CN114065539A - Seawater temperature and salt data vertical gradient correction method considering temperature and salt constitutive relation - Google Patents

Seawater temperature and salt data vertical gradient correction method considering temperature and salt constitutive relation Download PDF

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CN114065539A
CN114065539A CN202111394788.5A CN202111394788A CN114065539A CN 114065539 A CN114065539 A CN 114065539A CN 202111394788 A CN202111394788 A CN 202111394788A CN 114065539 A CN114065539 A CN 114065539A
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temperature
correction
salt
salinity
value
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吴昊
宋文昊
李自强
张丹
李孝伟
彭艳
谢少荣
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University of Shanghai for Science and Technology
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Abstract

The invention discloses a seawater temperature and salt data vertical gradient correction method considering temperature and salt constitutive relation, which comprises the steps of firstly identifying vertical gradient errors, and then correcting salinity of an area needing to be corrected until buoyancy frequency meets a minimum limit value; the salinity change and the temperature change follow the constitutive relation, the relation between the salinity change and the temperature change is obtained through linear fitting proportionality coefficients of local N profile data sets, finally, the temperature change quantity is obtained through salinity correction quantity through the proportionality coefficients, the result after the temperature and salt correction is used as an initial value of a cost function, and the temperature and salt value with the minimum cost function is solved through iteration circulation, namely the corrected temperature and salt gridding data is obtained. According to the invention, the vertical gradient correction algorithm of the seawater thermohaline structure is optimized by adding the constitutive relation between thermohalines, so that the authenticity of thermohaline data is improved; in addition, the method of solving the cost function is adaptive to the parameters, so that manual parameter setting is avoided, and the correction efficiency is improved.

Description

Seawater temperature and salt data vertical gradient correction method considering temperature and salt constitutive relation
Technical Field
The invention relates to a seawater thermohaline data vertical gradient correction method considering thermohaline constitutive relation.
Background
The structure of the warm salt of seawater is an important content about the research of physical oceanology. By knowing the time-space distribution of the temperature and salinity of the seawater layer, physical oceanographic phenomena such as fine structure, mesoscale vortex, ocean frontal surface, ocean inner wave formation and the like of the seawater layer can be researched. These phenomena are directly related to global environmental changes, marine transportation, marine military safety, marine fishery distribution and other major problems. The detection of thermohaline structures is usually carried out by arranging a certain number of thermohaline Depth measuring instruments (CTD sensors, The entire name of The Conductivity, Temperature, Depth sensors) on The survey line of The research sea area. The CTD can acquire thermohaline data through measurement for a period of time and perform interpolation in the transverse direction to obtain a thermohaline structure profile of the whole measuring line.
And (3) vertical gradient correction: the vertical gradient correction is that the temperature of the corrected area is reasonably changed along with the water depth by correcting the temperature and salinity value after 3D lattice point formation, and the deeper the depth is, the lower the section temperature is. The vertical gradient correction is to correct the deviation caused by the observation times of the grid depth and the vertical section of the grid. This correction is particularly effective in shallow coastal areas, where large deviations in offshore temperature or salinity gradients exist.
At present, most methods for performing vertical gradient correction on temperature and salt grid data are developed based on a buoyancy frequency calculation formula, and if the buoyancy frequency of a temperature profile along the depth direction is smaller than a set minimum value, it is indicated that an error exists in the vertical gradient at the position, and the vertical gradient correction is required. And then obtaining the corrected temperature and salinity through a minimum cost function. However, the previous research does not consider the temperature-salt constitutive relation of the temperature salt in the process of correcting and the automatic adjustment work of the temperature and temperature gradient weight when minimizing the cost function, for example, when Michael R.Carnes performs Vertical gradient correction in Description and Evaluation of GDEM-V3.0 and You-Soon Chang performs Vertical gradient correction in Vertical gradient correction for the ocean impedance of the East Asian Seas, the method firstly judges the buoyancy frequency and then minimizes the cost function.
Most of the existing methods for performing vertical gradient correction based on thermohaline data solve the problem by a method of minimizing a cost function, but the constitutive relation between thermohaline is ignored in the solving process, and the correction has deviation and low accuracy due to the neglect of the relation. In addition, in the conventional method, when the cost function is solved, the temperature and the temperature gradient weight in the formula cannot be adjusted in a self-adaptive manner, and manual adjustment is needed. The method which needs manual adjustment makes the corrected buoyancy frequency difficult to meet the requirement on the whole area, has narrow application range, can not be widely applied to various sea areas, and has lower correction efficiency and limitation.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a seawater temperature and salt data vertical gradient correction method considering the temperature and salt constitutive relation, which can correct the gridding data of ocean temperature and salt which does not meet the buoyancy frequency requirement, correct the measured value which does not meet the temperature and salinity with the depth change and has correct change in the gridding data, and finally enable the corrected temperature and salt data to meet the buoyancy frequency requirement and be widely applied in various fields of the ocean.
