Method for inversely researching seasonal change rule of depth of Sailuer dome thermocline of South Indian Ocean based on artificial intelligence

Abstract

The invention discloses a method for inversely researching a seasonal change rule of the depth of a Sailuer dome thermocline of South Indian Ocean based on artificial intelligence. The method comprises the following steps: acquiring sea surface data of Sailuer dome of South Indian Ocean and global earth-to-ocean real-time observation matrix data, and processing the sea surface data and the global earth-to-ocean real-time observation matrix data; establishing three models, and selecting and analyzing input variables by using the data; selecting a lightweight gradient lifting model, and confirming an input variable; verifying the lightweight gradient lifting model; estimating the change of the isotherm depth at 20 DEG C; and obtaining the seasonal change of the South India Ocean Sailuer dome by using the estimation result. According to the method, the problem that the 20 DEG C isotherm depth is not estimated from sea surface data obtained from satellites by using a machine learning method in the Indian Ocean region in the prior art is solved; the seasonal change of the Sailuer dome of the south India Ocean is reflected through the change of the depth of the 20 DEG C isotherm of the Sailuer dome of the India Ocean estimated by using a lightweight gradient lifting model.

Description

Technical Field

[0001] The present invention relates to a method for studying the seasonal variation law of the thermocline depth, and in particular to a method for studying the seasonal variation law of the thermocline depth in the Seychelles Dome in the South Indian Ocean based on artificial intelligence inversion. Background Art

[0002] The Seychelles Dome in the South Indian Ocean is a prominent ocean-atmosphere coupled system in the southwestern tropical Indian Ocean. Its dynamic variability on seasonal and interannual scales has long been a focus of physical oceanography. The unique wind stress curl field in this region drives the formation of a dynamic thermocline, making the spatiotemporal variability of the 20°C isotherm depth a key diagnostic parameter for understanding the Indian Ocean thermostratification and atmospheric response.

[0003] In recent years, with the rapid development of multi-source satellite remote sensing observation technology (such as sea surface temperature, sea surface salinity, and sea surface height), deep learning-based nonlinear modeling methods have made breakthrough progress in the field of ocean subsurface temperature inversion. In the Indian Ocean region, the existing literature 1 (Su H, Huang L, Li W, et al. Retrieving Ocean Subsurface Temperature Using a Satellite-Based Geographically Weighted Regression Model [J]. Journal of Geophysical Research-Oceans, 2018, 123 (8): 5180-5193) proposed a geographically weighted regression model to invert the subsurface temperature anomaly in the Indian Ocean and used the extreme gradient enhancement model to study the temperature and salinity anomalies of the global ocean in different seasons in 2015. Reference 2 (Zhang SY, Yang YZ, Xie KW, et al. Spatial-Temporal Siamese Convolutional Neural Network for Subsurface Temperature Reconstruction [J]. IEEE Transactions on Geoscience and Remote Sensing, 2024, 62) proposes a new spatiotemporal twin convolutional neural network model to improve the accuracy of Indian Ocean subsurface reconstruction. Reference 3 (Su H, Wu XB, Yan XH, et al. Estimation of subsurface temperature anomaly in the Indian Ocean during recent global surface warming hiatus from satellite measurements: A support vector machine approach [J]. Remote Sensing of Environment, 2015, 160: 63-71) proposes a support vector machine approach to estimate subsurface temperature anomaly in the Indian Ocean using satellite remote sensing data such as sea surface temperature anomaly, sea surface height anomaly, and sea surface salinity anomaly. The approach successfully achieves accurate estimation of subsurface temperature anomaly in the upper 1000 meters of the Indian Ocean.Reference 4 (Qi J, Xie B, Li D, et al. Estimating thermohaline structures in the tropical Indian Ocean from surface parameters using an improved CNN model [J]. Frontiers in Marine Science, 2023, 10) proposes a novel neural network model based on a convolutional block attention module and a convolutional neural network to simultaneously invert the subsurface thermal and salinity structures of the tropical Indian Ocean using satellite observation data. Reference 5 (Feng Z, Qi J, Li D, et al. Attention-enhanced deep learning model for reconstruction and downscaling of thermocline depth in the tropical Indian Ocean [J]. Ocean Modelling, 2025, 196) proposes a novel deep learning model called an enhanced block attention module and a convolutional neural network to reconstruct the thermocline depth in the tropical Indian Ocean from 1993 to 2022. Globally, Reference 6 (Lu W, Su H, Yang X, et al. Subsurface temperature estimation from remote sensing data using a clustering-neural network method [J]. Remote Sensing of Environment, 2019, 229: 213-222) proposed a method combining K-means clustering and artificial neural networks to invert global subsurface temperature anomalies. The results showed that the pre-clustered model has better performance than the unclustered counterpart. Reference 7 (Wang A, Su H, Huang ZC, et al. Knowledge-Informed Deep Learning Model for Subsurface Thermohaline Reconstruction From Satellite Observations [J]. IEEE Transactions on Geoscience and Remote Sensing, 2024, 62) proposed a novel clustering-guided and knowledge distillation network model based on an ocean knowledge-driven model for reconstructing global subsurface temperature and salinity.Reference 8 (Su H, Jiang J, Wang A, et al. Subsurface Temperature Reconstruction for theGlobal Ocean from 1993 to 2020 Using Satellite Observations and Deep Learning[J]. Remote Sensing, 2022, 14 (13)) uses a convolutional long short-term memory neural network to combine multi-source remote sensing observations and global geostrophic oceanography real-time observation grid data to reconstruct and generate a new long-term series of global ocean upper 2000 meters temperature dataset (covering 1993-2020) and named it deep ocean remote sensing product. Reference 9 (Su H, Zhang FY, Teng JC, et al. Reconstructing high-resolution subsurface temperature of the global ocean using deep forest with combined remote sensing and in situ observations [J]. Isprs Journal of Photogrammetry and Remote Sensing, 2024, 218: 389-404) combined a variety of remote sensing data with field observations, compared four types of models under the two major frameworks of gradient enhancement and deep learning, and determined the optimal model, deep forest, after screening, to construct a global 1 / 4 degree high-resolution subsurface temperature dataset at a depth of 0-2000 meters from 1993 to 2023. Reference 10 (Su H, Yang X, LuW F, et al. Estimating Subsurface Thermohaline Structure of the Global Ocean Using Surface Remote Sensing Observations [J]. Remote Sensing, 2019, 11 (13)) proposed a new ensemble learning algorithm, extreme gradient boosting, to invert surface temperature and salinity anomalies in the upper 2000 meters of the global ocean.To achieve transparent ocean observation, the paper 11 (Jiang JW, Wang J, Liu YP, et al. SWO: A Lightweight Window Spatiotemporal Attention Network Reconstructs Subsurface Temperature Structure[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2024, 17: 19274-19287) innovatively uses artificial intelligence to reconstruct global three-dimensional ocean structure from remote sensing data using a spatiotemporal attention mechanism. To address the significant computational challenges posed by high-resolution satellite imagery, a spatiotemporal window ocean network was proposed, which employs a special computational strategy and a spatiotemporal window attention mechanism to reduce complexity.

