishing triple data of the TC algorithm; calculating the error root mean square of the triple data and the correlation between the error root mean square and the sea ice thickness truth value; the method comprises the following steps: extracting an abnormal data set of triple data, recalibrating the abnormal data set, calculating an error variance, an abnormal value fusion weight and an abnormal value fusion time sequence of the abnormal data set, and finally calculating a multi-source fusion SIT data set to realize sea ice thickness product data fusion. According to the evaluation and fusion method, evaluation and fusion can be carried out on sea ice satellite data under a finite true value condition by utilizing a TC algorithm, large-range and long-time series sea ice thickness data can be accurately evaluated, and the precision and spatial resolution of result data are remarkably improved by optimizing a data fusion process.

Description

Technical Field

[0001] The present invention belongs to the field of polar sea ice, and in particular to a method for evaluating and fusing sea ice thickness product data based on finite true values. Background Art

[0002] As a key environmental factor in the climate system, sea ice acts as a barrier to the exchange of energy, water and materials between the ocean and the atmosphere. It has a profound impact on the global climate system through complex physical feedback mechanisms, including atmospheric circulation, ocean water cycle, and the regulation of temperature, salinity and heat balance. The reduction of Arctic sea ice not only affects global climate patterns, but also has many impacts on human society, including promoting the opening of shipping routes, the exploitability of natural resources and the enhancement of the region's strategic position. With the reduction of Arctic sea ice, seasonal navigation becomes possible, while providing opportunities for the exploration of new shipping routes. The rich natural resources in the Arctic region, which were previously difficult to reach due to the thick ice cover, are now feasible to develop as the sea ice melts. This not only promotes trade between energy-demanding countries, but also enhances the importance of Arctic shipping routes in the global economy and geopolitics.

[0003] Although there are a variety of sea ice thickness observation technologies, they have limitations in terms of time span, spatial resolution and observation accuracy, resulting in incompleteness and poor reliability of observation data. At present, it is costly to obtain high-quality measured data, and it is difficult to achieve continuous spatiotemporal observations. At present, the existing sea ice thickness data mainly come from satellite remote sensing and numerical models. Although these methods have their advantages, they still have shortcomings in accuracy and resolution. Field observations, as a key means to assess the reliability of these data products, are difficult to be widely used due to their high cost, limited resolution and uneven distribution. This limits the comprehensive evaluation of the performance of polar sea ice thickness data products. Therefore, researchers currently rely more on comparing the differences in characteristics of different data sources, using measured data as an auxiliary reference rather than directly using them for accurate assessment of sea ice thickness and data fusion.

[0004] Multi-source data fusion technology can complement each other's strengths, reduce uncertainty and improve the temporal and spatial resolution of data by integrating data from different sources and accuracies. This method can integrate high-precision measured products when measured data is sufficient, or integrate data sets of different accuracies when data is insufficient. At present, weighted average (WM) and optimal interpolation (OI) are two commonly used data fusion methods, although they may have errors in specific sea areas. The TC algorithm is an effective means to estimate satellite product errors in the absence of measured data. It estimates the time series error and correlation coefficient of sea ice thickness based on three sets of data that are independent of each other and linearly correlated with the true value. This method does not require extensive measured data, which is particularly important for verifying the thickness of sea ice in unobserved areas, and has been applied in many fields, such as the measurement of sea surface wind speed, soil moisture and land snow depth. Summary of the invention

[0005] The purpose of the invention is to provide a method for evaluating and fusing sea ice thickness product data based on finite true values, which can accurately evaluate sea ice thickness data over a large range and for a long time series, and can improve the accuracy and spatial resolution of the resulting data by optimizing the data fusion process.

[0006] Technical solution: The method for evaluating and fusing sea ice thickness product data based on finite true value of the present invention comprises the following steps:

[0007] Step 1: Perform a prerequisite test of the TC algorithm on the product data to be evaluated and fused, obtain product data that meets the data requirements of the TC algorithm, and then use the product data that meets the data requirements to establish the triple data of the TC algorithm;

[0008] Step 2, calculating the root mean square error of the triplet data and the correlation between the triplet data and the true value of the sea ice thickness, so as to realize the evaluation and processing of the triplet data;

[0009] Step 3: extract the anomaly data set of the triple data, recalibrate the anomaly data set of the triple data, calculate the error variance and outlier fusion weight of the recalibrated anomaly data set of the triple data, calculate the outlier fusion time series, and finally use the outlier fusion time series and the climatological mean to calculate the multi-source fused SIT data set to realize the fusion of sea ice thickness product data.

