CN105910587B - A kind of tide prediction method based on tidal parameter inverting - Google Patents

A kind of tide prediction method based on tidal parameter inverting Download PDF

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CN105910587B
CN105910587B CN201610222434.5A CN201610222434A CN105910587B CN 105910587 B CN105910587 B CN 105910587B CN 201610222434 A CN201610222434 A CN 201610222434A CN 105910587 B CN105910587 B CN 105910587B
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CN105910587A (en
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张瑰
刘凤
杜华栋
张梅
刘希强
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PLA University of Science and Technology
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Abstract

The present invention relates to a kind of tide prediction method based on tidal parameter inverting, determine phenomenon for uncomfortable caused by variational Assimilation method, utilize the Tikhonov regularization methods in Inverse Problems in Mathematical Physics, regularization parameter is introduced in cost functional, appropriate stability functional is constructed, common variational Assimilation method is improved；The variational Assimilation method for combining regularization thought is applied in tidal model, optimizes tide prediction mode parameter, achievees the purpose that to improve tidal model forecast precision；Wherein, for two kinds of unknown parameters in tidal model --- bottom-friction factor and the depth of water implement joint inversion, Synchronous fluorimetry, since obtained inverted parameters are obtained by solving the minimum problem of cost functional, therefore the optimal solution of the problem can be obtained, that is, effectively increases the precision of tidal model forecast.

Description

A kind of tide prediction method based on tidal parameter inverting
Technical field
The present invention relates to a kind of tide prediction method based on tidal parameter inverting, belongs to ocean remote sensing inversion technique neck Domain.
Background technology
The Tides And Tidal Currents in continental shelf marine site can be simulated and forecast using two-dimentional tidal model, and it is pre- to improve paralic tide numerical value The precision of report, key are given appropriate mode parameter.
Tide numerical model result of calculation compared with tidal observation data, manual calibration is carried out to pattern by past, people. With the increase of the unconventional data such as satellite altimetry data and continuously improving for data processing methods, now, people can utilize More advanced data assimilation method come be automatically performed tide numerical model with observe data fitting, for some in correction mode Harmonic component, the depth of water and bottom-friction factor in uncertain parameter, such as open boundaryconditions.Using data assimilation method, compared with It is efficient, objective that traditional manual synchronizing method has the advantages that.
Research to data assimilation problem, the especially research to adjoint method, foreign countries' starting is more early, and development is very fast.To adjoint The theory and application study that method carries out are Chavent etc. (1975) earlier, are discussed in text this method being applied to permeable Jie The parameter Estimation of fluid model in matter.After Marchuk (1974) is introduced into meteorology field, since it is considered as gram Taken optimum interpolation method there are the problem of, nonlinear problem can be perfectly suitable for, be particularly suitable for Real-time Forecasting System, Thus enjoy meteorological boundary to pay close attention to, widely studied and applied.A large amount of with Value of Remote Sensing Data obtain and its measure The raising of precision, people it is interested be that actual measurement satellite altimetry data individually or is combined normal water level Data Assimilation to numerical value In model.Lv Xianqing and Zhang Jie (1999) carries out the preferable adjoint of the linear tidal model open boundaryconditions optimization of mean depth Experiment；Han Guijun etc. (2000) opens perimeter strip using the non-linear tidal model of " twin " the experiment discussion optimization of Adjoint data assimilation Part, while they have carried out the variation Adjoint assimilation of tidal station water-level observation data and TOPEX/POSEIDON Altimetry Datas Experiment, optimizes the open boundaryconditions of non-linear tidal model；Wu Ziku etc. (2003a, 2003b) utilizes orthogonal damp response method pair Satellite altimeter data carries out assimilating along rail partial tide harmonic constant to two-dimension non linearity tide numerical model for tidal wave analysis extraction In, open boundaryconditions and bottom-friction factor in Optimized model, simulate the South Sea and Tide In Beibu Bay.Gu Yi etc. (2005) profits With adjoint method, according to tidal station water level prediction, the bottom-friction factor of optimization two-dimension non linearity tidal model.Wu Ziku etc. (2007) in Northeastern South China Sea tidal model, deep-sea altimeter data has been assimilated, has optimized bottom-friction factor and Kai Bian Boundary's condition.
As it was previously stated, data assimilation has extensive research and application in tide prediction, and have been achieved for Very ten-strike, but still there are some theory and technology problems not solve well, one of key issue is exactly to solve not Well-posedness.So-called ill-posedness, i.e. variational problem solution are not necessarily present, even if in the presence of also not necessarily unique, in solution existence anduniquess When also not necessarily stablize, can so cause cost functional decrease speed slow, low precision.
The content of the invention
The technical problems to be solved by the invention are to provide one kind and are directed to tide using variational Assimilation combination regularization method Forecast Mode Parametric optimization problem is studied, modification model error, effectively improve tide prediction precision based on tidal parameter The tide prediction method of inverting.
