Ocean three-dimensional temperature field inversion method based on Argo buoy

Abstract

The invention aims to explore a data-driven method for inverting an ocean three-dimensional temperature field based on an Argo buoy. The method comprises the following steps: firstly, reading an Argo buoy data file in a certain area, and extracting coordinate data and temperature and depth data in the file; secondly, substituting the temperature and depth data into a spline curve fitting function to obtain spline curve fitting parameters, and calculating fitted temperature data according to the parameters to obtain an ocean temperature vertical section model; thirdly, fitting temperature data of any depth are obtained according to spline curve fitting parameters, the temperature data and coordinate data corresponding to the temperature data are substituted into a Kriging interpolation function, and an ocean temperature horizontal section model is obtained; and finally, constructing the ocean three-dimensional temperature field by combining the steps. According to the method, the problem that the similarity requirement of an empirical model for an ocean internal structure and the like is high is solved, compared with a traditional empirical model and other methods, a data driving method is more convenient and faster, the model is established according to Argo actual measurement data, and the model is closer to real ocean temperature data.

Description

Technical Field

[0001] The invention relates to establishing a three-dimensional seawater temperature model based on an Argo buoy by utilizing a B-spline curve fitting and a Kriging interpolation method. Background Art

[0002] The ocean is an important part of the earth system. A deep understanding of the state of the ocean and its movement is of great significance to people's production and life. Ocean temperature is one of the most important basic parameters in the field of ocean research and is closely related to many oceanographic issues. In the early 21st century, a real-time global ocean observation system was established based on the Argo project, sampling the ocean above 2000 meters to obtain temperature profile data that can cover the world. In order to study the three-dimensional ocean, constructing a three-dimensional temperature field using Argo buoy data has become an important research topic.

[0003] The inversion of ocean three-dimensional temperature field based on Argo floats is mainly used to reconstruct the three-dimensional temperature field using sea surface information and develop real-time monthly average global grid three-dimensional temperature and salinity products, such as the JAMESTEC dataset, the Roemmich dataset, the EN4 dataset, and the global ocean Argo grid dataset (Barnes Objective Analysis_Array for Real-timeGeostrophic Oceanography, BOA_Argo). Among them, most of the existing technologies for constructing three-dimensional temperature fields based on Argo floats use empirical models, which require analysis of the internal structure and historical change laws of the ocean, and have high requirements for the similarity of the internal structure of the ocean. For oceans of different times, different regions, and different climates, empirical models may not accurately meet the conditions of the study area.

[0004] Therefore, the research of this patent is the first fully data-driven study on the inversion of the ocean three-dimensional temperature field based on Argo floats. Compared with traditional empirical models and other methods, the data-driven method is more convenient and faster, and the model is established based on Argo measured data, which is closer to the real ocean temperature data. At the same time, this method also overcomes the problem that the empirical model has high requirements for the similarity of the internal structure of the ocean. Summary of the invention

[0005] The present invention provides an ocean three-dimensional temperature field inversion method based on Argo buoys, adopts a completely data-driven method, and aims to establish a model based on Argo measured data, which is more convenient and quick.

[0006] The present invention provides an ocean three-dimensional temperature field inversion method based on Argo buoys, comprising the following steps:

[0007] Step 1: Analyze the Argo float data file and extract the depth and temperature data of each float;

[0008] Step 2: Use the B-spline curve fitting method to establish the vertical profile of seawater temperature;

[0009] Step 3: Use Kriging interpolation method to establish the horizontal profile of seawater temperature;

[0010] Step 4: Construct the three-dimensional ocean temperature field.