[0010] Furthermore, in step 1, the specific steps of performing the TC algorithm premise test on the product data to be evaluated and fused are as follows:

[0011] Step 1.1, select three sets of product data to be evaluated and integrated;

[0012] Step 1.2: Linearly fit the three selected product data sets with the reference data set, and determine the significance of the linear relationship of the linear fitting results through significance check. If the linear relationship is significant, indicating that the three product data sets are linearly correlated with the reference data set, then proceed to step 1.3; otherwise, return to step 1.1 and reselect three product data sets to be evaluated and fused;

[0013] Step 1.3, obtain the random errors of the three groups of product data based on the linear fitting results, and then use the random errors to further calculate the covariance, so as to evaluate the error correlation of the three groups of product data. If the errors of the three groups of product data are uncorrelated, the selected three groups of product data meet the TC algorithm data requirements, otherwise return to step 1.1 to reselect three groups of product data to be evaluated and fused.

[0014] Furthermore, in step 1.2, the fitting formula for linear fitting of the three selected product data sets with the reference data set is:

[0015] SIT i =α i +β i SIT true +ε i

[0016] In the formula, SIT i is the product data i in the triple data, i∈{X,Y,Z}, SIT true is the true value of sea ice thickness, ε i is the random error, β i is the deviation coefficient of the product data of sea ice thickness relative to the true value of sea ice thickness, α i is the deviation intercept of the sea ice thickness product data relative to the true value of sea ice thickness.

[0017] Furthermore, in step 1.2, the specific steps for judging the significance of the linear relationship of the linear fitting results through significance check are as follows:

[0018] Firstly, the linear fitting results of three sets of product data and the reference data set are obtained;

[0019] Then the test level α was set to 0.05, and the Mann-Whitney-U test method was used to calculate the significance and obtain the test result p value;

[0020] Finally, the p-value of the verification result is used to determine whether the linear relationship between the three groups of product data and the reference data set is significant. If the p-value of the verification result meets the set significance threshold, it is judged to be significant, otherwise it is not significant.

[0021] Furthermore, in step 1.3, the specific steps for evaluating the error correlation of the three sets of product data are as follows:

[0022] Firstly, the random errors of three groups of product data are extracted to obtain three groups of random errors;

[0023] Then calculate the correlation between the three groups of random errors and obtain the error correlation;

[0024] Finally, the error correlation is compared with the correlation threshold. If the error correlation ≤ the correlation threshold, it is considered that the error correlation between each data set is low, which meets the premise test of the TC algorithm and is qualified triple data. Otherwise, it does not meet the TC premise assumption and is unqualified triple data.

[0025] Furthermore, in step 2, the specific steps for calculating the root mean square error of the triplet data and the correlation with the true value of the sea ice thickness are:

[0026] Step 2.1: Calculate the covariance C for any two sets of product data in the triple data. i，j for:

[0027]

[0028] Where SIT i and SIT j are any two sets of product data in the triple data, Cov(·) represents the covariance operation, is the variance of the true value of sea ice thickness, β i and β j are the deviation coefficients of the two sets of sea ice thickness product data relative to the true value of sea ice thickness, For data SIT i The random error variance of

[0029] Step 2.2, calculate the root mean square error of the random errors of the three groups of data in the triple data respectively for:

[0030]

[0031] In the formula, C 11 , C 22 , C 33 , C 12 , C 13 and C 23 are the covariances of any two sets of product data in the triplet data;

[0032] Step 3.3, calculate the correlation coefficients between the three sets of product data and the true value of sea ice thickness respectively:

[0033]

[0034] In the formula, R T , i represents the correlation coefficient between product data i and the true value of sea ice thickness.

[0035] Furthermore, in step 3, the expression for extracting the abnormal data set of triple data is:

[0036]

[0037] In the formula, is the original time series data of product data i, is the climatological mean data of product data i, N is the valid number of years of triple data, YR is the year, DOY is a day in a year, i∈{X,Y,Z}.

[0038] Furthermore, in step 3, the specific steps for recalibrating the abnormal data set of triple data are as follows:

[0039] First set ANO X 、ANO Y and ANO Z There are three abnormal data sets for triplet data;

[0040] Then the abnormal data set ANO of the product data X of the triple data X As a reference dataset;

[0041] Then the other two abnormal data sets ANO Y and ANO Z Recalibrate to the reference data set, the specific calculation formula is:

[0042] ANO X * =ANO x

[0043]

[0044]

[0045] In the formula, ANO X * , ANO Y * and ANO Z * are the recalibrated abnormal data sets, and They are respectively the abnormal data set ANO Y and ANO Z The multiplicative calibration parameter is:

[0046]

[0047] In the formula, For the abnormal data set ANO X and ANO Y The time series covariance of For the abnormal data set ANO X and ANO Z The time series covariance of For the abnormal data set ANO Y and ANO Z The time series covariance of .

