A method for rapidly identifying the upper and lower boundaries of the ocean thermocline

Abstract

This invention relates to the field of physical oceanography, specifically to a method for rapidly identifying the upper and lower boundaries of the ocean thermocline. The method utilizes trigonometric functions as basis functions to construct a 10th-order trigonometric polynomial, and obtains the fitting parameters and results using the least squares method. Then, the first derivative of the trigonometric polynomial is calculated. The maximum value and its location, as well as all minimum values ​​and their locations, are determined. From the location of the maximum value, the two locations of the first minimum values ​​less than 1 / 10 of the maximum value are found on both sides. This yields the upper and lower boundaries of the ocean thermocline depth. This invention eliminates the subjectivity of parameter selection by eliminating the need for manually setting thresholds; it also avoids complex transformation and construction processes, resulting in a clear algorithm structure and high computational efficiency. It can operate stably in different sea areas and under various data precision conditions, significantly improving the automation, robustness, and computational efficiency of thermocline identification.

Description

Technical Field

[0001] This invention relates to the field of physical oceanography, and in particular to a method for rapidly identifying the upper and lower boundaries of the ocean thermocline. Background Technology

[0002] The lower boundary depth of seasonal thermoclines in global oceans generally does not exceed 200m, while the lower boundary depth of permanent thermoclines generally does not exceed 800m. Currently, methods for identifying ocean thermoclines can be mainly classified into two categories: gradient methods and curvature methods. Existing related patents (such as "A method and system for finding ocean thermoclines", "A method for determining the maximum and minimum values ​​of curvature regions based on thermocline boundary detection using ocean stratification spectra", "A wavelet transform method for determining the upper and lower boundaries of thermoclines based on ocean stratification spectra", "A method for artificial intervention in ocean thermo-salinity changes", and "A method for analyzing the dynamic changes of nearshore thermoclines") are all extensions and improvements of these two types of methods.

[0003] The basic idea of ​​the gradient method is to directly calculate the temperature gradient of seawater with depth and set an artificial threshold. When the temperature gradient is greater than the threshold, the layer is considered a thermocline. However, this method is highly subjective, and the selection of the threshold lacks a unified standard. The threshold often varies greatly in different sea areas and seasons, which limits its versatility.

[0004] The curvature rule identifies mesostomies by calculating the curvature at various points in a temperature profile. This can be done directly or by calculating the curvature after spectral transformation. Since the raw temperature data is usually coarse, directly calculating the gradient or curvature often results in an overly unsmooth image, making it difficult to determine an effective threshold or introducing multiple spurious peaks, thus affecting the accuracy of mesostomy identification. Therefore, researchers typically perform multiple smoothing processes on the data before calculation. However, the choice of the number of smoothing iterations is subjective: insufficient smoothing leads to too many spurious peaks, while excessive smoothing weakens the original signal characteristics and fails to accurately reflect the true structure of the mesostomy. Generally, multiple manual experiments are needed to determine a suitable smoothing parameter.

[0005] In summary, existing thermocline identification methods generally suffer from the following problems: lack of a unified standard for threshold selection, reliance on manual experience for data smoothing, complex transformation function construction, and high computational cost. These factors collectively increase the subjectivity and computational complexity of the thermocline identification process, necessitating a more automated, robust, and efficient identification method for improvement. Summary of the Invention

[0006] This invention provides a method for rapidly identifying the upper and lower boundaries of the ocean thermocline, thereby solving the problems of strong subjectivity, computational complexity, and low efficiency in existing ocean thermocline identification methods.

[0007] This invention provides a method for rapidly identifying the upper and lower boundaries of the ocean thermocline, comprising the following steps:

[0008] A method for rapidly identifying the upper and lower boundaries of the ocean thermocline, characterized by comprising the following steps:

[0009] Step 1: Obtain the maximum value of the depth data from the raw data and make a judgment to obtain the research data;

[0010] Step two: Using trigonometric functions as basis functions, select the number of terms in the polynomial. ,structure The first trigonometric polynomial is used, and the fitting parameters and fitting results are obtained by the least squares method.

[0011] Step 3: Substitute the obtained fitting parameters into the constructed... In the trigonometric polynomial of order 1, then find the first derivative of the trigonometric polynomial;

[0012] Step 4: Find the maximum value of the absolute value of the first derivative and its location, as well as all the minimum values ​​and their locations. Then, starting from the location of the maximum value, find the two locations of the first minimum value that is less than 1 / 10 of the maximum value.