In order to solve the above-mentioned technical problem the present invention uses following technical scheme：The present invention devises a kind of based on tide ginseng The tide prediction method of number inverting, includes the following steps：
Step 001. is directed to waters to be predicted, establishes two-dimensional coordinate, determines abscissa X-axis, and ordinate Y-axis, and In waters to be predicted, inverting target location is treated in selection, and is obtained and specified in historical time cycle T, treats the water of inverting target location Face relative to the position still water fluctuation altitude information set ζobs(x, y, t), and obtain and specify in historical time cycle T, Treat trend X-axis component set u of the trend in abscissa X-direction on inverting target locationobs(x, y, t), in ordinate Y-axis Trend Y-axis component set v on directionobs(x, y, t), wherein, t ∈ T, subsequently into step 002；
Step 002. is for the water surface relative to the fluctuation altitude information set ζ of the position still water, trend in abscissa X The trend Y-axis component set v of trend X-axis component set u, trend in ordinate Y direction on direction of principal axis, and treat inverting The water-bed friction coefficient Γ of target locationR, depth of water h, after being disturbedAnd define respectively ζ, u, v、ΓR, h derivativeSubsequently into step 003；
Step 003. is by after disturbanceSubstitute among two-dimentional tidal model, obtain water to be predicted The tangent linear mode of domain tide, enters back into step 004；
Step 004. is directed to ζ, u, v, ΓR, that h defines cost functional formula is as follows：
Meanwhile it is as follows according to the concept definition directional derivative of Gateaux differential, subsequently into step 005；Wherein, γ, η To preset regularization parameter, Ω represents waters to be predicted；
Step 005. obtains J'[Γ according to functional formula and directional derivativeR, h] and it is as follows：
Meanwhile according to Gateaux differential, obtain：
Subsequently into step 006；
Step 006. is directed to ζ, u, v, introduces adjoint variable U, V, W respectively, is multiplied by waters tide to be predicted respectively with U, V, W Tangent linear mode in three formula, and integrated on waters Ω to be predicted, and according to U, V, W in boundary face, with And the value of three formula is 0 in tide tangent linear mode in waters to be predicted, obtains such as drag：
Subsequently into step 007；Wherein, f represents Coriolis parameters, and A represents lateral eddy viscosity coefficient；
Step 007. obtains adjoint equation according to formula (4), (5), (6)：
And it is with initial BVP condition：
Subsequently into step 008；
Step 008. obtains the tidal water bottom-friction factor Γ in waters to be predicted according to formula (7), (8)RGradient table reaches Formula, depth of water h pressure gradient expression formulas are as follows, subsequently into step 009；
Step 009. is directed to the tidal water bottom-friction factor Γ in waters to be predictedRPressure gradient expression formula, depth of water h gradient tables reach Formula, is solved using Newton iteration method, obtains tidal water bottom-friction factor Γ respectivelyRTrend valueThe trend of depth of water h Value h*, and then willAs the optimal tidal water bottom-friction factor in waters to be predicted, h*As the optimal depth of water in waters to be predicted, Subsequently into step 010；
Step 010 is according to the optimal tidal water bottom-friction factor in waters to be predictedOptimal depth of water h*With two-dimentional tide mould Type, prediction is realized for the tide in waters to be predicted.
As a preferred technical solution of the present invention：It is described quiet relative to the position for the water surface in the step 002 Trend X-axis component set us of the fluctuation altitude information set ζ, trend in sealing face in abscissa X-direction, trend are sat vertical The trend Y-axis component set v in Y direction is marked, and treats the water-bed friction coefficient Γ of inverting target locationR, depth of water h, establish Shown in disturbance relation equation below (1)：
Thus, after being disturbed
As a preferred technical solution of the present invention：In the step 002, for ζ, u, v, ΓR, h, utilize following public affairs Shown in formula (2)：
ζ, u, v, Γ are defined respectivelyR, h derivativeWherein α is parameter preset.
As a preferred technical solution of the present invention：In the step 003, after disturbance Substitute among two-dimentional tidal model, shown in the tangent linear mode equation below (3) for obtaining waters tide to be predicted：
Wherein, f represents Coriolis parameters, and A represents lateral eddy viscosity coefficient.
As a preferred technical solution of the present invention：In the step 009, specifically comprise the following steps：
Step 00901. is according to the tidal water bottom-friction factor Γ in the waters to be predictedRPressure gradient expression formula, depth of water h gradients Expression formula, it is (Γ to define iteration initial guessR 0, h0), following steepest is designed using Newton iteration method and declines Iteration, Subsequently into step 00902；
Wherein, ρi、λiRepresent it is Γ respectivelyRWith the iteration step length of h；
Step 00902. defines J [ΓR 0,h0] it is cost functional, and define ρ0、λ0The respectively initial value of step-length, and start Iteration is performed, wherein each secondary iteration causes J [ΓR i+1,hi+1] ＜ J [ΓR i,hi], subsequently into step 00903；
Step 00903. is when meeting stopping criterion for iteration J≤ε, according to ΓR i+1→ΓR *,hi+1→h*, tide is obtained respectively Nighttide bottom friction coefficient ΓRTrend valueThe trend value h of depth of water h*, and then willOptimal tide as waters to be predicted Water-bed friction coefficient, h*As the optimal depth of water in waters to be predicted, subsequently into step 010, wherein ε represents default iteration ends Parameter.
A kind of tide prediction method based on tidal parameter inverting of the present invention is using above technical scheme and existing skill Art is compared, and has following technique effect：The designed tide prediction method based on tidal parameter inverting of the invention, it is same for variation It is uncomfortable caused by change method to determine phenomenon, using the Tikhonov regularization methods in Inverse Problems in Mathematical Physics, in cost functional Middle introduction regularization parameter, constructs appropriate stability functional, and common variational Assimilation method is improved；Canonical will be combined The variational Assimilation method for changing thought is applied in tidal model, optimizes tide prediction mode parameter, and it is pre- to reach raising tidal model Report the purpose of precision；Wherein, for two kinds of unknown parameters in tidal model --- bottom-friction factor and the depth of water implement joint instead Drill, Synchronous fluorimetry, since obtained inverted parameters are obtained by solving the minimum problem of cost functional, can obtain The optimal solution of the problem is obtained, that is, effectively increases the precision of tidal model forecast.
Brief description of the drawings
Fig. 1 is the flow diagram for the tide prediction method based on tidal parameter inverting that the present invention designs.
Embodiment
The embodiment of the present invention is described in further detail with reference to Figure of description.
