A thermocline identification method and system based on hyperbolic tangent function fitting

Abstract

The present invention belongs to the technical field of ocean temperature data identification, and discloses a thermocline identification method and system based on hyperbolic tangent function fitting. The method includes: data preparation and preprocessing; profile range selection; curve fitting; determining the upper boundary of the thermocline and the lower boundary of the thermocline by a rolling function. The present invention uses a hyperbolic tangent function to fit the S-shaped characteristic curve of the temperature-depth profile to accurately describe the structure of the ocean thermocline. Compared with the traditional Sigmoid function, the hyperbolic tangent function performs better in fitting steeply changing areas, and can more finely capture the rapid temperature changes in the central area of ​​the thermocline. The present invention uses a trust region reflection algorithm to optimize the fitting parameters (amplitude, steepness, center position, vertical offset) to ensure that the fitting results have higher accuracy and robustness, and are suitable for complex ocean profile data.

Description

Technical Field

[0001] The present invention belongs to the technical field of ocean temperature data identification, and in particular relates to a thermocline identification method and system based on hyperbolic tangent function fitting. Background Art

[0002] In the field of oceanography, the thermocline plays a vital role. As a layer in the ocean where the temperature changes dramatically, it is located between the surface mixed layer and the deep ocean strata, forming a distinct transition zone. Studying the thermocline is not only crucial for understanding the physical and chemical processes of the ocean, but also has great significance for military activities such as underwater navigation, communication, detection and concealment of aircraft.

[0003] At present, there are several main methods for identifying the thermocline boundary:

[0004] Entropy method: This method uses the vertical gradient method to calculate the temperature gradient of each layer underwater, with the absolute value of the temperature gradient greater than 0.05 As a screening condition, the potential location of the thermocline is determined, and then the calculated thermoclines are merged and screened. Finally, the importance of features such as latitude, longitude, depth, temperature, salinity and temperature intensity is analyzed based on the information entropy method, and the comprehensive score of each thermocline is calculated based on the weights of these features. Finally, the layer with the highest score is selected as the thermocline at this point. Although this method comprehensively evaluates the impact of multiple characteristic factors on the formation of the thermocline, it relies heavily on the weights of characteristic factors (such as temperature gradient, depth, salinity, etc.), which may lead to the inability to accurately capture the thermocline boundary in complex temperature profiles.

[0005] Tensor analysis method: This method represents the ocean temperature data as a three-dimensional tensor, and then uses tensor decomposition technology to calculate the depth pattern factor matrix. When new depth data is added, the pattern factor matrix of the tensor is updated by "folding" and significant changes in the newly added row vector are detected. If the change exceeds the threshold, it indicates that this depth may be the boundary of the thermocline. In addition, by comparing the abnormal temperature change tensor with the baseline tensor, the key change points are located, and finally the distribution of the upper and lower boundaries of the thermocline is determined. This method model relies on singular value decomposition (SVD), and the computational complexity is high when updating the temperature profile, which will lead to performance bottlenecks, especially when processing large-scale data.

[0006] Inflection point method: The inflection point method compresses the temperature-depth data into a piecewise linear model, and adjusts the endpoints of the line segment through algorithm iteration to ensure that the deviation of each depth point from its linear fitting value does not exceed the specified threshold. When the temperature gradient of a certain linear fitting reaches the maximum value, it is defined as the main part of the thermocline. However, this method is highly sensitive to the temperature gradient mutation point and is easily affected by noise data.

[0007] Variable representative isotherm method: This method estimates the depth of the thermocline by defining an isotherm representing the thermocline. The upper boundary of the thermocline is defined as the depth point when the sea surface temperature drops by 0.8°C, and the temperature at the lower boundary of the thermocline is calculated by the formula The corresponding depth is the lower boundary of the thermocline. This method is highly dependent on the predefined temperature difference threshold and has poor regional adaptability. It performs well in tropical regions, but has poor results in high-latitude regions (regions with small temperature changes).

[0008] Sigmoid function method: This method determines the boundary of the thermocline by fitting the shape of a typical ocean temperature profile to a Sigmoid function (i.e., an S-shaped function). This method has insufficient fitting accuracy when fitting complex temperature profiles (such as steep areas of the thermocline). In particular, the curve may not capture key features well in areas where the temperature gradient changes dramatically. Summary of the invention

[0009] In order to overcome the problems existing in the related art, the disclosed embodiments of the present invention provide a thermocline identification method and system based on hyperbolic tangent function fitting.

[0010] The technical solution is as follows: A thermocline identification method based on hyperbolic tangent function fitting comprises the following steps:

[0011] S1, data preparation and preprocessing; read the 3D grid data of Argo float, and use cubic spline interpolation to interpolate the original non-uniform grid data in the depth direction into 1-meter interval data in the screened depth range;

[0012] S2, profile range selection: convert the practical salinity and in-situ temperature in the three-dimensional grid data into absolute salinity and conservative temperature, and use them to calculate the Brunt-Väisälä frequency square, determine the depth of the maximum absolute value, and select the temperature profile from the ocean surface to twice the depth as the temperature profile to be fitted;

[0013] S3, curve fitting: the normalized temperature-depth profile is fitted using the hyperbolic tangent function, and the parameters are optimized using the trust region reflectance algorithm;

[0014] S4, determine the upper and lower boundaries of the thermocline by rolling function.

