CN108229060A - Parametrization Joint Distribution model based on significant wave height, average wave period and wave direction - Google Patents
Parametrization Joint Distribution model based on significant wave height, average wave period and wave direction Download PDFInfo
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Abstract
The present invention relates to wave energy resource assessment technology fields, and in particular to a kind of parametrization Joint Distribution model based on significant wave height, average wave period and wave direction includes the following steps, the edge distribution f of S1. structure linear variable significant wave heights and average wave periodHs(hs) and fTm(tm)；S2. the edge distribution f of round variable wave direction is builtΘ(θ)；S3. significant wave height and wave direction and the Joint Distribution c of average wave period and wave direction are builtHs‑Dir(u, v) and cTm‑DirThe condition distribution h of (v, w), significant wave height and wave direction and average wave period and wave directionHs|Dir(u | v) and hTm|Dir(v | w) and significant wave height, the averagely two-dimensional condition of wave period and wave direction distribution cHs‑Tm|Dir(hHs|Dir(u|v),hTm|Dir(v|w))；S4. the three-dimensional Joint Distribution model of significant wave height, average wave period and wave direction is built.The present invention considers three significant wave height, average wave period and wave direction main elements of wave, can more accurately describe wave condition.
Description
Technical field
The present invention relates to wave energy resource assessment technology fields, and in particular to one kind is based on significant wave height, average wave period
With the parametrization Joint Distribution model of wave direction.
Background technology
The stock assessment of wave energy and wave spectrum element are closely related, while wave spectrum element also influences the energy of equipment
The safety of capture rate and structure.The foundation of element of wave probabilistic model sets analysis wave energy feature and resource, device
Meter and generating efficiency assessment optimization are all particularly significant.
Wave energy assessment and follow up device, array optimization design in, significant wave height and feature wave period (such as spectral peak week
Phase, zero-crossing period or average period) it is two most important wave spectrum elements, the two is closely related, joint ensemble
Accurate structure, for many years always emphasis of correlative study.In the prior art, the structure of significant wave height and characteristic wave periodic model
It builds and can be used, such as original two dimensional Joint Distribution model, but the model needs data are normal distributions, to extreme wave height value simultaneously
It is inapplicable；Such as two-dimensional condition probabilistic model, that is, the one-dimension probability distribution of significant wave height under specific characteristic wave period is studied, is then built
The mathematical relationship of vertical feature wave period and significant wave height Probability Distribution Model Parameter, but be that structure is complicated the shortcomings that the model,
Mass data is needed to support, there are certain experiences with the function of significant wave height Probability Distribution Model Parameter for the feature wave period of foundation
Property, it is inaccurate for the estimation of extreme wave conditions.In addition to this, as Copula methods in recent years are using more and more extensive,
Based on dimensional Co pula functions, experts and scholars propose a variety of different probabilistic models for analyzing the two dimension joint of element of wave
Distribution, but correlative study passes through to conventional two-dimensional lognormal model, condition model and several ginsengs based on copula functions
Numberization model is compared, as a result display establish suitable statistical model or some difficulties.
In practice, the direction of wave is also an important parameter in marine environment.In view of by environmental factors such as monsoon
It influences, wave direction constantly changed in 1 year, and long term probability distribution often shows as multimodal form, i.e., there are multiple leading
Wave direction, and each dominate wave direction propagate the wave feature come influence it is significantly different, wave height-period joint probability distribution also it is each not
It is identical.Therefore it is more accurate to describe sea situation feature with the joint probability distribution model of wave direction, corresponding significant wave height and eigenperiod,
And compared with establishing the Two dimensional Distribution of significant wave height and feature wave period, people for this joint ensemble research also very
It is few.
Invention content
In order to which more accurately description wave condition, the present invention propose a kind of based on significant wave height, average wave period and wave
To parametrization Joint Distribution model.