The invention can be realized by the following technical scheme:
a method for correcting vertical gradient of seawater temperature and salt data in consideration of temperature and salt constitutive relation comprises the steps of firstly identifying vertical gradient errors, and then correcting salinity of an area needing to be corrected until buoyancy frequency meets a minimum limit value; the salinity change and the temperature change follow the constitutive relation, the relation between the salinity change and the temperature change is obtained through linear fitting proportionality coefficients of local N section data sets, finally, the temperature variation is obtained through salinity correction quantity through the proportionality coefficients, the result after the temperature and salt correction is used as an initial value of a cost function, the temperature and salt value with the minimum cost function is solved through iteration circulation, namely the corrected temperature and salt gridding data is obtained, in the process of minimizing the cost function, the coefficient A is automatically matched through an adaptive algorithm, and the vertical gradient correction is finished.
Further, the method for correcting the vertical gradient of the seawater temperature and salinity data by considering the temperature and salinity constitutive relation specifically comprises the following steps:
(1) firstly, determining a vertical gradient correction range: the step is to determine which measured section data around the lattice points are used for the range of gradient correction, wherein the screening range comprises three spatial scales, namely a warp scale, a weft scale and a vertical scale F, and a time scale, wherein the vertical scale represents the component of the cross-isopachrome and is a part of the potential vorticity, and the calculation formula is as follows
The following:
Figure BDA0003369879320000021
PV is positive pressure potential vorticity, f is Coriolis parameter, H is seabed depth at lattice point, i is actually measured section serial number, g is lattice point serial number;
(2) setting initial values of coefficients in the cost function: during vertical gradient correction, temperature and salt are continuously adjusted, then the adjusted temperature and salt value is substituted into the calculated temperature, density and buoyancy frequency, if the buoyancy frequency reaches a set value, circulation is stopped, otherwise, the temperature and salt value is continuously adjusted, during the adjustment of the temperature and salt value, firstly, salinity is iteratively corrected, then, the temperature is corrected according to the temperature and salt constitutive relation, the corrected temperature is set as an initial value for solving a minimum cost function, and finally, a temperature value which meets the minimum sum of temperature and temperature gradient variation is obtained through repeated iterative circulation and the minimum cost function;
in the solving process, the temperature and the temperature gradient are required to be in the same order in the cost function, an adjusting coefficient A is set for ensuring the balance between the temperature and the temperature gradient when the cost function is minimized, and an initial value is given to A before the vertical gradient correction, so that the adaptive parameter can be carried out on A when the vertical gradient correction is carried out on the thermohalite, and the balance between the temperature and the temperature gradient is searched again;
(3) calculating the bit temperature and the bit density: when the vertical gradient correction is carried out, whether the correction stopping requirement is met or not needs to be judged according to the variable of the buoyancy frequency, the buoyancy frequency is calculated to relate to two parameters of the bit density and the depth of a selected area, the bit density also needs a bit temperature parameter, the temperature of seawater micro-clusters at a certain depth in seawater when the seawater micro-clusters rise to the sea surface in an adiabatic way is called the bit temperature of the seawater at the depth, the corresponding density at the time is called the bit density,
the calculation formulas of the bit temperature theta and the bit density rho are respectively shown in formulas (1) and (2):
t＝T×1.00024
h＝Pr-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,Pr)＝{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+a2t2+a3t3+(b0+b1t)(S-35)+{c0+c1t+c2t2+c3t3+(d0+d1t)(S-35)}p+(e0+e1t+e2t2)p2
the parameters in the above formula are set as follows:
a0＝3.5803×10-5 a1＝8.5258×10-6 a2＝-6.8360×10-8 a3＝6.6228×10-10
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
e0＝-4.6206×10-13 e1＝1.8676×10-14 e2＝-2.1687×10-16
