A method for studying seasonal variation of thermocline depth in Seychelles Dome, southern Indian Ocean based on artificial intelligence inversion

Abstract

This invention discloses a method for studying the seasonal variation of the thermocline depth of the Seychelles Dome in the southern Indian Ocean based on artificial intelligence inversion. The method includes: acquiring and processing sea surface data and real-time global geostrophic oceanographic observation array data for the Seychelles Dome in the southern Indian Ocean; establishing three models and selecting and analyzing input variables using the aforementioned data; selecting a lightweight gradient boosting model and confirming the input variables; validating the lightweight gradient boosting model; estimating the change in the depth of the 20°C isotherm; and using the estimation results to obtain the seasonal variation of the Seychelles Dome in the southern Indian Ocean. This invention solves the problem in existing technologies for estimating the depth of the 20°C isotherm from satellite-acquired sea surface data in the Indian Ocean using machine learning methods. By using a lightweight gradient boosting model to estimate the change in the depth of the 20°C isotherm of the Seychelles Dome in the southern Indian Ocean, this invention reflects the seasonal variation of the Seychelles Dome.

Description

Technical Field

[0001] This invention relates to a method for studying the seasonal variation of thermocline depth, specifically a method based on artificial intelligence inversion to study the seasonal variation of thermocline depth in the Seychelles Dome in the southern Indian Ocean. Background Technology

[0002] The Seychelles Dome in the southern Indian Ocean, a significant ocean-atmosphere coupling system in the southwestern tropical Indian Ocean, has long been a focus of physical oceanography research due to its dynamic seasonal and interannual variations. The dynamic thermocline uplift driven by the unique wind stress curl field in this region makes the spatiotemporal variability at the depth of the 20°C isotherm a core diagnostic parameter for analyzing the thermal stratification and atmospheric response of the Indian Ocean.

[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), nonlinear modeling methods based on deep learning have made breakthrough progress in the field of ocean subsurface temperature inversion. In the Indian Ocean region, 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 of the Indian Ocean, and used a limiting 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 novel spatiotemporal twin convolutional neural network model aimed at improving the accuracy of subsurface reconstruction in the Indian Ocean. Reference 3 (Su H, Wu XB, Yan XH, et al. Estimation of subsurface temperature anomaly in the Indian Ocean during recent global surface warminghiatus from satellite measurements: A support vector machine approach[J]. Remote Sensing of Environment, 2015, 160: 63-71) proposes a support vector machine method that uses satellite remote sensing data such as sea surface temperature anomalies, sea surface height anomalies, and sea surface salinity anomalies to estimate subsurface temperature anomalies in the Indian Ocean, successfully achieving accurate estimation of subsurface temperature anomalies 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 convolutional block attention modules-convolutional neural networks, which uses satellite observation data to simultaneously invert the subsurface thermal and salinity structures of the tropical Indian Ocean. 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 enhanced block attention module-convolutional neural network, used to reconstruct the thermocline depth of 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 had better performance than similar methods without clustering. 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 a marine knowledge-driven model for reconstructing global subsurface temperature and salinity.Reference 8 (Su H, Jiang J, Wang A, et al. Subsurface Temperature Reconstruction for the Global 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 gridded data from a global geostrophic oceanographic real-time observation array to reconstruct and generate a new long-term global ocean upper 2000-meter temperature dataset (covering 1993-2020), which is named 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 multiple remote sensing data with in-situ observations, compared four types of models under the two major frameworks of gradient enhancement and deep learning, and selected the optimal model, deep forest, to construct a high-resolution subsurface temperature dataset of 1 / 4 degree at a depth of 0-2000 meters globally 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)) proposes a new ensemble learning algorithm, extreme gradient boosting, for inverting surface temperature and salinity anomalies at a depth of 2000 meters above the global ocean.To achieve the goal of transparent ocean observation, reference 11 (Jiang JW, Wang J, Liu YP, et al. SWO: A Lightweight Window Spatiotemporal Attention Network Reconstructs SubsurfaceTemperature Structure[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2024, 17: 19274-19287) innovatively utilizes artificial intelligence technology to reconstruct the global three-dimensional ocean structure from remote sensing data through a spatiotemporal attention mechanism. Addressing the significant computational challenges posed by high-resolution satellite imagery, a spatiotemporal window ocean network is proposed. This network employs a special computational strategy and a spatiotemporal window attention mechanism to reduce complexity.

[0004] In summary, in the Indian Ocean region, existing technologies do not utilize machine learning methods to estimate the depth of the 20°C isotherm from satellite-acquired sea surface data. Summary of the Invention

[0005] The purpose of this invention is to provide a method for studying the seasonal variation of the thermocline depth in the Seychelles Dome of the southern Indian Ocean based on artificial intelligence inversion. This method addresses the problem in existing technologies in the Indian Ocean region that do not utilize machine learning methods to estimate the 20°C isotherm depth from satellite-acquired sea surface data. By using a lightweight gradient boosting model to estimate the variation of the 20°C isotherm depth in the Seychelles Dome, the method reflects the seasonal variation of the Seychelles Dome in the southern Indian Ocean. Within a specific region, the 20°C isotherm depth estimated by the lightweight gradient boosting model shows a significant positive correlation with the 20°C isotherm depth calculated by drifting buoys from the Global Geostrophic Oceanographic Array (GGEO). The lightweight gradient boosting model's estimation of the 20°C isotherm depth exhibits low error and high correlation in most areas of the Seychelles Dome in the southern Indian Ocean.