[0015] In step S1, data preparation and preprocessing include:

[0016] S101, reading the three-dimensional grid data of the Argo float, where the three-dimensional grid data includes temperature and salinity data at different geographical locations and different depths;

[0017] S102, screening the depth range and using cubic spline interpolation to interpolate the original non-uniform gridded data in the depth direction into data at 1-meter intervals.

[0018] In step S2, the section range selection includes:

[0019] S201, based on the ocean thermodynamics equation, converts the practical salinity in the three-dimensional grid data into and in situ temperature Convert to absolute salinity and conservative temperature ;

[0020] S202, Calculate Brunt-Väisälä frequency squared , determine the depth of the maximum absolute value, and select the temperature profile from the ocean surface to twice the depth as the temperature profile to be fitted.

[0021] Furthermore, the Brunt-Väisälä frequency squared is calculated The expression is:

[0022] ;

[0023] In the formula, is the acceleration due to gravity, is the specific volume, is the absolute pressure, and are the thermal expansion coefficient and the brine contraction coefficient, is the conservative temperature difference between adjacent seawater layers, is the absolute salinity difference between adjacent seawater layers, It is the pressure difference between two adjacent seawater layers in the vertical direction.

[0024] In step S3, curve fitting includes:

[0025] S301, normalize the temperature data and map the value range to the interval [0,1];

[0026] S302, using a hyperbolic tangent function to fit the normalized temperature-depth profile, the function form is as follows:

[0027] ;

[0028] In the formula, is the curve amplitude, is the steepness of the curve, is the center position of the curve, is the vertical offset of the curve, is the sea water temperature, is the hyperbolic tangent function, and the definition formula is , is the seawater depth, and the depth data is , For the The depth of the seawater where the layer is located;

[0029] S303, optimizing various parameters by using a trust region reflective algorithm TRF.

[0030] In step S303, each parameter is optimized by using the trust region reflective algorithm TRF, including: optimizing parameters a, b, c, d by using the trust region reflective algorithm TRF, the specific steps are:

[0031] (1) Construction of objective function: the fitting objective is to minimize the fitting curve With normalized temperature data The residual sum of squares between defines the objective function, which is expressed as:

[0032] ;

[0033] In the formula, is the objective function, is the number of layers common to seawater, is the predicted value of the curve, is the parameter to be optimized, ;

[0034] (2) Establish and solve subproblems, at the current parameter value Nearby, construct a quadratic approximation model Instead of the objective function , approximate the change of the objective function in the local range, and the expression is:

[0035] ;

[0036] In the formula, is the objective function About the current iteration point The Jacobian matrix of , which represents the sensitivity of the objective function to the parameters, has a dimension of , expressed as ; is the residual vector, reflecting the deviation between the observed value and the model predicted value, with a dimension of , , is the normalized temperature data, representing the observed true temperature value, is the predicted temperature value of the curve model, based on the current parameters Calculated; is the update amount of the model parameters, and its dimension is , is the number of parameters to be optimized, , All are parameter increment vectors; for The transpose of is the transpose symbol;

[0037] The goal of this subproblem is to minimize the quadratic approximation model , in the trust region radius Solve the parameter increment under the restriction of , ensuring the optimal update step size No more than , the expression is:

[0038] ;

[0039] In the formula, For vector The norm of is defined as ;

[0040] (3) Update the iteration point according to the parameter increment obtained by the solution , update the model parameters as:

[0041] ;

[0042] In the formula, is the updated parameter, , the above parameters are used to recalculate ;

[0043] (4) Model evaluation: In each iteration, the quadratic approximation model is evaluated For the actual objective function Whether the decline prediction is accurate; by calculating the ratio of the actual objective function decline to the model predicted decline , determine the current step length the rationality of

[0044] ;

[0045] In the formula, The current iteration point The objective function value at represents the fitting error under the current parameters; The updated parameters The objective function value at represents the fitting error after updating the parameters; The quadratic approximation model exist The value at , that is, the model prediction value at the current iteration point; The quadratic approximation model In parameter increment The value at represents the model's prediction after the parameter update;

[0046] (5) Trust region radius adjustment, according to The value of adjusts the trust region radius , to control the parameter update range, when When , the current model fits well within the trust region, the radius of the trust region is expanded, and a larger step size is allowed to update; when When , the current model prediction is inaccurate and the trust region radius needs to be reduced; when When , the current trust region range is appropriate, and the trust region radius remains unchanged;

[0047] (6) Convergence judgment: when the parameter update amount The norm of Less than the preset threshold , or when the change in the objective function value is less than the preset threshold When the maximum number of iterations is reached Stop optimization.