To achieve these goals, the present invention adopts the following technical scheme that：Based on significant wave height, average wave period and wave direction
Parametrization Joint Distribution model, include the following steps,
S1. structure linear variable significant wave height and the edge distribution f of average wave periodHs(hs) and fTm(tm)；
S2. the edge distribution f of round variable wave direction is builtΘ(θ)；
S3. significant wave height and wave direction and the Joint Distribution c of average wave period and wave direction are builtHs-Dir(u, v) and cTm-Dir
The condition distribution h of (v, w), significant wave height and wave direction and average wave period and wave directionHs|Dir(u | v) and hTm|Dir(v | w) and
The two-dimensional condition distribution c of significant wave height, average wave period and wave directionHs-Tm|Dir(hHs|Dir(u|v),hTm|Dir(v|w))；
S4. the three-dimensional Joint Distribution model of significant wave height, average wave period and wave direction is built.
Further, in the step S1 using improve maximum entropy distribution come the edge distribution of linear variable.
Further, it is distributed in the step S2 using von Mises come the edge distribution of fitting circle deformation quantity.
Further, the step S3 is specifically included,
S31. significant wave height and wave direction and the Joint Distribution c of average wave period and wave direction are builtHs-Dir(u, v) and cTm-Dir
The condition distribution h of (v, w), significant wave height and wave direction and average wave period and wave directionHs|Dir(u | v) and hTm|Dir(v | w) and
Significant wave height；
S32. the two-dimensional condition distribution c of significant wave height, average wave period and wave direction is builtHs-Tm|Dir(hHs|Dir(u|v),
hTm|Dir(v|w))。
Further, the step S31 is specifically included,
S311. the probability density function of linear-circular distribution is built；
S312., linear-circular distribution is regarded to the Copula functions of special shape, i.e., linearly-circle Copula obtains it
Joint cumulative frequency is distributed；
S313. estimate round phase relation in linear-circle Copula joint cumulative frequency distributions using von Mises distributions
Several distribution functions；
S314. significant wave height and wave direction and the Joint Distribution c of average wave period and wave direction are obtainedHs-Dir(u, v) and
cTm-Dir(v, w) obtains significant wave height and wave direction and the conditional probability distribution h of average wave period and wave directionHs|Dir(u | v) and
hTm|Dir(v|w)。
Further, using Archimedean Copula models fittings significant wave height, average wave week in the step S32
The two-dimensional condition of phase and wave direction is distributed cHs-Tm|Dir(hHs|Dir(u|v),hTm|Dir(v|w))。
Further, the step S4 is specifically included,
S41. according to Copula functions, three-dimensional joint cumulative distribution function is built；
S42. the three-dimensional Joint Distribution model of significant wave height, average wave period and wave direction is obtained.
The parametrization Joint Distribution model based on significant wave height, average wave period and wave direction of the present invention has beneficial below
Effect：
(1) linear distribution and circular distribution are organically combined.
In engineer application, wind field or wave field are usually directed to several difference directions prevailing, and observation data cannot use unimodal point
Cloth is simulated, in order to overcome this difficulty, it is proposed that mixing von Mises distributions, and verified is a kind of flexible model.For
Linear-circular distribution with pair-copula is coupled, by linearly-circular distribution as the copula functions of special shape, is cried
Linear-circle copula is, using one using 2 π as the periodic function in period, obtains the connection of linear-circle copula functions
Close cumulative frequency distribution.
(2) consider three significant wave height, average wave period and wave direction main elements of wave, can more accurately describe wave
Unrestrained condition.
The Joint Distribution parameter model of a kind of wave period proposed by the present invention, wave height and wave direction.The model can be with
The correlation between three variables is considered, with vivider earth's surface oscillography wave-like condition；Have enough precision more to adapt to simultaneously
Member distribution can be applied in the calculating such as wave energy resource assessment.
