Error quadratic sum decomposition method and system for distinguishing seasonal influence of global average sea temperature

Abstract

The invention relates to the technical field of data analysis, and provides an error quadratic sum decomposition method and system for distinguishing seasonal influence of global average sea temperature, and the method comprises the steps: carrying out the processing based on a prediction time sequence of global average sea temperature over the years provided by a preset sea temperature prediction model and an observation time sequence of global average sea temperature over the years obtained through observation; according to the method, the error sum of squares is obtained through calculation and analysis, the error sum of squares is accurately decomposed into the multi-year mean deviation sum of squares, the multi-year linear trend deviation sum of squares and the residual sum of squares, the error source of the sea temperature forecasting model can be finely analyzed, and the interpretability is improved.

Description

Technical Field

[0001] This invention relates to the technical field of data analysis, and more specifically, to a method and system for decomposing the sum of squared errors of global average sea surface temperature to differentiate seasonal effects. Background Technology

[0002] Establishing reasonable evaluation indicators for sea surface temperature (SST) forecasting models is crucial for validating their predictive power and improving ensemble forecasting models. The sum of squared errors (SSEs) is widely used as an indicator for evaluating SST forecasting prowess due to its excellent statistical properties and computational simplicity. While this method allows for the overall performance evaluation and ranking of SST forecasting models using a single numerical value, its fundamental limitation lies in its inability to decompose the specific sources of SST forecasting model errors. This hinders a more refined analysis of these error sources, making it difficult to effectively utilize forecast information and impede effective decision-making. Summary of the Invention

[0003] To address the problem that existing technologies cannot provide a more refined analysis of the errors in sea surface temperature (SST) forecasting models, this invention proposes a method for decomposing the sum of squared errors of global average SST to differentiate seasonal influences. This method allows for a more refined analysis of the specific sources of errors in SST forecasting models, thereby enhancing the practical value of forecast information.

[0004] To achieve the above-mentioned technical effects, the technical solution of the present invention is as follows: A method for decomposing the sum of squared errors of global mean sea surface temperature to differentiate seasonal effects includes the following steps: S10: Based on the historical global average sea surface temperature forecast time series and historical global average sea surface temperature prediction time series, obtain the multi-year global average sea surface temperature error time series. S20: Seasonally group and decompose the multi-year global average sea surface temperature error time series to obtain multiple error subsequences; S30: Perform independent linear regression analysis on the multiple error subsequences to obtain multiple trend fitting values; S40: Analyze and calculate the multiple trend fitting values ​​and the multiple error subsequences to obtain multiple error sums of squares, and decompose the multiple error sums of squares into multi-year mean deviation sums of squares, multi-year linear trend deviation sums of squares and residual sums of squares, respectively. S50: Using the sum of squared deviations of the multi-year mean, the sum of squared deviations of the multi-year linear trend, and the sum of squared residuals, the global average sea surface temperature prediction performance of the preset sea surface temperature forecasting model is evaluated, and the performance analysis results are obtained.

[0005] Preferably, in S10, the processing procedure is as follows: Let the historical global average sea surface temperature prediction time series be denoted as... , Represents each point in time throughout the year. i The observational data; the historical global average sea surface temperature forecast time series is denoted as , Represents each point in time throughout the year. i Forecast data, i =1,2,……, t ; at each time point i The predicted data and the observed data are subtracted respectively to obtain t error data. Based on the t error data, the multi-year global average sea surface temperature error time series is obtained. .

[0006] Preferably, in S20, the process of seasonally grouping and decomposing the multi-year global average sea surface temperature error time series is as follows: Based on the time series of global average sea surface temperature error over many years Dividing by month, we obtain the error subsequences for each of the 12 months of the year, represented as follows: ,in, This represents the error data for the m-th month of each year, where m = 1, 2, ..., 12.