[0004] In conclusion, in the Indian Ocean region, there is no existing technology that uses machine learning methods to estimate the depth of the 20°C isotherm from satellite-derived sea surface data. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for studying the seasonal variation law of the thermocline depth of the Seychelles Dome in the South Indian Ocean based on artificial intelligence inversion, which solves the problem that the existing technology in the Indian Ocean region does not use machine learning methods to estimate the 20-degree Celsius isotherm depth from sea surface data obtained from satellites. The seasonal variation of the Seychelles Dome in the South Indian Ocean is reflected by using the changes in the 20-degree Celsius isotherm depth of the Seychelles Dome in the Indian Ocean estimated by a lightweight gradient lifting model. In a specific area, the 20-degree Celsius isotherm depth estimated by the lightweight gradient lifting model is significantly positively correlated with the 20-degree Celsius isotherm depth calculated by the drifting buoy of the Global Geostrophic Oceanography Real-Time Observation Array. The 20-degree Celsius isotherm depth estimated by the lightweight gradient lifting model has low error and high correlation in most areas of the Seychelles Dome in the South Indian Ocean.

[0006] To achieve the above objectives, the present invention provides a method for studying the seasonal variation of the thermocline depth in the Seychelles Dome in the South Indian Ocean based on artificial intelligence inversion, the method comprising: Step 1: Obtain sea surface data of the Seychelles Dome in the South Indian Ocean and global geostrophic oceanographic real-time observation array data, and process them into monthly average data; Step 2: Build lightweight gradient boosting models, extreme gradient boosting models, and category gradient boosting models, and use monthly average data to select and analyze input variables; Step 3: Select a lightweight gradient boosting model and determine the input variables based on feature importance. Step 4: Verify the lightweight gradient boosting model; Step 5: Use the validated lightweight gradient boosting model to estimate the change in isotherm depth; Step 6. Use the estimated isotherm depth changes to obtain the seasonal variation of the Seychelles Dome in the South Indian Ocean.

[0007] Preferably, in step one, the sea surface data of the Seychelles Dome in the South Indian Ocean are the fifth-generation global reanalysis data of the European Centre for Medium-Range Weather Forecasts meteorological reanalysis data, which include sea level height anomaly, latitudinal wind stress, latitudinal wind stress gradient, meridional wind stress and meridional wind stress gradient; the global geostrophic oceanography real-time observation array data include sea surface temperature, latitude, longitude, 20 degrees Celsius isotherm depth, 50-meter depth temperature and 100-meter depth temperature; the processing into monthly average data is to process the sea surface data of the Seychelles Dome in the South Indian Ocean and the global geostrophic oceanography real-time observation array data into monthly average data, and interpolate them to a spatial resolution of 1 degree × 1 degree, covering the Seychelles Dome area in the Indian Ocean, and the time period is from January 2004 to December 2022.

[0008] Preferably, the temporal resolution of the sea surface data of the Seychelles Dome in the South Indian Ocean is monthly, and the spatial resolution is 0.25 degrees × 0.25 degrees; the spatial resolution of the global geostrophic oceanographic real-time observation array data is 1 degree × 1 degree, the temporal resolution is monthly, and the depth is 0~2000 meters.

[0009] Preferably, in step 2, the Seychelles Dome in the South Indian Ocean is used as the study area, wherein the latitude of the study area is from 15 degrees south to the equator and the longitude is from 40 degrees east to 90 degrees east; the Seychelles Dome is an area where the depth of the 20 degrees Celsius isotherm is less than 100 meters and the core is as shallow as 60 meters; the analysis includes analyzing the seasonal variation of the input variables and the correlation between the depth of the 20 degrees Celsius isotherm and the input variables; the seasonal variation of the input variables is a seasonal fluctuation pattern; the role of the correlation between the depth of the 20 degrees Celsius isotherm and the input variables is to determine The variables of the lightweight gradient boosting model, the extreme gradient boosting model and the categorical gradient boosting model include the temperature at a depth of 100 meters, the temperature at a depth of 50 meters and the sea level anomaly; the input variables are wind stress curl, sea level anomaly, sea surface temperature, the temperature at a depth of 50 meters, the temperature at a depth of 100 meters, latitudinal wind stress, wind stress curl, latitudinal wind stress gradient, meridional wind stress gradient, and longitude and latitude; the wind stress curl is obtained by calculating the latitudinal component and meridional component of wind stress by the bulk formula and applying Stokes' theorem.

[0010] More preferably, the bulk formula is: ; in, is the meridional wind stress; is the zonal wind stress; is the wind speed in the surface layer of 10 meters; It faces east; It is north-facing; Indicates the air density; is the drag coefficient, which depends on the height of the wind.

[0011] Preferably, in step three, the feature importance is obtained by calculating the importance of the input variables to the inversion of the 20-degree Celsius isotherm depth; the confirmed input variables are the temperature at a depth of 100 meters, the sea surface temperature, the temperature at a depth of 50 meters, the sea level height anomaly, the meridional wind stress gradient, the latitudinal wind stress, the meridional wind stress, the longitude, the wind stress curl, the latitudinal wind stress gradient and the latitude as the input values ​​of the lightweight gradient boosting model, and the 20-degree Celsius isotherm depth of the Indian Ocean is estimated by the root mean square error, the mean absolute error and the coefficient of determination; the basis for selecting the lightweight gradient boosting model is that in the consistency calculation of the lightweight gradient boosting model, the extreme gradient boosting model and the category gradient boosting model with the measured data when inverting the 20-degree Celsius isotherm depth, only the lightweight gradient boosting model is consistent with the measured data.

[0012] Preferably, in step four, the lightweight gradient boosting model is verified in the Seychelles Dome area in the Indian Ocean in 2022, and the spatial distribution of the root mean square error and the determination coefficient between the 20-degree Celsius isotherm depth estimated by the lightweight gradient boosting model and the 20-degree Celsius isotherm depth calculated from the temperature data of the drifting buoy of the global geostrophic oceanography real-time observation array are analyzed; the root mean square error does not exceed 5 meters; the determination coefficient is greater than 0.8.

[0013] Preferably, in step five, the estimated change in isotherm depth is obtained by estimating the change in the 20-degree Celsius isotherm depth in the Seychelles Dome region of the Indian Ocean in April, July, October and January using a lightweight gradient boosting model; in April, July, October and January, the correlation coefficients between the results estimated using the lightweight gradient boosting model and the observations calculated by the drifting buoys of the Global Geostrophic Oceanography Real-Time Observation Array are not less than 0.85.

[0014] Preferably, in step five, the monthly average 20-degree Celsius isotherm depth data in 2022 measured by the drifting buoy of the Global Geostrophic Oceanography Real-Time Observation Array at longitudes of 50.5°E to 80.5°E and latitudes of 10.5°S to 5.5°S are consistent with the monthly average 20-degree Celsius isotherm depth data in 2022 estimated by the lightweight gradient boosting model.

[0015] Preferably, in step six, the correlation coefficients between the sea level anomaly, the temperature at a depth of 50 meters, the latitudinal wind stress, the meridional wind stress, the temperature at a depth of 100 meters, the wind stress curl, the sea surface temperature, the latitudinal wind stress gradient and the meridional wind stress gradient and the 20 degrees Celsius isotherm depth estimated by the lightweight gradient lifting model are calculated; the correlation coefficient between the temperature at a depth of 100 meters and the 20 degrees Celsius isotherm depth is 0.92; the correlation coefficient between the temperature at a depth of 50 meters and the 20 degrees Celsius isotherm depth is 0.54; and the correlation coefficient between the sea level anomaly and the 20 degrees Celsius isotherm depth is 0.40.