the temperature theta can be obtained according to the formula (1),
and next, solving a bit density value corresponding to the bit temperature by using the obtained bit temperature value theta, wherein a calculation formula is shown as (2):
Figure BDA0003369879320000031
t＝θ×1.00024
p＝P÷10
ρ(S,t,0)＝ρw+(b0+b1t+b2t2+b3t3+b4t4)S+(c0+c1t+c2t2)S3/2+d0S2
ρw＝a0+a1t+a2t2+a3t3+a4t4+a5t5
K(S,t,p)＝K(S,t,0)+Ap+Bp2
K(S,t,0)＝Kw+(f0+f1t+f2t2+f3t3)S+(g0+g1t+g2t2)S3/2
A＝Aw+(i0+i1t+i2t2)S+j0S3/2
B＝Bw+(m0+m1t+m2t2)S
Kw＝e0+e1t+e2t2+e3t3+e4t4
Aw＝h0+h1t+h2t2+h3t3
Bw＝k0+k1t+k2t2
the parameter coefficients related to the above formula are set as follows:
a0＝999.842594 a1＝6.793952×10-2 a2＝-9.095290×10-3 a3＝1.001685×10-4a4＝-1.120083×10-6 a5＝6.536332×10-9
b0＝8.24493×10-1 b1＝-4.0899×10-4 b2＝7.6438×10-5 b3＝-8.2467×10-7b4＝5.3875×10-9
c0＝-5.72466×10-3 c1＝1.0227×10-4 c2＝-1.6546×10-6
d0＝4.8314×10-4
e0＝19652.21 e1＝148.4206 e2＝-2.327105 e3＝1.360477×10-2 e4＝-5.155288×10-5
f0＝54.6746 f1＝-0.603459 f2＝1.09987×10-2 f3＝-6.1670×10-5
g0＝7.944×10-2 g1＝1.6483×10-2 g2＝-5.3009×10-4
h0＝3.239908 h1＝1.43713×10-3 h2＝1.16092×10-4 h3＝-5.77905×10-7
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 bit density value at the bit temperature theta can be obtained;
(4) calculating buoyancy frequency N2: the buoyancy frequency is calculated to judge whether the grid point data needs to be corrected in a vertical gradient manner, and if the buoyancy frequency N is obtained through calculation2When the cross section is smaller than the set value, vertical gradient correction is needed, the vertical gradient correction cross section range is the three-dimensional cube determined in the first step, then vertical gradient correction work can be carried out,
the buoyancy frequency calculation process is as follows: for an unmodified temperature profile T and salinity profile S, giving expressions of the temperature theta and the density rho of the i-1 th layer and the i-th layer, and solving the buoyancy frequency of each depth:
Figure BDA0003369879320000041
if N is present2Less than a set minimum value (N)2 min＝1.5×10-7) If so, indicating that an error exists in the vertical gradient and needing to be corrected;
(5) and (3) iterative correction of salinity: when the buoyancy frequency does not reach the minimum value, the salinity is iteratively corrected, and the iterative correction method comprises the following steps:
salinity value S for correcting depth of region to be iiAre increased by a set variation deltasiTo obtain Si+ΔSiThen judge thatWhether the buoyancy frequency reaches N under the salinity correction value2 min＝1.5×10-7If not, continue to SiMaking correction until the buoyancy frequency satisfies N2 minThe salinity correction is finished;
(6) setting an initial value of the temperature in the cost function according to the temperature-salt constitutive relation: since salinity and temperature changes follow constitutive relations, namely:
ΔTk+γkΔSk＝0，k＝1，2，…，K
before correcting the temperature-salinity value, the temperature-salinity relationship, i.e. the T-S relationship, is first calculated, which defines
Figure BDA0003369879320000051
T-S relationship gammakUsually, local N profile data sets are used
Figure BDA0003369879320000052
Is calculated before correction and then corrected by step 5, the salinity value and gammakCombine to obtain Delta TkAnd then giving an initial value T for the temperature correction using the minimum cost functionk+ΔTkSo that the corrected time temperature salt still meets the constitutive relation;
(7) minimizing the cost function: the cost function is set as shown in equation (3):
Figure BDA0003369879320000053
wherein the content of the first and second substances,
Figure BDA0003369879320000054
is a seawater temperature correction value at a certain depth, T is the temperature before correction, sigma is the standard deviation, D is the difference between the temperatures at adjacent depths k and k-1, delta is the standard deviation of D,
in the above step, we have obtained A and
Figure BDA0003369879320000055
corrected amount in the cost function
Figure BDA0003369879320000056
Also setting an initial value, finally minimizing a cost function, and obtaining a corrected temperature value
Figure BDA0003369879320000057
After the correction, judging whether the gradient of the lattice point is changed little, if not, automatically correcting the coefficient A to make A equal to A + deltaAWherein δASetting the parameter as an adjusting parameter according to the sea area characteristics; if yes, the A is not modified, then the temperature and the density are continuously calculated under the two conditions, whether the corrected temperature and salt buoyancy frequency meets the requirement or not is judged, and finally the buoyancy frequency N is used2>N2 minAnd finishing the correction.