[0006] To achieve the above objectives, this invention provides a method for studying the seasonal variation of the thermocline depth in the Seychelles Dome of the southern Indian Ocean based on artificial intelligence inversion. This method includes: Step 1: Obtain sea surface data of the Seychelles Dome in the southern Indian Ocean and data from the global geostrophic oceanography real-time observation array, and process them into monthly average data respectively; Step 2: Establish lightweight gradient boosting model, extreme gradient boosting model and categorical gradient boosting model, and select and analyze input variables using monthly average data; Step 3: Select a lightweight gradient boosting model and confirm the input variables based on feature importance; Step 4: Validate the lightweight gradient boosting model; Step 5: Using the validated lightweight gradient boosting model, estimate the change in isotherm depth; Step 6: Calculate the seasonal variation of the Seychelles Dome in the southern Indian Ocean by estimating the changes in isotherm depth.

[0007] Preferably, in step one, the sea surface data of the Seychelles Dome in the southern Indian Ocean is the fifth generation of European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis data, which includes sea level height anomalies, zonal wind stress, zonal wind stress gradient, meridional wind stress, and meridional wind stress gradient; the global geostrophic oceanographic real-time observation array data includes sea surface temperature, latitude, longitude, 20°C isotherm depth, 50-meter depth temperature, and 100-meter depth temperature; the processing into monthly average data involves processing both the sea surface data of the Seychelles Dome in the southern Indian Ocean and the global geostrophic oceanographic real-time observation array data into monthly average data and interpolating them to a spatial resolution of 1 degree × 1 degree, covering the Seychelles Dome region of the Indian Ocean, and the time period from January 2004 to December 2022.

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

[0009] Preferably, in step two, the Seychelles Dome in the southern Indian Ocean is used as the study area, which ranges from 15 degrees south latitude to the equator and from 40 degrees east longitude to 90 degrees east longitude; the Seychelles Dome is a region where the 20°C isotherm depth 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 20°C isotherm depth and the input variables; the seasonal variation of the input variables follows a seasonal fluctuation pattern; the correlation between the 20°C isotherm depth and the input variables is used to determine... The variables in the lightweight gradient boosting model, the extreme gradient boosting model, and the categorical gradient boosting model include temperature at a depth of 100 meters, temperature at a depth of 50 meters, and sea level anomaly. The input variables are wind stress curl, sea level anomaly, sea surface temperature, temperature at a depth of 50 meters, temperature at a depth of 100 meters, zonal wind stress, wind stress curl, zonal wind stress gradient, meridional wind stress gradient, longitude, and latitude. The wind stress curl is calculated by the bulk formula for the zonal and meridional components of wind stress and obtained by applying Stokes' theorem.

[0010] More preferably, the bulk formula is: ; in, For meridional wind stress; This refers to zonal wind stress; The surface wind speed is 10 meters per second. Facing east; North-facing; Indicates air density; This is the drag coefficient, which depends on the wind height.

[0011] Preferably, in step three, the feature importance is obtained by calculating the importance of the input variables to the inversion of the 20°C isotherm depth; the confirmed input variables are obtained by using the 100-meter depth temperature, sea surface temperature, 50-meter depth temperature, sea level height anomaly, meridional wind stress gradient, zonal 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°C isotherm depth in the Indian Ocean, and obtaining the results through root mean square error, mean absolute error, and coefficient of determination; the basis for selecting the lightweight gradient boosting model is that, in the consistency calculation between the lightweight gradient boosting model, the extreme gradient boosting model, and the categorical gradient boosting model and the measured data when inverting the 20°C isotherm depth, only the lightweight gradient boosting model is consistent with the measured data.

[0012] Preferably, in step four, the verification of the lightweight gradient lift model involves analyzing the spatial distribution of the root mean square error and coefficient of determination between the 20°C isotherm depth estimated by the lightweight gradient lift model and the 20°C isotherm depth calculated from the temperature data of the drifting buoys of the Global Geostrophic Oceanographic Observatory in the Seychelles Dome region of the Indian Ocean in 2022; the root mean square error does not exceed 5 meters; and the coefficient of determination is greater than 0.8.

[0013] Preferably, in step five, the estimated change in isotherm depth is obtained by using a lightweight gradient boosting model to estimate the change in 20°C isotherm depth in the Seychelles Dome region of the Indian Ocean in April, July, October, and January; and in April, July, October, and January, the correlation coefficient between the result estimated by the lightweight gradient boosting model and the observed value calculated by the drifting buoy of the Global Geostrophic Oceanographic Array is not less than 0.85.

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

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

[0016] This invention provides a method for studying the seasonal variation of the depth of the Seychelles Dome thermocline in the southern Indian Ocean based on artificial intelligence inversion. This method solves the problem in existing technologies in the Indian Ocean region that do not utilize machine learning methods to estimate the depth of the 20°C isotherm from sea surface data obtained from satellites. It has the following advantages: This invention reflects the seasonal variation of the Seychelles Dome in the southern Indian Ocean by using a lightweight gradient lifting model to estimate the depth of the 20°C isotherm. The depth of the 20°C isotherm in this region reaches its maximum in spring, at approximately 100 meters, while shrinking to its minimum in winter, at approximately 60 meters, exhibiting significant seasonal variation characteristics.

[0017] This invention demonstrates a significant positive correlation between the 20°C isotherm depth estimated by the lightweight gradient lift model and the 20°C isotherm depth calculated by drifting buoys from the Global Geostrophic Oceanographic Array (GGEO) within a specific region (longitude 50.5°E to 80.5°E, latitude 10.5°S to 5.5°S). The R² values ​​for these four seasons are 0.93, 0.90, 0.92, and 0.98, respectively. This shows the effectiveness and reliability of the lightweight gradient lift model across different seasons. Spatially, the lightweight gradient lift model's estimation of the 20°C isotherm depth exhibits low error (root mean square error < 5 meters) and high correlation (coefficient of determination > 0.8) in most of the Seychelles Dome region of the southern Indian Ocean.