As shown in Figure 1, designed by the present invention it is a kind of based on the tide prediction method of tidal parameter inverting in practical application mistake Cheng Dangzhong, specifically comprises the following steps：
Step 001. is directed to waters to be predicted, establishes two-dimensional coordinate, determines abscissa X-axis, and ordinate Y-axis, wherein, X-axis takes direction just eastwards, and Y-axis takes direction just northwards；And in waters to be predicted, inverting target location is treated in selection, and Obtain and specify in historical time cycle T, treat that the water surface of inverting target location (x, y) is high relative to the fluctuation of the position still water Degrees of data set ζobs(x, y, t), and obtain and specify in historical time cycle T, treat that trend is in horizontal stroke on inverting target location (x, y) Trend X-axis component set u in coordinate X-directionobs(x, y, t), the trend Y-axis component set in ordinate Y direction vobs(x, y, t), wherein, t ∈ T, subsequently into step 002.
Described in step 002. for the water surface relative to the fluctuation altitude information set ζ of the position still water, trend in horizontal stroke The trend Y-axis component set v of trend X-axis component set u, trend in ordinate Y direction in coordinate X-direction, and Treat the water-bed friction coefficient Γ of inverting target locationR, depth of water h, establish shown in disturbance relation equation below (1)：
Thus, after being disturbedAnd it is directed to ζ, u, v, ΓR, h, utilize equation below (2) shown in：
ζ, u, v, Γ are defined respectivelyR, h derivativeWherein α is parameter preset, subsequently into step Rapid 003.
Step 003. two dimension tidal model is as follows：
Wherein, f represents Coriolis parameters, and f=2 β sin φ, β represent rotational-angular velocity of the earth, and φ represents geographic logitude, A represents lateral eddy viscosity coefficient；Expression treats that inverting target location (x, y) considers the tide generating potential after earth tide effect； Then by after disturbanceSubstitute among two-dimentional tidal model, obtain the tangent line of waters tide to be predicted Shown in sexual norm equation below (3)：Step 004 is entered back into afterwards.
Boundary condition is given according to usual way, it is 0 that normal direction flow velocity is made on border is closed, i.e., does not enter on border is closed Flow and go out stream；Water level value is on border is opened
Wherein, ωm(m=1,2 ..., M) be partial tide angular frequency, a0, am, bm(m=1,2 ..., M) it is Fourier systems Number.
Consider the linear bottom-friction factors of Rayleigh (ray) it is assumed that i.e.
P=ΓRU, Q=ΓRv,
Wherein ΓRFor bottom-friction factor.
Step 004. is directed to ζ, u, v, ΓR, that h defines cost functional formula is as follows：
Meanwhile it is as follows according to the concept definition directional derivative of Gateaux differential, subsequently into step 005；Wherein, γ, η To preset regularization parameter, Ω represents waters to be predicted；
Step 005. obtains J'[Γ according to functional formula and directional derivativeR, h] and it is as follows：
Meanwhile according to Gateaux differential, obtain：
Subsequently into step 006.
Step 006. is directed to ζ, u, v, introduces adjoint variable U, V, W respectively, is multiplied by waters tide to be predicted respectively with U, V, W Tangent linear mode in three formula, and integrated on waters Ω to be predicted, and according to U, V, W in boundary face, with And the value of three formula is 0 in tide tangent linear mode in waters to be predicted, obtains such as drag：
Subsequently into step 007；Wherein, f represents Coriolis parameters, and A represents lateral eddy viscosity coefficient.
Step 007. obtains adjoint equation according to formula (4), (5), (6)：
And it is with initial BVP condition：
Subsequently into step 008.
Step 008. obtains the tidal water bottom-friction factor Γ in waters to be predicted according to formula (7), (8)RGradient table reaches Formula, depth of water h pressure gradient expression formulas are as follows, subsequently into step 009.
Step 009. is directed to the tidal water bottom-friction factor Γ in waters to be predictedRPressure gradient expression formula, depth of water h gradient tables reach Formula, is solved using Newton iteration method, obtains tidal water bottom-friction factor Γ respectivelyRTrend valueThe trend of depth of water h Value h*, and then willAs the optimal tidal water bottom-friction factor in waters to be predicted, h*As the optimal depth of water in waters to be predicted, Subsequently into step 010.
Wherein, in the step 009, specifically comprise the following steps：
Step 00901. is according to the tidal water bottom-friction factor Γ in the waters to be predictedRPressure gradient expression formula, depth of water h gradients Expression formula, it is (Γ to define iteration initial guessR 0,h0), following steepest is designed using Newton iteration method and declines Iteration, Subsequently into step 00902.
Wherein, ρi、λiRepresent it is Γ respectivelyRWith the iteration step length of h；
Step 00902. defines J [ΓR 0,h0] it is cost functional, and define ρ0、λ0The respectively initial value of step-length, and start Iteration is performed, wherein each secondary iteration causes J [ΓR i+1,hi+1] ＜ J [ΓR i,hi], subsequently into step 00903.
Step 00903. is when meeting stopping criterion for iteration J≤ε, according to ΓR i+1→ΓR *,hi+1→h*, tide is obtained respectively Nighttide bottom friction coefficient ΓRTrend valueThe trend value h of depth of water h*, and then willOptimal tide as waters to be predicted Water-bed friction coefficient, h*As the optimal depth of water in waters to be predicted, subsequently into step 010, wherein ε represents default iteration ends Parameter.
Step 010 is according to the optimal tidal water bottom-friction factor in waters to be predictedOptimal depth of water h*With two-dimentional tide mould Type, prediction is realized for the tide in waters to be predicted.