[0013] Step 5: Locate the two locations found in the water depth data to obtain the upper and lower bounds of the seawater thermocline depth.

[0014] As a preferred technical solution, in step one, the raw seawater temperature and depth profile data are obtained. The maximum value of the mid-depth data is used. If the maximum value is greater than 1000m, then the seawater temperature and depth data at ≤1000m are used as the research data. If the maximum value is less than or equal to 1000m, then the original data as a whole is used as the research data.

[0015] in, Because of the water depth, For seawater temperature, The length of a single profile data point.

[0016] As a preferred technical solution, in step two, a 1 / 2 multiple wavenumber term is introduced using trigonometric functions as basis functions. Choose the number of terms in the polynomial. The structure is as follows: Trigonometric polynomial of order 1.

[0017] As a preferred technical solution The trigonometric polynomial of order 1 is shown in formula (1):

[0018] (1)

[0019] in:

[0020] ,

[0021] In formula (1), let:

[0022]

[0023]

[0024]

[0025] Then formula (1) can be rewritten as:

[0026]

[0027] According to the least squares method, let:

[0028] (2)

[0029] Taking the first derivative of formula (2) and setting it to 0, we have:

[0030] (3)

[0031] The fitting parameters are obtained using the above formula. and fitting results .

[0032] As a preferred technical solution, the obtained fitting parameters Substituting into formula (1), and then taking the first derivative of formula (1), we obtain formula (4):

[0033]

[0034] in, .

[0035] As a preferred technical solution, the following formula (4) is used to obtain the desired result. maximum point And its position ST1, all local minima and their positions, and then find the first value less than ST1 on both sides. Location of the minimum value and .

[0036] As a preferred technical solution, in step five, and In the water depth data, the corresponding water layer is the upper and lower boundary depth of the thermocline.

[0037] This invention provides a method for rapidly identifying the upper and lower boundaries of the ocean thermocline. It fully utilizes the differentiability and smoothness of trigonometric functions, fitting seawater temperature profile data with a trigonometric polynomial and obtaining a smooth derivative curve by differentiating the fitted function. Subsequently, the upper and lower boundaries of the thermocline are automatically determined by identifying the nearest peak points on either side of the maximum value point in the derivative curve. Compared with traditional gradient and curvature methods, this method significantly reduces the need for manually setting thermocline discrimination thresholds, greatly eliminating the subjectivity of parameter selection; it also avoids complex transformation construction processes, resulting in a clear algorithm structure and high computational efficiency. With its strong robustness and smooth fitting characteristics, this method can operate stably in different sea areas and under various data accuracy conditions, significantly improving the automation, robustness, and computational efficiency of thermocline identification, and has broad prospects for promotion and application. Specifically:

[0038] 1. High degree of automation: This method uses trigonometric function polynomial fitting and derivative analysis to automatically identify the boundary of the jump layer, which significantly reduces manual intervention and improves the intelligence level of the identification process.

[0039] 2. Strong robustness: By utilizing the smooth and differentiable properties of trigonometric functions, the influence of noise in the original temperature data is effectively suppressed, and the resulting derivative curve is smooth and continuous, maintaining high recognition accuracy and stability under different sea areas, seasons and data resolutions.

[0040] 3. High computational efficiency: The method has a simple process and avoids the complex multiple smoothing and threshold trial calculations in traditional gradient and curvature methods, which greatly reduces the amount of computation and parameter debugging. It is suitable for batch or real-time data processing.

[0041] 4. Wide applicability: This method is not only applicable to conventional CTD (temperature, salinity, depth) profile data, but can also be extended to multi-source ocean observation data, such as the identification of layer transitions in buoy, mooring and numerical model output data.

[0042] 5. The results have clear physical meaning: The upper and lower boundaries of the thermocline are determined by the extreme points of the derivative and their neighboring peak points. The identification results are intuitive and clear, and can better reflect the true changing characteristics of the ocean's thermal structure.

[0043] In summary, this invention has significant advantages in improving automation, enhancing robustness of identification, and increasing computational efficiency, and can provide an efficient and reliable new approach for the rapid and accurate identification of the ocean thermocline. Attached Figure Description

[0044] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 It is temperature data that is the original seawater temperature data fitted with a trigonometric polynomial;

[0046] Figure 2 It is a comparison between the absolute value of the derivative of the trigonometric polynomial and the absolute gradient of the original seawater temperature data;

[0047] Figure 3 It contains the raw data of seawater temperature and the identified upper and lower boundaries of the thermocline. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0049] Furthermore, the term "and / or" in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article, unless otherwise specified, generally indicates that the preceding and following related objects have an "or" relationship.