Description of the drawings
Fig. 1 by research marine site Various Seasonal data Seasonal Distribution scatter plot；Wherein, the shape representation of data is not
With average wave cycle T m (" o "：0-2、“+”：2-4、“*”：4-6、“x”：6-8、“□”：8-10、“◇”：10-12、“△”：12-
14)；
Fig. 2 is significant wave height HsEdge distribution fitted figure；
Fig. 3 is equal wave period TmEdge distribution fitted figure；
Fig. 4 is the fitted figure of the edge distribution of wave direction θ；
Fig. 5 is significant wave height and wave direction HsThe Joint Distribution fitted figure of-θ；
Fig. 6 is average wave period and the Joint Distribution fitted figure of wave direction Tm- θ；
Fig. 7 is significant wave height and the fitting of distribution figure of CHs-Tm average period (u, w)；
Fig. 8 is PPi the and PFi images of model.
Specific embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is right below in conjunction with drawings and examples
The present invention is further elaborated.It should be appreciated that specific embodiment described herein is only to explain the present invention, not
For limiting the present invention.
The parametrization Joint Distribution model based on significant wave height, average wave period and wave direction of the present invention, including walking as follows
Suddenly,
S1. structure linear variable significant wave height and the edge distribution f of average wave periodHs(hs) and fTm(tm)；
Wherein, the edge distribution of linear variable, specific steps are simulated using maximum entropy distribution is improved in the step S1
For：
Linear variable includes significant wave height Hs and average cycle T m, it is assumed that the annual frequency of occurrences of variable for n (0,1,
2 ..., k ...), corresponding probability is P (n=k)=Pk(Pk=P0,P1,P2,…,Pk...), and multiple malformation function
ForCorresponding Poisson distribution isPoisson distribution function is substituted into Compound Extreme Value
It is distributed：
In order to obtain maximum entropy distribution, the following conditions are proposed：
Y=f (x) is enabled, then its Eulerian equation is
It enables
Then lny=α '+γ lnx- β xξ, therefore, under the constraint of above three condition, the probability density of maximum entropy distribution
Function is
Maximum entropy distribution function is
If the mathematic expectaion of stochastic variableSecond-order moment around mean V and third central moment B is present in arbitrary statistics sequence
Row, then its expression formula is as follows：
G (x) is substituted into F (x) to obtain
The probability density function for then improving maximum entropy distribution is：
In formula, beta, gamma, ξ and a0(location parameter) is all the parameter of function, and parameter Estimation uses maximum
Likelihood estimate (MLE) method.
S2. the edge distribution f of round variable wave direction is builtΘ(θ)；
In probability theory, von Mises distributions are because it is close to the normal distribution for being used as round variable during normal distribution.It is given
One ideal value z=eiθ, von Mises distributions are the maximum entropy densities of z.The probability density function and Bezier of von Mises
The series of function is：
θ ∈ in formula [0,2 π) be random round variable arc pattern, 0≤μ<2 π are mean values, reflection von Mises distributions
Symmetrical centre；К>0 is Center Parameter, reflects the dense degree away from center of round variable.Ij(К) is jth(j=0,1,
2 ...) improved Bessel function of the first kind, expression formula are as follows：
Herein on basis, the probability density function of mixing von Mises distributions is：
In formula, wh>0 is the non-negative weight parameter of mixed distribution, summation 1.H is the number of required von Mises distributions.It is mixed
Closing the cumulative frequency function that von Mises are distributed is：
Based on principle of maximum entropy, EM algorithm can be used in parameter Estimation, according to Akaike ' s information
Criterion (AIC) sees below formula, estimates parameter.
