A vertical gradient correction method for seawater temperature-salinity data considering temperature-salinity constitutive relation

Abstract

The present invention discloses a vertical gradient correction method for seawater temperature-salinity data considering the temperature-salinity constitutive relationship. First, the vertical gradient error is identified, and then the salinity correction is performed on the area to be corrected until the buoyancy frequency meets the minimum limit value. Since the salinity change and the temperature change follow the constitutive relationship, the relationship between the two is obtained by the linear fitting proportional coefficient of the local N profile data sets. Finally, the temperature change is obtained from the salinity correction through this proportional coefficient. The result after the temperature-salinity correction is used as the initial value of a cost function. The temperature-salinity value that minimizes the cost function is solved through an iterative cycle, which is the corrected temperature-salinity grid data. The present invention optimizes the vertical gradient correction algorithm for the temperature-salinity structure of seawater by adding the constitutive relationship between temperature and salt, thereby improving the authenticity of the temperature-salinity data. In addition, by allowing the solved cost function to adapt to the parameters, it avoids manually setting parameters and improves the correction efficiency.

Description

Technical Field

[0001] The invention relates to a vertical gradient correction method for seawater temperature-salinity data taking into account a temperature-salinity constitutive relationship. Background Art

[0002] The temperature and salinity structure of seawater is an important part of physical oceanography. By understanding the spatial and temporal distribution of the temperature and salinity of the seawater layer, we can study physical oceanographic phenomena such as the fine structure of the seawater layer, mesoscale vortices, ocean fronts, and the formation of internal ocean waves. These phenomena are directly related to major issues such as global environmental change, marine transportation, marine military security, and marine fishery distribution. The detection of temperature and salinity structure is usually carried out by arranging a certain number of temperature and salinity depth sensors (CTD sensors, full name The Conductivity, Temperature, Depth sensor) on the survey line of the research sea area. CTD can obtain temperature and salinity data through a period of measurement, and interpolate horizontally to obtain the temperature and salinity structure profile of the entire survey line.

[0003] Vertical gradient correction: Vertical gradient correction is to correct the temperature and salinity values ​​after 3D gridding so that the temperature in the correction area changes reasonably with the water depth. The deeper the depth, the lower the profile temperature. Vertical gradient correction is actually to correct the deviation caused by the number of observations at the grid depth and the vertical profile of the grid. This correction is particularly effective in shallow coastal areas because there are large offshore temperature or salinity gradient deviations in such sea areas.

[0004] At present, most methods for vertical gradient correction of temperature-salinity grid data are based on the buoyancy frequency calculation formula. If the buoyancy frequency of the temperature profile along the depth direction is less than the set minimum value, it means that there is an error in the vertical gradient at that location and vertical gradient correction is required. Then the corrected temperature-salinity is obtained by minimizing the cost function. However, previous studies did not consider the temperature-salinity constitutive relationship of temperature-salinity during the correction process and the automatic adjustment of temperature and temperature gradient weights when minimizing the cost function. For example, when Michael R. Carnes performed vertical gradient correction in "Description and Evaluation of GDEM-V 3.0" and You-Soon Chang performed vertical gradient correction in "Vertical gradient correction for the oceanographic Atlas of the East Asian Seas", they both first determined the buoyancy frequency and then minimized the cost function.

[0005] At present, most of the methods for vertical gradient correction based on temperature and salinity data are solved by minimizing the cost function. However, the constitutive relationship between temperature and salinity is ignored in the solution process. Ignoring this relationship will lead to correction deviation and low accuracy. In addition, when solving the cost function in previous methods, the temperature and temperature gradient weights in the formula cannot be adjusted adaptively, and manual adjustment is required. This method that requires manual adjustment makes it difficult for the corrected buoyancy frequency to meet the requirements in the entire domain. It has a narrow application range and cannot be widely used in various sea areas. In addition, the correction efficiency is low and has limitations. Summary of the invention

[0006] In order to solve the problems existing in the above prior art, the present invention proposes a vertical gradient correction method for seawater temperature-salinity data taking into account the temperature-salinity constitutive relationship. The method can correct the ocean temperature-salinity grid data that does not meet the buoyancy frequency requirements, and correct the measured values ​​in the grid data that do not conform to the correct change of temperature and salinity with depth. Ultimately, the corrected temperature-salinity data meets the buoyancy frequency requirements and can be widely used in various marine fields.

[0007] The present invention can be implemented through the following technical solutions:

[0008] A vertical gradient correction method for seawater temperature-salinity data considering the temperature-salinity constitutive relationship is disclosed. First, vertical gradient error identification is performed, and then salinity correction is performed on the area to be corrected until the buoyancy frequency meets the minimum limit value. Since salinity changes and temperature changes follow the constitutive relationship, the relationship between the two is obtained through the linear fitting proportional coefficient of the local N profile data sets. Finally, the temperature change is obtained from the salinity correction through the proportional coefficient. The result after the temperature-salinity correction is used as the initial value of a cost function. The temperature-salinity value that minimizes the cost function is solved through an iterative cycle, which is the corrected temperature-salinity gridded data. In the process of minimizing the cost function, the coefficient A is automatically matched using an adaptive algorithm, and the vertical gradient correction is completed.