[0007] Preferably, in S30, the process of performing independent linear regression analysis on the plurality of error subsequences is as follows: For each error subsequence, the least squares method is used for fitting to obtain a linear trend line corresponding to each error subsequence. Based on the linear trend line, the error data of the m-th month of each year in each error subsequence is obtained. Trend fit value at time point t:

[0008] in, Represents the order of months. Representing the The trend fit value of each month at time point t, and Let represent the slope and intercept of the linear trend line for the m-th month, respectively, where m = 1, 2, ..., 12.

[0009] Preferably, in S40, the plurality of trend fitting values ​​and the plurality of error subsequences are analyzed and calculated to obtain a plurality of error sums of squares, and the plurality of error sums of squares are decomposed into multi-year mean deviation sums of squares, multi-year linear trend deviation sums of squares, and residual sums of squares, respectively. The process is as follows: S41: Calculate the average of the trend fitting values ​​for the m-th month at time t to obtain the multi-year mean deviation for the m-th month. The calculation expression is:

[0010] Where t represents a point in time, Indicates the first The trend fit value of each month at time point t; S42: Based on the trend fitting value of the m-th month and the multi-year mean deviation, the multi-year linear trend deviation of the m-th month is calculated, and the calculation expression is:

[0011] S43: Based on the error data of the m-th month of each year, the trend fitting value, and the multi-year linear trend deviation calculation in S42, obtain the residual of the m-th month. The calculation expression is:

[0012] in, Let represent the error data for the m-th month of each year; then the decomposition expression of the error data for the m-th month of each year in each error subsequence is:

[0013] Based on the error data decomposition expression for the m-th month of each year in each error subsequence, the expression is obtained as follows:

[0014] in, The sum of squares of the deviations from the multi-year mean. The sum of squares of the multi-year linear trend deviations. S1 is the sum of squared residuals, S2 is the intersection of the multi-year mean deviation and the multi-year linear trend deviation, and S3 is the intersection of the multi-year linear trend deviation and the residuals.

[0015] Preferably, S1 satisfies S1= S2 satisfies S2= S3 satisfies S3= Let n be the time length, then S1, S2, and S3 are all 0. The decomposition expression for the sum of squared errors in the m-th month is: .

[0016] This invention also proposes an error sum-of-squares decomposition system for distinguishing the seasonal effects of global average sea surface temperature (SST) to implement the aforementioned error sum-of-squares decomposition method for distinguishing the seasonal effects of global average SST. The system includes: The error time series processing module is used to obtain a multi-year global average sea surface temperature (SST) error time series based on the acquired historical global average SST forecast time series and historical global average SST prediction time series. The seasonal grouping decomposition module is used to perform seasonal grouping decomposition on the multi-year global average sea surface temperature error time series to obtain multiple error subsequences. A linear regression analysis model is used to perform independent linear regression analysis on the multiple error subsequences to obtain multiple trend fitting values. The error sum of squares decomposition module is used to analyze and calculate the multiple trend fitting values ​​and the multiple error subsequences to obtain multiple error sums of squares, and decompose the multiple error sums of squares into multi-year mean deviation sums of squares, multi-year linear trend deviation sums of squares and residual sums of squares, respectively. The sea surface temperature forecasting model evaluation module is used to evaluate the global average sea surface temperature prediction performance of the preset sea surface temperature forecasting model by using the sum of squares of the multi-year mean deviation, the sum of squares of the multi-year linear trend deviation, and the sum of squares of the residuals, and to obtain performance analysis results.

[0017] The present invention also proposes an electronic device, comprising: a memory, a processor, and a program stored in the memory and executable on the processor; the processor is configured to read the program in the memory to implement the steps in the method for decomposing the error sum of squares of global mean sea surface temperature to differentiate seasonal effects.

[0018] The present invention also proposes a readable storage medium for storing a program that, when executed by a processor, implements steps in a method for decomposing the error sum of squares that distinguishes the seasonal effects of global average sea surface temperature.

[0019] The present invention also proposes a computer program product, including computer instructions, which, when executed by a processor, implement steps in a method for decomposing the error sum of squares that distinguishes the seasonal effects of global average sea surface temperature.