S3. significant wave height and wave direction and the Joint Distribution c of average wave period and wave direction are builtHs-Dir(u, v) and cTm-Dir
The condition distribution h of (v, w), significant wave height and wave direction and average wave period and wave directionHs|Dir(u | v) and hTm|Dir(v | w) and
The two-dimensional condition distribution c of significant wave height, average wave period and wave directionHs-Tm|Dir(hHs|Dir(u|v),hTm|Dir(v|w))；
S31. significant wave height and wave direction and the Joint Distribution c of average wave period and wave direction are builtHs-Dir(u, v) and cTm-Dir
The condition distribution h of (v, w), significant wave height and wave direction and average wave period and wave directionHs|Dir(u | v) and hTm|Dir(v | w) and
Significant wave height；
The step S31 is specifically included,
S311. the probability density function of linear-circular distribution is built；
The probability density function of linearly-circular distribution is：
fX,Θ=2 π g (ξ) fX(x)fΘ(θ)
In formula, fX(x) be linear variable probability density function, fΘ(θ) is the probability density function of angle variables, g (ξ)
It is the probability density function of round related coefficient ξ.It is respectively U and V to enable the cumulative frequency of linear variable and round variable, accordingly
Ground, ξ can be defined as：
S312., linear-circular distribution is regarded to the Copula functions of special shape, i.e., linearly-circle Copula obtains it
Joint cumulative frequency is distributed；
In order to which linear-circular distribution is coupled with the Copula functions of normal linear variable, so as to based on Pair-
Copula the Theory Construction three-dimensional Joint Distribution models, the present invention by linear-circular distribution as the Copula functions of special shape,
That is linear-circle Copula, is denoted as CL-C(u, v), probability density function are：
cL-C=2 π g (ξ)
But CL-CThe analytical function of (u, v) can not be directly obtained by the double integral of joint density function.Therefore, it enables G (ξ) is the circular distribution on a unit circle, i.e. g (ξ) is the periodicity using 2 π as the period
Function, for arbitrary v ' and θ ',Therefore joint accumulated probability CL-C(u, v) is represented by：
It is continuous.If the first derivative of g () is g1(), second dervative g2(), then
After simplification, the joint cumulative frequency distribution of linear-circle copula functions is：
CL-C(u, v)={ g2(2πu)-g2[2π(u-v)]+g2(-2πv)}/2π
Obtain CL-CAfter the analytical function of (u, v), conditional probability hL|C(u | v) it can be obtained by following formula：
cHs-Dir(u,v)、cTm-Dir(v, w) and cHs-Tm|Dir(hHs|Dir(u|v),hTm|Dir(v | w))
S313. estimate round phase relation in linear-circle Copula joint cumulative frequency distributions using von Mises distributions
Several distribution functions；
(GvM2) is distributed using broad sense von Mises for estimating the function g () of round related coefficient ξ
The single order of gGvM2 () and second order analytical function g1 () and g2 () in order to obtain, make Fourier change by above formula
It changes：
R (n μ in formula1) it is spin matrix, it is defined as below：
An, Bn are equal to
In formula, HnIt is defined as：
Sn=1 is enabled, if n/2 is nonnegative integer, and Sn=0, then Gn and Hn can be calculated by numerical method：
Therefore have：
S314. significant wave height and wave direction and the Joint Distribution c of average wave period and wave direction are obtainedHs-Dir(u, v) and
CTm-Dir(v, w) obtains significant wave height and wave direction and the conditional probability distribution h of average wave period and wave directionHs|Dir(u | v) and
hTm|Dir(v|w)；
The Joint Distribution and average period of significant wave height and wave direction and the Joint Distribution of wave direction can use linear-circle
Shape Copula functions are fitted.The maximal possibility estimation of broad sense von Mises distributions can be obtained substantially by following formula
In formula, A-1() is the inverse function of A (К), and A (К)=I1(К)/I0(К) be monotonic increasing function, A-1(·)
It needs to be calculated by numerical method.
S32. the two-dimensional condition distribution c of significant wave height, average wave period and wave direction is builtHs-Tm|Dir(hHs|Dir(u|v),
hTm|Dir(v|w))。
Wherein, using the two-dimensional strip of Archimedean Copula models fittings significant wave height, average wave period and wave direction
Part is distributed cHs-Tm|Dir(hHs|Dir(u|v),hTm|Dir(v|w))。
Final step is to establish two-dimensional condition distributed model cHs-Tm|Dir, using be usually used in be fitted significant wave height-eigenperiod
Archimedean Copula models (seeing the above table) the fitting c of Joint DistributionHs-Tm|Dir, the fitting of Copula parameter alphas according to it is maximum seemingly
Right method is estimated to obtain by following formula
Table.Archimedean Copula models
S4. the three-dimensional Joint Distribution model of significant wave height, average wave period and wave direction is built.