[0016] The present invention provides a method for studying the seasonal variation of the thermocline depth in the Seychelles Dome in the South Indian Ocean based on artificial intelligence inversion. This method solves the problem that the existing technology in the Indian Ocean region does not use machine learning methods to estimate the depth of the 20-degree Celsius isotherm from sea surface data obtained by satellites. It has the following advantages: This study uses a lightweight gradient boosting model to estimate the seasonal variation of the Seychelles Dome in the Indian Ocean. The 20°C isotherm depth in this region reaches a maximum of approximately 100 meters in spring and decreases to a minimum of approximately 60 meters in winter, demonstrating significant seasonal variation.

[0017] In a specific region (longitude 50.5°E to 80.5°E, latitude 10.5°S to 5.5°S), the 20°C isotherm depth estimated by the lightweight gradient boosting model (LGB) shows a significant positive correlation with the 20°C isotherm depth calculated by drifting buoys of the Global Geostrophic Oceanographic Array (GEORGA) in the four seasons. The R² values ​​for these four seasons were 0.93, 0.90, 0.92, and 0.98, respectively. This demonstrates the seasonal effectiveness and reliability of the LGBB model. Spatially, the 20°C isotherm depth estimated by the LGBB model exhibits low error (root mean square error <5 meters) and high correlation (coefficient of determination >0.8) across most of the Seychelles Dome region in the South Indian Ocean.

[0018] This paper uses a lightweight gradient boosting algorithm model with multiple parameters to estimate the depth of the 20°C isotherm in the Seychelles Dome in the South Indian Ocean with high accuracy. The lightweight gradient boosting algorithm is unique in that it can directly use multiple parameters to extract characteristic information for each variable despite its simple structure, thus fully considering the interactions between variables. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 This is a flow chart of the method for studying the seasonal variation of the thermocline depth in the Seychelles Dome in the South Indian Ocean based on artificial intelligence inversion.

[0020] Figure 2 This is the long-term average 20 degrees Celsius isotherm depth distribution map from January 2004 to December 2022 of the present invention.

[0021] Figure 3 This is a seasonal variation trend chart of each variable of the monthly average value from 2004 to 2022 of the present invention.

[0022] Figure 4 A heatmap of the Pearson correlation between the 20°C isotherm depth and variables, calculated for data from drifting buoys in the Global Geostrophic Oceanography Real-Time Observation Array. The numbers and colors represent the correlation coefficients between the various variables studied.

[0023] Figure 5 This is the horizontal distribution of the 20-degree Celsius isotherm depth in the Seychelles dome area in 2022 and its model evaluation results.

[0024] Figure 6 This is a scatter plot comparison of the 20-degree Celsius isotherm depths estimated by the three models of the present invention and the 20-degree Celsius isotherm depths calculated from the drifting buoy data of the Global Geostrophic Oceanography Real-Time Observation Array.

[0025] Figure 7 This is a comparison chart of the importance of each input variable to the lightweight gradient boosting model of the present invention.

[0026] Figure 8 This is a diagram showing the influence of different parameters on the 20°C isotherm depth inversion result estimated by the lightweight gradient boosting model of the present invention.

[0027] Figure 9 This is a horizontal distribution diagram of the 20-degree Celsius isotherm depth calculated from the temperature data of the drifting buoy of the global geostrophic oceanography real-time observation array of the present invention and the 20-degree Celsius isotherm depth estimated by lightweight gradient lifting.

[0028] Figure 10 This is the error map of the 20-degree Celsius isotherm depth calculated based on the drifting buoy data of the global geostrophic oceanography real-time observation array of the present invention.

[0029] Figure 11 This is a scatter plot of the 20-degree Celsius isotherm depth calculated from the temperature data of the drifting buoy of the global geostrophic oceanography real-time observation array of the present invention and the 20-degree Celsius isotherm depth of the four seasons estimated by lightweight gradient lifting.

[0030] Figure 12 This is a graph showing the difference between the 20-degree Celsius isotherm depth calculated from the drifting buoy data of the global geostrophic oceanography real-time observation array of the present invention and the true value.

[0031] Figure 13This is a scatter plot of the 20-degree Celsius isotherm depth calculated from the temperature data of the drifting buoy of the global geostrophic oceanography real-time observation array of the present invention and the 20-degree Celsius isotherm depth estimated by lightweight gradient lifting.

[0032] Figure 14 This is a monthly average graph of the 20-degree Celsius isotherm depth calculated from the temperature data of the drifting buoys of the global geostrophic oceanography real-time observation array of the present invention and the 20-degree Celsius isotherm depth estimated by the lightweight gradient lifting model.

[0033] Figure 15 This is a correlation coefficient diagram between various parameters of the present invention and the 20 degrees Celsius isotherm depth estimated by the lightweight gradient lifting model.

[0034] Figure 16 It is the spatial root mean square error and spatial correlation coefficient between the various parameters of the present invention and the 20 degrees Celsius isotherm depth estimated by the lightweight gradient boosting model. DETAILED DESCRIPTION

[0035] The following is a clear and complete description of the technical solutions in the embodiments of the present invention. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of the present invention.

[0036] Example 1 A method based on artificial intelligence inversion to study the seasonal variation of the thermocline depth in the Seychelles Dome in the South Indian Ocean, such as Figure 1 As shown in FIG, a flow chart of a method for studying the seasonal variation of the thermocline depth in the Seychelles Dome in the South Indian Ocean based on artificial intelligence inversion is provided. The method comprises: Step 1: Obtain sea surface data of the Seychelles Dome in the South Indian Ocean and global geostrophic oceanographic real-time observation array data, and process them into monthly average data.

[0037] This method utilizes two sources of ocean observation data: satellite-based sea level data (such as sea level anomaly, latitudinal wind stress, latitudinal wind stress gradient, meridional wind stress, meridional wind stress gradient, and wind stress curl) and Global Geostrophic Oceanographic Array (GEO) data (such as sea surface temperature, latitude, longitude, 20°C isotherm depth, temperature at 50 meters, and temperature at 100 meters). Longitude and latitude are derived from gridded GEO data provided by the International Pacific Center from January 2004 to December 2022. The GEO data have a spatial resolution of 1 degree by 1 degree, a monthly temporal resolution, and a depth range of 0 to 2000 meters. Sea level anomaly is a monthly gridded dataset provided by satellite altimeters, with a spatial resolution of 0.25 degrees by 0.25 degrees. The zonal wind stress, meridional wind stress, wind stress curl, meridional wind stress gradient, and wind stress curl are all derived from the fifth generation of the European Centre for Medium-Range Weather Forecasts global meteorological reanalysis data with a temporal resolution of monthly and a spatial resolution of 0.25° × 0.25°.

[0038] Given the differences in resolution and time period between available input and output data for the Indian Ocean, all data used in this paper were processed into monthly averages and interpolated to a spatial resolution of 1 degree × 1 degree. The coverage of the Seychelles Dome region in the Indian Ocean is identical, covering the period from January 2004 to December 2022. To ensure data uniformity, null values ​​for some variables were filled with the mean value. All data used in this paper are shown in Table 1.

[0039] Table 1 Summary of data used in this invention

[0040] Step 2: Establish lightweight gradient boosting model, extreme gradient boosting model and category gradient boosting model, and use monthly average data to select and analyze input variables.