[0020] Compared with the prior art, the beneficial effects of the technical solution of the present invention are: This invention proposes a method and system for decomposing the sum of squares of errors in global average sea surface temperature (SST) to differentiate seasonal effects. Based on the forecast time series of global average SST provided by the SST forecast model and the observed time series of global average SST obtained through observation, a multi-year global average SST error time series is calculated. This error time series is then seasonally grouped and decomposed to obtain multiple error subsequences reflecting seasonal error characteristics, grouped monthly. Independent linear regression analysis is performed on each error subsequence to obtain a linear trend line and trend fitting value. Further analysis yields the sum of squares of errors, which is then precisely decomposed into the sum of squares of multi-year mean deviation, the sum of squares of multi-year linear trend deviation, and the sum of squares of residuals. This allows for a refined analysis of the error sources in the SST forecast model, improving interpretability and the utilization value of forecast information, thus facilitating effective decision-making. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating the error sum of squares decomposition method for differentiating seasonal effects of global average sea surface temperature proposed in this embodiment of the invention. Figure 2 This is a comparison chart of the monthly global average sea surface temperature forecast data and observational data presented in the embodiments of the present invention; Figure 3 This diagram illustrates the interannual variation of the sum of squared deviations of the multi-year average for each month as presented in this embodiment of the invention. Figure 4 This diagram illustrates the interannual variation of the sum of squared deviations of the multi-year linear trend for each month, as presented in this embodiment of the invention. Figure 5 This diagram illustrates the interannual variation of the sum of squared residuals for each month as presented in this embodiment of the invention. Figure 6 This diagram illustrates the composition of the error sum-of-squares decomposition system for differentiating seasonal effects of global mean sea surface temperature as proposed in this embodiment of the invention. Figure 7 This diagram illustrates the structure of the electronic device proposed in the embodiments of the present invention. Detailed Implementation

[0022] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent. To better illustrate this embodiment, some parts of the accompanying drawings may be omitted, enlarged, or reduced, and do not represent the actual dimensions; It is understandable to those skilled in the art that some well-known details may be omitted from the accompanying drawings.

[0023] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0024] The positional relationships depicted in the accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent. Example 1 This embodiment provides a method for decomposing the sum of squared errors of global mean sea surface temperature to differentiate seasonal effects. The flowchart of this method can be found in [link to flowchart]. Figure 1 This includes the following steps: S10: Based on the historical global average sea surface temperature forecast time series and historical global average sea surface temperature prediction time series, obtain the multi-year global average sea surface temperature error time series. S20: Seasonally group and decompose the multi-year global average sea surface temperature error time series to obtain multiple error subsequences; S30: Perform independent linear regression analysis on the multiple error subsequences to obtain multiple trend fitting values; S40: Analyze and calculate the multiple trend fitting values ​​and the multiple error subsequences to obtain multiple error sums of squares, and decompose the multiple error sums of squares into multi-year mean deviation sums of squares, multi-year linear trend deviation sums of squares and residual sums of squares, respectively. S50: Using the sum of squared deviations of the multi-year mean, the sum of squared deviations of the multi-year linear trend, and the sum of squared residuals, the global average sea surface temperature prediction performance of the preset sea surface temperature forecasting model is evaluated, and the performance analysis results are obtained.

[0025] In this embodiment, the sea surface temperature (SST) forecast model is preset. Commonly used SST forecast models include HYCOM+NCODA (HYbrid Coordinate Ocean Model + Navy Coupled Ocean Data Assimilation), FOAM (Forecast Ocean Assimilation Model), and MOM (Modular Ocean Data Assimilation Model). Using models such as Model (MOM6), the historical global average sea surface temperature (SST) forecast time series and the historical global average SST observation time series obtained from observation are acquired and processed to obtain a multi-year global average SST error time series. This multi-year global average SST error time series is then seasonally grouped and decomposed to obtain multiple error subsequences grouped by month that reflect seasonal error characteristics. Independent linear regression analysis is performed on each error subsequence to obtain the linear trend line of each month's error subsequence and the trend fitting value of each error data point in the error subsequence. Further analysis and calculation yield the sum of squared errors for each month of the year, and this sum of squared errors is precisely decomposed into the multi-year mean deviation sum of squared errors, the multi-year linear trend deviation sum of squared errors, and the residual sum of squared errors. This allows for the differentiation of seasonal error sources in the SST forecast model, enabling refined analysis and improving interpretability.