S41. according to Copula functions, three-dimensional joint cumulative distribution function is built；
If H is a joint cumulative frequency function for having the edge distribution there are two stochastic variable x and y, then there are one
Copula function C, meet any (x, y)：
H (x, y)=C (FX(x),FY(y))
If Fx and Fy are continuous, then C is unique；Conversely, C can also uniquely determine Fx and Fy.If u=FX(x),
V=FY(y), copula functions C (u, v) may be defined as：
C (u, v)=FXY(x, y)=FXY[FX -1(u),FY -1(v)]
Enable fXY(x, y) represents joint probability density function, cUV(u, v) represents copula density functions, according to copula letters
Several definition, fXY(x, y) can be obtained by following formula：
Assuming that the cumulative frequency distribution function of ternary (X, Y, Z) is defined as F (), edge cumulative distribution u=F (x) is enabled,
V=F (y), w=F (z), according to pair-copula theories, the joint cumulative distribution function F about (X, Y, Z)XYZUnder
Formula defines：
In formula, FX|ZAnd FY|ZIt is distributed for condition, is calculated by following formula：
In above-mentioned equation, F is being calculatedXYZDuring, it is noted that three copula functions：CXZ(u,w),CYZ(v, w) and
One-dimensional condition distribution function is denoted as CXY|Z, the Joint Distribution of mono- timings (X, Y) of expression Z.Z is a key variables, because when Z becomes
During change, the Joint Distribution of X and Y can also change.Wave direction meets Z, because the state of the wave of different directions is significantly different, especially
It is the area of leading wave direction.If other two linear variable X and Y is significant wave height Hs and average cycle T m, then Hs, Tm and θ
Joint probability density can be estimated by following formula：
fHs-Tm-Dir(hs, tm, θ)=fHs(hs)·fTm(tm)·fΘ(θ)×cHs-Dir(u,w)·cTm-Dir(v,w)·
cHs-Tm|Dir(hHs|Dir(u|w),hTm|Dir(v|w))
U=F in formulaHs(hs), v=FTm(tm), w=FDir(θ), f represent the density function of edge distribution, and h is copula
The abbreviation of conditional probability function, to acquire fHs-Tm-Dir(hs, tm, θ), as long as acquiring f respectivelyHs(hs)、fTm(tm)、fΘ(θ)、
cHs-Dir(u,v)、cTm-Dir(v, w) and cHs-Tm|Dir(hHs|Dir(u|v),hTm|Dir(v | w)).
Given array [hsn,tmn,θn]N=1 ..., T, then log-likelihood function be
S42. the three-dimensional Joint Distribution model of significant wave height, average wave period and wave direction is obtained；
By fHs(hs)、fTm(tm)、fΘ(θ)、cHs-Dir(u,v)、cTm-Dir(v,w)、hHs|Dir(u|v)、hTm|Dir(v | w) and
cHs-Tm|Dir(hHs|Dir(u|v),hTm|Dir(v | w)) bring formula into：
fHs-Tm-Dir(hs, tm, θ)=fHs(hs)·fTm(tm)·fΘ(θ)×
cHs-Dir(u,w)·cTm-Dir(v,w)·cHs-Tm|Dir(hHs|Dir(u|w),hTm|Dir(v|w))
Obtain the three-dimensional Joint Distribution model of significant wave height, average wave period and wave direction.
In order to verify the validity of the method for the present invention, verified by following instance.
