CN107103173A - A kind of Design Wave projectional technique for embodying the influence of the factor of typhoon three - Google Patents
A kind of Design Wave projectional technique for embodying the influence of the factor of typhoon three Download PDFInfo
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Abstract
The present invention relates to calculation method of parameters, more particularly to a kind of Design Wave projectional technique for embodying the influence of the factor of typhoon three.It includes calculating step as follows：(1) the analyzed vortex unique characteristics factor, i.e. the typhoon factor；The reason for causing disaster for typhoon and the characteristic of typhoon, occur three factors of the beeline of the frequency and center of typhoon away from observation station as influence wave height water level using intensity of typhoon, typhoon；Wherein intensity of typhoon can be further represented as center of typhoon nearby barometric minimum or maximum wind velocity again.The present invention analyzes the influence of a variety of typhoon factor pair wave height and water level, and then more fully accurately describe influence of the typhoon to ocean environment parameter, ocean environment parameter and relevant design data are calculated by the model of foundation, the design result of more preferable ocean elevation is further tried to achieve, certain foundation is provided to prevent and reduce natural disasters.
Description
Technical field
The present invention relates to calculation method of parameters, more particularly to a kind of Design Wave reckoning side for embodying the influence of the factor of typhoon three
Method.
Background technology
Threat of the Oceanic disasters to coastal cities can not look down upon.Wave can throw ship, destroy coastal engineering, to seashore
Damage, or even also injure villages and small towns nearby and the people's lives and property safety.Wherein destruction of the extreme sea condition to breakwater
Maximum, especially when Extreme Wave and extreme water level are acted on simultaneously.
Typhoon is a kind of diastrous weather, the disaster of typhoon by three aspects the reason for constitute：(1) strong wind, is attacked coastal
Typhoon custom be usually up to 40~60m/s, the customs of some typhoons even can reach 100m/s；(2) heavy rain, general platform
Wind can cause 150~300mm rainfall when passing through；(3) storm tide, when typhoon landwards move by direction, due to very low
Air pressure and strong wind action can make littoral seawater rise suddenly and sharply, and this phenomenon is storm tide.
Immediate vicinity barometric minimum, immediate vicinity maximum wind velocity and the caused tide before and after Landed Typhoon of typhoon
(also cry and surge) is coefficient mainly due to the high wind in typhoon, low pressure and continental shelf neritic area and coastal landform feature
As a result.Calculated and shown by static pressure, when air pressure does not have 1 millibar of reduction, it will make that sea level rise 1 centimetre.Can be with from data observation
Find out, typhoon is stronger, surge bigger；Typhoon-scale is bigger, and tide coverage is wider caused by typhoon.By analysis,
Typhoon highest wave is obviously appeared near center of typhoon, is successively decreased to surrounding.The construction of breakwater is to prevent this area
Thus building, people's property etc. is known during design breakwater, reasonable consideration this area typhoon is sent out from the influence of wave
Raw process is also very necessary.
In marine engineering design, sea wave height is important Marine Environment Factors, accurately determines Return period design
Wave height value, it is significant for preventing and reducing natural disasters.
Influence in order to avoid artificial a priori assumption to Design Wave value, also has scientist to propose wave height maximum entropy distribution
Function, this method is to be based on entropy principle.But this method does not account for influence of the typhoon factor to wave height, have ignored
Extreme sea condition is frequently experienced in this objective fact in typhoon or cyclonic process.
2005, the theory of entropy was introduced into by Wang Liping, Xu Delun etc., is deduced based on principle of maximum entropy
New One-dimensional probability function.The introducing of principle of maximum entropy is more enriched and the perfect theory mode.Moreover, by practice
The density function for examining entropy theory to derive more conforms to reality, also more identical with measured data, can more reflect that extreme value environment is joined
Effect of the number when calculating the Return period return period.The hydrometric station in the typical case marine site such as this theoretical practical application Huanghai Sea East Sea
Measured data, with the distribution previously assumed by being compared, the compellent achievement of acquirement.More it is to derive two by one-dimensional
Tie up joint maximum entropy probability-distribution function after, marine environment design on practical application illustrate by Marine Environment Factors come
Design altitude is calculated just more to tally with the actual situation than ever.