[0050] The embodiments of the present invention will now be described in further detail with reference to the accompanying drawings.

[0051] This invention provides a method for rapidly identifying the upper and lower boundaries of the ocean thermocline, comprising the following steps:

[0052] Step 1: Obtain the maximum value of the depth data in the original data. If the maximum value is greater than 1000m, then take the seawater temperature and depth data ≤1000m as the research data. If the maximum value is less than or equal to 1000m, then take the original data as the research data.

[0053] Specifically, acquiring raw seawater temperature and depth profile data. For mid-depth data, if the maximum value is greater than 1000m, then seawater temperature and depth data at depths ≤1000m are used as research data; if the maximum value is ≤1000m, then the entire original data is used as research data. Because of the water depth, For seawater temperature, The length of a single profile data point.

[0054] Since the lower limit depth of the seasonal thermocline in the global ocean is generally no more than 200m and the lower limit depth of the permanent thermocline is generally no more than 800m, in order to reduce the number of terms in the trigonometric polynomial and improve the smoothness of the fitted data, seawater temperature and depth data with a depth ≤1000m from the seawater temperature and depth profile data were selected as the research data.

[0055] Step two: Using the research data obtained in step one, select the number of polynomial terms using trigonometric functions as basis functions. ,structure The trigonometric polynomial of order 1 is used, and the fitting parameters and fitting results are obtained by the least squares method, as shown in formula (1):

[0056] (1)

[0057] in:

[0058] ,

[0059] For water depth;

[0060] For the fitting constant term;

[0061] Let be the fitting coefficients of the k-th cosine term, where k = 1, 2, ..., m;

[0062] Let be the fitting coefficients of the k-th order sine term, where k = 1, 2, ..., m;

[0063] Let be the k-th order angular frequency;

[0064] For the first water depth The fitting results for the seawater temperature at that location.

[0065] In formula (1), let:

[0066]

[0067]

[0068]

[0069] Then formula (1) can be rewritten as:

[0070]

[0071] in: The weight matrix is ​​a triangular polynomial.

[0072] These are the fitting parameters, i.e., the column vector consisting of all the fitting parameters;

[0073] The result is the fitting result, which is a column vector consisting of all the fitted temperature values.

[0074] According to the least squares method, let:

[0075] (2)

[0076] Taking the first derivative of formula (2) and setting it to 0, we have:

[0077] (3)

[0078] The fitting parameters are obtained using the above formula. and fitting results ,like Figure 1 As shown by the red curve in the middle;

[0079] The basis functions in this step introduce a 1 / 2 multiple wavenumber term. This effectively solves the boundary fitting oscillation problem.

[0080] Step 3, obtain the fitting parameters Substitution of the construction In the trigonometric polynomial of order 1, then for Find the first derivative of a trigonometric polynomial of order 1.

[0081] Specifically, the obtained fitting parameters Substituting into formula (1), and then taking the first derivative of formula (1), we obtain formula (4), as follows: Figure 2 As shown by the red curve in the middle.

[0082]

[0083] in, .

[0084] Step 4: Find the maximum value of the absolute value of the first derivative and its location, as well as all the minimum values ​​and their locations. Then, starting from the location of the maximum value, find the two locations of the first minimum value that is less than 1 / 10 of the maximum value.

[0085] Specifically, the result is obtained according to formula (4). maximum point And its position ST1, all local minima and their positions, and then find the first value less than ST1 on both sides. Location of the minimum value and ,like Figure 2 As shown by the green dot.

[0086] Step 5: By mapping the two locations to the water depth data, the upper and lower bounds of the seawater thermocline depth can be obtained. and In the water depth data, the corresponding water layer, i.e., the upper and lower bounds of the thermocline depth, are as follows: Figure 3 As shown by the green dot. This is the boundary between the thermocline layer and the upper mixed layer; This represents the boundary between the thermocline layer and the underlying mixed layer.