[0048] Furthermore, in step 3, the specific steps of calculating the error variance of the abnormal data set of the recalibrated triple data and the outlier fusion weight are:

[0049] First, the error variance of the abnormal data set of the recalibrated triple data is calculated as:

[0050]

[0051] In the formula, is the recalibrated abnormal data set ANO X * The error variance is is the recalibrated abnormal data set ANO Y * The error variance is is the recalibrated abnormal data set ANO Z * The error variance of , <·> represents the time average;

[0052] Then the outlier fusion weight of the abnormal data set of the recalibrated triple data is calculated as:

[0053]

[0054] In the formula, and They are respectively the abnormal data set ANO X 、ANO Y and ANO Z The outlier fusion weights.

[0055] Furthermore, in step 3, the specific steps of calculating the multi-source fused SIT dataset using the outlier fusion time series and the climatological mean are as follows:

[0056] First, the outlier fusion time series is calculated as:

[0057]

[0058] In the formula, ANO Fuse Fusion of time series for outliers;

[0059] Then the multi-source fused SIT dataset is calculated as:

[0060]

[0061] Where SIT Fuse It is a multi-source fusion SIT dataset. It is the climatological mean data of the product data X of the triple data.

[0062] Compared with the prior art, the present invention has the following beneficial effects: the TC algorithm can be used to evaluate and fuse sea ice satellite data under finite truth conditions, and can accurately evaluate sea ice thickness data over a large range and for a long time series, and by optimizing the data fusion process, the accuracy and spatial resolution of the result data are significantly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 is a flow chart of the method of the present invention;

[0064] Figure 2 is the linear fitting result of the true value of sea ice thickness and product data

[0065] Figure 3 This is the spatial difference map between OIB and SIT fusion products during the period 2012-2019;

[0066] Figure 4 This is the meridional wavenumber spectrum of the triplet data in the [78. N-80. N, 343. E-355. E] sea area on November 21, 2017. DETAILED DESCRIPTION

[0067] The technical solution of the present invention is described in detail below with reference to the accompanying drawings, but the protection scope of the present invention is not limited to the embodiments.

[0068] Embodiment 1:

[0069] like Figure 1 As shown, the method for evaluating and fusing sea ice thickness product data based on finite truth values ​​disclosed in the present invention comprises the following steps:

[0070] Step 1: Perform a prerequisite check of the TC (Triple Collocation) algorithm on the product data to be evaluated and fused, obtain product data that meets the data requirements of the TC algorithm, and then use the product data that meets the data requirements to establish the triple data of the TC algorithm;

[0071] Step 2, calculating the root mean square error of the triplet data and the correlation between the triplet data and the true value of the sea ice thickness, so as to realize the evaluation and processing of the triplet data;

[0072] Step 3: extract the anomaly data set of the triple data, recalibrate the anomaly data set of the triple data, calculate the error variance and outlier fusion weight of the recalibrated anomaly data set of the triple data, calculate the outlier fusion time series, and finally use the outlier fusion time series and the climatological mean to calculate the multi-source fused SIT data set to realize the fusion of sea ice thickness product data.

[0073] The present invention can fuse sea ice thickness data of different sources and accuracies into daily sea ice thickness data with a spatial resolution of 5 km, and the data accuracy can be improved compared with its climatological parent product data, thereby providing more accurate and reliable data support for global climate change research and resource development in the Arctic region.

[0074] Furthermore, in step 1, the specific steps of performing the TC algorithm premise test on the product data to be evaluated and fused are as follows:

[0075] Step 1.1, select three sets of product data to be evaluated and integrated;

[0076] Step 1.2: Linearly fit the three selected product data sets with the reference data set, and determine the significance of the linear relationship of the linear fitting results through significance check. If the linear relationship is significant, indicating that the three product data sets are linearly correlated with the reference data set, then proceed to step 1.3; otherwise, return to step 1.1 and reselect three product data sets to be evaluated and fused;

[0077] Step 1.3, obtain the random errors of the three groups of product data based on the linear fitting results, and then use the random errors to further calculate the covariance, so as to evaluate the error correlation of the three groups of product data. If the errors of the three groups of product data are uncorrelated, the selected three groups of product data meet the TC algorithm data requirements, otherwise return to step 1.1 to reselect three groups of product data to be evaluated and fused.

[0078] Furthermore, in step 1.2, the fitting formula for linear fitting of the three selected product data sets with the reference data set is:

[0079] SIT i =α i +β i SIT true +ε i

[0080] Where SIT i is the product data i in the triple data, i∈{X,Y,Z}, SITtrue is the true value of sea ice thickness, ε i is the random error, β i is the deviation coefficient of the product data of sea ice thickness relative to the true value of sea ice thickness, α i is the deviation intercept of the sea ice thickness product data relative to the true value of sea ice thickness.