[0011] 2. Preferably, in step 2, for a single buoy, a B-spline curve is used to fit the relationship between seawater temperature and depth, and a vertical profile model of seawater temperature is established. The principle is as follows:

[0012]

[0013] Where P(t) represents the temperature curve corresponding to the temperature profile, t is the normalization parameter, that is, the normalized value of the depth, n+1 is the number of control points, P i is the characteristic point of the control curve, F i，k (t) is the i-th k-order B-spline curve basis function, i is the serial number of the B-spline curve, and k is the order of the B-spline curve. The basis function in the B-spline curve equation is:

[0014]

[0015] Where i is the serial number of the B-spline curve basis function, k is the order of the B-spline curve, and t is the normalization parameter.

[0016] Preferably, in step 3, the seawater temperature horizontal profile is established using the Kriging interpolation method based on the fitted temperature data, and the principle is as follows:

[0017]

[0018] Where x0 is the coordinate of any interpolation point in space, Z * (x0) is the estimated temperature at the interpolation point x0, which can be expressed as a linear combination of the observed values ​​around the space; x i is the coordinate of the i-th observation point in space, N is the number of observation points, i is the serial number of the known observation point, Z(x i ) is the temperature value of the i-th observation point, λ i is the weighting coefficient of the i-th observation point.

[0019] Assume that the spatial attribute Z(x) has the same distribution at each point, that is, for any point x in space, Z(x) has the same expectation c and variance σ 2 , that is, E[Z(x)]=c, Var[Z(x)]=σ2 In order to ensure the optimal estimate, the estimated value Z at the interpolation point x0 * The difference between (x0) and the true value Z(x0) is the smallest, which must satisfy Var[Z * (x0)-Z(x0)]=min, and in order to ensure the unbiasedness of the estimate, it is necessary to satisfy E[Z * (x0)-Z(x0)]=0, we get The variance expression of the error to be estimated is as follows:

[0020] Z var =Var[Z * (x0)-Z(x0)]

[0021]

[0022] Where Z var is the estimated variance, x0 is any interpolation coordinate in the space, Z * (x0) is the estimated temperature at the interpolation point x0, Z(x0) is the true temperature at the interpolation point x0, Cov(Z(x i ), Z(x j )) is Z(x i ) and Z(x j ), x i and x j is the coordinate of a known point in space, Z(x i ) and Z(x j ) is a known point x i and x j The corresponding temperature value, λ i and λ j is the weighting coefficient, i is the known observation point x i The serial number of j is the known observation point x j The sequence number of n is the number of known observation points. In order to make the estimated value equal to the actual value, the estimated variance must be minimized, that is, satisfy We must also ensure that the obtained λ i satisfy The Lagrange multiplier method is used to solve the problem, and the solution is to construct a new objective function.

[0023]

[0024] where μ is the Lagrange multiplier, Z var is the estimated variance, λ i is the weight coefficient, i is the weight coefficient λ i The serial number, n is the weight coefficient λ i The number of. Then

[0025]

[0026] where r ij is the semivariogram function, r ij =σ 2 -Cov(Z(x i ), Z(x j )), r i0 =σ 2 -Cov(Z(x i ), Z(x0)), σ 2 is the variance of any point in space, Cov(Z(x i ), Z(x j )) is Z(x i ) and Z(x j ), Cov(Z(x i ), Z(x0)) is Z(x i ) and the cross-covariance of Z(x0), where Z(x0) is the true temperature value at the interpolation point x0, i and x j is the coordinate of the known observation point in space, Z(x i ) and Z(x j ) is a known point x i and x j The temperature value at j is the weighting coefficient, j is the weighting coefficient λ j The serial number, n is the weighting coefficient λ j and λ i The number of. Combining the above conditions, we can get the following equations:

[0027]

[0028] By solving the above equation using the theoretical variation function model, we can get the weight coefficient λ of all interpolation points. i and Lagrange multiplier μ, and substitute it into the Kriging interpolation formula to obtain the estimated value Z * (x0), substitute the variance expression of the error to be estimated to obtain the estimated variance Z var .