[0009] Furthermore, the vertical gradient correction method of seawater temperature-salinity data considering the temperature-salinity constitutive relationship of the present invention specifically comprises the following steps:

[0010] (1) First, determine the vertical gradient correction range: This step is to determine which measured profile data around the grid point are used for gradient correction. The screening range includes three spatial scales, namely the longitudinal scale, the latitudinal scale and the vertical scale F, and a time scale. The vertical scale represents the component across the isobath and is a part of the potential vorticity. The calculation formula is as follows:

[0011]

[0012] PV = f / H is the barotropic potential vorticity, f is the Coriolis parameter, H is the seafloor depth at the grid point, i is the measured profile number, and g is the grid point number;

[0013] (2) Setting the initial value of the coefficient in the cost function: When correcting the vertical gradient, the temperature and salinity are continuously adjusted, and then the adjusted temperature and salinity values ​​are brought into the calculation of potential temperature, potential density and buoyancy frequency. If the buoyancy frequency reaches the set value, the cycle is stopped, otherwise the temperature and salinity value is continued to be adjusted. When adjusting the temperature and salinity value, the method is to iteratively correct the salinity first, and then correct the temperature according to the temperature-salinity constitutive relationship. The corrected temperature is set as the initial value for solving the minimization cost function. After multiple iterative cycles, the cost function is finally minimized to obtain the temperature value that satisfies the minimum sum of the temperature and temperature gradient changes.

[0014] In the solution process, the temperature and the temperature gradient must be at the same order of magnitude in the cost function. To ensure the balance between the temperature and the temperature gradient when minimizing the cost function, we set an adjustment coefficient A. Before the vertical gradient is corrected, A is given an initial value so that A can be adaptively adjusted when the vertical gradient of the temperature-salinity is corrected, and the balance between the temperature and the temperature gradient can be re-found.

[0015] (3) Calculation of potential temperature and potential density: When performing vertical gradient correction, it is necessary to determine whether the correction stop requirement is met based on the buoyancy frequency variable. The calculation of buoyancy frequency involves two parameters, the potential density and depth of the selected area. The calculation of potential density also requires the potential temperature parameter. The temperature of a seawater micro-group at a certain depth in the seawater when it rises adiabatically to the sea surface is called the potential temperature of the seawater at that depth, and the corresponding density at this time is called the potential density.

[0016] The calculation formulas of potential temperature θ and potential density ρ are shown in equations (1) and (2) respectively:

[0017] t=T×1.00024

[0018] h=P r -P

[0019] xk=h×Γ(S,t,P)

[0020] t=t+0.5×xk

[0021] q=xk

[0022] p=P+0.5×h

[0023] xk=h×Γ(S,t,p)

[0024] t=t+0.29289322×(xk-q)

[0025] q=0.58578644×xk+0.121320344×q

[0026] xk=h×Γ(S,t,p)

[0027] t=t+1.707106781×(xk-q)

[0028] q=3.414213562×xk-4.121320344×q

[0029] p=p+0.5×h

[0030] xk=h×Γ(S,t,p)

[0031] θ(S,T,P,P r )={t+(xk-2.0×q)÷6.0}×0.99976 (1)

[0032] where Γ(S, t, p) is defined as follows:

[0033] Γ(S,t,p)=a 0 +a 1 t+a 2 t 2 +a 3 t 3 +(b 0 +b 1 t)(S-35)+{c 0 +c 1 t+c 2 t 2 +c 3 t 3 +(d 0 +d 1 t)(S-35)}p+(e 0 +e 1 t+e 2 t 2 ) 2

[0034] The parameters in the above formula are set as follows:

[0035] a 0 =3.5803×10 -5 a 1 =8.5258×10 -6 a 2 =-6.8360×10 -8 a 3 =6.6228×10 -10

[0036] b 0 =1.8932×10 -6 b 1 =-4.2393×10-8

[0037] c 0 =1.8741×10 -8 c 1 =-6.7795×10 -10 c 2 =8.7330×10 -12 c 3 =-5.4481×10 -14

[0038] d 0 =-1.1351×10 -10 d 1 =2.7759×10 -12

[0039] e 0 =-4.6206×10 -13 e 1 =1.8676×10 -14 e 2 =-2.1687×10 -16

[0040] According to formula (1), the potential temperature θ can be obtained:

[0041] The next step is to use the obtained potential temperature value θ to calculate the potential density value corresponding to the potential temperature. The calculation formula is shown in (2):

[0042]

[0043] t=θ×1.00024

[0044] p=P÷10

[0045] ρ(S,t,0)=ρ w +(b 0 +b 1 t+b 2 t 2 +b 3 t 3 +b 4 t 4 )S+(c 0 +c 1 t+c 2 t 2 )S 3 / 2 +d 0 S 2

[0046] ρ w =a 0 +a 1 t+a 2t 2 +a 3 t 3 +a 4 t 4 +a 5 t 5

[0047] K(S,t,p)=K(S,t,0)+Ap+Bp 2

[0048] K(S,t,0)=K w +(f 0 +f 1 t+f 2 t 2 +f 3 t 3 )S+(g 0 +g 1 t+g 2 t 2 )S 3 / 2