[0048] In step S4, the upper boundary of the thermocline is determined by a rolling function, including:

[0049] First, after fitting the temperature curve using the hyperbolic tangent function, calculate the temperature value at a depth of 10 meters , and set it as the reference temperature;

[0050] Secondly, the temperature is de-normalized to restore to the original temperature unit;

[0051] Then, the temperature data of each depth point is traversed in positive order and compared with The depth where the difference is 0.2℃ is determined as the depth of the upper boundary of the thermocline and is determined as TTD. The expression is:

[0052] ;

[0053] In the formula, To take the minimum value, it is used to find the minimum depth that meets the conditions , For Depth Temperature The temperature at a depth of 10 meters The absolute difference is greater than or equal to 0.2℃.

[0054] In step S4, the lower boundary of the thermocline is determined by a rolling function, including:

[0055] First, the depth of 10 meters above the deepest point of the hyperbolic tangent function fitting curve is selected as the reference depth. The temperature at this depth As a reference temperature, this reference temperature is denormalized to restore its original units;

[0056] Then, traverse each depth point in reverse order. When the temperature of a certain depth point is When the temperature difference reaches 0.2℃, the depth is defined as the depth BTD of the lower boundary of the thermocline; the calculation formula of depth BTD is:

[0057] ;

[0058] In the formula, To take the maximum value, it is used to find the maximum depth that meets the conditions , For Depth Temperature The temperature at a depth of 10 meters above the deepest point of the fitting curve The absolute difference is greater than or equal to 0.2℃.

[0059] After step S4, the boundary calculation result is performed, and the selected multiple grid points are calculated respectively to obtain a curve fitted by a hyperbolic tangent function.

[0060] Another object of the present invention is to provide a thermocline identification system based on hyperbolic tangent function fitting, the system implements the thermocline identification method based on hyperbolic tangent function fitting, the system comprising:

[0061] Data preparation and preprocessing module, used to read the three-dimensional grid data of Argo float, and use cubic spline interpolation to interpolate the original non-uniform grid data in the depth direction into 1-meter interval data in the screened depth range;

[0062] The profile range selection module is used to convert the practical salinity and in-situ temperature in the three-dimensional grid data into absolute salinity and conservative temperature, and to calculate the Brunt-Väisälä frequency square, determine the depth of the maximum absolute value, and select the temperature profile from the ocean surface to twice the depth as the temperature profile to be fitted;

[0063] A curve fitting module is used to fit the normalized temperature-depth profile using a hyperbolic tangent function and to optimize various parameters using a trust region reflectance algorithm;

[0064] The module for determining the upper and lower boundaries of the thermocline is used to determine the upper and lower boundaries of the thermocline through a rolling function.

[0065] Combining all the above technical solutions, the beneficial effects of the present invention are as follows: the present invention uses the hyperbolic tangent function to fit the S-shaped characteristic curve of the temperature-depth profile and accurately describes the structure of the ocean thermocline. Compared with the traditional Sigmoid function, the hyperbolic tangent function performs better in fitting steeply changing areas and can more finely capture the rapid temperature changes in the central area of ​​the thermocline. The present invention uses the trust region reflective algorithm (TRF) to optimize the fitting parameters (amplitude, steepness, center position, vertical offset) to ensure that the fitting results have higher accuracy and robustness, and are suitable for complex ocean profile data.

[0066] Compared with the prior art, the advantages of the present invention further include:

[0067] Higher fitting accuracy: The hyperbolic tangent function has excellent performance in simulating the complex temperature change characteristics of the thermocline, especially in the steeply changing area in the middle of the thermocline, and its fitting accuracy is better than that of the Sigmoid function.

[0068] Strong robustness: Able to adapt to the thermocline characteristics of different regions and seasons, including high-latitude regions and multi-layer thermocline profiles.

[0069] Intuitive and flexible parameters: The four parameters of the hyperbolic tangent function (amplitude, slope, center point, and vertical offset) all have clear physical meanings and can be easily adjusted to suit different temperature profiles.

[0070] Low computational complexity: It is more efficient in processing large-scale data, has low computational cost, and is suitable for global climatological analysis.

[0071] Wide applicability: The performance in the equatorial and subtropical regions is particularly stable, while being able to accurately capture seasonal changes, providing a solid foundation for long-term monitoring and dynamic studies of the thermocline boundary.