The invention has the following beneficial effects:
1) during the vertical gradient correction, the salinity is corrected first, and then the temperature is corrected. The salinity is corrected firstly because the vertical change of the salinity is small and basically monotonous, and then the temperature is corrected on the basis, so that the accuracy of the corrected temperature can be improved;
2) when the warm salt is corrected, a method for iteratively correcting the warm salt is adopted, so that the minimum change quantity of the warm salt on the premise that the buoyancy frequency meets the requirement can be ensured, and the accuracy after the warm salt correction is further ensured;
3) by adding the condition of the temperature-salt constitutive relation, the variation between the temperature salts has correlation instead of random value taking of the temperature salts during correction, so that the temperature-salt adjustment work is more accurate, and the correction precision is improved;
4) the work of self-adaptive adjustment of the weight A between the temperature and the temperature gradient is added when the cost function is minimized, so that manual parameter adjustment is not needed, the self-adaptation of global temperature correction is realized, and the efficiency of solving the optimal solution is improved.
Drawings
FIG. 1 is a diagram of the present invention for determining a vertical gradient correction zone based on depth range;
FIG. 2-1 is a graph of the temperature change of the present invention before correction;
FIG. 2-2 is a graph of temperature change after modification in accordance with the present invention;
FIG. 3-1 is a graph of buoyancy frequency prior to correction in accordance with the present invention;
FIG. 3-2 is a graph of buoyancy frequency after modification in accordance with the present invention;
FIG. 4 is a flow chart of a vertical gradient correction method according to the present invention.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification.
The invention relates to a seawater temperature and salt data vertical gradient correction method considering temperature and salt constitutive relation, which comprises the steps of firstly identifying vertical gradient errors, and then correcting salinity of an area needing to be corrected until buoyancy frequency meets a minimum limit value; the salinity change and the temperature change follow the constitutive relation, the relation between the salinity change and the temperature change is obtained through linear fitting proportionality coefficients of local N section data sets, finally, the temperature variation is obtained through salinity correction quantity through the proportionality coefficients, the result after the temperature and salt correction is used as an initial value of a cost function, the temperature and salt value with the minimum cost function is solved through iteration circulation, namely the corrected temperature and salt gridding data is obtained, in the process of minimizing the cost function, the coefficient A is automatically matched through an adaptive algorithm, and the vertical gradient correction is finished. FIG. 4 is a flow chart of the vertical gradient correction method according to the present invention.
The invention relates to a seawater temperature and salt data vertical gradient correction method considering temperature and salt constitutive relation, which comprises the following steps:
(1) firstly, determining a vertical gradient correction range: this step is to determine which measured profile data around the grid points are used for the range of gradient correction. Wherein the screening range comprises three spatial scales (a warp scale, a weft scale and a vertical scale F) and a time scale. Wherein, the vertical dimension represents the component of the cross-equal water depth line, which is a part of potential vorticity, and the calculation formula is as follows:
Figure BDA0003369879320000061
and PV is the positive pressure potential vorticity, f is a Coriolis parameter, H is the depth of the sea bottom at the lattice point, i is the serial number of the actually measured section, and g is the serial number of the lattice point.
In actual calculation, specific calculation needs to be performed for the characteristics of seawater in different sea areas, for example, in the east asian sea area, the latitudinal scale is 1 °, the longitudinal scale is 0.5 °, and the F is 0.5 °. The three-dimensional correction range thus obtained is:
Figure BDA0003369879320000062
Figure BDA0003369879320000071
-0.25(Hi+Hg)≤Hi-Hg≤0.25(Hi+Hg)
Figure BDA0003369879320000072
Figure BDA0003369879320000073
from this formula, the measured profile range determined by the local water depth (local ocean depth) for gradient correction can be calculated. Constructing a three-dimensional cube as a correction interval according to the section range, and obtaining the temperature mean value D of the correction areakAs shown in fig. 1.
Note that the correction range determined here is set for lattice point data in which the buoyancy frequency does not reach the minimum limit, the range is determined, and D is obtainedkThe method is used for preparing for vertical gradient correction of abnormal points.