[0018] This invention utilizes a lightweight gradient boosting algorithm model with multiple parameters, demonstrating high accuracy in estimating the depth of the 20°C isotherm in the Seychelles Dome of the southern Indian Ocean. The unique feature of this lightweight gradient boosting algorithm model lies in its simple structure, yet it can directly extract feature information from each variable using multiple parameters, thus more fully considering the interactions between variables. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the method of the present invention for studying the seasonal variation of the depth of the thermocline in the Seychelles Dome in the southern Indian Ocean based on artificial intelligence inversion.

[0020] Figure 2 This is a depth distribution map of the long-term average 20°C isotherm from January 2004 to December 2022, based on the present invention.

[0021] Figure 3 This is a chart showing the seasonal variation trend of various variables for the monthly average values ​​from 2004 to 2022 in this invention.

[0022] Figure 4 This is a heatmap showing the correlation between the 20°C isotherm depth and the variable Pearson, calculated using data from drifting buoys of the Global Geostrophic Oceanography Real-Time Observation Array (GGEO) of this invention. The numbers and shaded areas represent the correlation coefficients between the various research variables.

[0023] Figure 5 This is a diagram showing the horizontal distribution of the 20°C isotherm depth in the Seychelles dome region in 2022 and the model evaluation results.

[0024] Figure 6 This is a scatter plot comparing the 20°C isotherm depth estimated by the three models of this invention with the 20°C isotherm depth calculated from the drifting buoy data of the Global Geostrophic Oceanography Real-Time Observation Array.

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

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

[0027] Figure 9 This is a horizontal distribution map showing the depth of the 20°C isotherm calculated from the temperature of drifting buoy data from the global geostrophic oceanographic real-time observation array of this invention, and the depth of the 20°C isotherm estimated by the lightweight gradient lift.

[0028] Figure 10 This is an error diagram of the 20°C isotherm depth calculated from drifting buoy data of the global geostrophic oceanographic real-time observation array of this invention.

[0029] Figure 11 This is a scatter plot of the 20°C isotherm depth calculated from the drifting buoy data of the Global Geostrophic Oceanographic Observation Array (GGEO) of this invention, and the estimated 20°C isotherm depth for each of the four seasons using lightweight gradient boosting.

[0030] Figure 12 This is a graph showing the difference between the depth of the 20°C isotherm calculated from the drifting buoy data of the global geostrophic oceanographic real-time observation array of this invention and the actual value.

[0031] Figure 13This is a scatter plot of the 20°C isotherm depth calculated from the temperature of drifting buoy data from the global geostrophic oceanographic real-time observation array of this invention, and the 20°C isotherm depth estimated by the lightweight gradient boost.

[0032] Figure 14 The image shows the monthly average depth of the 20°C isotherm calculated from the drifting buoy data of the global geostrophic oceanographic real-time observation array of this invention, and the depth of the 20°C isotherm estimated by the lightweight gradient boosting model.

[0033] Figure 15 This is a graph showing the correlation coefficients between the various parameters of this invention and the depth of the 20°C isotherm estimated by the lightweight gradient boosting model.

[0034] Figure 16 The spatial root mean square error and spatial correlation coefficient between the various parameters of this invention and the 20°C isotherm depth estimated by the lightweight gradient boosting model are given. Detailed Implementation

[0035] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] Example 1 A method for studying the seasonal variation of the thermocline depth in the Seychelles Dome in the southern Indian Ocean based on artificial intelligence inversion, such as... Figure 1 The flowchart shown is a method for studying the seasonal variation of the thermocline depth in the Seychelles Dome in the southern Indian Ocean based on artificial intelligence inversion. The method includes: Step 1: Obtain sea surface data of the Seychelles Dome in the southern Indian Ocean and data from the Global Geostrophic Oceanography Real-Time Observation Array, and process them into monthly average data.

[0037] This invention utilizes two sources of oceanographic data: satellite-observed sea level data (such as sea level anomalies, zonal wind stress, zonal wind stress gradient, meridional wind stress, meridional wind stress gradient, and wind stress curl) and real-time global geostrophic oceanography (GGE) data (such as sea surface temperature, latitude, longitude, 20°C isotherm depth, 50-meter depth temperature, and 100-meter depth temperature). The longitude and latitude data are derived from gridded GGE data provided by the International Pacific Centre from January 2004 to December 2022, with a spatial resolution of 1° × 1° and a temporal resolution of monthly, covering depths from 0 to 2000 meters. The sea level anomalies are obtained from a monthly gridded dataset provided by a satellite altimeter, with a spatial resolution of 0.25° × 0.25°. 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 global EMC reanalysis data from the European Centre for Medium-Range Weather Forecasts (ECMWF). The temporal resolution is monthly, and the spatial resolution is 0.25 degrees × 0.25 degrees.

[0038] Considering the differences in data resolution and time period between the available input and output data for the Indian Ocean, all data used in this invention were processed into monthly averages and interpolated to a spatial resolution of 1 degree × 1 degree. The coverage area of ​​the Seychelles Dome region in the Indian Ocean is the same, covering the period from January 2004 to December 2022. It should be noted that, to ensure data uniformity, if any variable at a data point has a null value, it is filled with the average value. All data used in this invention are shown in Table 1.

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

[0040] Step 2: Establish lightweight gradient boosting models, extreme gradient boosting models, and categorical gradient boosting models, and select and analyze input variables using monthly average data.

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

[0042] In addition to using a lightweight gradient boosting model, this invention also establishes a limiting gradient boosting model and a class gradient boosting model.