[0072] As auxiliary evidence of the inventiveness of the claims of the present invention, it is also reflected in the following important aspects:

[0073] The present invention can be widely used in the fields of marine environment monitoring, marine resource development, climate change research and military covert communication, etc., to improve the accuracy of thermocline identification and reduce the cost of data analysis. In particular, in the fields of marine detection and submarine stealth technology, it can provide more accurate thermocline information and enhance the optimization of underwater acoustic performance. Existing methods (such as entropy method, tensor analysis method, inflection point method, etc.) have problems such as low accuracy, high computational complexity and poor adaptability when identifying thermocline boundaries in complex marine environments. The present invention introduces the hyperbolic tangent function to fit the thermocline structure for the first time, and combines the trust region reflection algorithm (TRF) to optimize the calculation to achieve a high-precision, low-computational-cost thermocline identification technology. The present invention effectively solves the problems of low fitting accuracy and insufficient boundary recognition ability in the steeply changing area of ​​the thermocline. The traditional Sigmoid function fitting is limited in accuracy in the thermocline mutation area, while the hyperbolic tangent function fitting method of the present invention can more accurately capture the temperature gradient drastic change point. At the same time, the rolling function identifies the upper and lower boundaries, avoiding the problem of traditional methods relying on empirical parameters in specific areas, and improving the accuracy of thermocline identification. Sigmoid function or linear segmentation method is commonly used in this field to fit temperature profiles, which is considered to be sufficient to describe the characteristics of the thermocline. However, these methods perform poorly in steep areas of the thermocline and are easily interfered by noise. The present invention breaks through this technical bias and innovatively adopts the hyperbolic tangent function, which not only improves the fitting accuracy, but also can flexibly adjust parameters to adapt to different sea areas and seasonal changes, significantly improving the adaptability and robustness of thermocline identification. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] The accompanying drawings herein are incorporated in and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the description, serve to explain the principles of the present disclosure;

[0075] Figure 1 is a flow chart of a thermocline identification method based on hyperbolic tangent function fitting provided by an embodiment of the present invention;

[0076] Figure 2 It is a schematic diagram of a thermocline identification method based on hyperbolic tangent function fitting provided by an embodiment of the present invention;

[0077] Figure 3 Schematic diagram of a thermocline identification system based on hyperbolic tangent function fitting provided by an embodiment of the present invention;

[0078] Figure 4 is a schematic diagram of selected grid points provided by an embodiment of the present invention;

[0079] Figure 5 is a graph of the relationship between temperature, depth and month in a global ocean context provided by an embodiment of the present invention;

[0080] Figure 6It is a comparison diagram of the upper boundary position of the thermocline determined in June 2011 and the temperature profile fitted by the hyperbolic tangent function and the sigmoid function with the original data provided by the embodiment of the present invention;

[0081] Figure 7 It is a comparison diagram of the lower boundary position of the thermocline determined in June 2011 and the temperature profile fitted by the hyperbolic tangent function and the sigmoid function with the original data provided by the embodiment of the present invention;

[0082] In the figure: 1. Data preparation and preprocessing module; 2. Profile range selection module; 3. Curve fitting module; 4. Thermocline upper and lower boundary determination module. DETAILED DESCRIPTION

[0083] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present invention, so the present invention is not limited by the specific implementation disclosed below.

[0084] The innovation of the thermocline identification method and system based on hyperbolic tangent function fitting provided by the embodiments of the present invention is that: the present invention adopts the hyperbolic tangent function to accurately fit the temperature-depth profile, thereby improving the fitting accuracy of the steep area of ​​the thermocline; introduces the trust region reflectance algorithm (TRF) to optimize the fitting parameters, thereby ensuring that the fitting results have higher accuracy and robustness, and are suitable for complex ocean profile data.

[0085] Embodiment 1, as Figure 1 As shown, the thermocline identification method based on hyperbolic tangent function fitting provided by the embodiment of the present invention includes:

[0086] S1, data preparation and preprocessing.

[0087] S101, reading the three-dimensional grid data of the Argo float, which should include different geographical locations (latitude and longitude), depths, and temperature and salinity data at different depths.

[0088] S102, screening the depth range and using cubic spline interpolation to interpolate the original non-uniform gridded data in the depth direction into data at 1-meter intervals.

[0089] S2, section range selection.

[0090] S201, according to the definition in the Ocean Thermodynamics Equation-2010, the practical salinity in the three-dimensional grid data ( ) and in situ temperature ( ) to absolute salinity ( ) and conservative temperature ( ), in order to ensure the accuracy and consistency of thermodynamic calculations.

[0091] S202, calculate the Brunt-Väisälä frequency square ( ), determine the depth where its maximum absolute value is located, and select the temperature profile from the ocean surface to twice the depth as the temperature profile to be fitted.

[0092] S3, curve fitting.

[0093] S301, normalize the temperature data and map its value range to the interval [0,1].

[0094] S302, using a hyperbolic tangent function to fit the normalized temperature-depth profile, the function form is as follows:

[0095] ;

[0096] In the formula, is the curve amplitude, is the steepness of the curve, is the center position of the curve, is the vertical offset of the curve, is the sea water temperature, is the hyperbolic tangent function, and the definition formula is , is the seawater depth, and the depth data is , For the The depth of the seawater where the layer is located;

[0097] S303, optimizing various parameters by using a trust region reflective algorithm (TRF).

[0098] S4, determine the upper and lower boundaries of the thermocline by rolling function.