[0081] Furthermore, in step 1.2, the specific steps for judging the significance of the linear relationship of the linear fitting results through significance check are as follows:

[0082] Firstly, the linear fitting results of the three sets of product data and the reference data set are obtained, wherein the linear fitting results include the values ​​of various parameters in the fitting formula of the linear fitting;

[0083] Then the test level θ=0.05 was set, and the Mann-Whitney-U test method was used to calculate the significance and obtain the test result p value;

[0084] Finally, the p-value of the verification result is used to determine whether the linear relationship between the three groups of product data and the reference data set is significant. If the p-value of the verification result meets the set significance threshold, that is, p<0.05, it is judged to be significant, otherwise it is not significant.

[0085] Furthermore, in step 1.3, the specific steps for evaluating the error correlation of the three sets of product data are as follows:

[0086] Firstly, the random errors of three groups of product data are extracted to obtain three groups of random errors;

[0087] Then the correlation between the three groups of random errors is calculated to obtain the error correlation. The correlation is solved using the corr function in Matlab.

[0088] Finally, the error correlation is compared with the correlation threshold. If the error correlation is ≤ the correlation threshold, it is considered that the error correlation between each data set is low, which meets the premise test of the TC algorithm and is qualified triple data. Otherwise, it does not meet the TC premise assumption and is unqualified triple data, and the TC algorithm cannot be evaluated and fused.

[0089] Furthermore, in step 2, the specific steps for calculating the root mean square error of the triplet data and the correlation with the true value of the sea ice thickness are:

[0090] Step 2.1, calculate the covariance C for any two sets of data in the triple data i，j for:

[0091]

[0092] Where SIT iand SIT j are any two sets of product data in the triple data, Cov(·) represents the covariance operation, is the variance of the true value of sea ice thickness, β i and β j are the deviation coefficients of the two sets of sea ice thickness product data relative to the true value of sea ice thickness, For data SIT i The random error variance of

[0093] Step 2.2, calculate the root mean square error of the random errors of the three groups of data in the triple data respectively for:

[0094]

[0095] In the formula, C 11 , C 22 , C 33 , C 12 , C 13 and C 23 are the covariances of any two sets of data in the triplet data;

[0096] Step 3.3, calculate the correlation coefficients between the three sets of product data and the true value of sea ice thickness respectively:

[0097]

[0098] In the formula, R T , i represents the correlation coefficient between product data i and the true value of sea ice thickness, thus calculating the correlation coefficients R between the three sets of product data 1-3 and the true value of sea ice thickness respectively T，1 , R T,2 and R T，3 .

[0099] Furthermore, in step 3, the expression for extracting the abnormal data set of triple data is:

[0100]

[0101] In the formula, is the original time series data of product data i, is the climatological mean data of product data i, N is the valid number of years of triple data, YR is the year, DOY is a day in a year, i∈{X,Y,Z}.

[0102] Furthermore, in step 3, the specific steps for recalibrating the abnormal data set of triple data are as follows:

[0103] First set ANOX 、ANO Y and ANO Z There are three abnormal data sets for triplet data;

[0104] Then the abnormal data set ANO of the product data X of the triple data X As a reference dataset;

[0105] Then the other two abnormal data sets ANO Y and ANO Z Recalibrate to the reference data set, the specific calculation formula is:

[0106] ANO X * =ANO X

[0107]

[0108] In the formula, ANO X * , ANO Y * and ANO Z * are the recalibrated abnormal data sets, and They are respectively the abnormal data set ANO Y and ANO Z The multiplicative calibration parameter is:

[0109]

[0110] In the formula, For the abnormal data set ANO X and ANO Y The time series covariance of For the abnormal data set ANO X and ANO Z The time series covariance of For the abnormal data set ANO Y and ANO Z The time series covariance of .

[0111] Furthermore, in step 3, the specific steps of calculating the error variance of the abnormal data set of the recalibrated triple data and the outlier fusion weight are:

[0112] First, the error variance of the abnormal data set of the recalibrated triple data is calculated as:

[0113]

[0114] In the formula, is the recalibrated abnormal data set ANO X * The error variance is is the recalibrated abnormal data set ANO Y * The error variance is is the recalibrated abnormal data set ANO Z * The error variance of , <·> represents the time average;

[0115] Then the outlier fusion weight of the abnormal data set of the recalibrated triple data is calculated as:

[0116]

[0117]

[0118] In the formula, and They are respectively the abnormal data set ANO X 、ANO Y and ANO Z The outlier fusion weights.

[0119] Furthermore, in step 3, the specific steps of calculating the multi-source fused SIT dataset using the outlier fusion time series and the climatological mean are as follows:

[0120] First, the outlier fusion time series is calculated as:

[0121]

[0122] In the formula, ANO Fuse Fusion of time series for outliers;

[0123] Then the multi-source fused SIT dataset is calculated as:

[0124]

[0125] In the formula, SIT Fuse It is a multi-source fusion SIT dataset. It is the climatological mean data of the product data X of the triple data.