The tide prediction method based on tidal parameter inverting of the invention designed, for caused by variational Assimilation method not It is suitable to determine phenomenon, using the Tikhonov regularization methods in Inverse Problems in Mathematical Physics, regularization parameter is introduced in cost functional, Appropriate stability functional is constructed, common variational Assimilation method is improved；The variational Assimilation of regularization thought will be combined Method is applied in tidal model, optimizes tide prediction mode parameter, achievees the purpose that to improve tidal model forecast precision；Its In, for two kinds of unknown parameters in tidal model --- bottom-friction factor and the depth of water implement joint inversion, Synchronous fluorimetry, due to Obtained inverted parameters are obtained by solving the minimum problem of cost functional, therefore can obtain the optimal of the problem Solution, that is, effectively increase the precision of tidal model forecast.
Embodiments of the present invention are explained in detail above in conjunction with attached drawing, but the present invention is not limited to above-mentioned implementation Mode, within the knowledge of a person skilled in the art, can also be on the premise of present inventive concept not be departed from Make a variety of changes.

Claims (5)

  1. A kind of 1. tide prediction method based on tidal parameter inverting, it is characterised in that include the following steps：
    Step 001. is directed to waters to be predicted, establishes two-dimensional coordinate, determines abscissa X-axis, and ordinate Y-axis, and treat it is pre- Survey in waters, inverting target location is treated in selection, and is obtained and specified in historical time cycle T, treats the water surface phase of inverting target location Fluctuation altitude information set ζ for the position still waterobs(x, y, t), and obtain and specify in historical time cycle T, treat anti- Drill trend X-axis component set u of the trend in abscissa X-direction on target locationobs(x, y, t), in ordinate Y direction On trend Y-axis component set vobs(x, y, t), wherein, t ∈ T, subsequently into step 002；
    Step 002. is for the water surface relative to the fluctuation altitude information set ζ of the position still water, trend in abscissa X-axis side Trend Y-axis component set vs of the upward trend X-axis component set u, trend in ordinate Y direction, and treat inverting target The water-bed friction coefficient Γ of positionR, depth of water h, after being disturbedAnd define respectively ζ, u, v, ΓR, h derivativeSubsequently into step 003；
    Step 003. is by after disturbanceSubstitute among two-dimentional tidal model, obtain waters tide to be predicted The tangent linear mode of nighttide, enters back into step 004；
    Step 004. is directed to ζ, u, v, ΓR, that h defines cost functional formula is as follows：
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    Meanwhile it is as follows according to the concept definition directional derivative of Gateaux differential, subsequently into step 005；Wherein, γ, η are pre- If regularization parameter, Ω represents waters to be predicted, and α represents parameter preset；
    <mrow> <msup> <mi>J</mi> <mo>&amp;prime;</mo> </msup> <mo>&amp;lsqb;</mo> <msub> <mi>&amp;Gamma;</mi> <mi>R</mi> </msub> <mo>,</mo> <mi>h</mi> <mo>&amp;rsqb;</mo> <mo>=</mo> <munder> <mi>lim</mi> <mrow> <mi>&amp;alpha;</mi> <mo>&amp;RightArrow;</mo> <mn>0</mn> </mrow> </munder> <mfrac> <mrow> <mi>J</mi> <mo>&amp;lsqb;</mo> <msub> <mover> <mi>&amp;Gamma;</mi> <mo>~</mo> </mover> <mi>R</mi> </msub> <mo>,</mo> <mover> <mi>h</mi> <mo>~</mo> </mover> <mo>&amp;rsqb;</mo> <mo>-</mo> <msup> <mi>J</mi> <mo>&amp;prime;</mo> </msup> <mo>&amp;lsqb;</mo> <msub> <mi>&amp;Gamma;</mi> <mi>R</mi> </msub> <mo>,</mo> <mi>h</mi> <mo>&amp;rsqb;</mo> </mrow> <mi>&amp;alpha;</mi> </mfrac> </mrow>
    Step 005. obtains J'[Γ according to functional formula and directional derivativeR, h] and it is as follows：
    <mrow> <mtable> <mtr> <mtd> <mrow> <msup> <mi>J</mi> <mo>&amp;prime;</mo> </msup> <mo>&amp;lsqb;</mo> <msub> <mi>&amp;Gamma;</mi> <mi>R</mi> </msub> <mo>,</mo> <mi>h</mi> <mo>&amp;rsqb;</mo> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>T</mi> </msubsup> <munder> <mrow> <mo>&amp;Integral;</mo> <mo>&amp;Integral;</mo> </mrow> <mi>&amp;Omega;</mi> </munder> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <mi>&amp;zeta;</mi> <mo>-</mo> <msup> <mi>&amp;zeta;</mi> <mrow> <mi>o</mi> <mi>b</mi> <mi>s</mi> </mrow> </msup> <mo>)</mo> </mrow> <mover> <mi>&amp;zeta;</mi> <mo>^</mo> </mover> <mo>+</mo> <mrow> <mo>(</mo> <mi>u</mi> <mo>-</mo> <msup> <mi>u</mi> <mrow> <mi>o</mi> <mi>b</mi> <mi>s</mi> </mrow> </msup> <mo>)</mo> </mrow> <mover> <mi>u</mi> <mo>^</mo> </mover> <mo>+</mo> <mrow> <mo>(</mo> <mi>v</mi> <mo>-</mo> <msup> <mi>v</mi> <mrow> <mi>o</mi> <mi>b</mi> <mi>s</mi> </mrow> </msup> <mo>)</mo> </mrow> <mover> <mi>v</mi> <mo>^</mo> </mover> <mo>&amp;rsqb;</mo> <mi>d</mi> <mi>x</mi> <mi>d</mi> <mi>y</mi> <mi>d</mi> <mi>t</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mi>&amp;gamma;</mi> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>T</mi> </msubsup> <munder> <mrow> <mo>&amp;Integral;</mo> <mo>&amp;Integral;</mo> </mrow> <mi>&amp;Omega;</mi> </munder> <mfrac> <mo>&amp;part;</mo> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mo>(</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>&amp;zeta;</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mo>)</mo> <mover> <mi>&amp;zeta;</mi> <mo>^</mo> </mover> <mi>d</mi> <mi>x</mi> <mi>d</mi> <mi>y</mi> <mi>d</mi> <mi>t</mi> <mo>-</mo> <mi>&amp;eta;</mi> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>T</mi> </msubsup> <munder> <mrow> <mo>&amp;Integral;</mo> <mo>&amp;Integral;</mo> </mrow> <mi>&amp;Omega;</mi> </munder> <mfrac> <mo>&amp;part;</mo> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>&amp;zeta;</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mover> <mi>&amp;zeta;</mi> <mo>^</mo> </mover> <mi>d</mi> <mi>x</mi> <mi>d</mi> <mi>y</mi> <mi>d</mi> <mi>t</mi> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    Meanwhile according to Gateaux differential, obtain：