[0099] S401, for the thermocline upper boundary (TTD), the following steps are adopted: First, after fitting the temperature curve using the hyperbolic tangent function, the temperature value at a depth of 10 meters is calculated ( ) and set it as the reference temperature. Secondly, de-standardize the temperature to restore it to the original temperature unit. Then, traverse the temperature data of each depth point in positive order and compare it with The depth with a difference of 0.2℃ was determined as the depth of the upper boundary of the thermocline.

[0100] Among them, when calculating the upper boundary of the thermocline (TTD), the forward traversal refers to checking the temperature value of each depth point in order from shallow to deep until the position of the upper boundary of the thermocline that meets specific conditions is found.

[0101] S402, for the lower thermocline boundary (BTD), the following steps are adopted: First, a depth of 10 meters above the deepest point of the hyperbolic tangent function fitting curve is selected as the reference depth, and the temperature at this depth ( ) as the reference temperature. Similarly, this reference temperature needs to be de-normalized to restore its original unit. Then, traverse each depth point in reverse order. When the temperature difference reaches 0.2℃, the depth is defined as the depth of the lower boundary of the thermocline.

[0102] It can be understood that when calculating the lower boundary of the thermocline (BTD), the reverse traversal refers to checking the temperature value of each depth point in order from deep to shallow until the position of the lower boundary of the thermocline that meets the specific conditions is found.

[0103] For example, Figure 2 This is the principle of the thermocline identification method based on hyperbolic tangent function fitting provided by an embodiment of the present invention.

[0104] Embodiment 2, as Figure 3 As shown, the thermocline identification system based on hyperbolic tangent function fitting provided by the embodiment of the present invention includes:

[0105] The data preparation and preprocessing module 1 is used to read the three-dimensional grid data of the Argo float and use cubic spline interpolation to interpolate the screened depth range and the non-uniform grid data in the original depth direction into 1-meter interval data.

[0106] Profile range selection module 2 is used to convert practical salinity and in-situ temperature in three-dimensional gridded data into absolute salinity and conservative temperature, and to calculate the Brunt-Väisälä frequency square, determine the depth of the maximum absolute value, and select the temperature profile from the ocean surface to twice the depth as the temperature profile to be fitted.

[0107] The curve fitting module 3 is used to fit the normalized temperature-depth profile using a hyperbolic tangent function and to optimize various parameters using a trust region reflection algorithm.

[0108] The thermocline upper and lower bounds determination module 4 is used to determine the thermocline upper bound and the thermocline lower bound by a rolling function.

[0109] To further illustrate the effects of the embodiments of the present invention, the following experiment was conducted.

[0110] The study scope of this case is the eastern Pacific region from 170°W to 90°W, 30°S to 30°N. The Argo float 3D gridded data used is derived from the BOA_Argo dataset, which has a spatial resolution of 1°×1° and is unevenly distributed in the vertical direction from 0 to 1975 meters. It is divided into 58 layers, and the data are collected monthly. The time span is selected from January 2010 to March 2024. Ten grid points were randomly selected within the research scope as research samples, namely: 5.5°N, 139.5°W in June 2011, 21.5°S, 103.5°W in December 2013, 17.5°N, 158.5°W in February 2015, 1.5°S, 164.5°W in September 2017, 12.5°S, 91.5°W in April 2018, 7.5°N, 129.5°W in January 2020, 7.5°S, 99.5°W in November 2021, 2.5°N, 169.5°W in August 2022, 10.5°S, 116.5°W in March 2023, 10.5°N, 144.5°W in January 2024, and 15.5°N, 144.5°W in the next two months. Figure 4 is a schematic diagram of the selected grid points;

[0111] Step 1: Data preprocessing.

[0112] Figure 5 The correlation between temperature, depth and month in the context of the global ocean is shown. The results show that when the water depth exceeds 500 meters, the sea water temperature tends to stabilize, while the thermocline gradually weakens and eventually disappears. Therefore, in order to enhance the relevance of the study and the validity of the data, the analysis is limited to water layers with a depth of 500 meters or less, which includes the first 500 meters and is the most dynamic part of the thermocline. For each grid point, the original data depth ranges from 0 meters to 1975 meters and is stratified into 58 vertical standard layers. Since this study focuses on water layers with a depth of 500 meters or less, this part of the data is extracted for each grid point.

[0113] Next, the temperature and salinity data within the depth range were interpolated to a fixed 1-m interval using the cubic spline interpolation method to resolve the uneven depth distribution of the original data and generate smooth and continuous vertical profile data.

[0114] Step 2: Profile range selection. According to the ocean thermodynamics equation, use the convert_to_SA_TC function in Python to convert the practical salinity ( ) and in situ temperature ( ) to absolute salinity ( ) and conservative temperature ( ). Next, the Brunt-Väisälä frequency squared is calculated using the following formula ( ), determine the depth of its maximum absolute value, and select the temperature profile from the ocean surface to twice the depth as the temperature profile to be fitted:

[0115] ;

[0116] In the formula, is the acceleration due to gravity, is the specific volume, is the absolute pressure, and are the thermal expansion coefficient and the brine contraction coefficient, is the conservative temperature difference between adjacent seawater layers, is the absolute salinity difference between adjacent seawater layers, It is the pressure difference between two adjacent seawater layers in the vertical direction.