[0049] A=A w +(i 0 +i 1 t+i 2 t 2 )S+j 0 S 3 / 2

[0050] B=B w +(m 0 +m 1 t+m 2 t 2 )S

[0051] K w =e 0 +e 1 t+e 2 t 2 +e 3 t 3 +e 4 t 4

[0052] A w =h 0 +h 1 t+h 2 t 2 +h 3 t 3

[0053] B w =k 0 +k 1 t+k 2 t2

[0054] Among them, the parameter coefficients involved in the above formula are set as follows:

[0055] a 0 =999.842594 a 1 =6.793952×10 -2 a 2 =-9.095290×10 -3 a 3 =1.001685×10 - 4 a 4 =-1.120083×10 -6 a 5 =6.536332×10 -9

[0056] b 0 =8.24493×10 -1 b 1 =-4.0899×10 -4 b 2 =7.6438×10 -5 b 3 =-8.2467×10 -7 b 4 =5.3875×10 -9

[0057] c 0 =-5.72466×10 -3 c 1 =1.0227×10 -4 c 2 =-1.6546×10 -6

[0058] d 0 =4.8314×10 -4

[0059] e 0 =19652.21 e 1 =148.4206 e 2 =-2.327105 e 3 =1.360477×10 -2 e 4 =-5.155288×10 -5

[0060] f 0 =54.6746 f 1 =-0.603459 f2 =1.09987×10 -2 f 3 =-6.1670×10 -5

[0061] g 0 =7.944×10 -2 g 1 =1.6483×10 -2 g 2 =-5.3009×10 -4

[0062] h 0 =3.239908 h 1 =1.43713×10 -3 h 2 =1.16092×10 -4 h 3 =-5.77905×10 -7

[0063] i 0 =2.2838×10 -3 i 1 =-1.0981×10 -5 i 2 =-1.6078×10 -6

[0064] j 0 =1.91075×10 -4

[0065] k 0 =8.50935×10 -5 k 1 =-6.12293×10 -6 k 2 =5.2787×10 -8

[0066] m 0 =-9.9348×10 -7 m 1 =2.0816×10 -8 m 2 =9.1697×10 -10

[0067] The potential density value at potential temperature θ can be obtained;

[0068] (4) Calculate the buoyancy frequency N 2 :The purpose of calculating the buoyancy frequency is to determine whether the grid data needs vertical gradient correction. If the buoyancy frequency N is calculated2 When it is less than the set value, vertical gradient correction is required. The vertical gradient correction profile range is the three-dimensional cube determined in the first step, after which vertical gradient correction work can be carried out.

[0069] The calculation process of buoyancy frequency is as follows: for an uncorrected temperature profile T and salinity profile S, the expressions of potential temperature θ and potential density ρ of the i-1th layer and the ith layer are given, and the buoyancy frequency at each depth is calculated:

[0070]

[0071] If N 2 Less than the set minimum value (N 2 min =1.5×10 -7 ), it means that there is an error in the vertical gradient at that location and vertical gradient correction is required;

[0072] (5) Salinity iterative correction: When the buoyancy frequency does not reach the minimum value, salinity iterative correction is first performed. The iterative correction method is:

[0073] The salinity value S of the corrected area at depth i i Each increases by a set change value ΔS i , get S i +ΔS i Then determine whether the buoyancy frequency reaches N under the salinity correction value. 2 min =1.5×10 -7 If not, continue to S i Correct until the buoyancy frequency satisfies N 2 min , salinity correction ends;

[0074] (6) Set the initial value of the temperature in the cost function according to the temperature-salinity constitutive relationship: Since the salinity change and temperature change follow the constitutive relationship, that is:

[0075] ΔT k +γ k ΔS k =0, k=1, 2, ..., K

[0076] Before correcting the temperature-salinity value, we must first calculate the temperature-salinity relationship, that is, the TS relationship, which is defined as TS Relationships¶ k Usually a local N profile data set is used This calculation can be done before correction, and then the salinity value corrected in step 5 is compared with γ k Combined, we get ΔT k, and then give an initial temperature value T for correcting the temperature using the minimized cost function k +ΔT k , so that the modified temperature-salinity still satisfies the constitutive relationship;

[0077] (7) Minimize the cost function: The cost function is set as shown in formula (3):

[0078]

[0079] in, is the corrected value of seawater temperature at a certain depth, T is the temperature before correction, σ is the standard deviation, D is the temperature difference between adjacent depths k and k-1, δ is the standard deviation of D,

[0080] In the above steps, we have obtained A and The corrected amount in the cost function The initial value is also set, and the cost function is finally minimized to obtain the corrected temperature value

[0081] After the correction step is completed, it is determined whether the gradient of the grid point changes slightly. If not, the coefficient A is automatically corrected so that A = A + δ A , where δ A is an adjustment parameter, and the size of the parameter is set according to the characteristics of the sea area; if yes, A is not modified, and then the potential temperature and density are calculated in both cases to determine whether the corrected temperature-salinity buoyancy frequency meets the requirements. Finally, when the buoyancy frequency N 2 >N 2 min , the correction is completed.