[0126] In order to verify the effectiveness of the present invention, the evaluation and fusion method of the present invention was experimentally verified, and the data used in the experiment included true value data Upward-Looking Sonar (ULS), Operation IceBridge (OIB) in-situ measurement data and product data, wherein the product data sources include CPOM, CS2SMOS, PIOMAS and APP-x product data. Among them, CS2SMOS is the fusion product data of CryoSat-2 and the soil moisture and ocean salinity satellite SMOS, APP-x is the product data obtained by inverting the optical satellite AVHRR based on the energy budget model; PIOMAS is the ice-sea model product data that assimilates sea surface temperature and sea ice density; CPOM is the Arctic sea ice thickness product data based on CS2 radar altimeter data; in terms of spatial resolution, CS2SMOS is weekly product data, APP-x and PIOMAS are daily product data, and CPOM is monthly product data; gridded data include daily polar coordinate grid data released by the National Snow and Ice Data Center (NSIDC); ULS is data from 2010 to 2021, and OIB is data from March to April 2010-2019.

[0127] For the selection of the true value of sea ice thickness data, the present invention uses the measured data ULS and OIB as the true value data. However, the spatial range of OIB and ULS measured data is limited, and most of them are distributed in the western hemisphere of the Arctic. In order to make up for this defect, the present invention uses the product data as a pseudo-true value for premise inspection, making up for the defect of insufficient temporal and spatial resolution of the measured data, and solving the problem of insufficient representativeness of the measured data. When SIT true When ULS is selected, the present invention uses the time and space scales of the fixed points A, B and D of ULS as reference and uses the inverse distance weighted interpolation method for time and space matching; when SIT true When OIB is selected, the present invention uses the spatial distribution of the EASE2 grid of NSIDC as a reference and the temporal distribution of the OIB data as a reference, and uses the inverse distance weighted interpolation method for time-space matching; when SIT true When product data is selected, the present invention uses the spatiotemporal distribution of the product data as a reference, uses the inverse distance weighted interpolation method to perform spatiotemporal matching, and then performs a premise check.

[0128] When performing the premise test of the TC algorithm, the linear fitting results of the product data and the reference data set are as follows: Figure 2 As shown, the linear fitting results were subjected to Mann-Whitney-U test, and the results all showed p<0.001. The above linear fitting results had a significant relationship, and the linear relationship between the true value, pseudo-true value and product data was established.

[0129] Then, the error after linear fitting of the product is obtained, and the covariance between the errors of the product data is calculated. When the pseudo-true value method is used for testing, there are two error covariance calculation results for every two products, which are averaged. The true value and pseudo-true value test results are shown in Table 1.

[0130] Table 1. Calculation results of product data error covariance

[0131]

[0132] In Table 1, except for the error covariance between CS2SMOS and CPOM, the error covariance between other product data is less than 0.2, and the results of the correlation test on the product data errors are within the acceptable range of the study. According to the error covariance, two triplet data are selectively constructed, namely triplet data (A): APP-x, PIOMAS and CS2SMOS, and triplet data (B): APP-x, PIOMAS and CPOM. Triplet data A and B are used for multi-source sea ice data product evaluation and fusion.

[0133] The TC algorithm is used to evaluate the sea ice thickness data without true value, which is specifically manifested in two indicators: correlation coefficient R and root mean square error RMSE. At the same time, the measured data OIB and ULS are used to verify the evaluation results of the sea ice thickness data. The results of the evaluation of OIB measured data and TC algorithm products are shown in Table 2; the results of the evaluation of ULS measured data and TC algorithm products are shown in Tables 3 and 4.

[0134] Table 2 Comparison of measured data OIB and TC algorithm evaluation product results

[0135]

[0136] Table 3 Comparison of measured data ULS and TC algorithm evaluation product results (triplet A)

[0137]

[0138]

[0139] Table 4 Comparison of measured data ULS and TC algorithm evaluation product results (triplet B)

[0140]

[0141] As can be seen from the table above, compared with the actual data evaluation, the correlation values ​​judged by the TC algorithm are different, but the correlation order of different products is consistent with the actual data evaluation results. Therefore, product evaluation without true value based on the TC algorithm can achieve the comparison of the advantages and disadvantages between product data, providing a reliable reference for selecting appropriate product data in different scenarios.

[0142] In the fusion results, when the triple data (A) is TC fused, the climatology of each product APP-x, PIOMAS and CS2SMOS in the triple data (A) is selected and added to the corresponding SIT anomaly fusion dataset of the product to obtain three SIT fusion datasets, which are respectively represented as Fused-A1, Fused-A2 and Fused-A3 in the following text; when the triple data (B) is TC fused, the climatology of each product APP-x, PIOMAS and CPOM in the triple data (B) is selected and added to the corresponding SIT anomaly fusion dataset of the product to obtain three SIT fusion datasets, which are respectively represented as Fused-B1, Fused-B2 and Fused-B3 in the following text. The three SIT parent products in the triple data (A), namely APP-x, PIOMAS, and CS2SMOS, and the three fusion products Fused-A1, Fused-A2, and Fused-A3, are evaluated for accuracy using OIB measured data through correlation (R), RMSE, and MAE. The results are shown in Table 5. Similarly, the accuracy of the parent products and fusion products in the triple data (B) is evaluated, and the results are shown in Table 6. The accuracy of the fusion products is evaluated using ULS in the same way, and the results are shown in Tables 7 and 8.