    <mrow> <msup> <mi>J</mi> <mo>&amp;prime;</mo> </msup> <mo>&amp;lsqb;</mo> <msub> <mi>&amp;Gamma;</mi> <mi>R</mi> </msub> <mo>,</mo> <mi>h</mi> <mo>&amp;rsqb;</mo> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>T</mi> </msubsup> <munder> <mrow> <mo>&amp;Integral;</mo> <mo>&amp;Integral;</mo> </mrow> <mi>&amp;Omega;</mi> </munder> <mrow> <mo>(</mo> <msub> <mo>&amp;dtri;</mo> <msub> <mi>&amp;Gamma;</mi> <mi>R</mi> </msub> </msub> <mi>J</mi> <mo>&amp;CenterDot;</mo> <msub> <mover> <mi>&amp;Gamma;</mi> <mo>^</mo> </mover> <mi>R</mi> </msub> <mo>+</mo> <msub> <mo>&amp;dtri;</mo> <mi>h</mi> </msub> <mi>J</mi> <mo>&amp;CenterDot;</mo> <mover> <mi>h</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mi>d</mi> <mi>x</mi> <mi>d</mi> <mi>y</mi> <mi>d</mi> <mi>t</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    Subsequently into step 006；
    Step 006. is directed to ζ, u, v, introduces adjoint variable U, V, W respectively, is multiplied by cutting for waters tide to be predicted respectively with U, V, W Three formula in linear model, and integrated on waters Ω to be predicted, and according to U, V, W in boundary face, and treat The value for predicting three formula in the tide tangent linear mode of waters is 0, obtains such as drag：
    <mrow> <mtable> <mtr> <mtd> <mrow> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>T</mi> </msubsup> <munder> <mrow> <mo>&amp;Integral;</mo> <mo>&amp;Integral;</mo> </mrow> <mi>&amp;Omega;</mi> </munder> <mrow> <mo>(</mo> <mrow> <mo>-</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>U</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>t</mi> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>U</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mi>u</mi> <mo>-</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>U</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mi>v</mi> <mo>-</mo> <mi>g</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>V</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mo>-</mo> <mi>g</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>W</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mover> <mi>&amp;zeta;</mi> <mo>^</mo> </mover> <mi>d</mi> <mi>x</mi> <mi>d</mi> <mi>y</mi> <mi>d</mi> <mi>t</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>T</mi> </msubsup> <munder> <mrow> <mo>&amp;Integral;</mo> <mo>&amp;Integral;</mo> </mrow> <mi>&amp;Omega;</mi> </munder> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>&amp;zeta;</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mi>U</mi> <mo>-</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>V</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>t</mi> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>u</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mi>V</mi> <mo>-</mo> <mi>u</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>V</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mo>-</mo> <mi>v</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>V</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mo>+</mo> <msub> <mi>&amp;Gamma;</mi> <mi>R</mi> </msub> <mi>V</mi> <mo>-</mo> <mi>A</mi> <mi>&amp;Delta;</mi> <mi>V</mi> <mo>+</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>v</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mi>W</mi> <mo>+</mo> <mi>f</mi> <mi>W</mi> <mo>-</mo> <mi>h</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>U</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mover> <mi>u</mi> <mo>^</mo> </mover> <mi>d</mi> <mi>x</mi> <mi>d</mi> <mi>y</mi> <mi>d</mi> <mi>t</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>T</mi> </msubsup> <munder> <mrow> <mo>&amp;Integral;</mo> <mo>&amp;Integral;</mo> </mrow> <mi>&amp;Omega;</mi> </munder> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>&amp;zeta;</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mi>U</mi> <mo>+</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>u</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mi>V</mi> <mo>-</mo> <mi>f</mi> <mi>V</mi> <mo>-</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>W</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>t</mi> </mrow> </mfrac> <mo>-</mo> <mi>u</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>W</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>v</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mi>W</mi> <mo>-</mo> <mi>v</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>W</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mo>+</mo> <msub> <mi>&amp;Gamma;</mi> <mi>R</mi> </msub> <mi>W</mi> <mo>-</mo> <mi>A</mi> <mi>&amp;Delta;</mi> <mi>W</mi> <mo>-</mo> <mi>h</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>U</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mover> <mi>v</mi> <mo>^</mo> </mover> <mi>d</mi> <mi>x</mi> <mi>d</mi> <mi>y</mi> <mi>d</mi> <mi>t</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>T</mi> </msubsup> <munder> <mrow> <mo>&amp;Integral;</mo> <mo>&amp;Integral;</mo> </mrow> <mi>&amp;Omega;</mi> </munder> <mrow> <mo>(</mo> <mrow> <mi>u</mi> <mi>V</mi> <mo>+</mo> <mi>v</mi> <mi>W</mi> </mrow> <mo>)</mo> </mrow> <msub> <mover> <mi>&amp;Gamma;</mi> <mo>^</mo> </mover> <mi>R</mi> </msub> <mi>d</mi> <mi>&amp;sigma;</mi> <mi>d</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>T</mi> </msubsup> <munder> <mrow> <mo>&amp;Integral;</mo> <mo>&amp;Integral;</mo> </mrow> <mi>&amp;Omega;</mi> </munder> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>u</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mi>U</mi> <mo>+</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>v</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mi>U</mi> </mrow> <mo>)</mo> </mrow> <mover> <mi>h</mi> <mo>^</mo> </mover> <mi>d</mi> <mi>x</mi> <mi>d</mi> <mi>y</mi> <mi>d</mi> <mi>t</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