[0082] The present invention has the following beneficial effects:

[0083] 1) When correcting the vertical gradient, correct the salinity first and then the temperature. Correct the salinity first because the vertical change of salinity is small and basically monotonic, and then correct the temperature on this basis, which can improve the accuracy of the corrected temperature;

[0084] 2) When performing temperature-salinity correction, the method of iterative correction of temperature-salinity is adopted to ensure that the temperature-salinity has the minimum change under the premise that the buoyancy frequency meets the requirements, thereby ensuring the accuracy of the temperature-salinity correction;

[0085] 3) By adding the temperature-salinity constitutive relationship, the changes in temperature and salinity are correlated, rather than taking arbitrary values ​​of temperature and salinity during correction. This approach makes the temperature-salinity adjustment more accurate and improves the correction accuracy;

[0086] 4) When minimizing the cost function, the adaptive adjustment of the weight A between temperature and temperature gradient is added, which eliminates the need for manual parameter adjustment, realizes the adaptive global temperature correction, and improves the efficiency of solving the optimal solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Figure 1 The present invention determines the vertical gradient correction area based on the depth range;

[0088] Figure 2-1 This is a temperature variation diagram before the present invention is modified;

[0089] Figure 2-2 This is the temperature change diagram after correction of the present invention;

[0090] Figure 3-1 This is the buoyancy frequency diagram before correction of the present invention;

[0091] Figure 3-2 is the buoyancy frequency diagram after correction of the present invention;

[0092] Figure 4 The vertical gradient correction method of the present invention is a flow chart. DETAILED DESCRIPTION

[0093] The following describes the implementation methods of the present invention through specific implementation cases. Those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification.

[0094] The present invention provides a method for correcting the vertical gradient of seawater temperature-salinity data taking into account the temperature-salinity constitutive relationship. First, the vertical gradient error is identified. Then, the salinity correction is performed on the area that needs to be corrected until the buoyancy frequency meets the minimum limit value. Since the salinity change and temperature change follow the constitutive relationship, the relationship between the two is obtained through the linear fitting proportional coefficient of the local N profile data sets. Finally, the temperature change is obtained from the salinity correction through this proportional coefficient. The result after the temperature-salinity correction is used as the initial value of a cost function. The temperature-salinity value that minimizes the cost function is solved through an iterative cycle, which is the corrected temperature-salinity gridded data. In the process of minimizing the cost function, the coefficient A is automatically matched using an adaptive algorithm. At this point, the vertical gradient correction is completed. Figure 4 The figure shows a flow chart of the vertical gradient correction method of the present invention.

[0095] A method for correcting vertical gradient of seawater temperature-salinity data considering temperature-salinity constitutive relationship of the present invention comprises the following steps:

[0096] (1) First, determine the vertical gradient correction range: This step is to determine which measured profile data around the grid point are used for gradient correction. The screening range includes three spatial scales (longitudinal scale, latitudinal scale, and vertical scale F) and one time scale. The vertical scale represents the component across the isobath and is part of the potential vorticity. The calculation formula is as follows:

[0097]

[0098] PV=f / H is the barotropic potential vorticity, f is the Coriolis parameter, H is the seafloor depth at the grid point, i is the measured profile number, and g is the grid point number.

[0099] In actual calculations, it is necessary to perform specific calculations based on the seawater characteristics of different sea areas. For example, in the East Asian sea area, the latitudinal scale is 1°, the longitudinal scale is 0.5°, and F is 0.5. Therefore, the three-dimensional correction range is:

[0100]

[0101]

[0102] -0.25(H i +H g )≤H i -H g ≤0.25(H i +H g )

[0103]

[0104]

[0105] From this formula, the measured profile range determined by the local ocean depth for gradient correction can be calculated. A three-dimensional cube is constructed according to the profile range, which is the correction interval, and the temperature mean value D of the correction area is obtained. k like Figure 1 shown.

[0106] Note that the correction range determined here is set for the grid data whose buoyancy frequency does not reach the minimum limit. k This is to prepare for the vertical gradient correction work on abnormal points.

[0107] (2) Set the initial value of the coefficient in the cost function: When correcting the vertical gradient, the temperature and salinity are continuously adjusted, and then the adjusted temperature and salinity values ​​are brought into the calculation of potential temperature, potential density and buoyancy frequency. If the buoyancy frequency reaches the set value, the cycle is stopped, otherwise the temperature and salinity value is continued to be adjusted. When adjusting the temperature and salinity value, the method is to iteratively correct the salinity first, and then correct the temperature according to the temperature and salinity constitutive relationship, and set the corrected temperature as the initial value for solving the minimization cost function. After multiple iterative cycles, the cost function is finally minimized to obtain the temperature value that satisfies the minimum sum of the temperature and temperature gradient changes. The correction is now complete.

[0108] In the solution process, the temperature and temperature gradient must be at the same order of magnitude in the cost function, so that it is meaningful to solve the minimum value of the cost function. In order to ensure the balance between temperature and temperature gradient when minimizing the cost function, an adjustment coefficient is required. Let the adjustment coefficient be A. Before the vertical gradient is corrected, give A an initial value so that A can be adaptively adjusted when the vertical gradient of the temperature and salt is corrected, and the balance between temperature and temperature gradient can be re-found.

[0109] (3) Calculation of potential temperature and potential density: When performing vertical gradient correction, it is necessary to determine whether the correction stop requirement is met based on the variable of buoyancy frequency. The calculation of buoyancy frequency involves two parameters, the potential density and depth of the selected area. The calculation of potential density requires the potential temperature parameter. The temperature of a seawater micro-group at a certain depth in the seawater when it rises adiabatically to the sea surface is called the potential temperature of the seawater at that depth, and the corresponding density at this time is called the potential density.