But, all it is only to consider a factor of influence among those, it is impossible to depict typhoon well to influence marine site
The influence of wave height water level etc..It is envisaged that influence of the typhoon to Extreme Wave water level etc. be not the simple frequency can be with
Summarize.The several factors of typhoon all have such or such influence on marine environment factor extreme value.
With ocean engineering construction and the development of coastal economy, calculating of the people to Return period Design Wave value is proposed
Higher and higher required precision, typhoon how is taken into full account during reckoning, and this causes the extremes that disaster takes place frequently to many
Year one influence of Design Wave value is met, be that urgent need is opened while avoiding the artificial distribution pattern for assuming Marine Environmental Elements in advance again
The research work of exhibition.
The content of the invention
The technical problem to be solved in the present invention is how to overcome the deficiencies in the prior art to embody the factor of typhoon three there is provided one kind
The Design Wave projectional technique of influence.
The technical scheme that uses to achieve the above object of the present invention is：The Design Wave for embodying the influence of the factor of typhoon three is calculated
Method, including following reckoning step：
(1) the analyzed vortex unique characteristics factor, i.e. the typhoon factor；The reason for causing disaster for typhoon and the spy of typhoon
Property, intensity of typhoon, typhoon to that three of the beeline of the frequency and center of typhoon away from observation station as influence wave height water level occur
Factor；
Wherein intensity of typhoon can be further represented as center of typhoon nearby barometric minimum or maximum wind velocity again；
(2) by typhoon factor discretization, intensity of typhoon is carried out by the grade of barometric minimum near center of typhoon discrete
Be divided into 6 ranks, successively graduation for 1,2,3,4,5,6 grades, if so by the maximum wind velocity in generation Typhoon Process or
That barometric minimum is measured and can just define the intensity of typhoon, wherein the division of intensity of typhoon can also according to actual needs by
It is divided into arbitrary n grade；
Distance of the center of typhoon away from observation station represented using plane rectangular coordinate, i.e.,：
Wherein, Δ φ and Δ λ be respectively path distance observation station latitude away from through away from component；And d is divided into 9 etc.
Level, for describing influence of the typhoon to observation station, specially d ＜ 0.5, d ＜ 1, d ＜ 1.5, d ＜ 2, d ＜ 2.5, d ＜ 3, d ＜
3.5, d ＜ 4, other；
(3) the discrete maximum entropy model on the typhoon factor is set up, due to not being preferable independence between each factor of typhoon
Relation, according to maximum entropy theory, by the definition of entropy, if：
In formula：PijFor the probability of each discrete element of typhoon, i, j=1,2......
By the property of probability-distribution function, following four constraints is obtained：
In formula：m1、C1、m2、C2、C3For arbitrary parameter；
(4) 3) in constraints in, the entropy of probability reaches maximum, using method of Lagrange multipliers, constructs as follows
Functional：
J (f)=- ∫ f (x) lnf (x) dx+ λ0∫F(f(x))dx
Wherein, Part I is object function, and Part II is that each is each condition group on f on Part II
Into, integral domain is ignored in formula, and 0 is equal to f derivations, then it can solve the solution of place's functional；
In formula：
J --- object function；
λ0--- Lagrange multiplier；
F (f (x)) --- it is the function on f (x) constituted according to constraints；
(5) according to the knowledge of functional analysis, in solving 3) under constraints 4) in functional, that is, solve Euler-
Lagrange equations：
Wherein, n isOuter normal vector, PijFor the probability of each discrete element of typhoon, i, j=1,2...... λ1、λ2、λ3、
λ4Be arbitrary parameter, further, obtain probability-distribution function expression formula, i.e., on i, j joint probability distribution function：
(6) based on i, j probability-distribution function is further derived, it is determined that on i, j mixed moment is in (5)：
In formula：M, n are arbitrary parameter；
(7) by the reckoning of step (1)-step (6), it can obtain associated with wave height, water level on each factor of typhoon
Compound Distribution pattern：
F (x, y)=F0(x, y)+ε (x, y)-P (0,0,0),
In formula：ε (x, y) is error term,
Wherein m, n, r span be nonnegative integer, and (m, n, r) be a kind of discrete distribution, note p (m, n, r)=(i, j,
K) }=pijkI, j, k=0,1 ..., ∑ pijk=1；
(8) reckoning of step (1)-(7) is based on, intensity of typhoon, platform can be further associated by below equation
The calculating of the Design Wave value of the beeline of the frequency and center of typhoon away from observation station occurs for wind：
Further, i, j mixed moment can be drawn by measured data estimation, therefore by calculating i, and j each rank square can be with
Calculate the parameter lambda in i, j joint probability distribution functions1、λ4、m1、m2、λ2、λ3Value.