[0041] (1) Establish three models The lightweight gradient boosting model is an ensemble algorithm based on gradient boosting decision trees, derived from existing technology1 (Cessi P, Fantini M. The eddy-driven thermocline [J]. Journal of Physical Oceanography, 2004, 34 (12): 2642-2658). Compared to traditional gradient boosting decision tree algorithms, the lightweight gradient boosting model significantly improves efficiency, computational cost, and scalability. Its main improvements include a histogram algorithm and a leaf-by-leaf decision tree growth strategy with depth constraints. The advantages of the lightweight gradient boosting model are primarily reflected in its fast training speed, low memory usage, support for parallel training, and ability to effectively process large datasets.

[0042] In addition to selecting a lightweight gradient boosting model, the present invention also establishes an extreme gradient boosting model and a category gradient boosting model.

[0043] The extreme gradient boosting model is based on the gradient boosting decision tree algorithm. The categorical gradient boosting model is an additive model based on ensembles. During categorical gradient boosting model training, a forward distribution algorithm is used to achieve greedy learning. With each iteration, a classification tree is learned, and the residuals between the training results of the adjacent previous tree and the true values ​​of the training samples are fitted. The basic concept of the extreme gradient boosting model is consistent with that of the gradient boosting decision tree. The extreme gradient boosting model is also an additive model, but its node splitting criteria have been modified. Whether for regression or classification problems, a differentiable loss function must be defined first. Then, all tree structures are traversed, and the first-order and second-order derivatives of all samples under the tree structure are calculated. The loss of each tree structure is then calculated. By comparing the losses of all tree structures, the structure with the minimum loss is selected as the new learner. The categorical gradient boosting model is an open source machine learning library released in 2017 and belongs to the boosting algorithm family. Categorical gradient boosting is considered one of the three important improvements to the gradient boosting decision tree method, but it differs from the other two boosting algorithms. The Categorical Gradient Boosting model is a gradient boosting algorithm for processing categorical features. It uses a symmetric tree as its base model and supports categorical variables. This algorithm avoids overfitting by balancing the tree structure. In a symmetric tree, the index of each leaf node can be encoded using a binary vector of the same length as the tree depth. The Categorical Gradient Boosting model first performs binary conversion on all floating-point features, statistical information, and one-hot encoded features, and then uses these binary features to make predictions.

[0044] (2) Determine the research area for the three models mentioned above, select and analyze the input variables The application of the three models mentioned above typically requires the following types of data: training data, validation data, and test data. Training data is used to train the lightweight gradient boosting model, while validation data is used to evaluate the model's performance during training and effectively control overfitting.

[0045] The present invention randomly divides all the data from January 2004 to December 2022 into two parts: training data and verification data. Specifically, the present invention randomly divides the 216-month data from 2004.01 to 2021.12 as training data and the 12-month data from 2022.01 to 2022.12 as test data, uses the 216-month data for training, and the 12-month data for testing. The application process of the above three models includes two main steps: (1) training and verification; (2) using the trained lightweight gradient boosting model to estimate the depth of the 20-degree Celsius isotherm. Before applying the three models to invert the depth of the 20-degree Celsius isotherm, the present invention uses satellite sea surface data and global geostrophic oceanography real-time observation array marker data to train and verify them, as follows:

[0046] ①Select the research area This study uses the Seychelles Dome in the South Indian Ocean (15°S to the equator, 40°E to 90°E) as the research area. First, the depth of the 20°C isotherm was averaged over many years.

[0047] like Figure 2 As shown in the figure, the long-term average 20 degrees Celsius isotherm depth distribution map of the present invention from January 2004 to December 2022. Figure 2 It can be seen that the Seychelles Dome is an area where the 20-degree Celsius isotherm depth is less than 100 meters and the core is as shallow as 60 meters.

[0048] ②Calculate the sea surface wind stress curl In order to calculate the curl of sea surface wind stress, the present invention first uses the bulk formula of prior art 2 (Trenberth KE, Large W G, Olson J G. The Mean Annual Cycle in Global Ocean Wind Stress [J]. Journal of Physical Oceanography, 1990, 20 (11): 1742-1760) to calculate the latitudinal and longitudinal components of wind stress.

[0049] The bulk formula is as follows: ; in, is the meridional wind stress; is the zonal wind stress; is the wind speed in the surface layer of 10 meters; It faces east; It is north-facing; Indicates the air density; is the drag coefficient, which depends on the height of the wind.

[0050] Then applying Stokes' theorem we get The vertical component of , that is, the sea surface wind stress curl.

[0051] The present invention selects wind stress curl, sea level height anomaly, sea surface temperature, temperature at 50 meters depth, temperature at 100 meters depth, latitudinal wind stress, wind stress curl, latitudinal wind stress gradient, meridional wind stress gradient, as well as longitude and latitude as input variables of the above three models to estimate the depth of the 20 degrees Celsius isotherm in the Seychelles dome region of the South Indian Ocean.

[0052] ③Seasonal changes in input variables The present invention analyzes the seasonal variations of nine input variables (wind stress curl, latitudinal wind stress gradient, meridional wind stress gradient, sea level height anomaly, sea surface temperature, temperature at 50 m depth, temperature at 100 m depth, latitudinal wind stress, and meridional wind stress) to determine their seasonal fluctuation patterns.

[0053] like Figure 3 As shown in the figure, the seasonal variation trend diagram of each variable of the monthly average value from 2004 to 2022 is provided. Figure 3 The 19-year seasonal average of wind stress curl, zonal wind stress gradient, meridional wind stress gradient, sea level anomaly, sea surface temperature, 50-meter depth temperature, 100-meter depth temperature, zonal wind stress, and meridional wind stress reveals a significant annual cycle for wind stress curl, peaking in February and troughing in October. The zonal wind stress gradient exhibits similar trends to wind stress curl, also exhibiting significant annual fluctuations. Sea surface temperature, zonal wind stress, and meridional wind stress also exhibit annual cyclical variations. Furthermore, the 50-meter depth temperature, 100-meter depth temperature, meridional wind stress gradient, and sea surface anomaly exhibit significant semiannual cycles. These findings reveal the seasonal fluctuations of these variables in long-term observations, providing a foundation for further analysis of their interrelationships and their impacts on ocean phenomena.

[0054] ④Correlation analysis between the depth of the 20°C isotherm and input variables The present invention analyzes the correlation between the above-mentioned input variables (11 input variables: latitude, longitude, sea level anomaly, temperature at 50 meters depth, latitudinal wind stress, meridional wind stress, temperature at 100 meters depth, wind stress curl, sea surface temperature, latitudinal wind stress gradient and meridional wind stress gradient) and the depth of the 20 degrees Celsius isotherm, and determines that the temperature at 100 meters depth, the temperature at 50 meters depth and sea level anomaly are the key variables of the above-mentioned three models.