[0043] The Limit Gradient Boosting model is a gradient boosting decision tree algorithm. The Class Gradient Boosting model is an additive model based on the ensemble approach. During training, a forward distribution algorithm is used to achieve greedy learning. In each iteration, a new classification tree is learned, and the residuals between the training results of the previous neighboring trees and the true values ​​of the training samples are fitted. The basic idea of ​​the Limit Gradient Boosting model is consistent with that of the Gradient Boosting Decision Tree; it is also an additive model, but the criteria for node splitting have changed. For both regression and classification problems, a differentiable loss function needs to be defined first. Then, all tree structures are traversed, and the first and second derivatives of all samples under each tree structure are calculated to obtain the loss for each tree structure. By comparing the losses of all tree structures, the structure with the minimum loss is selected as the new learner. The Class Gradient Boosting model is an open-source machine learning library released in 2017 and belongs to the boosting algorithm family. The Class Gradient Boosting model 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 that handles categorical features. It uses a symmetric tree as its base model, supports categorical variables, and 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 for prediction.

[0044] (2) Determine the research area of ​​the above three models, and select and analyze the input variables. In applying the three models described above, the following types of data are typically required: 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 can effectively control overfitting.

[0045] This invention randomly divides all data from January 2004 to December 2022 into two parts: training data and validation data. Specifically, this invention randomly divides the data, using 216 months of data from January 2004 to December 2021 as training data and 12 months of data from January 2022 to December 2022 as test data. The 216 months of data are used for training, and the 12 months of data are used for testing. The application process of the above three models includes two main steps: (1) training and validation; (2) using the trained lightweight gradient boosting model to estimate the depth of the 20°C isotherm. Before applying the three models to invert the depth of the 20°C isotherm, this invention uses satellite sea surface data and marker data from the Global Geostrophic Oceanographic Array to train and validate them, as follows:

[0046] ① Selecting the research area This invention uses the Seychelles Dome in the southern Indian Ocean (from 15°S to the equator, and from 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, this invention presents a long-term average 20°C isotherm depth distribution map from January 2004 to December 2022. (From...) Figure 2 It is known that the Seychelles Dome is a region with a 20-degree Celsius isotherm depth of less than 100 meters and a core depth as shallow as 60 meters.

[0048] ② Calculate the wind stress curl at sea surface To calculate the wind stress curl at sea surface, this invention first uses the bulk formula of prior art 2 (Trenberth KE, LargeW 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 zonal and meridional components of wind stress.

[0049] The bulk formula is as follows: ; in, For meridional wind stress; This refers to zonal wind stress; The surface wind speed is 10 meters per second. Facing east; North-facing; Indicates air density; This is the drag coefficient, which depends on the wind height.

[0050] Then, applying Stokes' theorem, we obtain... The vertical component, namely the sea surface wind stress curl.

[0051] This invention selects wind stress curl, sea level height anomaly, sea surface temperature, temperature at 50 meters depth, temperature at 100 meters depth, zonal wind stress, wind stress curl, zonal wind stress gradient, meridional wind stress gradient, as well as longitude and latitude, as input variables for the above three models to estimate the depth of the 20-degree Celsius isotherm in the Seychelles Dome region of the southern Indian Ocean.

[0052] ③Seasonal variation of input variables This invention analyzes the seasonal variations of nine input variables (wind stress curl, zonal wind stress gradient, meridional wind stress gradient, sea level height anomaly, sea surface temperature, temperature at 50 meters depth, temperature at 100 meters depth, zonal wind stress, and meridional wind stress) to determine their seasonal fluctuation patterns.

[0053] like Figure 3 The figure shows the seasonal variation trend of various variables for the monthly average values ​​from 2004 to 2022 in this invention. Figure 3 It is evident that after 19 years of seasonal averaging of wind stress curl, zonal wind stress gradient, meridional wind stress gradient, sea level anomaly, sea surface temperature, temperature at 50 meters depth, temperature at 100 meters depth, zonal wind stress, and meridional wind stress, the wind stress curl data exhibits a significant annual cycle, peaking in February and troughing in October. The trend of the zonal wind stress gradient is largely consistent with that of the wind stress curl, also demonstrating a clear annual cycle. The data for sea surface temperature, zonal wind stress, and meridional wind stress also show an annual cycle. In addition, the trends of temperature at 50 meters depth, temperature at 100 meters depth, meridional wind stress gradient, and sea surface height anomaly exhibit a relatively significant semi-annual cycle. These findings reveal the seasonal fluctuation patterns of each variable in long-term observations, providing a foundation for further analysis of their interrelationships and their impact on ocean phenomena.

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

[0055] like Figure 4 As shown, this invention presents a heatmap of the correlation between the 20°C isotherm depth and the variable Pearson, calculated from data of drifting buoys in the Global Geostrophic Oceanography Real-Time Observation Array. The numbers and shaded areas represent the correlation coefficients between the various research variables. Figure 4 These coefficients, calculated through Pearson correlation analysis, reveal the strength of the linear relationship between the 20°C isotherm depth calculated from the temperature data of drifting buoys in the Global Geostrophic Oceanographic Array (GGEO) and various variables. Specifically, the correlation between the 20°C isotherm depth and the 100°C isotherm depth is the 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 anomalies are 0.56 and 0.45, respectively, indicating a strong positive correlation between them and the 20°C isotherm depth. However, 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, showing a relatively weak linear relationship. Overall, the estimation performance of the proposed model is closely related to the input variables. The strong correlation between variables such as temperature at a depth of 100 meters, temperature at a depth of 50 meters, and sea level height anomaly and the depth of the 20-degree Celsius isotherm suggests 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 highlight the necessity of considering these key variables in model construction.