Further, in step (2) the discrete division number range of barometric minimum grade is near center of typhoon：1019-
1006；1005-991；990-975；974-957；956-938；Totally 6 grades of ＜=937, unit is hundred handkerchiefs, or needed according to research
A range of barometric minimum near center of typhoon is subjected to discrete level division on demand..
Further, beeline of the typhoon away from observation station is represented using plane rectangular coordinate, and using coastal area of china typhoon road
The implementation standard that footpath is represented by plane rectangular coordinate is divided to research area.
The advantage of the invention is that the influence of a variety of typhoon factor pair wave height and water level is analyzed, so it is more fully accurate
Describe influence of the typhoon to ocean environment parameter, ocean environment parameter and relevant design number are calculated by the model of foundation
According to further trying to achieve the design result of more preferable ocean elevation, certain foundation provided to prevent and reduce natural disasters.
Brief description of the drawings
Combined effect of the frequency to wave height water level occurs for Fig. 1 typhoons.
Combined effect of the intensity to wave height water level occurs for Fig. 2 typhoons.
Fig. 3 center of typhoons are away from combined effect of the observation station beeline to wave height water level.
Embodiment
Describe the Design Wave projectional technique of the present invention-factor of embodiment typhoon three influence in detail below in conjunction with the accompanying drawings.
The typhoon factor is analyzed first：Typhoon is a kind of diastrous weather, the disaster of typhoon by three aspects original
Because constituting：(1) strong wind, attacks coastal typhoon wind speed and is usually up to 40-60 meter per seconds, the wind speed of some typhoons can even reach
To 100 meter per seconds or so.(2) heavy rain, can cause 150-300 millimeters of rainfall when general typhoon passes through.Individual other typhoon exists
Extra torrential rain can be caused under its advantage.The Camille hurricanes of such as in Augusts, 1969 part are made in Virginia, USA
Into the down-pour of 686 millimeters/day, explosive flood is brought.Counted according to the U.S., the U.S. there are 63 floods since 1886
Water is caused by hurricane heavy rain, average just to have within 15 years 1 time.It is also that the major casualty that causes extra torrential rain originates it in China's typhoon
One, many strong Persistent Heavy Rains are all relevant with typhoon.(3) storm tide, when typhoon landwards move by direction, due to very low
Air pressure and strong wind action littoral seawater can be made to rise suddenly and sharply, this phenomenon is storm tide.The storm tide of high wind can make the sea of bank
It is waterborne to gush as many as 5-6 meters.In deep-sea marine site, typhoon can start billow, and wave is high up to more than ten or even tens meters.In the shadow of typhoon
Under sound, anomalous variation occurs in marine hydrology phenomenon.The scope of appearance and its influence of typhoon, central pressure drop (or center
Wind speed greatest around) etc. the marine environment where it can all have been influenceed.Therefore, the reason for causing disaster for typhoon, this
Literary author plan the frequency of typhoon generation, center of typhoon wind speed greatest around, center of typhoon nearby barometric minimum and typhoon away from
Four factors of beeline of observation station.
Typhoon occurs and beeline of the typhoon away from observation station is all to belong to the external factor of typhoon, simply in Typhoon Process
In because consider region just return back out it is existing and by consideration regional effect the factor.These factor datas must attend the meeting because examine
The region of worry it is different and different, that is to say, that consider that region is different, the data of same typhoon are also different.Note simultaneously
To barometric minimum is all the inwardness of typhoon near center of typhoon wind speed greatest around and center of typhoon, is also typhoon
Internal factor.Typhoon is once produce, and it is just provided with the maximum wind velocity and barometric minimum of oneself.Its two factors are not
Change because of the difference in the region of consideration, but these factors of typhoon can be because of the different and different of the region passed through.Also
To say, even in same place generate the same terms typhoon because external factor difference cause by region differ
Sample, and the region that these pass through can feed back in Typhoon Process to typhoon, this feedback may make the wind speed of typhoon gentle
Pressure all changes.