[0143] Table 5 Precision evaluation results of (A) SIT parent product and fusion product based on OIB for triple data

[0144] APP-x PIOMAS CS2SMOS Fused-A1 Fused-A2 Fused-A3 N 6660 6660 6660 6660 6660 6660 R 0.57 0.64 0.73 0.69 0.67 0.72 RMSE 0.89 0.73 0.65 0.87 0.70 0.67 MAE 0.73 0.52 0.48 0.73 0.50 0.48

[0145] Table 6 Precision evaluation results of (B) SIT parent product and fusion product based on OIB for triple data

[0146]

[0147]

[0148] Table 7 Precision evaluation results of (A) SIT parent product and fusion product based on ULS for triple data

[0149] APP-x PIOMAS CS2SMOS Fused-A1 Fused-A2 Fused-A3 N 5805 5805 5805 5805 5805 5805 R 0.63 0.75 0.72 0.72 0.77 0.75 RMSE 0.80 0.59 0.40 0.74 0.57 0.37 MAE 0.66 0.50 0.29 0.62 0.50 0.27

[0150] Table 8 Precision evaluation results of (B) SIT parent product and fusion product based on ULS for triple data

[0151] APP-x PIOMAS CPOM Fused-B1 Fused-B2 Fused-B3 N 5698 5698 5698 5698 5698 5698 R 0.62 0.72 0.55 0.69 0.74 0.65 RMSE 0.80 0.59 0.55 0.75 0.59 0.50 MAE 0.66 0.51 0.43 0.63 0.50 0.40

[0152] First, the relationship between the evaluation results of different measured products is determined. Since OIB data has larger accidental errors than ULS data, the accuracy evaluation of the fusion product based on OIB data is used as a supplement to the accuracy evaluation results of the fusion product based on ULS data.

[0153] By analyzing the above table, it is found that the accuracy evaluation results of the fusion products are better than the accuracy evaluation results of the products corresponding to the climatological data themselves when comparing the climatological products with the corresponding fusion products. Among them, in the verification using OIB measured data, there is no significant difference between the comparison results of the fusion product Fused-A3 obtained based on the fusion of CS2SMOS climatological data and triple data (A) outliers and the original CS2SMOS product. In the verification using ULS measured data, the accuracy evaluation results of the fusion product Fused-A3 obtained based on the fusion of CS2SMOS climatological data and triple data (A) outliers are better than the original CS2SMOS product. According to the above-mentioned OIB-based data evaluation results, which are supplemented by the ULS data evaluation results, the present invention believes that the accuracy of all fusion products is better than the corresponding climatological products. By comparing the fusion results with the product data, it is found that the fusion results have achieved an improvement in the accuracy of the corresponding climatological mean products. In the triple data (A), the fusion result Fused-A3 based on CS2SMOS climatological data has the best accuracy. In the triple data (B), the fusion product Fused-B1 based on APP-x climatological data, the fusion results Fused-B2 based on PIOMAS and CPOM, and Fused-B3 have better accuracy.

[0154] In terms of spatial distribution, the present invention matches all OIB data from 2012 to 2019 with the fusion products in time and space, and then draws a spatial distribution map of the difference between the measured data OIB and the fusion products, as shown in Figure 2. Figure 3 shown. Figure 3 In the figure, Figure (a) is Fused-A1, Figure (b) is Fused-A2, Figure (c) is Fused-A3, Figure (d) is Fused-B1, Figure (e) is Fused-B2, and Figure (f) is Fused-B3.

[0155] Depend on Figure 3It can be seen that in the fusion results of triple data (A), compared with other fusion products, Fused-A1 shows a larger difference result with the measured data. In the Beaufort and Chukchi Seas, Fused-A3 shows a smaller difference result with the measured data than Fused-A2; in other sea areas, the difference results of Fused-A3 and Fused-A2 are close to the measured data. In the fusion results of triple data (B), compared with other fusion products, Fused-B1 shows a larger difference result with the measured data. In the Beaufort and Chukchi Seas, Fused-B3 shows a smaller difference result with the measured data than Fused-B2; in the central Arctic Sea, Fused-B2 shows a smaller difference result with the measured data than Fused-B3; in other sea areas, the difference results of Fused-A3 and Fused-A2 are close to the measured data.