    Subsequently into step 007；Wherein, f represents Coriolis parameters, and A represents lateral eddy viscosity coefficient；
    Step 007. is as follows according to formula (4), (5), (6) acquisition adjoint equation, wherein, g represents acceleration of gravity, and Δ V represents V Laplace operator, Δ W represent W Laplace operator：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>U</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>t</mi> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>U</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mi>u</mi> <mo>+</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>U</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mi>v</mi> <mo>+</mo> <mi>g</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>V</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mo>+</mo> <mi>g</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>W</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mi>&amp;zeta;</mi> <mo>-</mo> <msup> <mi>&amp;zeta;</mi> <mrow> <mi>o</mi> <mi>b</mi> <mi>s</mi> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <mi>&amp;gamma;</mi> <mfrac> <mo>&amp;part;</mo> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>&amp;zeta;</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mi>&amp;eta;</mi> <mfrac> <mo>&amp;part;</mo> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>&amp;zeta;</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>V</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>t</mi> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>&amp;zeta;</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mi>U</mi> <mo>-</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>u</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mi>V</mi> <mo>+</mo> <mi>u</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>V</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mo>+</mo> <mi>v</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>V</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mo>-</mo> <msub> <mi>&amp;Gamma;</mi> <mi>R</mi> </msub> <mi>V</mi> <mo>+</mo> <mi>A</mi> <mi>&amp;Delta;</mi> <mi>V</mi> <mo>-</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>v</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mi>W</mi> <mo>-</mo> <mi>f</mi> <mi>W</mi> <mo>+</mo> <mi>h</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>U</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mo>=</mo> <mi>u</mi> <mo>-</mo> <msup> <mi>u</mi> <mrow> <mi>o</mi> <mi>b</mi> <mi>s</mi> </mrow> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>W</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>t</mi> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>&amp;zeta;</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mi>U</mi> <mo>-</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>u</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mi>V</mi> <mo>+</mo> <mi>f</mi> <mi>V</mi> <mo>+</mo> <mi>u</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>W</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>v</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mi>W</mi> <mo>+</mo> <mi>v</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>W</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mo>-</mo> <msub> <mi>&amp;Gamma;</mi> <mi>R</mi> </msub> <mi>W</mi> <mo>+</mo> <mi>A</mi> <mi>&amp;Delta;</mi> <mi>W</mi> <mo>+</mo> <mi>h</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>U</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mo>=</mo> <mi>v</mi> <mo>-</mo> <msup> <mi>v</mi> <mrow> <mi>o</mi> <mi>b</mi> <mi>s</mi> </mrow> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
    And it is with initial BVP condition：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>U</mi> <msub> <mo>|</mo> <mrow> <mi>t</mi> <mo>=</mo> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mi>V</mi> <msub> <mo>|</mo> <mrow> <mi>t</mi> <mo>=</mo> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mi>W</mi> <msub> <mo>|</mo> <mrow> <mi>t</mi> <mo>=</mo> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>U</mi> <msub> <mo>|</mo> <mrow> <mo>&amp;part;</mo> <mi>&amp;Omega;</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mi>V</mi> <msub> <mo>|</mo> <mrow> <mo>&amp;part;</mo> <mi>&amp;Omega;</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mi>W</mi> <msub> <mo>|</mo> <mrow> <mo>&amp;part;</mo> <mi>&amp;Omega;</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
    Subsequently into step 008；
    Step 008. obtains the tidal water bottom-friction factor Γ in waters to be predicted according to formula (7), (8)RPressure gradient expression formula, the depth of water H pressure gradient expression formulas are as follows, subsequently into step 009；
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mo>&amp;dtri;</mo> <msub> <mi>&amp;Gamma;</mi> <mi>R</mi> </msub> </msub> <mi>J</mi> <mo>=</mo> <mi>u</mi> <mi>V</mi> <mo>+</mo> <mi>v</mi> <mi>W</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mo>&amp;dtri;</mo> <mi>h</mi> </msub> <mi>J</mi> <mo>=</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>u</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mi>U</mi> <mo>+</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>v</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mi>U</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
    Step 009. is directed to the tidal water bottom-friction factor Γ in waters to be predictedRPressure gradient expression formula, depth of water h pressure gradient expression formulas, use Newton iteration method is solved, and obtains tidal water bottom-friction factor Γ respectivelyRTrend valueThe trend value h of depth of water h*, into And incite somebody to actionAs the optimal tidal water bottom-friction factor in waters to be predicted, h*As the optimal depth of water in waters to be predicted, Ran Houjin Enter step 010；
    Step 010 is according to the optimal tidal water bottom-friction factor in waters to be predictedOptimal depth of water h*With two-dimentional tidal model, pin Prediction is realized to the tide in waters to be predicted.