(2) Setting initial values of coefficients in the cost function: and during vertical gradient correction, continuously adjusting the temperature and the salt, then substituting the adjusted temperature and salt value into the calculation of the temperature, the density and the buoyancy frequency, stopping circulation if the buoyancy frequency reaches a set value, and otherwise, continuously adjusting the temperature and salt value. When the temperature and salt value is adjusted, the method comprises the steps of carrying out iterative correction on the salinity, then correcting the temperature according to the temperature and salt constitutive relation, setting the corrected temperature as an initial value for solving the minimum cost function, and finally solving the temperature value which meets the minimum sum of the temperature and the temperature gradient variation through multiple iterative cycles by using the minimum cost function. And finishing the correction.
In the solving process, the temperature and the temperature gradient are required to be in the same order in the cost function, so that the minimum value of the cost function is meaningful to solve. In order to ensure the balance between the temperature and the temperature gradient when the cost function is minimized, an adjustment coefficient is required to exist, the adjustment coefficient is set to be A, and an initial value is given to A before the vertical gradient correction, so that the adaptive parameter can be performed on A when the vertical gradient correction is performed on the temperature salt, and the balance between the temperature and the temperature gradient is searched again.
(3) Calculating the bit temperature and the bit density: when the vertical gradient correction is carried out, whether the correction stopping requirement is met or not needs to be judged according to the variable of the buoyancy frequency, the buoyancy frequency is calculated to relate to two parameters of bit density and depth of a selected area, and the bit density is calculated to need a bit temperature parameter. The temperature of the seawater micro-cluster at a certain depth in the seawater when the seawater micro-cluster adiabatically rises to the sea surface is called the temperature of the seawater at the depth, and the corresponding density at the time is called the bit density.
The calculation formulas of the bit temperature theta and the bit density rho are respectively shown in formulas (1) and (2):
t＝T×1.00024
h＝Pr-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,Pr)＝{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+a2t2+a3t3+(b0+b1t)(S-35)+{c0+c1t+c2t2+c3t3+(d0+d1t)(S-35)}p+(e0+e1t+e2t2)p2
the parameters in the above formula are set as follows:
a0＝3.5803×10-5 a1＝8.5258×10-6 a2＝-6.8360×10-8 a3＝6.6228×10-10
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
e0＝-4.6206×10-13 e1＝1.8676×10-14 e2＝-2.1687×10-16
although the listed coefficients are large, it is known that the temperature θ can be finally obtained according to equation (1).
And next, solving a bit density value corresponding to the bit temperature by using the obtained bit temperature value theta, wherein a calculation formula is shown as (2):
Figure BDA0003369879320000081
t＝θ×1.00024
p＝P÷10
ρ(S,t,0)＝ρw+(b0+b1t+b2t2+b3t3+b4t4)S+(c0+c1t+c2t2)S3/2+d0S2
ρw＝a0+a1t+a2t2+a3t3+a4t4+a5t5
K(S,t,p)＝K(S,t,0)+Ap+Bp2
K(S,t,0)＝Kw+(f0+f1t+f2t2+f3t3)S+(g0+g1t+g2t2)S3/2
A＝Aw+(i0+i1t+i2t2)S+j0S3/2
B＝Bw+(m0+m1t+m2t2)S
Kw＝e0+e1t+e2t2+e3t3+e4t4
Aw＝h0+h1t+h2t2+h3t3
Bw＝k0+k1t+k2t2
the parameter coefficients related to the above formula are set as follows:
a0＝999.842594 a1＝6.793952×10-2 a2＝-9.095290×10-3 a3＝1.001685×10-4a4＝-1.120083×10-6 a5＝6.536332×10-9
b0＝8.24493×10-1 b1＝-4.0899×10-4 b2＝7.6438×10-5 b3＝-8.2467×10-7b4＝5.3875×10-9
c0＝-5.72466×10-3 c1＝1.0227×10-4 c2＝-1.6546×10-6
d0＝4.8314×10-4
e0＝19652.21 e1＝148.4206 e2＝-2.327105 e3＝1.360477×10-2 e4＝-5.155288×10-5
f0＝54.6746 f1＝-0.603459 f2＝1.09987×10-2 f3＝-6.1670×10-5
g0＝7.944×10-2 g1＝1.6483×10-2 g2＝-5.3009×10-4
h0＝3.239908 h1＝1.43713×10-3 h2＝1.16092×10-4 h3＝-5.77905×10-7
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
in the process of solving the bit density, although the coefficient is large in each formula, it is known that the bit density value at the bit temperature θ can be obtained.
(4) Calculating buoyancy frequency N2: the buoyancy frequency is calculated to judge whether the grid point data needs to be corrected in a vertical gradient manner, and if the buoyancy frequency is calculated, the buoyancy frequency is obtainedFrequency N2And when the cross section is smaller than the set value, vertical gradient correction is required, the vertical gradient correction cross section range is the three-dimensional cube determined in the first step, and then the vertical gradient correction work can be carried out.
The buoyancy frequency calculation process is as follows: for an unmodified temperature profile T and salinity profile S, giving expressions of the temperature theta and the density rho of the i-1 th layer and the i-th layer, and solving the buoyancy frequency of each depth:
Figure BDA0003369879320000091
if N is present2Less than a set minimum value (N)2 min＝1.5×10-7) If so, indicating that an error exists in the vertical gradient and needing to be corrected;
the vertical gradient correction uses the gradient calculation judgment standard of the bit density, namely the buoyancy frequency, because the bit density is obtained by calculating the temperature and the salinity, the gradient of the bit density used for calculating the buoyancy frequency is the balanced average of the temperature and the salinity, and can represent the gradient of the temperature and the salinity without bias. Therefore, the correction of the temperature salinity value to the buoyancy frequency abnormal point is a reasonable operation.
(5) And (3) iterative correction of salinity: when the buoyancy frequency does not reach the minimum value, the salinity is iteratively corrected, and the iterative correction method comprises the following steps: salinity value S for correcting depth of region to be iiAre increased by a set variation deltasiTo obtain Si+ΔSiThen judging whether the buoyancy frequency reaches N under the salinity correction value2 min＝1.5×10-7If not, continue to SiMaking correction until the buoyancy frequency satisfies N2 minAnd the salinity correction is finished.
(6) Setting an initial value of the temperature in the cost function according to the temperature-salt constitutive relation: since salinity and temperature changes follow constitutive relations, namely:
ΔTk+γkΔSk＝0，k＝1，2，…，K
before correcting the temperature and salinity value, firstly, the calculation is carried outTemperature-salinity relationship, i.e. T-S relationship, definition thereof
Figure BDA0003369879320000101
T-S relationship gammakUsually, local N profile data sets are used
Figure BDA0003369879320000102
Is calculated before correction and then corrected by step 5, the salinity value and gammakCombine to obtain Delta TkAnd then giving an initial value T for the temperature correction using the minimum cost functionk+ΔTkSo that the corrected time temperature salt still satisfies the constitutive relation. The method can improve the accuracy of correction and has usability in practical application.
(7) Minimizing the cost function: the cost function is set as shown in equation (3):
Figure BDA0003369879320000103
wherein the content of the first and second substances,
Figure BDA0003369879320000104
the corrected value of the seawater temperature at a certain depth is obtained. T is the pre-correction temperature, σ is the standard deviation, D is the difference between the temperatures at adjacent depths k and k-1, and δ is the standard deviation of D.
In the above step, we have obtained A and
Figure BDA0003369879320000105
corrected amount in the cost function
Figure BDA0003369879320000106
Also setting an initial value, finally minimizing a cost function, and obtaining a corrected temperature value
Figure BDA0003369879320000107
After the step of correction is finished, judging whether the gradient of the grid point changes comparativelyIf not, the coefficient A is automatically corrected to make A equal to A + deltaAWherein δASetting the size of a regulating parameter by self so that the parameter A can be regulated in a self-adaptive manner; if yes, the A is not modified, then the temperature and the density are continuously calculated under the two conditions, and whether the corrected temperature and salt buoyancy frequency meets the requirements or not is judged.
Final buoyancy frequency N2>N2 minAnd finishing the correction.
(8) The vertical gradient correction based on the thermohaline structure is realized: when the effect of the method is verified, the selected area is 125.5E yellow sea area (24N-40N), the time is monthly January data of a certain year, the buoyancy frequency calculated by the temperature and salt value in the data does not reach the standard, so that vertical gradient correction is carried out, and the temperature change before and after correction is shown in figure 2.
As shown in fig. 2-1, in the range of latitude 28N to 34N, the temperature value increases with the depth, which indicates that the region has abnormal vertical gradient, so the result shown in fig. 2-2 is obtained according to the summarized vertical gradient correction method.