[0056] Step 3: Select a lightweight gradient boosting model and confirm the input variables based on feature importance. (1) Model selection This invention further analyzes and compares the aforementioned 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 depth of the 20°C isotherm based on sea surface data. The specific process is as follows: like Figure 5As shown, this invention presents the horizontal distribution of the 20°C isotherm depth in the Seychelles Dome region in 2022 and its model evaluation results. (a), (d), and (g) represent the 20°C isotherm depth of drifting buoys (three identical subplots are provided for easy comparison with subsequent subplots); (b) shows the lightweight gradient boosting model's evaluation of the 20°C isotherm depth in the Seychelles Dome region in 2022; (c) shows the inversion value of the 20°C isotherm depth in the Seychelles Dome region in 2022 obtained by the lightweight gradient boosting model and its comparison with the global geostrophic oceanographic real-time observation array. The difference between the true and false values; (e) is the depth inversion of the 20°C isotherm in the Seychelles Dome region in 2022 by the categorical gradient boosting model; (f) is the difference between the inverted value of the 20°C isotherm depth in the Seychelles Dome region in 2022 by the categorical gradient boosting model and the true value from the Global Geostrophic Oceanography Real-Time Observation Array; (h) is the depth inversion of the 20°C isotherm in the Seychelles Dome region in 2022 by the limiting gradient boosting model; (i) is the difference between the inverted value of the 20°C isotherm depth in the Seychelles Dome region in 2022 by the limiting gradient boosting model and the true value from the Global Geostrophic Oceanography Real-Time Observation Array. Figure 5 (a), (d), and (g) are measured values ​​of the 20°C isotherm depth calculated from drifting buoy temperature data from the Global Geostrophic Oceanographic Array (GGEO), revealing that the 20°C isotherm depth in this region is less than 100 meters, with the core area as shallow as 60 meters. Figure 5 Figures (b), (e), and (h) respectively present the inversion results of the lightweight gradient boosting model, the categorical gradient boosting model, and the ultimate gradient boosting model for the depth of the 20°C isotherm in this year. 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 reproduce the spatial distribution characteristics of the depth of the 20°C isotherm in the Seychelles Dome region quite well. Figure 5 (c), (f), and (i) further compared the model accuracy through the difference analysis between the model inversion values ​​and the measured values. The results show that the depth of the 20°C isotherm inverted by the lightweight gradient boosting model is consistent with the measured data.

[0057] Therefore, in the subsequent depth inversion analysis of the 20°C isotherm in the Seychelles Dome region, this invention selected the lightweight gradient boosting model. The evaluation process of this model fully demonstrated the advantages of lightweight gradient boosting in integrating multi-source ocean data to improve the accuracy of the 20°C isotherm depth inversion, providing strong validation for its application in oceanographic research.

[0058] like Figure 6As shown, a scatter plot comparing the 20°C isotherm depth estimated by the three models of this invention with the 20°C isotherm depth calculated from drifting buoy data of the Global Geostrophic Oceanographic Array (GGEO), where (a) is the lightweight gradient boosting model; (b) is the categorical gradient boosting model; and (c) is the ultimate gradient boosting model. Figure 6 As shown in (a), the lightweight gradient boosting model exhibits significant advantages, with a coefficient of determination as high as 0.97 and a root mean square error of only 2.46 meters; Figure 6 From (b), we can see that the coefficient of determination for the categorical gradient boosting model is 0.96, and the root mean square error is 2.53 m; Figure 6 As shown in (c), the coefficient of determination of the limiting gradient lift model is 0.93, and the root mean square error reaches 4.08 meters. This indicates that the lightweight gradient lift model has higher accuracy and stronger correlation when estimating the depth of the 20°C isotherm.

[0059] (2) Determine input variables based on feature importance Since the importance of various variables in the 20°C isotherm depth inversion model of the Seychelles Dome region in the Indian Ocean varies, in order to explore the weights of different inversion factors in the training of the lightweight gradient boosting model and to more effectively adjust the regression fitting of the inversion factors to make it closer to the measured 20°C isotherm depth value of the Global Geostrophic Oceanographic Array, the importance of 11 variables (temperature at 100m depth, sea surface temperature, temperature at 50m depth, sea level height anomaly, meridional wind stress gradient, zonal wind stress, longitude, wind stress curl, zonal wind stress gradient, and latitude) to the 20°C isotherm depth inversion was calculated and two significant figures were retained for analysis. The higher the importance of the result, the greater the contribution of the variable to the 20°C isotherm depth inversion.

[0060] like Figure 7 The figure shows a comparison of the importance of each input variable to the lightweight gradient boosting model in this invention. Figure 7 The results show that the top five variables are the 100℃ isotherm depth, sea surface temperature, 50℃ isotherm depth, sea level height anomaly, and meridional wind stress gradient, with importance scores of 0.98, 0.91, 0.83, 0.82, and 0.60, respectively. Other parameters, such as zonal wind stress, meridional wind stress, longitude, wind stress curl, zonal 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 20℃ isotherm depth inversion, providing a scientific basis for model optimization and determining the focus of subsequent research.

[0061] Since the selection of the above-mentioned input variables has a significant impact on the performance of the lightweight gradient boosting model, this invention uses 10 different combinations of variables as input values ​​for 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 using statistical indicators such as root mean square error, mean absolute error, and coefficient of determination.

[0062] This invention selects different combinations of variables as input variables based on the importance of the aforementioned features. 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, as detailed in Table 2.

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

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

[0065] like Figure 8 As shown, this diagram illustrates the influence of different parameters of the present invention on the depth inversion results of the 20°C isotherm estimated by the lightweight gradient boosting model. The horizontal axis represents different combinations (combination 1 to combination 10), the left side of the vertical axis represents the mean absolute error (in meters) and root mean square error (in meters), and the right side represents the correlation coefficient and coefficient of determination. The red bars represent the mean absolute error, the blue bars represent the root mean square error, and the black dotted lines represent the coefficient of determination values. Figure 8 It can be seen that the mean absolute error and root mean square error of combination 1 are 6.79 meters and 10.36 meters, respectively, with a coefficient of determination of 0.81. In contrast, the mean absolute error of combination 10 decreases to 0.78 meters, the root mean square error decreases to 1.11 meters, and the coefficient of determination reaches 0.99. This indicates that parameter selection has a significant impact on 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, longitude, wind stress curl, zonal wind stress gradient, and latitude) was selected as the input variables. Its parameter configuration can significantly improve the accuracy of the 20°C isotherm depth inversion, providing an important reference for subsequent research.