[0055] like Figure 4 As shown in the figure, the Pearson correlation heat map of the 20-degree Celsius isotherm depth and variables calculated from the drifting buoy data of the global geostrophic oceanography real-time observation array of the present invention. The numbers and colors represent the correlation coefficients between the various research variables. Figure 4 These coefficients, calculated using Pearson correlation analysis, reveal the strength of the linear relationship between the 20°C isotherm depth, calculated from temperature data from drifting buoys in the Global Geostrophic Oceanographic Real-Time Array, and various variables. Specifically, the results show that the correlation between the 20°C isotherm depth and the 100°C isotherm depth is most significant, with a correlation coefficient as high as 0.91, indicating a very strong positive correlation. Furthermore, the correlation coefficients between the 20°C isotherm depth and the 50°C isotherm depth and sea level anomaly are 0.56 and 0.45, respectively, indicating a strong positive correlation with the 20°C isotherm depth. The correlation coefficients between the 20°C isotherm depth and sea surface temperature, zonal wind stress, longitude, latitude, meridional wind stress, zonal wind stress gradient, and meridional wind stress gradient are -0.1, -0.11, -0.25, -0.056, 0.03, 0.21, and 0.032, respectively, indicating relatively weak linear relationships. Overall, the estimated effects of the proposed model are closely related to the input variables entered. The strong correlations between variables such as 100-meter depth temperature, 50-meter depth temperature and sea level height anomaly and the depth of the 20-degree Celsius isotherm indicate that they may be of great significance in subsequent modeling and inversion. These findings provide strong support for understanding how variables affect the depth of the 20-degree Celsius isotherm and emphasize the necessity of considering these key variables in model construction.

[0056] Step 3: Select a lightweight gradient boosting model and determine the input variables based on feature importance (1) Model selection The present invention further analyzes and compares the above-mentioned lightweight gradient boosting model, extreme gradient boosting model, and category gradient boosting model, and ultimately determines to use the lightweight gradient boosting model to estimate the 20 degrees Celsius isotherm depth based on sea surface data. The specific process is as follows: like Figure 5As shown in the figure, the horizontal distribution of the 20-degree Celsius isotherm depth in the Seychelles dome area in 2022 and its model evaluation results, among which (a), (d) and (g) are the 20-degree Celsius isotherm depth of the drifting buoy (three identical small figures are set for the convenience of comparison with the subsequent small figures); (b) is the evaluation of the 20-degree Celsius isotherm depth in the Seychelles dome area in 2022 by the lightweight gradient lifting model; (c) is the inversion value of the 20-degree Celsius isotherm depth in the Seychelles dome area in 2022 by the lightweight gradient lifting model and the global geostrophic oceanography real-time observation array. The difference between the true value; (e) is the inversion of the 20-degree Celsius isotherm depth in the Seychelles Dome area by the category gradient lifting model; (f) is the difference between the inversion value of the 20-degree Celsius isotherm depth in the Seychelles Dome area in 2022 by the category gradient lifting and the true value of the global geostrophic oceanography real-time observation array; (h) is the inversion of the 20-degree Celsius isotherm depth in the Seychelles Dome area by the extreme gradient lifting model; (i) is the difference between the inversion value of the 20-degree Celsius isotherm depth in the Seychelles Dome area in 2022 by the extreme gradient lifting and the true value of the global geostrophic oceanography real-time observation array. Figure 5 (a), (d) and (g) are the measured values ​​of the 20-degree Celsius isotherm depth calculated based on the temperature data of the drifting buoys of the Global Geostrophic Oceanography Real-time Observation Array, which reveal that the 20-degree Celsius isotherm depth in this area is less than 100 meters, and the core area is as shallow as 60 meters. Figure 5 (b), (e) and (h) show the inversion results of the 20-degree Celsius isotherm depth for that year using the lightweight gradient boosting model, the categorical gradient boosting model and the extreme gradient boosting model, respectively. The input variables used cover multi-source satellite observation data from 2004 to 2021, including sea level anomalies, temperatures at different depths, wind stress curl and its components, etc. The inversion results show that all three models can well reproduce the spatial distribution characteristics of the 20-degree Celsius isotherm depth in the Seychelles dome region. Figure 5 (c), (f) and (i) further compared the model accuracy through difference analysis between the model inversion value and the measured value. The results show that the 20°C isotherm depth inverted by the lightweight gradient lifting model is consistent with the measured data.

[0057] Therefore, in the subsequent inversion analysis of the 20-degree Celsius isotherm depth in the Seychelles dome area, the present invention selected the lightweight gradient boosting model. The model evaluation process fully demonstrated the advantages of lightweight gradient boosting in integrating multi-source ocean data to improve the inversion accuracy of the 20-degree Celsius isotherm depth, providing strong verification for its application in oceanographic research.

[0058] like Figure 6As shown in the figure, the scatter plot comparison between the 20-degree Celsius isotherm depth estimated by the three models of the present invention and the 20-degree Celsius isotherm depth calculated by the global geostrophic oceanographic real-time observation array drifting buoy data, where (a) is the lightweight gradient boosting model; (b) is the class gradient boosting model; and (c) is the extreme gradient boosting model. Figure 6 As shown in (a), the lightweight gradient boosting model shows significant advantages, with a determination coefficient of 0.97 and a root mean square error of only 2.46 meters; Figure 6 From (b), we can see that the determination coefficient of the category gradient boosting model is 0.96 and the root mean square error is 2.53 meters; Figure 6 As shown in (c), the coefficient of determination of the extreme gradient boosting model is 0.93, and the root mean square error reaches 4.08 meters. This shows that the lightweight gradient boosting model has higher accuracy and stronger correlation in estimating the depth of the 20°C isotherm.

[0059] (2) Determine input variables based on feature importance Due to the different importance of various variables in the inversion model of the 20°C isotherm depth in the Seychelles Dome region in the Indian Ocean, in order to explore the weights of different inversion factors in the training of the lightweight gradient boosting model and more effectively adjust the regression fitting of the inversion factors to make them close to the 20°C isotherm depth values ​​measured by the Global Geostrophic Oceanographic Real-Time Observation Array, the importance of 11 variables (temperature at 100 m depth, sea surface temperature, temperature at 50 m depth, sea level anomaly, meridional wind stress gradient, zonal wind stress, meridional wind stress, longitude, wind stress curl, zonal wind stress gradient, and latitude) to the inversion of the 20°C isotherm depth was calculated, and the results were analyzed with two significant figures retained. The higher the importance of the result, the greater the contribution of the variable to the inversion of the 20°C isotherm depth.

[0060] like Figure 7 As shown in Figure 2, the importance comparison chart of each input variable to the lightweight gradient boosting model of the present invention is shown in Figure 2. Figure 7 The top five variables are the 100°C isotherm depth, sea surface temperature, 50°C isotherm depth, sea level anomaly, and meridional wind stress gradient, with corresponding importance scores of 0.98, 0.91, 0.83, 0.82, and 0.60, respectively. The remaining parameters, such as zonal wind stress, meridional wind stress, longitude, wind stress curl, latitudinal component, and latitude, contribute relatively little to the model, with importance scores of 0.55, 0.51, 0.43, 0.38, 0.23, and 0.10, respectively. This result highlights the different roles of the 11 variables in the inversion of the 20°C isotherm depth, providing a scientific basis for model optimization and the identification of subsequent research priorities.

[0061] Since the selection of the above-mentioned input variables has an important influence on the performance of the lightweight gradient boosting model, the present invention uses 10 different variable combinations as the input values ​​of the lightweight gradient boosting model to estimate the depth of the 20°C isotherm in the Indian Ocean. The performance of the lightweight gradient boosting model is evaluated by statistical indicators such as root mean square error, mean absolute error and coefficient of determination.