[0110] The calculation formulas of potential temperature θ and potential density ρ are shown in equations (1) and (2) respectively:

[0111] t=T×1.00024

[0112] h=P r -P

[0113] xk=h×Γ(S,t,P)

[0114] t=t+0.5×xk

[0115] q=xk

[0116] p=P+0.5×h

[0117] xk=h×Γ(S,t,p)

[0118] t=t+0.29289322×(xk-q)

[0119] q=0.58578644×xk+0.121320344×q

[0120] xk=h×Γ(S,t,p)

[0121] t=t+1.707106781×(xk-q)

[0122] q=3.414213562×xk-4.121320344×q

[0123] p=p+0.5×h

[0124] xk=h×Γ(S,t,p)

[0125] θ(S,T,P,P r )={t+(xk-2.0×q)÷6.0}×0.99976 (1)

[0126] where Γ(S, t, p) is defined as follows:

[0127] Γ(S,t,p)=a 0 +a 1 t+a 2 t 2 +a 3 t 3 +(b 0 +b 1 t)(S-35)+{c 0 +c 1 t+c 2 t 2 +c 3 t 3 +(d 0 +d 1 t)(S-35)}p+(e 0 +e 1 t+e 2 t 2 ) 2

[0128] The parameters in the above formula are set as follows:

[0129] a 0 =3.5803×10 -5 a 1 =8.5258×10 -6 a 2 =-6.8360×10 -8 a 3 =6.6228×10 -10

[0130] b 0 =1.8932×10 -6 b 1 =-4.2393×10 -8

[0131] c 0 =1.8741×10 -8 c 1 =-6.7795×10 -10 c 2 =8.7330×10 -12 c 3 =-5.4481×10 -14

[0132] d 0 =-1.1351×10 -10 d 1 =2.7759×10 -12

[0133] e 0 =-4.6206×10 -13 e 1 =1.8676×10 -14 e 2 =-2.1687×10 -16

[0134] Although there are many coefficients listed, they are all known, and the potential temperature θ can be finally obtained according to formula (1).

[0135] The next step is to use the obtained potential temperature value θ to calculate the potential density value corresponding to the potential temperature. The calculation formula is shown in (2):

[0136]

[0137] t=θ×1.00024

[0138] p=P÷10

[0139] ρ(S,t,0)=ρ w +(b 0 +b 1 t+b 2 t 2 +b 3 t 3 +b 4 t 4 )S+(c 0 +c 1 t+c 2 t 2 )S 3 / 2 +d 0 S 2

[0140] ρ w =a 0 +a 1 t+a 2 t2 +a 3 t 3 +a 4 t 4 +a 5 t 5

[0141] K(S,t,p)=K(S,t,0)+Ap+Bp 2

[0142] K(S,t,0)=K w +(f 0 +f 1 t+f 2 t 2 +f 3 t 3 )S+(g 0 +g 1 t+g 2 t 2 )S 3 / 2

[0143] A=A w +(i 0 +i 1 t+i 2 t 2 )S+j 0 S 3 / 2

[0144] B=B w +(m 0 +m 1 t+m 2 t 2 )S

[0145] K w =e 0 +e 1 t+e 2 t 2 +e 3 t 3 +e 4 t 4

[0146] A w =h 0 +h 1 t+h 2 t 2 +h 3 t 3

[0147] B w =k 0 +k 1 t+k 2 t 2

[0148] Among them, the parameter coefficients involved in the above formula are set as follows:

[0149] a 0 =999.842594 a 1 =6.793952×10 -2 a 2 =-9.095290×10 -3 a 3 =1.001685×10 - 4 a 4 =-1.120083×10 -6 a 5 =6.536332×10 -9

[0150] b 0 =8.24493×10 -1 b 1 =-4.0899×10 -4 b 2 =7.6438×10 -5 b 3 =-8.2467×10 -7 b 4 =5.3875×10 -9

[0151] c 0 =-5.72466×10 -3 c 1 =1.0227×10 -4 c 2 =-1.6546×10 -6

[0152] d 0 =4.8314×10 -4

[0153] e 0 =19652.21 e 1 =148.4206 e 2 =-2.327105 e 3 =1.360477×10 -2 e 4 =-5.155288×10 -5

[0154] f 0 =54.6746 f 1 =-0.603459 f 2=1.09987×10 -2 f 3 =-6.1670×10 -5

[0155] g 0 =7.944×10 -2 g 1 =1.6483×10 -2 g 2 =-5.3009×10 -4

[0156] h 0 =3.239908 h 1 =1.43713×10 -3 h 2 =1.16092×10 -4 h 3 =-5.77905×10 -7

[0157] i 0 =2.2838×10 -3 i 1 =-1.0981×10 -5 i 2 =-1.6078×10 -6

[0158] j 0 =1.91075×10 -4

[0159] k 0 =8.50935×10 -5 k 1 =-6.12293×10 -6 k 2 =5.2787×10 -8

[0160] m 0 =-9.9348×10 -7 m 1 =2.0816×10 -8 m 2 =9.1697×10 -10

[0161] In the process of solving the potential density, although there are many coefficients in each formula, they are all known, and the potential density value at the potential temperature θ can be obtained.