After the vertical gradient correction is carried out, the buoyancy frequency is not less than zero, and the buoyancy frequency is compared before and after the correction as shown in figures 3-1 and 3-2, so that the correction effect meets the requirement.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (2)

1. A seawater temperature and salt data vertical gradient correction method considering temperature and salt constitutive relation is characterized in that vertical gradient error identification is firstly carried out, and then salinity correction is firstly carried out on an area needing to be corrected until buoyancy frequency meets a minimum limit value; the salinity change and the temperature change follow the constitutive relation, the relation between the salinity change and the temperature change is obtained through linear fitting proportionality coefficients of local N section data sets, finally, the temperature variation is obtained through salinity correction quantity through the proportionality coefficients, the result after the temperature and salt correction is used as an initial value of a cost function, the temperature and salt value with the minimum cost function is solved through iteration circulation, namely the corrected temperature and salt gridding data is obtained, in the process of minimizing the cost function, the coefficient A is automatically matched through an adaptive algorithm, and the vertical gradient correction is finished.
2. The method for correcting the vertical gradient of the seawater temperature and salinity data by considering the temperature-salinity constitutive relation, according to claim 1, is characterized by comprising the following steps:
(1) firstly, determining a vertical gradient correction range: the step is to determine which measured section data around the lattice points are used in a range of gradient correction, wherein the screening range comprises three spatial scales, namely a warp scale, a weft scale and a vertical scale F, and a time scale, wherein the vertical scale represents a component of the cross-isophotic line and is a part of potential vorticity, and a calculation formula is as follows:
Figure FDA0003369879310000011
PV is positive pressure potential vorticity, f is Coriolis parameter, H is seabed depth at lattice point, i is actually measured section serial number, g is lattice point serial number;
(2) setting initial values of coefficients in the cost function: during vertical gradient correction, temperature and salt are continuously adjusted, then the adjusted temperature and salt value is substituted into the calculated temperature, density and buoyancy frequency, if the buoyancy frequency reaches a set value, circulation is stopped, otherwise, the temperature and salt value is continuously adjusted, during the adjustment of the temperature and salt value, firstly, salinity is iteratively corrected, then, the temperature is corrected according to the temperature and salt constitutive relation, the corrected temperature is set as an initial value for solving a minimum cost function, and finally, a temperature value which meets the minimum sum of temperature and temperature gradient variation is obtained through repeated iterative circulation and the minimum cost function;
in the solving process, the temperature and the temperature gradient are required to be in the same order in the cost function, an adjusting coefficient A is set for ensuring the balance between the temperature and the temperature gradient when the cost function is minimized, and an initial value is given to A before the vertical gradient correction, so that the adaptive parameter can be carried out on A when the vertical gradient correction is carried out on the thermohalite, and the balance between the temperature and the temperature gradient is searched again;
(3) calculating the bit temperature and the bit density: when the vertical gradient correction is carried out, whether the correction stopping requirement is met or not needs to be judged according to the variable of the buoyancy frequency, the buoyancy frequency is calculated to relate to two parameters of the bit density and the depth of a selected area, the bit density also needs a bit temperature parameter, the temperature of seawater micro-clusters at a certain depth in seawater when the seawater micro-clusters rise to the sea surface in an adiabatic way is called the bit temperature of the seawater at the depth, the corresponding density at the time is called the bit density,
the calculation formulas of the bit temperature theta and the bit density rho are respectively shown in formulas (1) and (2):
t＝T×1.00024
h＝Pr-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,Pr)＝{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+a2t2+a3t3+(b0+b1t)(S-35)+{c0+c1t+c2t2+c3t3+(d0+d1t)(S-35)}p+(e0+e1t+e2t2)p2
the parameters in the above formula are set as follows:
a0＝3.5803×10-5 a1＝8.5258×10-6 a2＝-6.8360×10-8 a3＝6.6228×10-10
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
e0＝-4.6206×10-13 e1＝1.8676×10-14 e2＝-2.1687×10-16
the temperature theta can be obtained according to the formula (1),