Because center of typhoon air pressure drop has approximation relation as follows with its center wind speed greatest around：
vmax=K (p∞-p0)1/2
Wherein, K is the function of density.Near center of typhoon, K values average is 5.7.p0For the minimum gas of center of typhoon
Pressure, p∞For typhoon peripheral environment air pressure.Therefore, center barometric minimum to a certain specified sea areas typhoon and the pass of maximum wind velocity
It is that formula is substantially determination.That is, when discussing the characterization factor of typhoon in itself, center barometric minimum and maximum wind velocity
Value needs to consider one.This can regard the measure coefficient of intensity of typhoon as.The frequency and typhoon occur for typhoon away from observation station
Beeline between there is no the relation that can be used for reference, by its discrete figure it is also seen that the relation between them is also suitable
It is fuzzy.Therefore two extrinsic factors of typhoon should be all taken into account.
Occur the frequency and typhoon consequently, it is possible to allow for four original factors and become three, i.e. intensity of typhoon, typhoon
The beeline of centre-to-centre spacing observation station.
To sum up, the beeline of the frequency and center of typhoon away from observation station is occurred into for intensity of typhoon, typhoon as performance typhoon
Three factors.
Intensity of typhoon can be further represented as center of typhoon nearby barometric minimum or maximum wind velocity again.
Will be with reference to the division methods of tropical depression, tropical storm, severe tropical storm, typhoon, violent typhoon and Super Typhoon
Typhoon bottom immediate vicinity maximum wind velocity is divided into 6 grades：10.8-17.1；17.2-24.4；24.5-32.6；32.7-41.4；41.5-
50.9；＞=51 (unit：m/s).It is worth noting that, the discrete division of intensity of typhoon can also by near center of typhoon most
Low pressure is divided, and is followed successively by：1019-1006；1005-991；990-975；974-957；956-938；＜=937 (unit：
Hundred handkerchiefs).As long as typhoon can just be defined by so measuring the maximum wind velocity or barometric minimum that occur in Typhoon Process
The division of intensity, wherein intensity of typhoon can also be divided into arbitrary n grade according to actual needs.Drawn more than
Divide order, graduation successively is 1-6 grades, and higher grade, it is dangerous bigger.
By the understanding to typhoon and typhoon to the influence to calamity, we are observed using intensity and the typhoon distance of typhoon
The distance of point describes influence of the typhoon to observation station.
In the same manner, typhoon track can also be described using plane rectangular coordinate apart from observation station apart from this typhoon factor, and
And the implementation standard that the coastal typhoon track of only one China is represented by plane rectangular coordinate can be found, using this standard come to wanting research area
Typhoon make division, its describing mode is as follows：
Typhoon track represented apart from the distance of observation station using plane rectangular coordinate, i.e.,：
Wherein, Δ φ and Δ λ be respectively path distance observation station latitude away from through away from component；And d is divided into 9 etc.
Level, for describing influence of the typhoon to observation station, specially d ＜ 0.5, d ＜ 1, d ＜ 1.5, d ＜ 2, d ＜ 2.5, d ＜ 3, d ＜
3.5, d ＜ 4, other.Calculating so is done to the path of each process typhoon, considered in this, as discrete variable.And give
Go out the discrete division result of the beeline of intensity of typhoon and center of typhoon away from observation station, such as table 1：
It is after an effective way of Research on typhoon, typhoon factor discretization, to establish to the research of typhoon each factor
Model come to describe the typhoon factor be one of main method of Research on typhoon.According to Such analysis, the intensity of typhoon and apart from sight
The beeline of measuring point is all that the major reason of heavy losses is caused to architectural engineering etc..
Notice between each factor of typhoon it is not preferable independence simultaneously, thus it is independent except to study each factor
Rule outside, also to study the rule of agents.This allows for being necessary property of Research on typhoon agents probabilistic model.
The discrete maximum entropy model on the typhoon factor is set up, by the definition of entropy, if：
In formula：PijFor the probability of each discrete element of typhoon, i, j=1,2......