[0162] (4) Calculate the buoyancy frequency N 2:The purpose of calculating the buoyancy frequency is to determine whether the grid data needs vertical gradient correction. If the buoyancy frequency N is calculated 2 When it is less than the set value, vertical gradient correction is required. The vertical gradient correction profile range is the three-dimensional cube determined in the first step, after which the vertical gradient correction work can be carried out.

[0163] The calculation process of buoyancy frequency is as follows: for an uncorrected temperature profile T and salinity profile S, the expressions of potential temperature θ and potential density ρ of the i-1th layer and the ith layer are given, and the buoyancy frequency at each depth is calculated:

[0164]

[0165] If N 2 Less than the set minimum value (N 2 min =1.5×10 -7 ), it means that there is an error in the vertical gradient at that location and vertical gradient correction is required;

[0166] The reason why vertical gradient correction uses the gradient calculation judgment standard of position density - buoyancy frequency, is because position density is calculated through temperature and salinity, so the gradient of position density used in buoyancy frequency calculation is the balanced average of temperature and salinity, which can represent the gradient of temperature and salinity impartially. Therefore, it is a reasonable operation to correct the temperature and salinity value for the abnormal point of buoyancy frequency.

[0167] (5) Salinity iterative correction: When the buoyancy frequency does not reach the minimum value, the salinity iterative correction is first performed. The iterative correction method is: the salinity value S of the correction area with a depth of i is i Each increases by a set change value ΔS i , get S i +ΔS i Then determine whether the buoyancy frequency reaches N under the salinity correction value. 2 min =1.5×10 -7 If not, continue to S i Correct until the buoyancy frequency satisfies N 2 min , salinity correction ends.

[0168] (6) Set the initial value of the temperature in the cost function according to the temperature-salinity constitutive relationship: Since the salinity change and temperature change follow the constitutive relationship, that is:

[0169] ΔT k +γ k ΔS k =0, k=1, 2, ..., K

[0170] Before correcting the temperature-salinity value, we must first calculate the temperature-salinity relationship, that is, the TS relationship, which is defined as TS Relationships¶ k Usually a local N profile data set is used This calculation can be done before correction, and then the salinity value corrected in step 5 is compared with γ k Combined, we get ΔT k , and then give an initial temperature value T for correcting the temperature using the minimized cost function k +ΔT k , so that the temperature and salinity still satisfy the constitutive relationship during correction. This approach can improve the accuracy of correction and is applicable in practical applications.

[0171] (7) Minimize the cost function: The cost function is set as shown in formula (3):

[0172]

[0173] in, is the corrected value of seawater temperature at a certain depth. T is the temperature before correction, σ is the standard deviation, D is the temperature difference between adjacent depths k and k-1, and δ is the standard deviation of D.

[0174] In the above steps, we have obtained A and The corrected amount in the cost function The initial value is also set, and the cost function is finally minimized to obtain the corrected temperature value

[0175] After the correction step is completed, it is determined whether the gradient of the grid point changes slightly. If not, the coefficient A is automatically corrected so that A = A + δ A , where δ A As an adjustment parameter, set the size yourself so that A can adaptively adjust the parameters; if so, do not modify A, and then continue to calculate the potential temperature and potential density in these two cases to determine whether the corrected temperature-salinity buoyancy frequency meets the requirements.

[0176] Finally, when the buoyancy frequency N 2 >N 2 min , the correction is completed.

[0177] (8) Implementation of vertical gradient correction based on temperature-salinity structure: When verifying the effect of this method, the area selected was the Yellow Sea area of ​​125.5E (24N-40N), and the time was the data of January of a certain year. The buoyancy frequency calculated by the temperature-salinity value in this data did not meet the standard, so a vertical gradient correction was performed. The comparison of temperature changes before and after the correction is shown in Figure 2.

[0178] like Figure 2-1 As shown in the figure, in the latitude range of 28N-34N, the temperature value increases with the depth, which indicates that there is an abnormal vertical gradient in this area. Therefore, according to the vertical gradient correction method summarized, the following is obtained: Figure 2-2 The results in .

[0179] After vertical gradient correction, the buoyancy frequency should be no less than zero. Figure 3-1 and 3-2 The comparison of buoyancy frequency before and after correction is shown, and the correction effect meets the requirements.