[0029] Preferably, in step 4, the three-dimensional temperature field of the ocean is constructed in combination with step 2 and step 3. According to the spline curve fitting parameters of each buoy obtained in step 2, the temperature data of any depth of each coordinate can be calculated, and according to step 3, the horizontal temperature field of the ocean is constructed by Kriging interpolation, and finally the three-dimensional temperature field of the ocean is constructed.

[0030] In the invention, first, the Argo buoy data files are analyzed, and the depth and temperature data of each buoy are extracted; secondly, the data are fitted with a B-spline curve to establish a vertical profile of seawater temperature; then, the fitted temperature data at any depth is used to establish a horizontal profile of seawater temperature using the Kriging interpolation method; finally, a three-dimensional ocean temperature field is constructed. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 A schematic diagram of a flow chart of a method for inverting a three-dimensional ocean temperature field based on Argo buoys provided in an embodiment of the present invention;

[0032] Figure 2 A polynomial fitting of the vertical temperature profile of seawater in the three-dimensional ocean temperature field inversion method based on Argo buoys provided in an embodiment of the present invention;

[0033] Figure 3 The B-spline curve fitting of the vertical temperature profile of seawater of the ocean three-dimensional temperature field inversion method based on Argo buoy provided in the embodiment of the present invention;

[0034] Figure 4 The Kriging interpolation seawater horizontal temperature profile of the ocean three-dimensional temperature field inversion method based on Argo buoy provided in an embodiment of the present invention;

[0035] Figure 5 The SVR seawater horizontal temperature profile of the ocean three-dimensional temperature field inversion method based on Argo buoy provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0036] This patent aims to explore a data-driven method for inverting the three-dimensional ocean temperature field based on Argo buoys. This patent first uses B-spline curve fitting to establish an ocean temperature model in the vertical direction, and then establishes an ocean temperature model in the horizontal direction based on the temperature data of any depth in the area obtained by fitting, and finally establishes a three-dimensional ocean temperature field.

[0037] In order to better understand the above technical solution, the above technical solution will be described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0038] This embodiment provides an ocean three-dimensional temperature field inversion method based on Argo buoys, which mainly includes the following steps:

[0039] Step 1: Analyze the Argo float data file and extract the depth and temperature data of each float.

[0040] Step 2: Use the B-spline curve fitting method to establish the vertical profile of seawater temperature. Specifically, for a single buoy, use the B-spline curve to fit the relationship between seawater temperature and depth, and establish a vertical profile model of seawater temperature. The principle is as follows:

[0041]

[0042] Where P(t) represents the temperature curve corresponding to the temperature profile, t is the normalization parameter, that is, the normalized value of the depth, n+1 is the number of control points, P i is the characteristic point of the control curve, F i，k (t) is the i-th k-order B-spline curve basis function, i is the serial number of the B-spline curve, and k is the order of the B-spline curve. The basis function in the B-spline curve equation is:

[0043]

[0044] Where i is the serial number of the B-spline curve basis function, k is the order of the B-spline curve, and t is the normalization parameter.

[0045] Step 3: Use Kriging interpolation to establish the horizontal profile of seawater temperature. Specifically, based on the fitted temperature data, use Kriging interpolation to establish the horizontal profile model of seawater temperature. The principle is as follows:

[0046]

[0047] Where x0 is the coordinate of any interpolation point in space, Z * (x0) is the estimated temperature at the interpolation point x0, which can be expressed as a linear combination of the observed values ​​around the space; x i is the coordinate of the i-th observation point in space, N is the number of observation points, i is the serial number of the known observation point, Z(x i ) is the temperature value of the i-th observation point, λ i is the weighting coefficient of the i-th observation point.