In order to ensure that data are enough, representative strong, by Atlantic Ocean observation station every three hours 1997 to 2001 continuous 5 years
Significant wave height Hs, average wave cycle T m and the wave direction θ data applications of observation are to the method.Due to wave climate seasonal variety,
Northern Hemisphere most area winter (December to February) is wave energy most abundant season, and the data count in winter is 3608,
It is further analyzed enough, therefore by taking the Wave Data in winter as an example.Fig. 1 shows the distribution scatter plots of data used.
Radius in figure represents significant wave height Hs.
First, single factor analysis
Fig. 2 and Fig. 3 show the fitting image of the linear edge distribution of significant wave height Hs and average wave period Tm.As a result table
It is bright, it improves maximum entropy distribution and the fitting of Hs, Tm data is good.
Fig. 4 show the fitting image of wave direction edge distribution, winter degree of fitting relative drop in H=5,6.
2nd, two-dimentional Joint Distribution
Fig. 5 and Fig. 6 show the joint empirical cumulative frequency of Hs- θ and Tm- θ and the figure of corresponding theory profile accumulation frequency
Picture.As shown in the figure, the range of regression coefficient R2 is 0.9137-0.9729, show that the model established and initial data are very close.
Fig. 7 is average wave period and the Joint Distribution fitted figure of wave direction Tm- θ.
3rd, three dimensional analysis
In order to estimate model and observation data X=(Hs obs,Tm obs,θobs)N×3Between similarity (N is data
Number), while testing model validity, it needs to establish an a fairly large number of joint pseudo random number Y=(Hs sim,Tm sim,θsim),
Hs,TmIt may be defined as with the joint empirical cumulative frequency of θ：
I is indicator function in formula, its value is 1 when the conditions are met, is otherwise 0.Utilize the data of simulation, PFiTheoretical value
It can be estimated by following formula
Fig. 8 shows PP of the model in winteriAnd PFiImage.The PP in winteriAnd PFiRelated coefficient for 0.9954, its table
Representation model and fitting algorithm can be simulated with higher confidence level research marine site sea situation.
The present invention proposes a kind of wave direction and same period significant wave height, the three-dimensional joint probability distribution model of feature wave period.
Circular distribution is efficiently converted into linear distribution, and using one using 2 π as the period in period using von Mises distributions are mixed
Property function, obtain the joint cumulative frequency distribution of linear-circle copula functions.The present invention is it is contemplated that between three variables
Correlation with vivider earth's surface oscillography wave-like condition, there is enough precision to adapt to polynary distribution.Meanwhile it is tested by example
Card, it is of the invention represent model and fitting algorithm can be simulated with higher confidence level research marine site sea situation.
It should be understood that for those of ordinary skills, can be improved or converted according to the above description,
And all these modifications and variations should all belong to the protection domain of appended claims of the present invention.
Claims (7)
1. the parametrization Joint Distribution model based on significant wave height, average wave period and wave direction, which is characterized in that including walking as follows
Suddenly,
S1. structure linear variable significant wave height and the edge distribution f of average wave periodHs(hs) and fTm(tm)；
S2. the edge distribution f of round variable wave direction is builtΘ(θ)；
S3. significant wave height and wave direction and the Joint Distribution c of average wave period and wave direction are builtHs-Dir(u, v) and cTm-Dir(v,
W), the condition distribution h of significant wave height and wave direction and average wave period and wave directionHs|Dir(u | v) and hTm|Dir(v | w) and effectively
The two-dimensional condition distribution c of wave height, average wave period and wave directionHs-Tm|Dir(hHs|Dir(u|v),hTm|Dir(v|w))；
S4. the three-dimensional Joint Distribution model of significant wave height, average wave period and wave direction is built.
2. the parametrization Joint Distribution model according to claim 1 based on significant wave height, average wave period and wave direction,
It is characterized in that, using improvement maximum entropy distribution come the edge distribution of linear variable in the step S1.
3. the parametrization Joint Distribution model according to claim 2 based on significant wave height, average wave period and wave direction,
It is characterized in that, is distributed in the step S2 using von Mises come the edge distribution of fitting circle deformation quantity.