[0087] This invention provides a method for rapidly identifying the upper and lower boundaries of the ocean thermocline. It fully utilizes the differentiability and smoothness of trigonometric functions, fitting seawater temperature profile data with a trigonometric polynomial and obtaining a smooth derivative curve by differentiating the fitted function. Subsequently, the upper and lower boundaries of the thermocline are automatically determined by identifying the nearest peak points on either side of the maximum value point in the derivative curve. Compared with existing technologies: It boasts a high degree of automation, utilizing trigonometric polynomial fitting and derivative analysis to automatically identify thermocline boundaries, significantly reducing the need for manually set thresholds and human intervention, thus improving the intelligence level of the identification process. It exhibits strong robustness, effectively suppressing noise in the original temperature data through the smooth and differentiable properties of trigonometric functions. The resulting derivative curve is smooth and continuous, maintaining high accuracy and stability under different sea areas, seasons, and data resolutions. It offers high computational efficiency, with a simple process that avoids the complex multiple smoothing and threshold calculation processes of traditional gradient and curvature methods, significantly reducing computational load and parameter debugging workload, making it suitable for batch or real-time data processing. With a wide range of applications, this method is not only applicable to conventional CTD (temperature, salinity, depth) profile data, but can also be extended to multi-source ocean observation data, such as the identification of thermoclines (thermoclines, haloclines, myclines, and soniclines) in buoy, mooring, and numerical model output data. The results have clear physical meaning; the upper and lower boundaries of the thermocline are determined by the extreme points of the derivative and their neighboring peak points. The identification results are intuitive and clear, and can better reflect the true changing characteristics of the ocean's thermal structure.

[0088] In summary, this invention has significant advantages in improving automation, enhancing robustness of identification, and increasing computational efficiency, and can provide an efficient and reliable new approach for the rapid and accurate identification of the ocean thermocline.

[0089] Of course, the present invention may have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and modifications according to the present invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A method for rapidly identifying the upper and lower boundaries of the ocean thermocline, characterized in that, Includes the following steps: Step 1: Obtain the maximum value of the depth data from the raw data and make a judgment to obtain the research data; Step two: Using trigonometric functions as basis functions, select the number of terms in the polynomial. ,structure The first trigonometric polynomial is used, and the fitting parameters and fitting results are obtained by the least squares method. Step 3: Substitute the obtained fitting parameters into the constructed... In the trigonometric polynomial of order 1, then find the first derivative of the trigonometric polynomial; Step 4: Find the maximum value of the absolute value of the first derivative and its location, as well as all the minimum values ​​and their locations. Then, starting from the location of the maximum value, find the two locations of the first minimum value that is less than 1 / 10 of the maximum value. Step 5: Locate the two locations found in the water depth data to obtain the upper and lower bounds of the seawater thermocline depth.

2. The method for rapidly identifying the upper and lower boundaries of the ocean thermocline according to claim 1, characterized in that, In step one, raw seawater temperature and depth profile data are obtained. The maximum value of the mid-depth data is used. If the maximum value is greater than 1000m, then the seawater temperature and depth data at ≤1000m are used as the research data. If the maximum value is less than or equal to 1000m, then the original data as a whole is used as the research data. in, Because of the water depth, For seawater temperature, The length of a single profile data point.

3. The method for rapidly identifying the upper and lower boundaries of the ocean thermocline according to claim 1, characterized in that, In step two, trigonometric functions are used as basis functions to introduce a 1 / 2 multiple wavenumber term. Choose the number of terms in the polynomial. ,structure Trigonometric polynomial of order 1.

4. The method for rapidly identifying the upper and lower boundaries of the ocean thermocline according to claim 3, characterized in that, The trigonometric polynomial of order 1 is shown in formula (1): （1） in: ; ； In formula (1), let: Then formula (1) can be rewritten as: According to the least squares method, let: （2） Taking the first derivative of formula (2) and setting it to 0, we have: （3） The fitting parameters are obtained using the above formula. and fitting results .

5. The method for rapidly identifying the upper and lower boundaries of the ocean thermocline according to claim 4, characterized in that, The obtained fitting parameters Substituting into formula (1), and then taking the first derivative of formula (1), we obtain formula (4): in, .

6. The method for rapidly identifying the upper and lower boundaries of the ocean thermocline according to claim 5, characterized in that, Calculate according to formula (4) maximum point And its position ST1, all local minima and their positions, and then find the first value less than ST1 on both sides. Location of the minimum value and .

7. The method for rapidly identifying the upper and lower boundaries of the ocean thermocline according to claim 6, characterized in that, In step five, and In the water depth data, the corresponding water layer is the upper and lower boundary depth of the thermocline.

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