[0026] Example 2 In this embodiment, the global average monthly ocean surface temperature (OST) dataset from 1979 to 2025, derived from The National Centers for Environmental Prediction Climate Forecast System Version 2, is read using the `read_csv` function of the Python third-party library Pandas and stored in a Dataframe variable named `obs` in CSV format as a historical global average OST forecast time series. The global average monthly OST dataset from 1991 to 2025, derived from Optimum Interpolation Sea Surface Temperature Version 2, is read using the `open_dataset` function of the Python third-party library Xarray. The data dimensions include dataset members, starting month, year, and forecast lead time. Data with a forecast lead time of 0 is selected and stored in a Dataset variable named `ens` in NetCDF format as a historical global average OST forecast time series. In S10, the processing procedure is as follows: Let the historical global average sea surface temperature prediction time series be denoted as... , Represents each point in time throughout the year. i The observational data; the historical global average sea surface temperature forecast time series is denoted as , Represents each point in time throughout the year. i Forecast data, i =1,2,……, t ; at each time point i The predicted data and the observed data are subtracted respectively to obtain t error data. Based on the t error data, the multi-year global average sea surface temperature error time series is obtained. .

[0027] In S20, the process of performing seasonal grouping decomposition on the multi-year global average sea surface temperature error time series is as follows: Based on the time series of global average sea surface temperature error over many years Dividing by month, we obtain the error subsequences for each of the 12 months of the year, represented as follows: ,in, This represents the error data for the m-th month of each year, where m = 1, 2, ..., 12.

[0028] Specifically, in the multi-year global average sea surface temperature error time series, the `sel` method in the Pandas library is used to extract the error data for January of each year, forming an error subsequence. The error data from February of each year are extracted and grouped into an error subsequence. This process is repeated to obtain the error subsequences for the corresponding 12 months.

[0029] In S30, the process of performing independent linear regression analysis on the multiple error subsequences is as follows: For each error subsequence, the least squares method is used for fitting to obtain a linear trend line corresponding to each error subsequence. Based on the linear trend line, the error data of the m-th month of each year in each error subsequence is obtained. Trend fit value at time point t:

[0030] in, Represents the order of months. Representing the The trend fit value of each month at time point t, and Let represent the slope and intercept of the linear trend line for the m-th month, respectively, where m = 1, 2, ..., 12.

[0031] Specifically, the polyfit function in the Numpy library is used to fit the error subsequence for each month using the least squares method, resulting in multiple linear trend lines representing the changes in global average sea surface temperature for each month over the years. This can distinguish the impact of monthly differences on the sea surface temperature forecast model's prediction of global average sea surface temperature. Then, based on the multiple linear trend lines, the polyval function in the Numpy library is used to calculate the trend fitting value corresponding to the error data at time point t for each month.

[0032] In S40, the multiple trend fitting values ​​and the multiple error subsequences are analyzed and calculated to obtain multiple sums of squared errors, which are then decomposed into sums of squared errors of multi-year mean deviation, sums of squared errors of multi-year linear trend deviation, and sums of squared residuals. The process is as follows: S41: Calculate the average of the trend fitting values ​​for the m-th month at time t to obtain the multi-year mean deviation for the m-th month. The calculation expression is:

[0033] Where t represents a point in time, Indicates the first The trend fit value of each month at time point t; S42: Based on the trend fitting value of the m-th month and the multi-year mean deviation, the multi-year linear trend deviation of the m-th month is calculated, and the calculation expression is:

[0034] S43: Based on the error data of the m-th month of each year, the trend fitting value, and the multi-year linear trend deviation calculation in S42, obtain the residual of the m-th month. The calculation expression is:

[0035] in, Let represent the error data for the m-th month of each year; then the decomposition expression for the error data of the m-th month of each year is:

[0036] Based on the error data decomposition expression for the m-th month of each year in each error subsequence, the expression is obtained as follows:

[0037] in, The sum of squares of the deviations from the multi-year mean. The sum of squares of the multi-year linear trend deviations. S1 is the sum of squared residuals, S2 is the intersection of the multi-year mean deviation and the multi-year linear trend deviation, and S3 is the intersection of the multi-year linear trend deviation and the residuals.