By the property of probability-distribution function, following four constraints is obtained：
In formula：m1、C1、m2、C2、C3For arbitrary parameter；
Above-mentioned requirements are in above-mentioned constraints, and the entropy of probability reaches maximum, can use method of Lagrange multipliers, structure
Make following functional：
J (f)=- ∫ f (x) lnf (x) dx+ λ0∫F(f(x))dx
In formula：
J --- object function；
λ0--- Lagrange multiplier；
F (f (x)) --- it is the function on f (x) constituted according to constraints；
Wherein, Part I is object function in above formula, and it is each on f that Part II, which is each on Part II,
Condition composition, integral domain is ignored in formula, and 0 is equal to f derivations, then the solution of the functional can be solved, according to functional analysis
Knowledge, solve constraints under functional, that is, solve Euler-Lagrange equations：
Wherein, n isOuter normal vector, PijFor the probability of each discrete element of typhoon, i, j=1,2...... λ1、λ2、λ3、
λ4It is arbitrary parameter,
Order
Then
Therefore, probability-distribution function expression formula is obtained：
I.e. on i, j joint probability distribution function：
I and j mixed moment is calculated below：
Wherein,
Order
Then
That is,
It can similarly obtain：
Derived more than and understand i, j mixed moment is：
In formula：M, n are arbitrary parameter；
On i, j mixed moment can be estimated by measured data, that is to say, that by calculating i, j each rank is mixed
Closing square can be with the i that calculates of numerical value, the parameter in j joint distribution functions.Discrete division result in table 1, applied to i, j
Joint distribution function, obtains the model profile parameter calculated value such as table 2：
The characteristics of due to wave itself, the very big sight of the Marine Environmental Elements observed every year (such as wave height, water level)
The beeline of the frequency, maximum intensity and center of typhoon away from observation station that measured value occurs from annual typhoon in different sea areas etc. is all
It is not a constant but a stochastic variable.Under typhoon influence, other adjoint environmental key-elements such as extreme sea condition such as wave height, such as
Water level etc. constitutes a kind of polynary continuous type probability distribution again.
Definition：(m, n, r) is a kind of discrete distribution, note
P { (m, n, r)=(i, j, k) }=pijkI, j, k=0,1 ... ∑ pijk=1.
Theorem：
If ξ, η,For stochastic variable, random vector (ξ1, ξ2, ξ3) andDistribution Q (x, y, z) and G is obeyed respectively
(x, y, z).G (x, y, z) joint probability density function is present, and is designated as g (x, y, z).Remember ξ1In factor of influence (i, j, k) altogether
Independent of observation and remaining stochastic variable adjoint with it in the case of same-action are designated as (ξ1ijk, ξ2ijk, ξ3ijk).P (i) refers to P
The edge distribution of (i, j, k), G1(u) be Q (x, y, z) edge distribution, H1(u) be G (x, y, z) edge distribution；M, n, r take
Value scope is nonnegative integer.Define stochastic variable：
Then
F (x, y, z)=F0(x, y, z)+ε (x, y, z)-P (0,0,0)
Wherein,
ε (x, y) is error
.
Application of the multiple malformation in engineering design：
It is commonly used discrete Poisson distributions, single-point distribution, binomial distribution and discrete maximum entropy distribution etc. to be distributed with.
Because discrete variable selected by us is the intensity (maximum wind velocity or lowest center air pressure) of typhoon, the frequency and according to observation station most
Short distance.Here we are converted into discrete variable first by the intensity in these three variables and beeline discretization.
The discretization of intensity (so that typhoon is maximum as an example)：According to the maximum wind velocity of wind scale and typhoon by the typhoon etc.
Level, which is marked, to be come, and wind scale is 1 in 5-6 grades of intensity of typhoon；Similar 2,3,4,5 be followed successively by 7-8,9-10,11-12,13 with
On.Thus the grade classification of typhoon is come out according to the maximum wind velocity of typhoon.
Such as table 3, the discretization of beeline：
Such as table 4, intensity of typhoon, the maximum entropy fitting parameter table away from observation station beeline and the frequency
Application of the Compound Extreme Value in Return period parameters of engineering design is calculated：
In actual applications, discrete distribution can be replaced with continuously distributed with different influence factors, wherein discrete
Distribution is the effect that it represents the continuous factor of factor pair.Such as it is continuously distributed can take wind speed, wave height, water level；Discrete distribution
Its intensity of typhoon, the frequency and deflection of influence etc. can be taken.Wave height or water level all can be by differences in different environment
The influence of factor, the effect of various factors influence is also not quite similar.More all-sidedly and accurately consideration has influence on the work of the continuous factor
With, more accurate design altitude is calculated, it is more preferable to engineering offer to ensure.The formula to calculating above derived is just utilized now
The design load of ocean environment parameter.Formula expression is as follows：
Consider effect of the typhoon multifactor impact relative to consideration typhoon single-factor influence to preferably illustrate, here
The return period of wave height under single-factor influence, water level is listed as follows.The selection of following table medium wave high water level is same according to wave height water level
Obtained Deng being calculated in the case of status (influence to design altitude is identical).