[0048] Assume that the spatial attribute Z(x) has the same distribution at each point, that is, for any point x in space, Z(x) has the same expectation c and variance σ 2 , that is, E[Z(x)]=c, Var[Z(x)]=σ 2 In order to ensure the optimal estimate, the estimated value Z at the interpolation point x0 * The difference between (x0) and the true value Z(x0) is the smallest, which must satisfy Var[Z * (x0)-Z(x0)]=min, and in order to ensure the unbiasedness of the estimate, it is necessary to satisfy E[Z * (x0)-Z(x0)]=0, we get The variance expression of the error to be estimated is as follows:

[0049] Z var =Var[Z * (x0)-Z(x0)]

[0050]

[0051] Where Z var is the estimated variance, x0 is any interpolation coordinate in the space, Z * (x0) is the estimated temperature at the interpolation point x0, Z(x0) is the true temperature at the interpolation point x0, Cov(Z(x i ), Z(x j )) is Z(x i ) and Z(x j ), x i and x j is the coordinate of a known point in space, Z(x i ) and Z(x j ) is a known point x i and x j The corresponding temperature value, λ i and λ j is the weighting coefficient, i is the known observation point x i The serial number of j is the known observation point x j The sequence number of n is the number of known observation points. In order to make the estimated value equal to the actual value, the estimated variance must be minimized, that is, satisfy We must also ensure that the obtained λ i satisfy The Lagrange multiplier method is used to solve the problem, and the solution is to construct a new objective function.

[0052]

[0053] where μ is the Lagrange multiplier, Z var is the estimated variance, λ i is the weight coefficient, i is the weight coefficient λ i The serial number, n is the weight coefficient λ i The number of. Then

[0054]

[0055] where r ij is the semivariogram function, r ij =σ 2 -Cov(Z(x i ), Z(x j )), r i0 =σ 2 -Cov(Z(xi ), Z(x0)), σ 2 is the variance of any point in space, Cov(Z(x i ), Z(x j )) is Z(x i ) and Z(x j ), Cov(Z(x i ), Z(x0)) is Z(x i ) and the cross-covariance of Z(x0), where Z(x0) is the true temperature value at the interpolation point x0, i and x j is the coordinate of the known observation point in space, Z(x i ) and Z(x j ) is a known point x i and x j The temperature value at j is the weighting coefficient, j is the weighting coefficient λ j The serial number, n is the weighting coefficient λ j and λ i The number of. Combining the above conditions, we can get the following equations:

[0056]

[0057] By solving the above equation using the theoretical variation function model, we can get the weight coefficient λ of all interpolation points. i and Lagrange multiplier μ, and substitute it into the Kriging interpolation formula to obtain the estimated value Z * (x0), substitute the variance expression of the error to be estimated to obtain the estimated variance Z var .

[0058] Step 4: Construct the three-dimensional ocean temperature field. Combine steps 2 and 3 to construct the three-dimensional ocean temperature field. According to the spline curve fitting parameters of each buoy obtained in step 2, the temperature data at any depth of each coordinate can be calculated. According to step 3, the ocean horizontal temperature field is constructed by Kriging interpolation, and finally the three-dimensional ocean temperature field is constructed.

[0059] The present invention is further described below.

[0060] See also Figure 1The method for inverting the three-dimensional ocean temperature field based on Argo buoys provided in this embodiment mainly includes the following steps: first, reading the Argo buoy data file of a certain area, and extracting the coordinate data and temperature and depth data in the file; second, substituting the temperature and depth data into the spline curve fitting function to obtain the spline curve fitting parameters, calculating the fitted temperature data according to the parameters, and establishing the ocean temperature vertical profile model; then, according to the spline curve fitting parameters, obtaining the fitted temperature data of any depth, substituting the temperature data and its corresponding coordinate data into the Kriging interpolation function, and establishing the ocean temperature horizontal profile model; finally, combining the above steps, constructing the three-dimensional ocean temperature field.

[0061] Several main parts of this embodiment are explained below.

[0062] 1.1 Model construction

[0063] First, the original Argo data files are analyzed to extract the coordinate data as well as the temperature and depth data in the files.