  2. A kind of 2. tide prediction method based on tidal parameter inverting according to claim 1, it is characterised in that the step In 002, it is described for the water surface relative to the fluctuation altitude information set ζ of the position still water, trend in abscissa X-direction On trend Y-axis component set v in ordinate Y direction of trend X-axis component set u, trend, and treat inverting target position The water-bed friction coefficient Γ putR, depth of water h, establish shown in disturbance relation equation below (1)：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mover> <mi>&amp;zeta;</mi> <mo>~</mo> </mover> <mo>=</mo> <mi>&amp;zeta;</mi> <mo>+</mo> <mi>&amp;alpha;</mi> <mover> <mi>&amp;zeta;</mi> <mo>^</mo> </mover> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <mi>u</mi> <mo>~</mo> </mover> <mo>=</mo> <mi>u</mi> <mo>+</mo> <mi>&amp;alpha;</mi> <mover> <mi>u</mi> <mo>^</mo> </mover> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <mi>v</mi> <mo>~</mo> </mover> <mo>=</mo> <mi>v</mi> <mo>+</mo> <mi>&amp;alpha;</mi> <mover> <mi>v</mi> <mo>^</mo> </mover> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>&amp;Gamma;</mi> <mo>~</mo> </mover> <mi>R</mi> </msub> <mo>=</mo> <msub> <mi>&amp;Gamma;</mi> <mi>R</mi> </msub> <mo>+</mo> <mi>&amp;alpha;</mi> <msub> <mover> <mi>&amp;Gamma;</mi> <mo>^</mo> </mover> <mi>R</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <mi>h</mi> <mo>~</mo> </mover> <mo>=</mo> <mi>h</mi> <mo>+</mo> <mi>&amp;alpha;</mi> <mover> <mi>h</mi> <mo>^</mo> </mover> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    Thus, after being disturbed
  3. 3. a kind of tide prediction method based on tidal parameter inverting according to claim 1 or claim 2, it is characterised in that described In step 002, for ζ, u, v, ΓR, h, using equation below (2) Suo Shi：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mover> <mi>&amp;zeta;</mi> <mo>^</mo> </mover> <mo>=</mo> <munder> <mi>lim</mi> <mrow> <mi>&amp;alpha;</mi> <mo>&amp;RightArrow;</mo> <mn>0</mn> </mrow> </munder> <mfrac> <mrow> <mover> <mi>&amp;zeta;</mi> <mo>~</mo> </mover> <mo>-</mo> <mi>&amp;zeta;</mi> </mrow> <mi>&amp;alpha;</mi> </mfrac> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <mi>u</mi> <mo>^</mo> </mover> <mo>=</mo> <munder> <mi>lim</mi> <mrow> <mi>&amp;alpha;</mi> <mo>&amp;RightArrow;</mo> <mn>0</mn> </mrow> </munder> <mfrac> <mrow> <mover> <mi>u</mi> <mo>~</mo> </mover> <mo>-</mo> <mi>u</mi> </mrow> <mi>&amp;alpha;</mi> </mfrac> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <mi>v</mi> <mo>^</mo> </mover> <mo>=</mo> <munder> <mi>lim</mi> <mrow> <mi>&amp;alpha;</mi> <mo>&amp;RightArrow;</mo> <mn>0</mn> </mrow> </munder> <mfrac> <mrow> <mover> <mi>v</mi> <mo>~</mo> </mover> <mo>-</mo> <mi>u</mi> </mrow> <mi>&amp;alpha;</mi> </mfrac> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>&amp;Gamma;</mi> <mo>^</mo> </mover> <mi>R</mi> </msub> <mo>=</mo> <munder> <mi>lim</mi> <mrow> <mi>&amp;alpha;</mi> <mo>&amp;RightArrow;</mo> <mn>0</mn> </mrow> </munder> <mfrac> <mrow> <msub> <mover> <mi>&amp;Gamma;</mi> <mo>~</mo> </mover> <mi>R</mi> </msub> <mo>-</mo> <msub> <mi>&amp;Gamma;</mi> <mi>R</mi> </msub> </mrow> <mi>&amp;alpha;</mi> </mfrac> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <mi>h</mi> <mo>^</mo> </mover> <mo>=</mo> <munder> <mi>lim</mi> <mrow> <mi>&amp;alpha;</mi> <mo>&amp;RightArrow;</mo> <mn>0</mn> </mrow> </munder> <mfrac> <mrow> <mover> <mi>h</mi> <mo>~</mo> </mover> <mo>-</mo> <mi>h</mi> </mrow> <mi>&amp;alpha;</mi> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    ζ, u, v, Γ are defined respectivelyR, h derivativeWherein α is parameter preset.