[0117] Step 3: Curve fitting. Normalize the temperature data selected at each grid point and map its value range to the interval [0,1] using the formula: ,(in Represents depth, represents temperature, and Represent the maximum and minimum values ​​of the temperature data respectively). Using the hyperbolic tangent function As a fitting model, the present invention innovatively optimizes parameters a, b, c, and d through a trust region reflective algorithm (TRF). The specific operation steps are as follows:

[0118] (1) Construction of objective function: the fitting objective is to minimize the fitting curve With normalized temperature data The residual sum of squares between , defines the objective function:

[0119] ;

[0120] In the formula, is the objective function, is the number of layers common to seawater, is the predicted value of the curve, is the parameter to be optimized, ;

[0121] (2) Establish and solve subproblems. Since the nonlinear objective function may have multiple local extreme values, it is relatively difficult to directly solve the global optimal solution. Therefore, Nearby, construct a quadratic approximation model Instead of the objective function , approximate the change of the objective function in the local range (within the trust region):

[0122] ;

[0123] In the formula, is the objective function About the current iteration point The Jacobian matrix of , which represents the sensitivity of the objective function to the parameters, has a dimension of , expressed as ; is the residual vector, reflecting the deviation between the observed value and the model predicted value, with a dimension of , , is the normalized temperature data, representing the observed true temperature value, is the predicted temperature value of the curve model, based on the current parameters Calculated; is the update amount of the model parameters, and its dimension is , is the number of parameters to be optimized, , All are parameter increment vectors; for The transpose of is the transpose symbol;

[0124] The goal of this subproblem is to minimize the quadratic approximation model , in the trust region radius Solve the parameter increment under the restriction of , ensuring the optimal update step size No more than :

[0125] ;

[0126] In the formula, For vector The norm of is defined as ;

[0127] (3) Update the iteration point according to the parameter increment obtained by the solution , update the model parameters:

[0128] ;

[0129] In the formula, is the updated parameter, , the above parameters are used to recalculate ;

[0130] (4) Model evaluation: In each iteration, the quadratic approximation model is evaluated For the actual objective function Whether the decline prediction is accurate; by calculating the ratio of the actual objective function decline to the model predicted decline , determine the current step length the rationality of

[0131] ;

[0132] In the formula, The current iteration point The objective function value at represents the fitting error under the current parameters; The updated parameters The objective function value at represents the fitting error after updating the parameters; The quadratic approximation model exist The value at , that is, the model prediction value at the current iteration point; The quadratic approximation model In parameter increment The value at represents the model's prediction after the parameter update;

[0133] (5) Trust region radius adjustment, according to The value of adjusts the trust region radius , to control the parameter update range, when When , the current model fits well within the trust region, the radius of the trust region is expanded, and a larger step size is allowed to update; when When , the current model prediction is inaccurate and the trust region radius needs to be reduced; when When , the current trust region range is appropriate, and the trust region radius remains unchanged;

[0134] (6) Convergence judgment: when the parameter update amount The norm of Less than the preset threshold , or when the change in the objective function value is less than the preset threshold When the maximum number of iterations is reached Stop optimization.

[0135] Step 4: Determination of the thermocline boundary.

[0136] The upper boundary of the thermocline is determined by a rolling function, including:

[0137] First, after fitting the temperature curve using the hyperbolic tangent function, calculate the temperature value at a depth of 10 meters , and set it as the reference temperature;

[0138] Secondly, the temperature is de-normalized to restore to the original temperature unit;

[0139] Then, the temperature data of each depth point is traversed in positive order and compared with The depth with a difference of 0.2℃ is determined as the depth TTD of the upper boundary of the thermocline, and the expression is:

[0140] ;

[0141] In the formula, To take the minimum value, it is used to find the minimum depth that meets the conditions , For Depth Temperature The temperature at a depth of 10 meters The absolute difference is greater than or equal to 0.2℃…….

[0142] The lower boundary of the thermocline is determined by a rolling function, including:

[0143] First, the depth of 10 meters above the deepest point of the hyperbolic tangent function fitting curve is selected as the reference depth. The temperature at this depth As a reference temperature, this reference temperature is denormalized to restore its original units;

[0144] Then, traverse each depth point in reverse order. When the temperature of a certain depth point is When the temperature difference reaches 0.2℃, the depth is defined as the depth BTD of the lower boundary of the thermocline; the calculation formula of depth BTD is:

[0145] ;

[0146] In the formula, To take the maximum value, it is used to find the maximum depth that meets the conditions , For Depth Temperature The temperature at a depth of 10 meters above the deepest point of the fitting curve The absolute difference is greater than or equal to 0.2℃.