[0066] Step 4: Validate the lightweight gradient boosting model After comparing the category-based boosting model and the ultimate gradient boosting model, this invention found that the lightweight gradient boosting model exhibits superior performance in retrieving the 20°C isotherm depth. To further explore the model's retrieval capability in the Indian Ocean region, this 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 from the temperature data of drifting buoys of the Global Geostrophic Oceanographic Array.

[0067] like Figure 9 As shown, this invention presents a horizontal distribution map of the 20°C isotherm depth calculated from the temperature of drifting buoy data from the global geostrophic oceanographic real-time observation array, and a horizontal distribution map of the 20°C isotherm depth estimated by lightweight gradient lifting. (a) is the horizontal distribution map of the root mean square error; (b) is the horizontal distribution map of the coefficient of determination. Figure 9 It is evident that the root mean square error (RMSE) of the estimated 20°C isotherm depth by the lightweight gradient boosting model is generally low (less than 5 meters) across most of the Seychelles Dome in the southern Indian Ocean, while the coefficient of determination (COP) is high (greater than 0.8), indicating the accuracy and relevance of the altitude. Regions with relatively high RMSE and COP are mainly located in the southern Indian Ocean, with RMSE exceeding 20 meters and COP below 0.2. These findings further demonstrate the reliability of the lightweight gradient boosting model in accurately predicting the seasonality of the Seychelles Dome.

[0068] Step 5: Using the validated lightweight gradient boosting model, estimate the change in depth of the 20°C isotherm. To evaluate the effectiveness of the lightweight gradient boosting algorithm in retrieving seasonal variations in the depth of the 20°C isotherm, this invention uses a lightweight gradient boosting model to estimate the depth of the 20°C isotherm in the Seychelles Dome region of the Indian Ocean.

[0069] like Figure 10 As shown, this invention presents an error map of the 20°C isotherm depth calculated from drifting buoy data of the Global Geostrophic Oceanographic Observation Array (GGEO). (a) represents the drifting buoy in spring; (b) represents the lightweight gradient rise in spring; (c) represents the spring difference; (d) represents the drifting buoy in summer; (e) represents the lightweight gradient rise in summer; (f) represents the summer difference; (g) represents the drifting buoy in autumn; (h) represents the lightweight gradient rise in autumn; (i) represents the autumn difference; (j) represents the drifting buoy in winter; (k) represents the lightweight gradient rise in winter; and (l) represents the winter difference. Figure 10 From (a), (d), (g), and (j), it can be seen that the depth of the 20°C isotherm in the Seychelles vault reaches its maximum in spring, approximately 100 meters, and shrinks to its minimum in winter, approximately 60 meters, demonstrating significant seasonal variation. Figure 10As shown in (b), (e), (h), and (k), the spatial distribution of the 20°C isotherm depth estimates by the lightweight gradient boosting model for spring, summer, autumn, and winter is highly consistent with the spatial distribution of the measured data from the Global Geostrophic Oceanographic Array (GGEO), demonstrating the accuracy of the lightweight gradient boosting model in capturing the seasonal variations in the 20°C isotherm depth. Further analysis of the differences between the estimated and measured values ​​from the lightweight gradient boosting model... Figure 10 As shown in (c), (f), (i), and (l), the differences between the two are generally small. Specifically, the differences in spring and winter are both controlled within 5 meters, while the differences in summer and autumn, although slightly increased, still do not exceed 10 meters. These results highlight the high accuracy and reliability of the lightweight gradient boosting model in the depth inversion of the 20°C isotherm.

[0070] like Figure 11 As shown, this invention presents a scatter plot of the 20°C isotherm depth calculated from drifting buoy data of the Global Geostrophic Oceanography Real-Time Observation Array (GGEO) and the estimated 20°C isotherm depth for each of the four seasons using lightweight gradient lifting. (a) represents spring; (b) summer; (c) autumn; and (d) winter. Figure 11 It can be seen that the depth of the 20°C isotherm estimated by the lightweight gradient boosting model is significantly positively correlated with the depth of the 20°C isotherm calculated by the drifting buoys of the Global Geostrophic Oceanography Real-Time Observation Array. The scatter points are densely distributed near the isotherm, indicating a high goodness of fit of the model. Specifically, Figure 11 The coefficient of determination for (a) spring is 0.93, indicating that the model has high accuracy in retrieving the depth of the 20°C isotherm in spring; Figure 11 (b) The coefficient of determination for summer is 0.90, indicating that the model still maintains good inversion ability in summer; Figure 11 The coefficient of determination for (c) autumn is 0.92, further validating the model's stability; while Figure 11 The coefficient of determination for (d) winter is as high as 0.98, highlighting the model's excellent performance in retrieving the depth of the 20°C isotherm during winter. Overall, the lightweight gradient boosting model demonstrates excellent retrieval results in different seasons, proving its reliability and effectiveness in retrieving the depth of the 20°C isotherm.

[0071] To further verify the ability of the lightweight gradient boosting model to retrieve the seasonal variation of the depth of the 20°C isotherm in the Seychelles Dome region of the southern Indian Ocean, this invention selected four key months—April, July, October, and January—for detailed evaluation.