[0062] This method selects different variable combinations as input variables based on the aforementioned feature importance. Each row represents a combination, and each column represents a parameter. For example, combination 1 selects two variables (temperature at 100 meters depth and sea surface temperature), combination 2 selects three variables (temperature at 100 meters depth, sea surface temperature, and sea level anomaly), and so on, until combination 10 selects all parameters. See Table 2 for details.

[0063] Table 2 shows the importance distribution of each parameter in different models

[0064] In order to accurately evaluate and select appropriate input variables, the present invention further analyzes combinations 1 to 10 in Table 2 using root mean square error, mean absolute error, and coefficient of determination as key indicators.

[0065] like Figure 8 As shown in the figure, the influence of different parameters of the present invention on the inversion results of the 20 degrees Celsius isotherm depth estimated by the lightweight gradient lifting model is shown, where the horizontal axis represents different combinations (combination 1 to combination 10), the left side of the vertical axis represents the mean absolute error (unit: meter) and the root mean square error (unit: meter), and the right side represents the correlation coefficient determination coefficient; the red bar graph represents the mean absolute error, the blue bar graph represents the root mean square error, and the black dotted line represents the determination coefficient value. Figure 8 The mean absolute error and root mean square error for combination 1 are 6.79 meters and 10.36 meters, respectively, with a coefficient of determination of 0.81. For combination 10, the mean absolute error drops to 0.78 meters, the root mean square error drops to 1.11 meters, and the coefficient of determination reaches 0.99. This indicates that parameter selection significantly influences model performance. Therefore, combination 10 (temperature at 100 meters depth, sea surface temperature, temperature at 50 meters depth, sea level anomaly, meridional wind stress gradient, zonal wind stress, meridional wind stress, longitude, wind stress curl, zonal wind stress gradient, and latitude) was selected as the input variables. Its parameter configuration significantly improves the accuracy of the 20°C isotherm depth inversion, providing an important reference for subsequent research.

[0066] Step 4: Verify the lightweight gradient boosting model After comparing the category boosting model with the extreme gradient boosting model, the present invention found that the lightweight gradient boosting model demonstrated superior performance in inverting the 20°C isotherm depth. To further explore the inversion capabilities of this model in the Indian Ocean, the present invention analyzed the spatial distribution of the root mean square error and coefficient of determination between the 20°C isotherm depth estimated by the lightweight gradient boosting model in the Seychelles Dome region of the Indian Ocean in 2022 and the 20°C isotherm depth calculated using temperature data from drifting buoys of the Global Geostrophic Oceanographic Real-Time Observation Array.

[0067] like Figure 9 As shown in the figure, the horizontal distribution diagram of the 20-degree Celsius isotherm depth calculated from the temperature data of the drifting buoy of the global geostrophic oceanography real-time observation array of the present invention and the 20-degree Celsius isotherm depth estimated by lightweight gradient lifting, where (a) is the horizontal distribution diagram of the root mean square error; (b) is the horizontal distribution diagram of the determination coefficient. Figure 9 The 20°C isotherm depth estimated by the lightweight gradient boosting model has a generally low root mean square error (RMS) of less than 5 meters across most of the Seychelles Dome in the southern Indian Ocean, and a high coefficient of determination (CDR) greater than 0.8, indicating high accuracy and correlation. The regions with relatively high RMS and CDR are primarily located in the southern Indian Ocean, with RMS errors exceeding 20 meters and CDRs below 0.2. These findings further demonstrate the reliability of the lightweight gradient boosting model in accurately forecasting the Seychelles Dome season.

[0068] Step 5: Use the validated lightweight gradient boosting model to estimate the change in the depth of the 20°C isotherm In order to evaluate the effectiveness of the lightweight gradient boosting algorithm in inverting the seasonal variation of the 20°C isotherm depth, the present invention uses the lightweight gradient boosting model to estimate the 20°C isotherm depth in the Seychelles Dome region of the Indian Ocean.

[0069] like Figure 10 As shown in the figure, the error diagram of the 20-degree Celsius isotherm depth calculated from the drifting buoy data of the global geostrophic oceanography real-time observation array of the present invention, wherein (a) is the drifting buoy in spring; (b) is the lightweight gradient lifting in spring; (c) is the spring difference; (d) is the drifting buoy in summer; (e) is the lightweight gradient lifting in summer; (f) is the summer difference; (g) is the drifting buoy in autumn; (h) is the lightweight gradient lifting in autumn; (i) is the autumn difference; (j) is the drifting buoy in winter; (k) is the lightweight gradient lifting in winter; and (l) is the winter difference. Figure 10 From (a), (d), (g) and (j), we can see that the depth of the 20-degree Celsius isotherm in the Seychelles Dome region reaches its maximum value of about 100 meters in spring and decreases to its minimum value of about 60 meters in winter, reflecting a significant seasonal variation. Figure 10As shown in (b), (e), (h) and (k), the estimated depths of the 20°C isotherm in spring, summer, autumn and winter by the lightweight gradient boosting model are highly consistent with the spatial distribution of the measured data from the global geostrophic oceanographic real-time observation array, proving the accuracy of the lightweight gradient boosting model in capturing the seasonal variation of the 20°C isotherm depth. Further analysis of the differences between the estimated values ​​and the measured values ​​by the lightweight gradient boosting model shows that the depths of the 20°C isotherm in spring, summer, autumn and winter are highly consistent with the spatial distribution of the measured data from the global geostrophic oceanographic real-time observation array, proving the accuracy of the lightweight gradient boosting model in capturing the seasonal variation of the 20°C isotherm depth. Figure 10 As can be seen from (c), (f), (i), and (l), the differences between the two are generally small. Specifically, the differences in spring and winter are both within 5 meters, while the differences in summer and autumn increase slightly but still do not exceed 10 meters. These results highlight the high accuracy and reliability of the lightweight gradient boosting model in retrieving the depth of the 20°C isotherm.

[0070] like Figure 11 As shown in the figure, the scatter plot of the 20-degree Celsius isotherm depth calculated from the temperature data of the drifting buoy of the global geostrophic oceanography real-time observation array of the present invention and the 20-degree Celsius isotherm depth estimated by lightweight gradient lifting in four seasons, where (a) is spring; (b) is summer; (c) is autumn; and (d) is winter. Figure 11 It can be seen that the 20-degree Celsius isotherm depth estimated by the lightweight gradient lifting model is significantly positively correlated with the 20-degree Celsius isotherm depth calculated by the global geostrophic oceanography real-time observation array drifting buoy, and the scattered points are densely distributed near the isotherm, indicating that the model has a high degree of goodness of fit. Specifically, Figure 11 The coefficient of determination for (a) spring is 0.93, indicating that the model has a high accuracy in retrieving the depth of the 20°C isotherm in spring; Figure 11 The determination coefficient of (b) in summer is 0.90, which shows that the model still maintains good retrieval ability in summer; Figure 11 The coefficient of determination of (c) autumn is 0.92, which further verifies the stability of the model; Figure 11 The coefficient of determination for (d) in winter is as high as 0.98, highlighting the model's excellent performance in retrieving the 20°C isotherm depth in winter. Overall, the lightweight gradient boosting model exhibits excellent inversion results across seasons, demonstrating its reliability and effectiveness in retrieving the 20°C isotherm depth.

[0071] In order to further verify the inversion capability of the lightweight gradient boosting model for the seasonal variation of the 20°C isotherm depth in the Seychelles Dome region of the South Indian Ocean, four key months, April, July, October and January, were selected for detailed evaluation.