[0038] Specifically, in S43, the difference between the error data and the trend fit value for the m-th month of each year is first calculated. Then, the expression obtained in S42 is substituted into this expression to obtain the residual expression represented by the error data for the m-th month of each year, the multi-year linear trend deviation, and the multi-year mean deviation, i.e.: By rearranging the residual expression, we obtain the decomposed expression for the error data of the m-th month of each year, namely: Finally, squaring both sides of the decomposition expression yields a preliminary decomposition expression for the sum of squared errors in the m-th month of each year, namely: .

[0039] In this embodiment, S1 satisfies S1= S2 satisfies S2= S3 satisfies S3= Let n be the time length, then S1, S2, and S3 are all 0. The decomposition expression for the sum of squared errors in the m-th month is: .

[0040] Specifically, the derivation process to prove that S1 is 0 is as follows: C11: Will writing ,but writing The expression obtained is: ; C12: Set constant Extracting the expression outside the parentheses yields:

[0041] C13: The expression is derived from the definition of the mean. ,but Thus obtain If , then S1 is 0.

[0042] The derivation process for proving that S2 is 0 is as follows: C21: Will writing Then the constant Extracting the summation calculation, we obtain the expression:

[0043] C22: According to the fundamental property of least squares, the sum of the residuals is 0, that is... Thus obtain If , then S2 is 0.

[0044] The derivation process to prove that S3 is 0 is as follows: C31: Will writing The expression obtained by calculation is: ; C32: Due to and ,in ,but Substituting into the expression in C31, we get the expression:

[0045] C33: Based on the fundamental property of ordinary least squares, the covariance of the residuals with all explanatory variables is 0, therefore... If , then S3 is 0.

[0046] In summary, since S1, S2, and S3 are all 0, we obtain the decomposition expression for the sum of squared errors in the m-th month of each year: The system successfully decomposed the sum of squared errors for the m-th month of each year into three orthogonal components: the sum of squared deviations of the multi-year mean, the sum of squared deviations of the multi-year linear trend, and the sum of squared residuals. These components were then saved in NetCDF format to the file decomposition_results.nc.

[0047] In this embodiment, the data visualization operation steps based on the plotting methods in Python's Matplotlib library are as follows: 1. For example Figure 2 As shown, using the ocean heatwave level calculated from observed climatology as a background, a comparison chart of monthly global average sea surface temperature (SST) forecast data and observed data is plotted. The vertical axis represents SST, and the horizontal axis represents the year: January, February, March, April, May, Jane, July, August, September, October, November, and December represent January to December, respectively. The red dots represent the historical global average SST forecast time series, and the red curve represents the linear trend line of the historical global average SST forecast time series. The blue bars represent forecast ensembles, of which there are 24 ensembles. Based on the 10th, 25th, 50th, 75th, and 90th quantiles of the forecast ensembles, they are divided into light blue and dark blue sections. The blue curve represents the linear trend line of the historical global average SST forecast time series.