[0072] like Figure 12As shown, this invention presents a graph illustrating the difference between the depth of the 20°C isotherm calculated from drifting buoy data of the Global Geostrophic Oceanographic Observation Array (GGEO). (a) represents the drifting buoy depth in April; (b) represents the light gradient rise in April; (c) represents the difference in April; (d) represents the drifting buoy depth in July; (e) represents the light gradient rise in July; (f) represents the seasonal difference in July; (g) represents the drifting buoy depth in October; (h) represents the light gradient rise in October; (i) represents the difference in October; (j) represents the drifting buoy depth in January; (k) represents the light gradient rise in January; and (l) represents the difference in January. Figure 12 From (a), (d), (g), and (j), it can be seen that the depth of the 20°C isotherm reaches its deepest point in April, approximately 100 meters, while it reaches its shallowest point in January, approximately 50 meters, demonstrating a significant seasonal variation in the depth of the 20°C isotherm in this region. Figure 12 As shown in (b), (e), (h), and (k), the spatial distribution of the lightweight gradient boosting model's estimations of the 20°C isotherm depth for these four months is highly consistent with the measured data from the Global Geostrophic Oceanographic Array, indicating that the model can effectively capture the spatial variations in the 20°C isotherm depth. Further discrepancy analysis is conducted 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 controlled within 5 meters, while the differences in July and October are controlled within 10 meters. These results fully demonstrate the accuracy and reliability of the lightweight gradient lift model in retrieving the depth of the 20°C isotherm in the Seychelles Dome region in different seasons.

[0073] To verify the accuracy of the lightweight gradient boosting model in retrieving the depth of the 20°C isotherm in April, July, October, and January, this invention utilizes the relationship between the estimated values ​​from the lightweight gradient boosting model and the observed values ​​calculated by drifting buoys from the Global Geostrophic Oceanographic Observatory, and uses the R² value to quantify the goodness of fit of the model.

[0074] like Figure 13 As shown, this invention presents a scatter plot of the 20°C isotherm depth calculated from the temperature of drifting buoy data from the Global Geostrophic Oceanography Real-Time Observation Array (GGEO) and the 20°C isotherm depth estimated by lightweight gradient lifting, where (a) represents April; (b) July; (c) October; and (d) January. Figure 13 It can be seen that the lightweight gradient boosting model exhibits some differences in inversion performance across different seasons. Overall, the correlation coefficient between the simulated 20°C isotherm depth in January and the 20°C isotherm depth calculated from drift buoy data reached 0.96. The correlation coefficient was 0.95 in April, and 0.85 in both July and October, indicating that the model can accurately invert the seasonal variations in the 20°C isotherm depth.

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

[0076] like Figure 14 As shown, this invention uses data from drifting buoys of the Global Geostrophic Oceanography Real-Time Observation Array to calculate the depth of the 20°C isotherm and the monthly average depth of the 20°C isotherm estimated by a lightweight gradient lifting model. The horizontal axis represents the month, and the vertical axis represents the depth. From... Figure 14 It is evident that the seasonal variation of the 20°C isotherm depth within this region (longitude range 50.5°E to 80.5°E, latitude range 10.5°S to 5.5°S) exhibits a clear semi-annual cycle: data from the Global Geostrophic Oceanographic Array (GGEO) shows 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, before rising again to 84.93 meters in August, and then falling again to 74.67 meters in December. The 20°C isotherm depth inverted by the lightweight gradient enhancement model also reveals a semi-annual cycle trend, with the 20°C isotherm depth reaching its maximum of 88.30 meters in April, but the minimum occurring slightly earlier in June at 74.39 meters, then rising again to 85.31 meters in August, and then falling again to 77.05 meters in December. Although there are slight differences in the months in which the minimum values ​​occur, overall, the 20°C isotherm depth estimated by the lightweight gradient boosting model and the 20°C isotherm depth measured by the drifting buoys of the Global Geostrophic Oceanography Real-Time Observation Array maintain a high degree of consistency in the trend of change, verifying the accuracy and reliability of the model in seasonal inversion in this region.

[0077] Step Six: Calculate the seasonal variations of the Seychelles Dome in the southern Indian Ocean by estimating the changes in the depth of the 20°C isotherm. Next, in the data preprocessing stage, this invention can perform feature selection or dimensionality reduction operations, utilizing the strong correlation between variables to improve the inversion accuracy and stability of the lightweight gradient boosting model. This invention calculates the correlation coefficients between nine different variables (sea level anomaly, temperature at 50 meters depth, zonal wind stress, meridional wind stress, temperature at 100 meters depth, wind stress curl, sea surface temperature, zonal wind stress gradient, and meridional wind stress gradient) and the 20°C isotherm depth estimated by the lightweight gradient boosting model.

[0078] like Figure 15As shown, this is a graph illustrating the correlation coefficients between various parameters of the present invention and the depths of the 20°C isotherm estimated by the lightweight gradient lifting model. The horizontal axis represents, in order, sea level anomaly, temperature at 50 meters depth, zonal wind stress, meridional wind stress, temperature at 100 meters depth, wind stress curl, sea surface temperature, zonal wind stress gradient, and meridional wind stress gradient; the vertical axis represents the correlation coefficients. Figure 15 The results show that the temperature at a depth of 100 meters has the strongest correlation with the depth of the 20°C isotherm, with a correlation coefficient of 0.92. This is followed by the temperature at a depth of 50 meters and sea level anomalies, with correlation coefficients of 0.54 and 0.40, respectively. The weakest correlation is with sea surface temperature, with a correlation coefficient of -0.21. In contrast, the correlation coefficients for sea surface temperature, longitude, and latitude (which have a weaker correlation with the depth of the 20°C isotherm) are -0.21, -0.08, and -0.12, respectively. Furthermore, other variables such as meridional wind stress, zonal wind stress, wind stress curl, and the zonal and meridional components of wind stress curl also show varying degrees of correlation. These correlation analysis results indicate that the temperature at a depth of 100 meters, the temperature at a depth of 50 meters, and sea level anomalies are key factors affecting the depth of the 20°C isotherm and can be considered as key features for feature selection, helping to improve the accuracy and stability of the model's inversion.