[0156] In summary, the TC algorithm can improve the accuracy of the original products corresponding to climatology. The fusion product with the highest accuracy has improved accuracy compared to all parent products. Before using the TC algorithm for product data fusion, it is important to select high-quality parent products to achieve high-precision fusion products.

[0157] In addition, the effective spatial resolution of the fusion result is studied. The present invention will take the fusion result of triple data (B) as an example to analyze the spatial resolution. First, the present invention will resample the APP-x and PIOMAS sea ice thickness product data in the triple data (B) into the CPOM product grid, fuse the three types of sea ice thickness data TC after resampling, and use the wavenumber spectrum method to measure the effective spatial resolution of the fusion product. Since the accuracy of the fusion product Fused-B1 based on APP-x climatological data is not as good as Fused-B2 and Fused-B3, and Fused-B3 is the fusion data based on CPOM climatological data, and the daily data of CPOM is obtained by copying and filling the monthly data, the present invention selects the fusion data Fused-B2 based on PIOMAS climatological data, and uses the wavenumber spectrum method to discuss its effective spatial resolution. First, the sequence data is detrended, and then the Black-Harris window is used to prevent spectral energy leakage, and the Burg method (MATLAB built-in function) is used to estimate its wavenumber spectrum. Taking November 21, 2017 as an example, the sea area with SIT measurement and latitude and longitude range of [78°N-80°N, 343°E-355°E] was selected as the study area to calculate the meridional spectra of CPOM, PIOMAS and the fusion product Fused-B2. The results are as follows: Figure 4 shown.

[0158] CPOM is a product data with a spatial resolution of 5km. The fused product Fused-B2 and CPOM show a relatively consistent energy attenuation law. Studies in the prior art show that the ideal spectral slope calculated by the quasi-geostrophic turbulence theory is about -2, and the wavenumber spectrum slope of the passive tracer moving along the isopycnal is also about -2. Sea ice is not a strict passive tracer. Studies in the prior art show that the thickness of sea ice is closely related to seawater temperature, salinity, etc., and the spectral slopes of the two are between -3 and -2. Therefore, the present invention believes that the reasonable spectral slope of SIT is also between -3 and -2. According to the nyquist folding frequency, the spatial resolution of the fused products Fused-B2 and CPOM can both reach 5km, while PIOMAS cannot identify mesoscale changes below 25km.

[0159] As described above, although the present invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the present invention itself. Various changes in form and details may be made without departing from the spirit and scope of the present invention as defined in the appended claims.

Claims

1. A method for evaluating and fusing sea ice thickness product data based on finite truth values, characterized in that: The steps include: Step 1: Perform a prerequisite test of the TC algorithm on the product data to be evaluated and fused, obtain product data that meets the data requirements of the TC algorithm, and then use the product data that meets the data requirements to establish the triple data of the TC algorithm; Step 2, calculating the root mean square error of the triplet data and the correlation between the triplet data and the true value of the sea ice thickness, so as to realize the evaluation and processing of the triplet data; Step 3: extract the anomaly data set of the triple data, recalibrate the anomaly data set of the triple data, calculate the error variance and outlier fusion weight of the recalibrated anomaly data set of the triple data, calculate the outlier fusion time series, and finally use the outlier fusion time series and the climatological mean to calculate the multi-source fused SIT data set to realize the fusion of sea ice thickness product data.

2. The method for evaluating and fusing sea ice thickness product data based on finite truth values ​​according to claim 1, characterized in that: In step 1, the specific steps for performing TC algorithm premise verification on the product data to be evaluated and fused are as follows: Step 1.1, select three sets of product data to be evaluated and integrated; Step 1.2: Linearly fit the three selected product data sets with the reference data set, and determine the significance of the linear relationship of the linear fitting results through significance check. If the linear relationship is significant, indicating that the three product data sets are linearly correlated with the reference data set, then proceed to step 1.3; otherwise, return to step 1.1 and reselect three product data sets to be evaluated and fused; Step 1.3, obtain the random errors of the three groups of product data based on the linear fitting results, and then use the random errors to further calculate the covariance, so as to evaluate the error correlation of the three groups of product data. If the errors of the three groups of product data are uncorrelated, the selected three groups of product data meet the TC algorithm data requirements, otherwise return to step 1.1 to reselect three groups of product data to be evaluated and fused.

3. The method for evaluating and fusing sea ice thickness product data based on finite truth values ​​according to claim 2, characterized in that: In step 1.2, the fitting formula for linear fitting of the three selected product data sets and the reference data set is: SIT i =α i +β i SIT true +ε i Where SIT i is the product data i in the triple data, i∈{X,Y,Z}, SIT true is the true value of sea ice thickness, ε i is the random error, β i is the deviation coefficient of the product data of sea ice thickness relative to the true value of sea ice thickness, α i is the deviation intercept of the sea ice thickness product data relative to the true value of sea ice thickness.