[0048] 2. For example Figure 3 , Figure 4 , Figure 5 As shown, linear trend lines are plotted for the sum of squared deviations of the multi-year mean, the sum of squared deviations of the multi-year linear trend, and the sum of squared residuals for each month of each year. Figure 3 , Figure 4 , Figure 5 January, February, March, April, May, Jane, July, August, September, October, November, and December represent the months from January to December, respectively, with the horizontal axis representing the year. Figure 3 The ordinate, Mean Component, represents the mean component. Figure 4 The vertical axis, Trend Component, represents the trend deviation component. Figure 5 The ordinate Residual Component represents the residual component; In this embodiment, according to Figure 2 , Figure 3 , Figure 4 , Figure 5 The performance of the preset sea surface temperature (SST) prediction model for global average SST was evaluated, and the performance analysis results were obtained: like Figure 2The chart showing the comparison between the monthly global average sea surface temperature forecast data and the observed data reveals that the preset sea surface temperature forecast model systematically underestimates the global sea surface temperature over many years. This underestimation is most severe from July to October, indicating that the preset sea surface temperature forecast model is not effective in simulating the sea surface temperature in late summer and early autumn and needs to be improved overall. like Figure 4 The graphs showing the interannual variation of the sum of squared deviations of the multi-year linear trend for each month are shown. For example, in July, August, September, and October, the trend lines are close to horizontal, indicating that the preset sea surface temperature (SST) forecast model has no systematic trend in error during these months, the systematic deviation is stable, and the performance is reliable. On the other hand, in March, April, May, November, and December, the trend lines rise significantly, indicating that the systematic deviation of the preset SST forecast model increases year by year during these months, the SST forecast performance continues to decline, and targeted adjustments to the model are needed.

[0049] Example 3 This embodiment provides an error sum-of-squares decomposition system for distinguishing the seasonal effects of global mean sea surface temperature (SST) to implement the aforementioned error sum-of-squares decomposition method for distinguishing the seasonal effects of SST. (See also...) Figure 6 The system includes: The error time series processing module is used to obtain a multi-year global average sea surface temperature (SST) error time series based on the acquired historical global average SST forecast time series and historical global average SST prediction time series. The seasonal grouping decomposition module is used to perform seasonal grouping decomposition on the multi-year global average sea surface temperature error time series to obtain multiple error subsequences. A linear regression analysis model is used to perform independent linear regression analysis on the multiple error subsequences to obtain multiple trend fitting values. The error sum of squares decomposition module is used to analyze and calculate the multiple trend fitting values ​​and the multiple error subsequences to obtain multiple error sums of squares, and decompose the multiple error sums of squares into multi-year mean deviation sums of squares, multi-year linear trend deviation sums of squares and residual sums of squares, respectively. The sea surface temperature forecasting model evaluation module is used to evaluate the global average sea surface temperature prediction performance of the preset sea surface temperature forecasting model by using the sum of squares of the multi-year mean deviation, the sum of squares of the multi-year linear trend deviation, and the sum of squares of the residuals, and to obtain performance analysis results.

[0050] This application also provides an electronic device, including: a processor, a memory, and a program stored in the memory and executable on the processor. When the program is executed by the processor, it implements the various processes of the above-described method embodiment for decomposing the error sum of squares of the seasonal effects of global average sea surface temperature, and can achieve the same technical effect. To avoid repetition, it will not be described again here.

[0051] For details, see Figure 7 This application also provides an electronic device, including a bus 401, a transceiver 402, an antenna 403, a bus interface 404, a processor 405, and a memory 406.

[0052] The transceiver 402 is used to acquire at least one of the historical global average sea surface temperature forecast time series and the historical global average sea surface temperature prediction time series. The processor 405 is used to seasonally group and decompose the multi-year global average sea surface temperature error time series to obtain multiple error subsequences, perform independent linear regression analysis on each of the multiple error subsequences to obtain multiple trend fitting values, analyze and calculate the multiple trend fitting values ​​and the multiple error subsequences to obtain multiple error sums of squares, and decompose the multiple error sums of squares into multi-year mean deviation sums of squares, multi-year linear trend deviation sums of squares, and residual sums of squares, respectively. Using the multi-year mean deviation sums of squares, the multi-year linear trend deviation sums of squares, and the residual sums of squares, the global average sea surface temperature prediction performance of the preset sea surface temperature forecast model is evaluated to obtain performance analysis results.