[0180] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for correcting the vertical gradient of seawater temperature and salinity data considering the temperature-salinity constitutive relationship, characterized in that: First, the vertical gradient error is identified, and then the salinity correction is performed on the area that needs to be corrected until the buoyancy frequency meets the minimum limit value; since the salinity change and temperature change follow the constitutive relationship, the relationship between the two is obtained through the linear fitting proportional coefficient of the local N profile data sets, and finally the temperature change is obtained from the salinity correction through this proportional coefficient. The above temperature-salinity correction result is used as the initial value of a cost function, and the temperature-salinity value that minimizes the cost function is solved through an iterative cycle, which is the corrected temperature-salinity grid data. In the process of minimizing the cost function, the coefficient A uses an adaptive algorithm to achieve automatic matching, and the vertical gradient correction is completed; The specific steps include: (1) First, determine the vertical gradient correction range: This step is to determine which measured profile data around the grid point are used for gradient correction. The screening range includes three spatial scales, namely the longitudinal scale, the latitudinal scale and the vertical scale F, and a time scale. The vertical scale represents the component across the isobath and is a part of the potential vorticity. The calculation formula is as follows: PV = f / H is the barotropic potential vorticity, f is the Coriolis parameter, H is the seafloor depth at the grid point, i is the measured profile number, and g is the grid point number; (2) Setting the initial value of the coefficient in the cost function: When correcting the vertical gradient, the temperature and salinity are continuously adjusted, and then the adjusted temperature and salinity values ​​are brought into the calculation of potential temperature, potential density and buoyancy frequency. If the buoyancy frequency reaches the set value, the cycle is stopped, otherwise the temperature and salinity value is continued to be adjusted. When adjusting the temperature and salinity value, the method is to iteratively correct the salinity first, and then correct the temperature according to the temperature-salinity constitutive relationship. The corrected temperature is set as the initial value for solving the minimization cost function. After multiple iterative cycles, the cost function is finally minimized to obtain the temperature value that satisfies the minimum sum of the temperature and temperature gradient changes. In the solution process, the temperature and the temperature gradient must be at the same order of magnitude in the cost function. To ensure the balance between the temperature and the temperature gradient when minimizing the cost function, we set an adjustment coefficient A. Before the vertical gradient is corrected, A is given an initial value so that A can be adaptively adjusted when the vertical gradient of the temperature-salinity is corrected, and the balance between the temperature and the temperature gradient can be re-found. (3) Calculation of potential temperature and potential density: When performing vertical gradient correction, it is necessary to determine whether the correction stop requirement is met based on the buoyancy frequency variable. The calculation of buoyancy frequency involves two parameters, the potential density and depth of the selected area. The calculation of potential density also requires the potential temperature parameter. The temperature of a seawater micro-group at a certain depth in the seawater when it rises adiabatically to the sea surface is called the potential temperature of the seawater at that depth, and the corresponding density at this time is called the potential density. The calculation formulas of potential temperature θ and potential density ρ are shown in equations (1) and (2) respectively: t=T×1.00024 h=P r -P xk=h×Γ(S,t,P) t=t+0.5×xk q=xk p=P+0.5×h xk=h×Γ(S,t,p) t=t+0.29289322×(xk-q) q=0.58578644×xk+0.121320344×q xk=h×Γ(S,t,p) t=t+1.707106781×(xk-q) q=3.414213562×xk-4.121320344×q p=p+0.5×h xk=h×Γ(S,t,p) θ(S,T,P,P r )={t+(xk-2.0×q)÷6.0}×0.99976 (1) where Γ(S, t, p) is defined as follows: Γ(S,t,p)=a0+a1t+a2t 2 +a3t 3 +(b0+b1t)(S-35)+{c0+c1t+c2t 2 +c3t 3 +(d0+d1t)(S-35)}p+(e0+e1t+e2t 2 )p 2 The parameters in the above formula are set as follows: <h2 style=";text-align:left;direction:ltr">a0 = 3.5803×10<h2 style=";text-align:left;direction:ltr"> -5 <h2 style=";text-align:left;direction:ltr"> a1 = 8.5258×10<h2 style=";text-align:left;direction:ltr"> -6 <h2 style=";text-align:left;direction:ltr"> a2 = 6.8360×10<h2 style=";text-align:left;direction:ltr"> -8 <h2 style=";text-align:left;direction:ltr"> a3 = 6.6228×10<h2 style=";text-align:left;direction:ltr"> -10 b0=1.8932×10 -6 b1=-4.2393×10 -8 c0=1.8741×10 -8 c1=-6.7795×10 -10 c2=8.7330×10 -12 c3=-5.4481×10 -14 d0=-1.1351×10 -10 d1=2.7759×10 -12 <h2 style=";text-align:left;direction:ltr">e0 = -4.6206×10<h2 style=";text-align:left;direction:ltr"> -13 <h2 style=";text-align:left;direction:ltr"> e1 = 1.8676×10<h2 style=";text-align:left;direction:ltr"> -14 <h2 style=";text-align:left;direction:ltr"> e2 = -2.1687×10<h2 style=";text-align:left;direction:ltr"> -16 According to formula (1), the potential temperature θ can be obtained: The next step is to use the obtained potential temperature value θ to calculate the potential density value corresponding to the potential temperature. The calculation formula is shown in (2): t=θ×1.00024 p=P÷10 ρ(S,t,0)=ρ w +(b0+b1t+b2t 2 +b3t 3 +b4t 4 )S+(c0+c1t+c2t 2 )S 3 / 2 +d0S 2 ρ w =a0+a1t+a2t 2 +a3t 3 +a4t 4 +a5t 5 K(S,t,p)=K(S,t,0)+Ap+Bp 2 K(S,t,0)=K w +(f0+f1t+f2t 2 +f3t 3 )S+(g0+g1t+g2t 2 )S 3 / 2 A=A w +(i0+i1t+i2t 2 )S+j0S 3 / 2 B=B w +(m0+m1t+m2t 2 )S K w =e0+e1t+e2t 2 +e3t 3 +e4t 4 A w =h0+h1t+h2t 2 +h3t 3 B w =k0+k1t+k2t 2 Among them, the parameter coefficients involved in the above formula are set as follows: <h2 style=";text-align:left;direction:ltr">a0=999.842594a1=6.793952×10<h2 style=";text-align:left;direction:ltr"> -2 <h2 style=";text-align:left;direction:ltr"> a2 = 9.095290×10<h2 style=";text-align:left;direction:ltr"> -3 <h2 style=";text-align:left;direction:ltr"> a3 = 1.001685×10<h2 style=";text-align:left;direction:ltr"> -4 <h2 style=";text-align:left;direction:ltr"> a4 = 1.120083×10<h2 style=";text-align:left;direction:ltr"> -6 <h2 style=";text-align:left;direction:ltr"> a5 = 6.536332×10<h2 style=";text-align:left;direction:ltr"> -9 <h2 style=";text-align:left;direction:ltr">b0 = 8.24493×10<h2 style=";text-align:left;direction:ltr"> -1 <h2 style=";text-align:left;direction:ltr"> b1 = -4.0899×10<h2 style=";text-align:left;direction:ltr"> -4 <h2 style=";text-align:left;direction:ltr"> b2 = 7.6438×10<h2 style=";text-align:left;direction:ltr"> -5 <h2 style=";text-align:left;direction:ltr"> b3 = -8.2467×10<h2 style=";text-align:left;direction:ltr"> -7 <h2 style=";text-align:left;direction:ltr"> b4 = 5.3875×10<h2 style=";text-align:left;direction:ltr"> -9 c0=-5.72466×10 -3 c1=1.0227×10 -4 c2=-1.6546×10 -6 d0＝4.8314×10 -4 e0=19652.21e1=148.4206e2=-2.327105e3=1.360477×10 -2 e4=-5.155288×10 -5 <h2 style=";text-align:left;direction:ltr">f0=54.6746f1=-0.603459f2=1.09987×10<h2 style=";text-align:left;direction:ltr"> -2 <h2 style=";text-align:left;direction:ltr"> f3 = 6.1670×10<h2 style=";text-align:left;direction:ltr"> -5 g0=7.944×10 -2 g1=1.6483×10 -2 g2=-5.3009×10 -4 <h2 style=";text-align:left;direction:ltr">h0 = 3.239908h1 = 1.43713×10<h2 style=";text-align:left;direction:ltr"> -3 <h2 style=";text-align:left;direction:ltr"> h2 = 1.16092×10<h2 style=";text-align:left;direction:ltr"> -4 <h2 style=";text-align:left;direction:ltr"> h3 = -5.77905×10<h2 style=";text-align:left;direction:ltr"> -7 i0=2.2838×10 -3 i1=-1.0981×10 -5 i2=-1.6078×10 -6 j0＝1.91075×10 -4 k0=8.50935×10 -5 k1=-6.12293×10 -6 k2=5.2787×10 -8 m0=-9.9348×10 -7 m1=2.0816×10 -8 m2=9.1697×10 -10 The potential density value at potential temperature θ can be obtained; (4) Calculate the buoyancy frequency N 2 :The purpose of calculating the buoyancy frequency is to determine whether the grid data needs vertical gradient correction. If the buoyancy frequency N is calculated 2 When it is less than the set value, vertical gradient correction is required. The vertical gradient correction profile range is the three-dimensional cube determined in the first step, after which vertical gradient correction work can be carried out. The calculation process of buoyancy frequency is as follows: for an uncorrected temperature profile T and salinity profile S, the expressions of potential temperature θ and potential density ρ of the i-1th layer and the ith layer are given, and the buoyancy frequency at each depth is calculated: If N 2 Less than the set minimum value N 2 min =1.5×10- 7 , it means that there is an error in the vertical gradient at that location and vertical gradient correction is required; (5) Salinity iterative correction: When the buoyancy frequency does not reach the minimum value, the salinity iterative correction is first performed. The iterative correction method is: the salinity value S of the correction area with a depth of i is i Each increases by a set change value ΔS i , get S i +ΔS i Then determine whether the buoyancy frequency reaches N under the salinity correction value. 2 min =1.5×10- 7 If not, continue to S i Correct until the buoyancy frequency satisfies N 2 min , salinity correction ends; (6) Set the initial value of the temperature in the cost function according to the temperature-salinity constitutive relationship: Since the salinity change and temperature change follow the constitutive relationship, that is: ΔT k +g k ΔS k =0,k=1,2,…,K Before correcting the temperature-salinity value, we must first calculate the temperature-salinity relationship, that is, the TS relationship, which is defined as TS Relationships¶ k Usually a local N profile data set is used This calculation can be done before correction, and then the salinity value corrected in step 5 is compared with γ k Combined, we get ΔT k , and then give an initial temperature value T for correcting the temperature using the minimized cost function k +ΔT k , so that the modified temperature-salinity still satisfies the constitutive relationship; (7) Minimize the cost function: The cost function is set as shown in formula (3): in, k = 1, 2, 3, ... N is the corrected value of seawater temperature at a certain depth, T is the temperature before correction, σ is the standard deviation, D is the temperature difference at adjacent depths k and k-1, δ is the standard deviation of D, In the above steps, we have obtained A and The corrected amount in the cost function The initial value is also set, and the cost function is finally minimized to obtain the corrected temperature value After the correction step is completed, it is determined whether the gradient of the grid point changes slightly. If not, the coefficient A is automatically corrected so that A = A + δ A , where δ A is an adjustment parameter, and the size of the parameter is set according to the characteristics of the sea area; if yes, A is not modified, and then the potential temperature and density are calculated in both cases to determine whether the corrected temperature-salinity buoyancy frequency meets the requirements. Finally, when the buoyancy frequency N 2 >N 2 min , the correction is completed.

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