4. the parametrization Joint Distribution based on significant wave height, average wave period and wave direction according to claims 1 or 2 or 3
Model, which is characterized in that the step S3 is specifically included,
S31. significant wave height and wave direction and the Joint Distribution c of average wave period and wave direction are builtHs-Dir(u, v) and cTm-Dir(v,
W), the condition distribution h of significant wave height and wave direction and average wave period and wave directionHs|Dir(u | v) and hTm|Dir(v | w) and effectively
Wave height；
S32. the two-dimensional condition distribution c of significant wave height, average wave period and wave direction is builtHs-Tm|Dir(hHs|Dir(u|v),hTm|Dir(v
|w))。
5. the parametrization Joint Distribution model according to claim 4 based on significant wave height, average wave period and wave direction,
It being characterized in that, the step S31 is specifically included,
S311. the probability density function of linear-circular distribution is built；
S312., linear-circular distribution is regarded to the Copula functions of special shape, i.e., linearly-circle Copula obtains its joint
Cumulative frequency is distributed；
S313. estimate round related coefficient in linear-circle Copula joint cumulative frequency distributions using von Mises distributions
Distribution function；
S314. significant wave height and wave direction and the Joint Distribution c of average wave period and wave direction are obtainedHs-Dir(u, v) and cTm-Dir(v,
W), significant wave height and wave direction and the conditional probability distribution h of average wave period and wave direction are obtainedHs|Dir(u | v) and hTm|Dir(v|
w)。
6. the parametrization Joint Distribution model according to claim 4 based on significant wave height, average wave period and wave direction,
It is characterized in that, using Archimedean Copula models fittings significant wave height, average wave period and wave direction in the step S32
Two-dimensional condition distribution cHs-Tm|Dir(hHs|Dir(u|v),hTm|Dir(v|w))。
7. the parametrization Joint Distribution model according to claim 6 based on significant wave height, average wave period and wave direction,
It is characterized in that,
S41. according to Copula functions, three-dimensional joint cumulative distribution function is built；
S42. the three-dimensional Joint Distribution model of significant wave height, average wave period and wave direction is obtained.
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| CN109583030A (en) * | 2018-11-01 | 2019-04-05 | 中国海洋大学 | A kind of superposition of wind wave and swell Distribution of wave height and period construction method based on mixed model |
| CN112307676A (en) * | 2020-11-04 | 2021-02-02 | 国家海洋局北海预报中心((国家海洋局青岛海洋预报台)(国家海洋局青岛海洋环境监测中心站)) | Wave height numerical prediction model result correction method |
| CN113405537A (en) * | 2021-07-20 | 2021-09-17 | 中国海洋大学 | Wave direction inversion method based on satellite navigation positioning |
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| CN112307676A (en) * | 2020-11-04 | 2021-02-02 | 国家海洋局北海预报中心((国家海洋局青岛海洋预报台)(国家海洋局青岛海洋环境监测中心站)) | Wave height numerical prediction model result correction method |
| CN112307676B (en) * | 2020-11-04 | 2022-10-14 | 国家海洋局北海预报中心((国家海洋局青岛海洋预报台)(国家海洋局青岛海洋环境监测中心站)) | Wave height numerical prediction model result correction method |
| CN113468726A (en) * | 2021-06-09 | 2021-10-01 | 山东电力工程咨询院有限公司 | Wave period-wave height combined distribution calculation method and system |
| CN113468726B (en) * | 2021-06-09 | 2024-05-03 | 山东电力工程咨询院有限公司 | Wave period-wave height combined distribution calculation method and system |
| CN113405537A (en) * | 2021-07-20 | 2021-09-17 | 中国海洋大学 | Wave direction inversion method based on satellite navigation positioning |
| CN114818390A (en) * | 2022-06-27 | 2022-07-29 | 中交第四航务工程勘察设计院有限公司 | Method for evaluating port inoperable time |
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