  4. A kind of 4. tide prediction method based on tidal parameter inverting according to claim 1, it is characterised in that the step In 003, after disturbanceSubstitute among two-dimentional tidal model, obtain cutting for waters tide to be predicted Shown in linear model equation below (3)：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mover> <mi>&amp;zeta;</mi> <mo>^</mo> </mover> </mrow> <mrow> <mo>&amp;part;</mo> <mi>t</mi> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mover> <mi>&amp;zeta;</mi> <mo>^</mo> </mover> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mi>u</mi> <mo>+</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>&amp;zeta;</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mover> <mi>u</mi> <mo>^</mo> </mover> <mo>+</mo> <mi>h</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mover> <mi>u</mi> <mo>^</mo> </mover> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mover> <mi>&amp;zeta;</mi> <mo>^</mo> </mover> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mi>v</mi> <mo>+</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>&amp;zeta;</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mover> <mi>v</mi> <mo>^</mo> </mover> <mo>+</mo> <mi>h</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mover> <mi>v</mi> <mo>^</mo> </mover> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mover> <mi>u</mi> <mo>^</mo> </mover> </mrow> <mrow> <mo>&amp;part;</mo> <mi>t</mi> </mrow> </mfrac> <mo>+</mo> <mover> <mi>u</mi> <mo>^</mo> </mover> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>u</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mo>+</mo> <mi>u</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mover> <mi>u</mi> <mo>^</mo> </mover> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mo>+</mo> <mover> <mi>v</mi> <mo>^</mo> </mover> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>u</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mo>+</mo> <mi>v</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mover> <mi>u</mi> <mo>^</mo> </mover> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mo>-</mo> <mi>f</mi> <mover> <mi>v</mi> <mo>^</mo> </mover> <mo>+</mo> <msub> <mi>&amp;Gamma;</mi> <mi>R</mi> </msub> <mover> <mi>u</mi> <mo>^</mo> </mover> <mo>+</mo> <msub> <mover> <mi>&amp;Gamma;</mi> <mo>^</mo> </mover> <mi>R</mi> </msub> <mi>u</mi> <mo>-</mo> <mi>A</mi> <mi>&amp;Delta;</mi> <mover> <mi>u</mi> <mo>^</mo> </mover> <mo>+</mo> <mi>g</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mover> <mi>&amp;zeta;</mi> <mo>^</mo> </mover> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mover> <mi>v</mi> <mo>^</mo> </mover> </mrow> <mrow> <mo>&amp;part;</mo> <mi>t</mi> </mrow> </mfrac> <mo>+</mo> <mover> <mi>u</mi> <mo>^</mo> </mover> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>v</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mo>+</mo> <mi>u</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mover> <mi>v</mi> <mo>^</mo> </mover> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mo>+</mo> <mover> <mi>v</mi> <mo>^</mo> </mover> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>v</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mo>+</mo> <mi>v</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mover> <mi>v</mi> <mo>^</mo> </mover> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mo>+</mo> <mi>f</mi> <mover> <mi>u</mi> <mo>^</mo> </mover> <mo>+</mo> <msub> <mi>&amp;Gamma;</mi> <mi>R</mi> </msub> <mover> <mi>v</mi> <mo>^</mo> </mover> <mo>+</mo> <msub> <mover> <mi>&amp;Gamma;</mi> <mo>^</mo> </mover> <mi>R</mi> </msub> <mi>v</mi> <mo>-</mo> <mi>A</mi> <mi>&amp;Delta;</mi> <mover> <mi>v</mi> <mo>^</mo> </mover> <mo>+</mo> <mi>g</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mover> <mi>&amp;zeta;</mi> <mo>^</mo> </mover> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, f represents Coriolis parameters, and A represents lateral eddy viscosity coefficient,RepresentLaplace operator,Table ShowLaplace operator.
  5. A kind of 5. tide prediction method based on tidal parameter inverting according to claim 1, it is characterised in that the step In 009, specifically comprise the following steps：
    Step 00901. is according to the tidal water bottom-friction factor Γ in the waters to be predictedRPressure gradient expression formula, depth of water h gradient tables reach Formula, it is (Γ to define iteration initial guessR 0,h0), following steepest is designed using Newton iteration method and declines Iteration, then Enter step 00902；
    <mrow> <mtable> <mtr> <mtd> <mrow> <msup> <msub> <mi>&amp;Gamma;</mi> <mi>R</mi> </msub> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <msup> <msub> <mi>&amp;Gamma;</mi> <mi>R</mi> </msub> <mi>i</mi> </msup> <mo>-</mo> <mrow> <mo>(</mo> <mrow> <msub> <mo>&amp;dtri;</mo> <msub> <mi>&amp;Gamma;</mi> <mi>R</mi> </msub> </msub> <mi>J</mi> </mrow> <mo>)</mo> </mrow> <msub> <mo>|</mo> <mrow> <mo>(</mo> <mrow> <msup> <msub> <mi>&amp;Gamma;</mi> <mi>R</mi> </msub> <mi>i</mi> </msup> <mo>,</mo> <msup> <mi>h</mi> <mi>i</mi> </msup> </mrow> <mo>)</mo> </mrow> </msub> <msup> <mi>&amp;rho;</mi> <mi>i</mi> </msup> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>h</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>h</mi> <mi>i</mi> </msup> <mo>-</mo> <mrow> <mo>(</mo> <mrow> <msub> <mo>&amp;dtri;</mo> <mi>h</mi> </msub> <mi>J</mi> </mrow> <mo>)</mo> </mrow> <msub> <mo>|</mo> <mrow> <mo>(</mo> <mrow> <msup> <msub> <mi>&amp;Gamma;</mi> <mi>R</mi> </msub> <mi>i</mi> </msup> <mo>,</mo> <msup> <mi>h</mi> <mi>i</mi> </msup> </mrow> <mo>)</mo> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msup> <mi>&amp;lambda;</mi> <mi>i</mi> </msup> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, ρi、λiRepresent it is Γ respectivelyRWith the iteration step length of h；
    Step 00902. defines J [ΓR 0,h0] it is cost functional, and define ρ0、λ0The respectively initial value of step-length, and start to perform Iteration, wherein each secondary iteration causes J [ΓR i+1,hi+1] ＜ J [ΓR i,hi], subsequently into step 00903；
    Step 00903. is when meeting stopping criterion for iteration J≤ε, according to ΓR i+1→ΓR *,hi+1→h*, tidal water bottom is obtained respectively Friction coefficient ΓRTrend valueThe trend value h of depth of water h*, and then willRub at optimal tidal water bottom as waters to be predicted Wipe coefficient, h*As the optimal depth of water in waters to be predicted, subsequently into step 010, wherein ε represents default iteration ends parameter.
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