[0064] 1) Construct a vertical fitting function for ocean temperature and store each coordinate data and its corresponding temperature and depth data in different series;

[0065] 2) Calculate the spline curve fitting parameters for each coordinate;

[0066] 3) Evaluate the spline curve fitting effect for each coordinate point and establish an ocean temperature vertical profile model;

[0067] 4) Construct a horizontal fitting function for ocean temperature, use spline curve fitting parameters to calculate the seawater temperature at any depth plane, and establish a vertical temperature model;

[0068] 5) Calculate Kriging interpolation parameters;

[0069] 6) Evaluate the effect of Kriging interpolation and draw a horizontal profile of ocean temperature;

[0070] 7) Construct a three-dimensional ocean temperature field.

[0071] 1.2 Effect evaluation

[0072] In the evaluation of the spline curve fitting effect, 80% of the temperature data and its corresponding depth data are randomly selected and substituted into the spline curve fitting function to obtain the spline curve fitting parameters. The fitted temperature data is calculated according to the parameters, and then the root mean square error (RMSE) is calculated as the error metric based on the remaining 20% ​​of the temperature and depth data. The calculation formula of RMSE is as follows:

[0073]

[0074] Among them, z i is the remaining 20% ​​of the original temperature data, i is the sequence number of the remaining 20% ​​of the original temperature data, zk i is the spline curve fitting result with z i Temperature data corresponding to depth, n is z i The number of

[0075] In the evaluation of the Kriging interpolation effect, 80% of the temperature data obtained by spline curve fitting and its corresponding depth data are randomly selected and substituted into the Kriging interpolation function to obtain the Kriging interpolation parameters. The temperature data after Kriging interpolation is calculated according to the parameters, and then the RMSE is calculated as the error metric based on the remaining 20% ​​of the temperature and depth data. The calculation formula of RMSE is as follows:

[0076]

[0077] Among them, z i is the temperature data obtained by B-spline curve fitting, i is the serial number of the temperature data obtained by B-spline curve fitting, zk i is the Kriging interpolation result and z i Temperature data corresponding to depth, n is z i The number of

[0078] In order to verify the effect of the present invention, the following is a description in conjunction with experimental results.

[0079] According to the requirements, the experimental effect evaluation was designed. The effect evaluation of the vertical direction fitting of the seawater temperature and the horizontal direction fitting of the seawater temperature both show the reliability of the present invention in inverting the three-dimensional ocean temperature field. Figure 3 As shown in the figure, the effect of horizontal fitting of seawater temperature is evaluated as follows: Figure 4 The present invention aims to explore a data-driven ocean three-dimensional temperature field inversion method based on Argo buoys. This method builds a model based on Argo measured data and is closer to the real ocean temperature data. Compared with traditional methods, this method has the advantages of being convenient and fast, and reducing the analysis of the internal structure and historical change laws of the ocean.

[0080] Finally, it should be noted that the above specific implementation methods are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to examples, a person of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the spirit and scope of the present invention, which should be covered by the scope of the patent claims of the present invention.

Claims

1. The method for inverting the ocean three-dimensional temperature field based on Argo buoys is characterized by: The following steps are included Step 1: Analyze the Argo float data file and extract the depth and temperature data of each float; Step 2: Use the B-spline curve fitting method to establish the vertical profile of seawater temperature; Step 3: Use Kriging interpolation method to establish the horizontal profile of seawater temperature; Step 4: Construct the three-dimensional ocean temperature field.

2. The method for inverting the ocean three-dimensional temperature field based on Argo buoys according to claim 1, characterized in that: In step 2, for a single buoy, a B-spline curve is used to fit the relationship between seawater temperature and depth, and a vertical profile model of seawater temperature is established. The principle is as follows: Where P(t) represents the temperature curve corresponding to the temperature profile, t is the normalization parameter, that is, the normalized value of the depth, n+1 is the number of control points, P i is the characteristic point of the control curve, F i，k (t) is the i-th k-order B-spline curve basis function, i is the serial number of the B-spline curve, and k is the order of the B-spline curve. The basis function in the B-spline curve equation is: Where i is the serial number of the B-spline curve basis function, k is the order of the B-spline curve, and t is the normalization parameter.