[0072] like Figure 12As shown in the figure, the difference between the 20-degree Celsius isotherm depth calculated from the drifting buoy data of the global geostrophic oceanography real-time observation array of the present invention and the true value, wherein (a) is the drifting buoy in April; (b) is the lightweight gradient boost in April; (c) is the difference in April; (d) is the drifting buoy in July; (e) is the lightweight gradient boost in July; (f) is the seasonal difference in July; (g) is the drifting buoy in October; (h) is the lightweight gradient boost in October; (i) is the difference in October; (j) is the drifting buoy in January; (k) is the lightweight gradient boost in January; and (l) is the difference in January. Figure 12 From (a), (d), (g) and (j), we can see that the depth of the 20-degree Celsius isotherm reaches its deepest depth in April, about 100 meters, and reaches its shallowest depth in January, about 50 meters, reflecting the obvious seasonal variation characteristics of the 20-degree Celsius isotherm depth in this area. Figure 12 As shown in (b), (e), (h) and (k), the spatial distribution of the 20°C isotherm depth estimation results of the lightweight gradient boosting model for these four months is highly consistent with the measured data of the global geostrophic oceanography real-time observation array, indicating that the model can effectively capture the spatial variation of the 20°C isotherm depth. Further difference analysis was carried out by Figure 12 Figures (c), (f), (i), and (l) show that the differences between the model estimates and the measured values ​​are small. Specifically, the differences in April and January are both within 5 meters, while the differences in July and October are within 10 meters. These results fully demonstrate the accuracy and reliability of the lightweight gradient lifting model in retrieving the 20°C isotherm depth in the Seychelles Dome region in different seasons.

[0073] To verify the accuracy of the lightweight gradient boosting model for the inversion of the 20°C isotherm depth in April, July, October, and January, the present invention uses the relationship between the lightweight gradient boosting model estimates and the observations calculated by the Global Geostrophic Oceanography Real-Time Array drifting buoys, and quantifies the model's goodness of fit using the R² value.

[0074] like Figure 13 As shown in the figure, the scatter plot of the 20-degree Celsius isotherm depth calculated from the temperature data of the drifting buoy of the global geostrophic oceanography real-time observation array of the present invention and the 20-degree Celsius isotherm depth estimated by lightweight gradient lifting, where (a) is April; (b) is July; (c) is October; and (d) is January. Figure 13 It can be seen that the inversion performance of the lightweight gradient boosting model in different seasons also has some differences. Overall, the correlation coefficient between the 20-degree Celsius isotherm depth simulated by the model in January and the 20-degree Celsius isotherm depth calculated from the drifting buoy data temperature reached 0.96. The correlation coefficient between the two in April was 0.95, and the correlation coefficients in July and October were both 0.85, indicating that the model can accurately invert the seasonal changes in the 20-degree Celsius isotherm depth.

[0075] This paper compares the 20-degree Celsius isotherm depth data measured by the drifting buoys of the Global Geostrophic Oceanography Real-Time Observation Array with the 20-degree Celsius isotherm depth data estimated by the lightweight gradient boosting model in a specific area (longitude range 50.5°E to 80.5°E, latitude range 10.5°S to 5.5°S) in the form of monthly average values ​​in 2022.

[0076] like Figure 14 As shown in the figure, the monthly average value of the 20-degree Celsius isotherm depth calculated from the temperature data of the drifting buoy of the global geostrophic oceanography real-time observation array of the present invention and the 20-degree Celsius isotherm depth estimated by the lightweight gradient lifting model, where the horizontal axis is the month and the vertical axis is the depth. Figure 14 The seasonal variation in the depth of the 20°C isotherm in this region (longitude range 50.5°E to 80.5°E, latitude range 10.5°S to 5.5°S) shows a clear semi-annual cycle: data from the Global Geostrophic Oceanographic Real-Time Observation Array indicate that the 20°C isotherm depth reaches its annual maximum of 86.93 meters in April, then drops to a minimum of 70.76 meters in July, then rises to 84.93 meters in August, and then drops again to 74.67 meters in December. The 20°C isotherm depth inverted by the lightweight gradient boosting model also reveals a semi-annual trend, with the 20°C isotherm depth reaching a maximum of 88.30 meters in April, but its minimum value occurs earlier in June at 74.39 meters, then rises to 85.31 meters in August, and then drops to 77.05 meters in December. Although there is a slight difference between the two in the months when the minimum values ​​occur, overall, the 20-degree Celsius isotherm depth estimated by the lightweight gradient boosting model and the 20-degree Celsius isotherm depth measured by the Global Geostrophic Oceanography Real-Time Observation Array drifting buoy maintain a high degree of consistency in their changing trends, verifying the accuracy and reliability of the model in seasonal inversion in this region.

[0077] Step 6: Use the estimated 20°C isotherm depth to derive seasonal variations in the Seychelles Dome in the South Indian Ocean. Next, during the data preprocessing phase, the present invention can perform feature selection or dimensionality reduction, leveraging the strong correlations between variables to improve the inversion accuracy and stability of the lightweight gradient boosting model. The present invention calculated the correlation coefficients between nine different variables (sea level anomaly, temperature at 50 meters, zonal wind stress, meridional wind stress, temperature at 100 meters, wind stress curl, sea surface temperature, zonal wind stress gradient, and meridional wind stress gradient) and the depth of the 20°C isotherm estimated using the lightweight gradient boosting model.

[0078] like Figure 15As shown in the figure, the correlation coefficients between the various parameters of the present invention and the depth of the 20-degree Celsius isotherm estimated by the lightweight gradient lifting model are plotted, where the horizontal axis represents the sea level height anomaly, 50-meter depth temperature, latitudinal wind stress, meridional wind stress, 100-meter depth temperature, wind stress curl, sea surface temperature, latitudinal wind stress gradient, and meridional wind stress gradient; the vertical axis represents the correlation coefficient. Figure 15 The strongest correlation is observed between the temperature at 100 meters and the depth of the 20°C isotherm, with a correlation coefficient of 0.92. This is followed by the temperature at 50 meters and sea level anomaly, with correlation coefficients of 0.54 and 0.40, respectively. The least correlated relationship is with sea surface temperature, with correlation coefficients of -0.21. In contrast, the correlation coefficients between sea surface temperature, longitude, and latitude (which have weaker correlations with the depth of the 20°C isotherm) are -0.21, -0.08, and -0.12, respectively. Other variables, such as meridional wind stress, zonal wind stress, wind stress curl, and the latitudinal and meridional components of wind stress curl, also exhibit varying degrees of correlation. These correlation analysis results indicate that the temperature at 100 meters, the temperature at 50 meters, and sea level anomaly are key factors influencing the depth of the 20°C isotherm and can be used as key features for feature selection, helping to improve the inversion accuracy and stability of the model.