[0053] exist Figure 7 In this context, a bus architecture (represented by bus 401) is used. Bus 401 can include any number of interconnected buses and bridges, linking various circuits including one or more processors represented by processor 405 and memory represented by memory 406. Bus 401 can also link various other circuits such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and therefore will not be described further herein. Bus interface 404 provides an interface between bus 401 and transceiver 402. Transceiver 402 can be a single element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by processor 405 is transmitted over a wireless medium via antenna 403, which further receives data and transmits data to processor 405.

[0054] Processor 405 is responsible for managing bus 401 and general processing, and can also provide various functions, including timing, peripheral interface, voltage regulation, power management, and other control functions. Memory 406 can be used to store data used by processor 405 during operation.

[0055] Optionally, the processor 405 may be a central processing unit (CPU), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or a complex programmable logic device (CPLD).

[0056] This application also provides a computer-readable storage medium storing a computer program. When executed by a processor, this computer program implements the various processes of the above-described embodiment of the error sum-of-squares decomposition method for differentiating the seasonal effects of global average sea surface temperature, and achieves the same technical effect. To avoid repetition, it will not be described again here. The computer-readable storage medium may be a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, etc.

[0057] This application also provides a computer program product, including computer instructions. When executed by a processor, these computer instructions implement the various processes of the above-described method embodiment for decomposing the error sum of squares that differentiates the seasonal effects of global average sea surface temperature, and achieve the same technical effect. To avoid repetition, they will not be described again here.

[0058] The embodiments described are merely examples to clearly illustrate the present invention and are not intended to limit the implementation of the invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively describe all possible implementations. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for decomposing the sum of squared errors of global mean sea surface temperature to differentiate seasonal effects, characterized in that, Includes the following steps: S10: Based on the historical global average sea surface temperature forecast time series and historical global average sea surface temperature prediction time series, obtain the multi-year global average sea surface temperature error time series. S20: Seasonally group and decompose the multi-year global average sea surface temperature error time series to obtain multiple error subsequences; S30: Perform independent linear regression analysis on the multiple error subsequences to obtain multiple trend fitting values; S40: Analyze and calculate the multiple trend fitting values ​​and the multiple error subsequences to obtain multiple error sums of squares, and decompose the multiple error sums of squares into multi-year mean deviation sums of squares, multi-year linear trend deviation sums of squares and residual sums of squares, respectively. S50: Using the sum of squared deviations of the multi-year mean, the sum of squared deviations of the multi-year linear trend, and the sum of squared residuals, the global average sea surface temperature prediction performance of the preset sea surface temperature forecasting model is evaluated, and the performance analysis results are obtained.

2. The method for decomposing the sum of squared errors in distinguishing seasonal effects of global mean sea surface temperature according to claim 1, characterized in that, In S10, the processing procedure is as follows: Let the historical global average sea surface temperature prediction time series be denoted as... , Represents each point in time throughout the year. i The observational data; the historical global average sea surface temperature forecast time series is denoted as , Represents each point in time throughout the year. i Forecast data, i =1,2,……, t ; Each time point i The predicted data and the observed data are subtracted respectively to obtain t error data. Based on the t error data, the multi-year global average sea surface temperature error time series is obtained. .

3. The method for decomposing the sum of squared errors in distinguishing seasonal effects of global average sea surface temperature according to claim 2, characterized in that, In S20, the process of performing seasonal grouping decomposition on the multi-year global average sea surface temperature error time series is as follows: Based on the time series of global average sea surface temperature error over many years Dividing by month, we obtain the error subsequences for each of the 12 months of the year, represented as follows: ,in, This represents the error data for the m-th month of each year, where m = 1, 2, ..., 12.

4. The method for decomposing the sum of squared errors in distinguishing seasonal effects of global mean sea surface temperature according to claim 2, characterized in that, In S30, the process of performing independent linear regression analysis on the multiple error subsequences is as follows: For each error subsequence, the least squares method is used for fitting to obtain a linear trend line corresponding to each error subsequence. Based on the linear trend line, the error data of the m-th month of each year in each error subsequence is obtained. Trend fit value at time point t: in, Represents the order of months. Representing the The trend fit value of each month at time point t, and Let represent the slope and intercept of the linear trend line for the m-th month, respectively, where m = 1, 2, ..., 12.