[0147] Step 5: Boundary calculation results. Perform the calculations of steps 1 to 4 on the ten selected grid points to obtain the curve fitted by the hyperbolic tangent function, the upper and lower bounds calculated by this method, and the comparison with other methods. The results are as follows: Figure 6 The upper boundary position of the thermocline determined in June 2011 and the comparison between the temperature profile fitted by the hyperbolic tangent function (red curve) and the sigmoid function (blue curve) and the original data (gray scattered points).

[0148] like Figure 7The lower boundary position of the thermocline determined in June 2011 and the comparison between the temperature profile fitted by the hyperbolic tangent function (red curve) and the sigmoid function (blue curve) and the original data (gray scattered points).

[0149] Specifically, Figure 6-Figure 7 In the figure, the gray scattered points are the original data of temperature changing with depth, the red curve represents the temperature profile fitted by the hyperbolic tangent function, the blue curve represents the temperature profile fitted by the sigmoid function, and the hyperbolic tangent function fitting R in the lower right corner 2 and Sigmoid function R 2 Represent the goodness of fit of the hyperbolic tangent function and the sigmoid function respectively. Different symbols in the figure mark the upper / lower bounds of the thermocline determined by each method: the green square represents the entropy method, the purple triangle represents the tensor analysis method, the orange diamond represents the inflection point method, the cyan inverted triangle represents the variable representative isotherm method, the magenta star represents the sigmoid function method, and the blue dot represents the hyperbolic tangent function fitting method. It can be seen that the present invention can capture the rapid temperature changes in the central area of ​​the thermocline more finely.

[0150] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered within the protection scope of the present invention.

Claims

1. A thermocline identification method based on hyperbolic tangent function fitting, characterized in that: The method comprises the following steps: S1, data preparation and preprocessing; read the 3D grid data of Argo float, and use cubic spline interpolation to interpolate the original non-uniform grid data in the depth direction into 1-meter interval data in the screened depth range; S2, profile range selection: convert the practical salinity and in-situ temperature in the three-dimensional grid data into absolute salinity and conservative temperature, and use them to calculate the Brunt-Väisälä frequency square, determine the depth of the maximum absolute value, and select the temperature profile from the ocean surface to twice the depth as the temperature profile to be fitted; S3, curve fitting: the normalized temperature-depth profile is fitted using the hyperbolic tangent function, and the parameters are optimized using the trust region reflectance algorithm; S4, determine the upper and lower boundaries of the thermocline by rolling function; In step S3, curve fitting includes: S301, normalize the temperature data and map the value range to the interval [0,1]; S302, using a hyperbolic tangent function to fit the normalized temperature-depth profile, the function form is as follows: ； In the formula, is the curve amplitude, is the steepness of the curve, is the center position of the curve, is the vertical offset of the curve, is the sea water temperature, is the hyperbolic tangent function, and the definition formula is , is the seawater depth, and the depth data is , For the The depth of the seawater where the layer is located; S303, optimizing various parameters by using a trust region reflective algorithm TRF.

2. The thermocline identification method based on hyperbolic tangent function fitting according to claim 1, characterized in that: In step S1, data preparation and preprocessing include: S101, reading the three-dimensional grid data of the Argo float, where the three-dimensional grid data includes temperature and salinity data at different geographical locations and different depths; S102, screening the depth range and using cubic spline interpolation to interpolate the original non-uniform gridded data in the depth direction into data at 1-meter intervals.

3. The thermocline identification method based on hyperbolic tangent function fitting according to claim 1 is characterized in that: In step S2, the section range selection includes: S201, based on the ocean thermodynamics equation, converts the practical salinity in the three-dimensional grid data into and in situ temperature Convert to absolute salinity and conservative temperature : S202, Calculate Brunt-Väisälä frequency squared , determine the depth of the maximum absolute value, and select the temperature profile from the ocean surface to twice the depth as the temperature profile to be fitted.

4. The thermocline identification method based on hyperbolic tangent function fitting according to claim 3 is characterized in that: Calculate the Brunt-Väisälä frequency squared The expression is: ； In the formula, is the acceleration due to gravity, is the specific volume, is the absolute pressure, and are the thermal expansion coefficient and the brine contraction coefficient, is the conservative temperature difference between adjacent seawater layers, is the absolute salinity difference between adjacent seawater layers, It is the pressure difference between two adjacent seawater layers in the vertical direction.