[0079] like Figure 16 As shown in FIG, the spatial root mean square error and spatial correlation coefficient between the various parameters of the present invention and the 20 degrees Celsius isotherm depth estimated by the lightweight gradient lifting model. Figure 16 The strongest spatial correlation is observed between the 100-meter depth temperature and the model-estimated 20°C isotherm depth, with a correlation coefficient of 0.9 and a root mean square error of 50 meters in the Seychelles Dome region. The next strongest correlations are with the 50-meter depth temperature and sea level anomaly, with correlation coefficients of 0.8 and 0.7, respectively, and root mean square errors of 60 and 70 meters, respectively. These results indicate that the 100-meter and 50-meter depth temperature and sea level anomalies are the primary variables influencing the seasonal variation in the thermocline depth over the Seychelles Dome in the South Indian Ocean. In contrast, the correlation coefficients for sea surface temperature, meridional wind stress, zonal wind stress, wind stress curl, meridional wind stress gradient, and zonal wind stress gradient are lower, at only 0.1, with a root mean square error of 80 meters, indicating that these variables have a lesser influence on the model-estimated 20°C isotherm depth.

[0080] Although the present invention has been described in detail through the above preferred embodiments, it should be understood that the above description is not intended to limit the present invention. After reading the above description, various modifications and substitutions of the present invention will become apparent to those skilled in the art. Therefore, the scope of protection of the present invention should be defined by the appended claims.

Claims

1. A method for studying the seasonal variation of the thermocline depth in the Seychelles Dome in the South Indian Ocean based on artificial intelligence inversion, characterized in that: The method includes: Step 1: Obtain sea surface data of the Seychelles Dome in the South Indian Ocean and global geostrophic oceanographic real-time observation array data, and process them into monthly average data; Step 2: Build lightweight gradient boosting models, extreme gradient boosting models, and category gradient boosting models, and use monthly average data to select and analyze input variables; Step 3: Select a lightweight gradient boosting model and determine the input variables based on feature importance. Step 4: Verify the lightweight gradient boosting model; Step 5: Use the validated lightweight gradient boosting model to estimate the change in isotherm depth; Step 6. Use the estimated isotherm depth changes to obtain the seasonal variation of the Seychelles Dome in the South Indian Ocean.

2. The method according to claim 1, characterized in that In step one, the sea surface data of the Seychelles Dome in the South Indian Ocean is the fifth-generation global reanalysis data of the European Centre for Medium-Range Weather Forecasts meteorological reanalysis data, which includes sea level height anomaly, latitudinal wind stress, latitudinal wind stress gradient, meridional wind stress and meridional wind stress gradient; the global geostrophic oceanography real-time observation array data includes sea surface temperature, latitude, longitude, 20 degrees Celsius isotherm depth, 50-meter depth temperature and 100-meter depth temperature; the processing into monthly average data is to process the sea surface data of the Seychelles Dome in the South Indian Ocean and the global geostrophic oceanography real-time observation array data into monthly average data, and interpolate to a spatial resolution of 1 degree × 1 degree, covering the Seychelles Dome area in the Indian Ocean, and the time period is from January 2004 to December 2022.

3. The method according to claim 2, characterized in that The temporal resolution of the sea surface data of the Seychelles Dome in the South Indian Ocean is monthly, and the spatial resolution is 0.25 degrees × 0.25 degrees; the spatial resolution of the global geostrophic oceanographic real-time observation array data is 1 degree × 1 degree, the temporal resolution is monthly, and the depth is 0~2000 meters.

4. The method according to claim 1, wherein In step 2, the Seychelles Dome in the South Indian Ocean is taken as the study area, where the latitude of the study area is from 15 degrees south to the equator and the longitude is from 40 degrees east to 90 degrees east; the Seychelles Dome is an area where the depth of the 20-degree Celsius isotherm is less than 100 meters and the core is as shallow as 60 meters; the analysis includes analyzing the seasonal variation of the input variables and the correlation between the depth of the 20-degree Celsius isotherm and the input variables; the seasonal variation of the input variables is a seasonal fluctuation pattern; the role of the correlation between the depth of the 20-degree Celsius isotherm and the input variables is to determine that the variables of the lightweight gradient boosting model, the extreme gradient boosting model and the category gradient boosting model include 100-meter depth temperature, 50-meter depth temperature and sea level height anomaly; the input variables are wind stress curl, sea level height anomaly, sea surface temperature, 50-meter depth temperature, 100-meter depth temperature, zonal wind stress, wind stress curl, zonal wind stress gradient, meridional wind stress gradient, and longitude and latitude; The wind stress curl is obtained by calculating the latitudinal and longitudinal components of wind stress using the bulk formula and applying Stokes' theorem.

5. The method according to claim 4, characterized in that The bulk formula is: ； in, is the meridional wind stress; is the zonal wind stress; is the wind speed in the surface layer of 10 meters; It faces east; It is north-facing; Indicates the air density; is the drag coefficient, which depends on the height of the wind.

6. The method according to claim 1, characterized in that In step three, the feature importance is obtained by calculating the importance of the input variables to the inversion of the 20-degree Celsius isotherm depth; the confirmed input variables are the 100-meter depth temperature, sea surface temperature, 50-meter depth temperature, sea level height anomaly, meridional wind stress gradient, zonal wind stress, meridional wind stress, longitude, wind stress curl, zonal wind stress gradient and latitude as input values ​​of the lightweight gradient boosting model to estimate the 20-degree Celsius isotherm depth in the Indian Ocean, which is obtained by the root mean square error, mean absolute error and determination coefficient; the basis for selecting the lightweight gradient boosting model is that the lightweight gradient boosting model, the extreme gradient boosting model and the category gradient boosting model are consistent with the measured data in the consistency calculation when inverting the 20-degree Celsius isotherm depth.

7. The method according to claim 1, characterized in that In step four, the lightweight gradient boosting model is verified in the Seychelles Dome area in the Indian Ocean in 2022 by analyzing the spatial distribution of the root mean square error and the determination coefficient between the 20-degree Celsius isotherm depth estimated by the lightweight gradient boosting model and the 20-degree Celsius isotherm depth calculated from the temperature data of the drifting buoy of the global geostrophic oceanography real-time observation array; the root mean square error does not exceed 5 meters; the determination coefficient is greater than 0.

8.

8. The method according to claim 1, characterized in that In step five, the estimated change in isotherm depth is obtained by estimating the change in the 20-degree Celsius isotherm depth in the Seychelles Dome region of the Indian Ocean in April, July, October, and January using a lightweight gradient boosting model; in April, July, October, and January, the correlation coefficient between the results estimated using the lightweight gradient boosting model and the observations calculated by the drifting buoys of the Global Geostrophic Oceanography Real-Time Observation Array is not less than 0.

85.

9. The method according to claim 1, characterized in that In step five, the monthly average 20-degree Celsius isotherm depth data for 2022 measured by the Global Geostrophic Oceanography Real-Time Observation Array drifting buoys at longitudes of 50.5°E to 80.5°E and latitudes of 10.5°S to 5.5°S are consistent with the monthly average 20-degree Celsius isotherm depth data for 2022 estimated by the lightweight gradient boosting model.

10. The method according to claim 1, characterized in that In step six, the correlation coefficients between the sea level anomaly, the temperature at 50 meters depth, the latitudinal wind stress, the meridional wind stress, the temperature at 100 meters depth, the wind stress curl, the sea surface temperature, the latitudinal wind stress gradient, and the meridional wind stress gradient and the 20 degrees Celsius isotherm depth estimated by the lightweight gradient lifting model are calculated; the correlation coefficient between the temperature at 100 meters depth and the 20 degrees Celsius isotherm depth is 0.92; the correlation coefficient between the temperature at 50 meters depth and the 20 degrees Celsius isotherm depth is 0.54; and the correlation coefficient between the sea level anomaly and the 20 degrees Celsius isotherm depth is 0.40.

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