3. The method for inverting the ocean three-dimensional temperature field based on Argo buoys according to claim 1, characterized in that: In step 3, according to the temperature data fitted in step 2, a seawater temperature horizontal profile model is established using the Kriging interpolation method, and the principle is as follows: Where x0 is the coordinate of any interpolation point in space, Z * (x0) is the estimated temperature at the interpolation point x0, which can be expressed as a linear combination of the observed values ​​around the space: i is the coordinate of the i-th observation point in space, N is the number of observation points, i is the serial number of the known observation point, Z(x i ) is the temperature value of the i-th observation point, λ i is the weighting coefficient of the i-th observation point. Assume that the spatial attribute Z(x) has the same distribution at each point, that is, for any point x in space, Z(x) has the same expectation c and variance σ 2 , that is, E[Z(x)]=c, Var[Z(x)]=σ 2 In order to ensure the optimal estimate, the estimated value Z at the interpolation point x0 * The difference between (x0) and the true value Z(x0) is the smallest, which must satisfy Var[Z * (x0)-Z(x0)]=min, and in order to ensure the unbiasedness of the estimate, it is necessary to satisfy E[Z * (x0)-Z(x0)]=0, we get The variance expression of the error to be estimated is as follows: Z var =Var[Z * (x0)-Z(x0)] Where Z var is the estimated variance, x0 is any interpolation coordinate in the space, Z * (x0) is the estimated temperature at the interpolation point x0, Z(x0) is the true temperature at the interpolation point x0, Cov(Z(x i ), Z(x j )) is Z(x i ) and Z(x j ), x i and x j is the coordinate of a known point in space, Z(x i ) and Z(x j ) is a known point x i and x j The corresponding temperature value, λ i and λ j is the weighting coefficient, i is the known observation point x i The serial number of j is the known observation point x j The sequence number of n is the number of known observation points. In order to make the estimated value equal to the actual value, the estimated variance must be minimized, that is, satisfy We must also ensure that the obtained λ i satisfy The Lagrange multiplier method is used to solve the problem, and the solution is to construct a new objective function. where μ is the Lagrange multiplier, Z var is the estimated variance, λ i is the weight coefficient, i is the weight coefficient λ i The serial number, n is the weight coefficient λ i The number of. Then where r ij is the semivariogram function, r ij =σ 2 -Cov(Z(x i ), Z(x j )), r i0 =σ 2 -Cov(Z(x i ), Z(x0)), σ 2 is the variance of any point in space, Cov(Z(x i ), Z(x j )) is Z(x i ) and Z(x j ), Cov(Z(x i ), Z(x0)) is Z(x i ) and the cross-covariance of Z(x0), where Z(x0) is the true temperature value at the interpolation point x0, i and x j is the coordinate of the known observation point in space, Z(x i ) and Z(x j ) is a known point x i and x j The temperature value at j is the weighting coefficient, j is the weighting coefficient λ j The number of n is the weighting coefficient λ j and λ i The number of. Combining the above conditions, we can get the following equations: By solving the above equation using the theoretical variation function model, we can get the weight coefficient λ of all interpolation points. i and Lagrange multiplier μ, and substitute it into the Kriging interpolation formula to obtain the estimated value Z * (x0), substitute the variance expression of the error to be estimated to obtain the estimated variance Z var .

4. The method for inverting the ocean three-dimensional temperature field based on Argo buoys according to claim 1, characterized in that: In step 4, the three-dimensional temperature field of the ocean is constructed by combining step 2 and step 3. According to the spline curve fitting parameters of each buoy obtained in step 2, the temperature data of any depth of each coordinate can be calculated, and according to step 3, the horizontal temperature field of the ocean is constructed by Kriging interpolation, and finally the three-dimensional temperature field of the ocean is constructed.

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