5. The thermocline identification method based on hyperbolic tangent function fitting according to claim 1 is characterized in that: In step S303, each parameter is optimized by using the trust region reflective algorithm TRF, including: optimizing parameters a, b, c, d by using the trust region reflective algorithm TRF, the specific steps are: (1) Construction of objective function: the fitting objective is to minimize the fitting curve With normalized temperature data The residual sum of squares between defines the objective function, which is expressed as: ； In the formula, is the objective function, is the number of layers common to seawater, is the predicted value of the curve, is the parameter to be optimized, ; (2) Establish and solve subproblems, at the current parameter value Nearby, construct a quadratic approximation model Instead of the objective function , approximate the change of the objective function in the local range, and the expression is: ； In the formula, is the objective function About the current iteration point The Jacobian matrix of , which represents the sensitivity of the objective function to the parameters, has a dimension of , expressed as ; is the residual vector, reflecting the deviation between the observed value and the model predicted value, with a dimension of , , is the normalized temperature data, representing the observed true temperature value, is the predicted temperature value of the curve model, based on the current parameters Calculated; is the update amount of the model parameters, and its dimension is , is the number of parameters to be optimized, , All are parameter increment vectors; for The transpose of is the transpose symbol; The goal of this subproblem is to minimize the quadratic approximation model , in the trust region radius Solve the parameter increment under the restriction of , ensuring the optimal update step size No more than , the expression is: ; In the formula, For vector The norm of is defined as ; (3) Update the iteration point according to the parameter increment obtained by the solution , update the model parameters as: ； In the formula, is the updated parameter, , the above parameters are used to recalculate ; (4) Model evaluation: In each iteration, the quadratic approximation model is evaluated For the actual objective function Whether the decline prediction is accurate; by calculating the ratio of the actual objective function decline to the model predicted decline , determine the current step length rationality; ； In the formula, The current iteration point The objective function value at represents the fitting error under the current parameters; The updated parameters The objective function value at represents the fitting error after updating the parameters; The quadratic approximation model exist The value at , that is, the model prediction value at the current iteration point; The quadratic approximation model In parameter increment The value at represents the model's prediction after the parameter update; (5) Trust region radius adjustment, according to The value of adjusts the trust region radius , to control the parameter update range, when When , the current model fits well within the trust region, the radius of the trust region is expanded, and a larger step size is allowed to update; when When , the current model prediction is inaccurate and the trust region radius needs to be reduced; when When , the current trust region range is appropriate, and the trust region radius remains unchanged; (6) Convergence judgment: when the parameter update amount The norm of Less than the preset threshold , or when the change in the objective function value is less than the preset threshold When the maximum number of iterations is reached Stop optimization.

6. The thermocline identification method based on hyperbolic tangent function fitting according to claim 1, characterized in that: In step S4, the upper boundary of the thermocline is determined by a rolling function, including: First, after fitting the temperature curve using the hyperbolic tangent function, calculate the temperature value at a depth of 10 meters , and set it as the reference temperature; Secondly, the temperature is de-normalized to restore to the original temperature unit; Then, the temperature data of each depth point is traversed in positive order and compared with The depth where the difference is 0.2℃ is determined as the depth of the upper boundary of the thermocline and is determined as TTD. The expression is: ； In the formula, To take the minimum value, used to find the minimum depth that meets the conditions , For Depth Temperature The temperature at a depth of 10 meters The absolute difference is greater than or equal to 0.2℃.

7. The thermocline identification method based on hyperbolic tangent function fitting according to claim 1 is characterized in that: In step S4, the lower boundary of the thermocline is determined by a rolling function, including: First, the depth of 10 meters above the deepest point of the hyperbolic tangent function fitting curve is selected as the reference depth. The temperature at this depth As a reference temperature, this reference temperature is denormalized to restore its original units; Then, traverse each depth point in reverse order. When the temperature of a certain depth point is When the temperature difference reaches 0.2℃, the depth is defined as the depth BTD of the lower boundary of the thermocline; the calculation formula of depth BTD is: ； In the formula, To take the maximum value, it is used to find the maximum depth that meets the conditions , For Depth Temperature The temperature at a depth of 10 meters above the deepest point of the fitting curve The absolute difference is greater than or equal to 0.2℃.

8. The thermocline identification method based on hyperbolic tangent function fitting according to claim 1 is characterized in that: After step S4, the boundary calculation result is performed, and the selected multiple grid points are calculated respectively to obtain a curve fitted by a hyperbolic tangent function.

9. A thermocline identification system based on hyperbolic tangent function fitting, characterized in that: The system implements the thermocline identification method based on hyperbolic tangent function fitting as claimed in any one of claims 1 to 8, and the system comprises: The data preparation and preprocessing module (1) is used to read the three-dimensional grid data of the Argo float and use cubic spline interpolation to interpolate the original non-uniform grid data in the depth direction into 1-meter interval data within the selected depth range; A profile range selection module (2) is used to convert the practical salinity and in-situ temperature in the three-dimensional grid data into absolute salinity and conservative temperature, and to calculate the Brunt-Väisälä frequency square, determine the depth of the maximum absolute value, and select the temperature profile within the range from the ocean surface to twice the depth as the temperature profile to be fitted; A curve fitting module (3) is used to fit the normalized temperature-depth profile using a hyperbolic tangent function and optimize various parameters using a trust region reflectance algorithm; The module for determining the upper and lower boundaries of the thermocline (4) is used to determine the upper and lower boundaries of the thermocline through a rolling function.

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