and next, solving a bit density value corresponding to the bit temperature by using the obtained bit temperature value theta, wherein a calculation formula is shown as (2):
Figure FDA0003369879310000021
t＝θ×1.00024
p＝P÷10
ρ(S,t,0)＝ρw+(b0+b1t+b2t2+b3t3+b4t4)S+(c0+c1t+c2t2)S3/2+d0S2
ρw＝a0+a1t+a2t2+a3t3+a4t4+a5t5
K(S,t,p)＝K(S,t,0)+Ap+Bp2
K(S,t,0)＝Kw+(f0+f1t+f2t2+f3t3)S+(g0+g1t+g2t2)S3/2
A＝Aw+(i0+i1t+i2t2)S+j0S3/2
B＝Bw+(m0+m1t+m2t2)S
Kw＝e0+e1t+e2t2+e3t3+e4t4
Aw＝h0+h1t+h2t2+h3t3
Bw＝k0+k1t+k2t2
the parameter coefficients related to the above formula are set as follows:
a0＝999.842594 a1＝6.793952×10-2 a2＝-9.095290×10-3 a3＝1.001685×10-4
a4＝-1.120083×10-6 a5＝6.536332×10-9
b0＝8.24493×10-1 b1＝-4.0899×10-4 b2＝7.6438×10-5 b3＝-8.2467×10-7 b4＝5.3875×10-9
c0＝-5.72466×10-3 c1＝1.0227×10-4 c2＝-1.6546×10-6
d0＝4.8314×10-4
e0＝19652.21 e1＝148.4206 e2＝-2.327105 e3＝1.360477×10-2 e4＝-5.155288×10-5
f0＝54.6746 f1＝-0.603459 f2＝1.09987×10-2 f3＝-6.1670×10-5
g0＝7.944×10-2 g1＝1.6483×10-2 g2＝-5.3009×10-4
h0＝3.239908 h1＝1.43713×10-3 h2＝1.16092×10-4 h3＝-5.77905×10-7
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 bit density value at the bit temperature theta can be obtained;
(4) calculating buoyancy frequency N2: the buoyancy frequency is calculated to judge whether the grid point data needs to be corrected in a vertical gradient manner, and if the buoyancy frequency N is obtained through calculation2When the cross section is smaller than the set value, vertical gradient correction is needed, the vertical gradient correction cross section range is the three-dimensional cube determined in the first step, then vertical gradient correction work can be carried out,
the buoyancy frequency calculation process is as follows: for an unmodified temperature profile T and salinity profile S, giving expressions of the temperature theta and the density rho of the i-1 th layer and the i-th layer, and solving the buoyancy frequency of each depth:
Figure FDA0003369879310000041
if N is present2Less than a set minimum value (N)2 min＝1.5×10-7) If so, indicating that an error exists in the vertical gradient and needing to be corrected;
(5) and (3) iterative correction of salinity: when the buoyancy frequency does not reach the minimum value, the salinity is iteratively corrected, and the iterative correction method comprises the following steps: salinity value S for correcting depth of region to be iiAre increased by a set variation deltasiTo obtain Si+ΔSiThen judging whether the buoyancy frequency reaches N under the salinity correction value2 min＝1.5×10-7If not, continue to SiMaking correction until the buoyancy frequency satisfies N2 minThe salinity correction is finished;
(6) setting an initial value of the temperature in the cost function according to the temperature-salt constitutive relation: since salinity and temperature changes follow constitutive relations, namely:
ΔTk+γkΔSk＝0，k＝1，2，…，K
before correcting the temperature-salinity value, the temperature-salinity relationship, i.e. the T-S relationship, is first calculated, which defines
Figure FDA0003369879310000042
T-S relationship gammakUsually, local N profile data sets are used
Figure FDA0003369879310000043
Is calculated before correction and then corrected by step 5, the salinity value and gammakCombine to obtain Delta TkAnd then giving an initial value T for the temperature correction using the minimum cost functionk+ΔTkSo that the corrected time temperature salt still meets the constitutive relation;
(7) minimizing the cost function: the cost function is set as shown in equation (3):
Figure FDA0003369879310000044
wherein the content of the first and second substances,
Figure FDA0003369879310000045
is a seawater temperature correction value at a certain depth, T is the temperature before correction, sigma is the standard deviation, D is the difference between the temperatures at adjacent depths k and k-1, delta is the standard deviation of D,
in the above step, we have obtained A and
Figure FDA0003369879310000046
corrected amount in the cost function
Figure FDA0003369879310000047
Also setting an initial value, finally minimizing a cost function, and obtaining a corrected temperature value
Figure FDA0003369879310000048
After the correction, judging whether the gradient of the lattice point is changed little, if not, automatically correcting the coefficient A to make A equal to A + deltaAWherein δASetting the parameter as an adjusting parameter according to the sea area characteristics; if yes, the A is not modified, then the temperature and the density are continuously calculated under the two conditions, whether the corrected temperature and salt buoyancy frequency meets the requirement or not is judged, and finally the buoyancy frequency N is used2>N2 minAnd finishing the correction.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114910150A (en) * 2022-04-20 2022-08-16 慕思健康睡眠股份有限公司 Calibration method and device of capacitive weight sensor, intelligent pad and storage medium
CN114910150B (en) * 2022-04-20 2023-08-01 慕思健康睡眠股份有限公司 Calibration method and device of capacitive weight sensor, intelligent pad and storage medium

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