Table 5：
Neutralized from table 5 and can be seen that the influence of each factor pair wave height water level of typhoon all with reference to the quantile plot of Fig. 1,2,3 three
It is present, and effect is not quite similar.All in all, beeline of the center of typhoon away from observation station is to wave height water level
Influence it is stronger than the frequency and intensity of typhoon.This meets with actual conditions, and maximum wave height water level is occurred from mostly
Center of typhoon surrounding waters.This not just merely because near center of typhoon wind maximum intensity, also as typhoon reach should
Typhoon has been acted on the marine site for a long time during marine site.Influence of the intensity to wave height water level is most weak, and this can be from the shape of ripple
Explained on into principle.The growth of ripple not only has relation with the intensity of wind, relevant also with the length of its duration.In other words
Say, even prolonged acted on sea of the wind of small intensity can also make wave growth be than larger wave.
Above-described embodiment is simply to illustrate that the technical concepts and features of the present invention, the purpose is to be to allow in the art
Those of ordinary skill can understand present disclosure and implement according to this, and it is not intended to limit the scope of the present invention.It is all
It is the equivalent change or modification according to made by the essence of present invention, should all covers within the scope of the present invention.
Claims (4)
1. embody the Design Wave projectional technique of the factor of typhoon three influence, it is characterised in that calculate step including following：
(1) the analyzed vortex unique characteristics factor, i.e. the typhoon factor；The reason for causing disaster for typhoon and the characteristic of typhoon, will
Three factors of the beeline of the frequency and center of typhoon away from observation station as influence wave height water level occur for intensity of typhoon, typhoon；
Wherein intensity of typhoon can be further represented as center of typhoon nearby barometric minimum or maximum wind velocity again；
(2) by typhoon factor discretization, intensity of typhoon is carried out by discrete division by the grade of barometric minimum near center of typhoon
For 6 ranks, successively graduation be 1,2,3,4,5,6 grades, as long as so by the maximum wind velocity in generation Typhoon Process or most
Low pressure, which is measured, can just define the intensity of typhoon, and the wherein division of intensity of typhoon can also be according to actual needs by its stroke
It is divided into arbitrary n grade；
Distance of the center of typhoon away from observation station represented using plane rectangular coordinate, i.e.,：
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(3) the discrete maximum entropy model on the typhoon factor is set up, due to not being preferable independence between each factor of typhoon,
According to maximum entropy theory, by the definition of entropy, if：
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By the property of probability-distribution function, following four constraints is obtained：
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<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>C</mi>
<mn>2</mn>
</msub>
<mo><</mo>
<mi>&infin;</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</munder>
<msub>
<mi>p</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mi>ln</mi>
<mi> </mi>
<mi>i</mi>
<mi>j</mi>
<mo>=</mo>
<msub>
<mi>C</mi>
<mn>3</mn>
</msub>
<mo><</mo>
<mi>&infin;</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula：m1、C1、m2、C2、C3For arbitrary parameter；
(4) in the constraints in (3), the entropy of probability reaches maximum, using method of Lagrange multipliers, constructs as follows general
Letter：
J (f)=- ∫ f (x) ln f (x) dx+ λ0∫F(f(x))dx
Wherein, Part I is object function, and Part II is that each is that each is constituted on f condition on Part II
, integral domain is ignored in formula, and 0 is equal to f derivations, then it can solve the solution of place's functional；
In formula：
J --- object function；
λ0--- Lagrange multiplier；
F (f (x)) --- it is the function on f (x) constituted according to constraints；