[0079] like Figure 16 As shown, the spatial root mean square error and spatial correlation coefficient between the various parameters of this invention and the 20°C isotherm depth estimated by the lightweight gradient lifting model are presented. Figure 16 The study found that the spatial correlation between the temperature at a depth of 100 meters and the estimated depth of the 20°C isotherm was the strongest, reaching a correlation coefficient of 0.9 in the Seychelles Dome region, with a root mean square error (RMSE) of 50 meters. This was followed by the temperature at 50 meters and sea level anomalies, with correlation coefficients of 0.8 and 0.7, respectively, and RMSEs of 60 and 70 meters. These results indicate that the temperature at 100 meters, the temperature at 50 meters, and the sea level anomaly are the main variables affecting the seasonal variation of the thermocline depth in the Seychelles Dome of the southern 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 were relatively low, at only 0.1, with an RMSE of 80 meters, suggesting that these variables had a smaller impact on the estimated depth of the 20°C isotherm.

[0080] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. 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 southern 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 southern Indian Ocean and data from the global geostrophic oceanography real-time observation array, and process them into monthly average data respectively; The temporal resolution of the sea surface data of the Seychelles Dome in the southern Indian Ocean is monthly, and the spatial resolution is 0.25 degrees × 0.25 degrees; the spatial resolution of the data of the global geostrophic oceanographic real-time observation array is 1 degree × 1 degree, the temporal resolution is monthly, and the depth is 0 to 2000 meters. Step 2: Establish lightweight gradient boosting model, extreme gradient boosting model and categorical gradient boosting model, and select and analyze input variables using monthly average data; The Seychelles Dome in the southern Indian Ocean is used as the study area, which ranges from 15°S to the equator and from 40°E to 90°E. The Seychelles Dome is defined as the region where the 20°C isotherm depth 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 20°C isotherm depth and the input variables. The seasonal variation of the input variables follows a seasonal fluctuation pattern. Step 3: Select a lightweight gradient boosting model and confirm the input variables based on feature importance; The importance of the features is calculated by evaluating the importance of the input variables to the inversion of the 20°C isotherm depth. The confirmed input variables are obtained by using the 100-meter depth temperature, sea surface temperature, 50-meter depth temperature, sea level anomaly, meridional wind stress gradient, zonal wind stress, longitude, wind stress curl, zonal wind stress gradient, and latitude as input values ​​for the lightweight gradient boosting model to estimate the 20°C isotherm depth in the Indian Ocean, and by using the root mean square error, mean absolute error, and coefficient of determination. The selection of the lightweight gradient boosting model is based on the consistency between the lightweight gradient boosting model, the extreme gradient boosting model, and the categorical gradient boosting model and the measured data when inverting the 20°C isotherm depth. Step 4: Validate the lightweight gradient boosting model; The validation of the lightweight gradient lift model was conducted in the Seychelles Dome region of the Indian Ocean in 2022. The spatial distribution of the root mean square error and coefficient of determination between the 20°C isotherm depth estimated by the lightweight gradient lift model and the 20°C isotherm depth calculated from the temperature data of drifting buoys from the Global Geostrophic Oceanographic Array was analyzed. The root mean square error did not exceed 5 meters, and the coefficient of determination was greater than 0.

8. Step 5: Using the validated lightweight gradient boosting model, estimate the change in isotherm depth; Step 6: Calculate the seasonal variation of the Seychelles Dome in the southern Indian Ocean by estimating the changes in isotherm depth.

2. The method according to claim 1, characterized in that, In step one, the sea surface data of the Seychelles Dome in the southern Indian Ocean is the fifth generation of European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis data, which includes sea level anomalies, zonal wind stress, zonal wind stress gradient, meridional wind stress, and meridional wind stress gradient. The data from the Global Geostrophic Oceanography Real-Time Observation Array (GGEO) includes sea surface temperature, latitude, longitude, 20°C isotherm depth, 50-meter depth temperature, and 100-meter depth temperature. The process of converting the data into monthly averages involves processing both the sea surface data of the Seychelles Dome in the southern Indian Ocean and the GGEO data into monthly averages and interpolating them to a spatial resolution of 1 degree × 1 degree, covering the Seychelles Dome region of the Indian Ocean, from January 2004 to December 2022.

3. The method according to claim 1, characterized in that, In step two, the correlation between the 20°C isotherm depth and the input variables is used to determine whether the variables of the lightweight gradient boosting model, the extreme gradient boosting model, and the categorical gradient boosting model include 100-meter depth temperature, 50-meter depth temperature, and sea level anomaly. The input variables are wind stress curl, sea level 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 calculated using the bulk formula to determine the zonal and meridional components of the wind stress, and then obtained by applying Stokes' theorem.

4. The method according to claim 3, characterized in that, The bulk formula is: ; in, For meridional wind stress; This refers to zonal wind stress; The surface wind speed is 10 meters per second. Facing east; North-facing; Indicates air density; This is the drag coefficient, which depends on the wind height.

5. The method according to claim 1, characterized in that, In step five, the estimated changes in isotherm depth are obtained by using a lightweight gradient boosting model to estimate the changes in the 20°C isotherm depth in the Seychelles Dome region of the Indian Ocean in April, July, October, and January. In April, July, October, and January, the correlation coefficient between the results estimated using the lightweight gradient boosting model and the observed values ​​calculated by the drifting buoys of the Global Geostrophic Oceanographic Observatory is no less than 0.

85.

6. The method according to claim 1, characterized in that, In step five, the monthly average 20°C isotherm depth data measured by the drifting buoys of the Global Geostrophic Oceanography Real-Time Observation Array in 2022 is consistent with the monthly average 20°C isotherm depth data estimated by the lightweight gradient lift model in 2022, within the longitude range of 50.5°E to 80.5°E and latitude range of 10.5°S to 5.5°S.

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

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