5. A method for decomposing the sum of squared errors in distinguishing seasonal effects of global mean sea surface temperature according to claim 3 or 4, characterized in that, In S40, the multiple trend fitting values ​​and the multiple error subsequences are analyzed and calculated to obtain multiple sums of squared errors, which are then decomposed into sums of squared errors of multi-year mean deviation, sums of squared errors of multi-year linear trend deviation, and sums of squared residuals. The process is as follows: S41: Calculate the average of the trend fitting values ​​for the m-th month at time t to obtain the multi-year mean deviation for the m-th month. The calculation expression is: Where t represents a point in time, Indicates the first The trend fit value of each month at time point t; S42: Based on the trend fitting value of the m-th month and the multi-year mean deviation, the multi-year linear trend deviation of the m-th month is calculated, and the calculation expression is: S43: Based on the error data of the m-th month of each year, the trend fitting value, and the multi-year linear trend deviation calculation in S42, obtain the residual of the m-th month. The calculation expression is: in, Let represent the error data for the m-th month of each year; then the decomposition expression of the error data for the m-th month of each year in each error subsequence is: Based on the error data decomposition expression for the m-th month of each year in each error subsequence, the expression is obtained as follows: in, The sum of squares of the deviations from the multi-year mean. The sum of squares of the multi-year linear trend deviations. S1 is the sum of squared residuals, S2 is the intersection of the multi-year mean deviation and the multi-year linear trend deviation, and S3 is the intersection of the multi-year linear trend deviation and the residuals.

6. The method for decomposing the sum of squared errors in distinguishing seasonal effects of global mean sea surface temperature according to claim 5, characterized in that, S1 satisfies S1= S2 satisfies S2= S3 satisfies S3= Let n be the time length, then S1, S2, and S3 are all 0. The decomposition expression for the sum of squared errors in the m-th month is: 。 7. A system for decomposing the error sum of squares of global mean sea surface temperature (SST) to differentiate seasonal effects, used to implement the method for decomposing the error sum of squares of global mean SST to differentiate seasonal effects according to any one of claims 1-6, characterized in that, include: The error time series processing module is used to obtain a multi-year global average sea surface temperature (SST) error time series based on the acquired historical global average SST forecast time series and historical global average SST prediction time series. The seasonal grouping decomposition module is used to perform seasonal grouping decomposition on the multi-year global average sea surface temperature error time series to obtain multiple error subsequences. A linear regression analysis model is used to perform independent linear regression analysis on the multiple error subsequences to obtain multiple trend fitting values. The error sum of squares decomposition module is used to analyze and calculate the multiple trend fitting values ​​and the multiple error subsequences to obtain multiple error sums of squares, and decompose the multiple error sums of squares into multi-year mean deviation sums of squares, multi-year linear trend deviation sums of squares and residual sums of squares, respectively. The sea surface temperature forecasting model evaluation module is used to evaluate the global average sea surface temperature prediction performance of the preset sea surface temperature forecasting model by using the sum of squares of the multi-year mean deviation, the sum of squares of the multi-year linear trend deviation, and the sum of squares of the residuals, and to obtain performance analysis results.

8. An electronic device, comprising: A memory, a processor, and a program stored in the memory and executable on the processor; characterized in that the processor is configured to read the program from the memory to implement the steps in the error sum-of-squares decomposition method for differentiating seasonal effects of global mean sea surface temperature as described in any one of claims 1 to 6.

9. A readable storage medium for storing a program, characterized in that, When the program is executed by the processor, it implements the steps in the error sum-of-squares decomposition method for distinguishing seasonal effects of global mean sea surface temperature as described in any one of claims 1 to 6.

10. A computer program product, characterized in that, Includes computer instructions, which, when executed by a processor, implement the steps in the error sum-of-squares decomposition method for differentiating seasonal effects of global mean sea surface temperature as described in any one of claims 1 to 6.

Images