4. The method for evaluating and fusing sea ice thickness product data based on finite truth values ​​according to claim 2, characterized in that: In step 1.2, the specific steps for judging the significance of the linear relationship of the linear fitting results through significance test are as follows: Firstly, the linear fitting results of three sets of product data and the reference data set are obtained; Then the test level α was set to 0.05, and the Mann-Whitney-U test method was used to calculate the significance and obtain the test result p value; Finally, the p-value of the verification result is used to determine whether the linear relationship between the three groups of product data and the reference data set is significant. If the p-value of the verification result meets the set significance threshold, it is judged to be significant, otherwise it is not significant.

5. The method for evaluating and fusing sea ice thickness product data based on finite truth values ​​according to claim 2, characterized in that: In step 1.3, the specific steps for evaluating the error correlation of the three sets of product data are: Firstly, the random errors of three groups of product data are extracted to obtain three groups of random errors; Then calculate the correlation between the three groups of random errors and obtain the error correlation; Finally, the error correlation is compared with the correlation threshold. If the error correlation ≤ the correlation threshold, it is considered that the error correlation between each data set is low, which meets the premise test of the TC algorithm and is qualified triple data. Otherwise, it does not meet the TC premise assumption and is unqualified triple data.

6. The method for evaluating and fusing sea ice thickness product data based on finite truth values ​​according to claim 1, characterized in that: In step 2, the specific steps for calculating the root mean square error of the triplet data and the correlation with the true value of sea ice thickness are: Step 2.1: Calculate the covariance C for any two sets of product data in the triple data. i,j for: Where SIT i and SIT j are any two sets of product data in the triple data, Cov(·) represents the covariance operation, is the variance of the true value of sea ice thickness, β i and β j are the deviation coefficients of the two sets of sea ice thickness product data relative to the true value of sea ice thickness, For data SIT i The random error variance of Step 2.2, calculate the root mean square error of the random errors of the three groups of data in the triple data respectively for: In the formula, C 11 , C 22 , C 33 , C 12 , C 13 and C 23 are the covariances of any two sets of product data in the triplet data; Step 3.3, calculate the correlation coefficients between the three sets of product data and the true value of sea ice thickness respectively: In the formula, R T,i Represents the correlation coefficient between product data i and the true value of sea ice thickness.

7. The method for evaluating and fusing sea ice thickness product data based on finite truth values ​​according to claim 1, characterized in that: In step 3, the expression for extracting the abnormal data set of triple data is: In the formula, is the original time series data of product data i, is the climatological mean data of product data i, N is the valid number of years of triple data, YR is the year, DOY is a day in a year, i∈{X,Y,Z}.

8. The method for evaluating and fusing sea ice thickness product data based on finite truth values ​​according to claim 7, characterized in that: In step 3, the specific steps for recalibrating the abnormal data set of triple data are as follows: First set ANO X 、ANO Y and ANO z There are three abnormal data sets for triplet data; Then the abnormal data set ANO of the product data X of the triple data X As a reference dataset; Then the other two abnormal data sets ANO Y and ANO Z Recalibrate to the reference data set, the specific calculation formula is: YEAR X * =YEAR X In the formula, ANO X * , ANO Y * and ANO Z * are the recalibrated abnormal data sets, and They are respectively the abnormal data set ANO Y and ANO Z The multiplicative calibration parameter is calculated as follows: In the formula, For the abnormal data set ANO X and ANO Y The time series covariance of For the abnormal data set ANO X and ANO Z The time series covariance of For the abnormal data set ANO Y and ANO Z The time series covariance of .

9. The method for evaluating and fusing sea ice thickness product data based on finite truth values ​​according to claim 8, characterized in that: In step 3, the specific steps of calculating the error variance of the abnormal data set of the recalibrated triple data and the outlier fusion weight are: First, the error variance of the abnormal data set of the recalibrated triple data is calculated as: In the formula, is the recalibrated abnormal data set ANO X * The error variance is is the recalibrated abnormal data set ANO Y * The error variance is is the recalibrated abnormal data set ANO Z * The error variance of , <·> represents the time average; Then the outlier fusion weight of the abnormal data set of the recalibrated triple data is calculated as: In the formula, and They are respectively the abnormal data set ANO X 、ANO Y and ANO Z The outlier fusion weights.

10. The method for evaluating and fusing sea ice thickness product data based on finite truth values ​​according to claim 9, characterized in that: In step 3, the specific steps of calculating the multi-source fused SIT dataset using outlier fusion time series and climatological mean are as follows: First, the outlier fusion time series is calculated as: In the formula, ANO Fus Fusion of time series for outliers; Then the multi-source fused SIT dataset is calculated as: Where SIT Fuse It is a multi-source fusion SIT dataset. It is the climatological mean data of the product data X of the triple data.

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