(5) according to the knowledge of functional analysis, in solving 3) under constraints 4) in functional, that is, solve Euler-Lagrange side
Journey：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>p</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mi>log</mi>
<mi> </mi>
<msub>
<mi>p</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&lambda;</mi>
<mn>1</mn>
</msub>
<mo>&part;</mo>
<msub>
<mi>p</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
<mo>&part;</mo>
<msup>
<mi>i</mi>
<msub>
<mi>m</mi>
<mn>1</mn>
</msub>
</msup>
<msub>
<mi>p</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&lambda;</mi>
<mn>3</mn>
</msub>
<mo>&part;</mo>
<msup>
<mi>j</mi>
<msub>
<mi>m</mi>
<mn>2</mn>
</msub>
</msup>
<msub>
<mi>p</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>4</mn>
</msub>
<mo>&part;</mo>
<msub>
<mi>p</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mi>ln</mi>
<mi> </mi>
<mi>i</mi>
<mi>j</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>p</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>&Element;</mo>
<mi>R</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>p</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mi>log</mi>
<mi> </mi>
<msub>
<mi>p</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&lambda;</mi>
<mn>1</mn>
</msub>
<mo>&part;</mo>
<msub>
<mi>p</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
<mo>&part;</mo>
<msup>
<mi>i</mi>
<msub>
<mi>m</mi>
<mn>1</mn>
</msub>
</msup>
<msub>
<mi>p</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&lambda;</mi>
<mn>3</mn>
</msub>
<mo>&part;</mo>
<msup>
<mi>j</mi>
<msub>
<mi>m</mi>
<mn>2</mn>
</msub>
</msup>
<msub>
<mi>p</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>4</mn>
</msub>
<mo>&part;</mo>
<msub>
<mi>p</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mi>ln</mi>
<mi> </mi>
<mi>i</mi>
<mi>j</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>p</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>&CenterDot;</mo>
<mi>n</mi>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>&Element;</mo>
<mo>&part;</mo>
<mi>R</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein, n isOuter normal vector, PijFor the probability of each discrete element of typhoon, i, j=1,2...... λ1、λ2、λ3、λ4
For arbitrary parameter, further, obtain probability-distribution function expression formula, i.e., on i, j joint probability distribution function：
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>&lambda;</mi>
<mn>1</mn>
</msub>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
<mo>)</mo>
</mrow>
<msub>
<mi>&lambda;</mi>
<mn>4</mn>
</msub>
</msup>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mrow>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
<msup>
<mi>i</mi>
<msub>
<mi>m</mi>
<mn>1</mn>
</msub>
</msup>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>3</mn>
</msub>
<msup>
<mi>j</mi>
<msub>
<mi>m</mi>
<mn>2</mn>
</msub>
</msup>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
(6) based on i, j probability-distribution function is further derived, it is determined that on i, j mixed moment is in (5)：
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mi>m</mi>
<mo>,</mo>
<mi>n</mi>
</mrow>
</msub>
<mo>=</mo>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</munder>
<msup>
<mi>i</mi>
<mi>m</mi>
</msup>
<msup>
<mi>j</mi>
<mi>n</mi>
</msup>
<msub>
<mi>p</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</munder>
<msub>
<mi>&lambda;</mi>
<mn>1</mn>
</msub>
<msup>
<mi>i</mi>
<mrow>
<mi>m</mi>
<mo>+</mo>
<msub>
<mi>&lambda;</mi>
<mn>4</mn>
</msub>
</mrow>
</msup>
<msup>
<mi>j</mi>
<mrow>
<mi>n</mi>
<mo>+</mo>
<msub>
<mi>&lambda;</mi>
<mn>4</mn>
</msub>
</mrow>
</msup>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mrow>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
<msup>
<mi>i</mi>
<msub>
<mi>m</mi>
<mn>1</mn>
</msub>
</msup>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>3</mn>
</msub>
<msup>
<mi>j</mi>
<msub>
<mi>m</mi>
<mn>2</mn>
</msub>
</msup>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<mfrac>
<msub>
<mi>&lambda;</mi>
<mn>1</mn>
</msub>
<mrow>
<msub>
<mi>m</mi>
<mn>1</mn>
</msub>
<msub>
<mi>m</mi>
<mn>2</mn>
</msub>
<msubsup>
<mi>&lambda;</mi>
<mn>2</mn>
<mfrac>
<mrow>
<mi>m</mi>
<mo>+</mo>
<msub>
<mi>&lambda;</mi>
<mn>4</mn>
</msub>
<mo>+</mo>
<mn>1</mn>
</mrow>
<msub>
<mi>m</mi>
<mn>1</mn>
</msub>
</mfrac>
</msubsup>
<msubsup>
<mi>&lambda;</mi>
<mn>3</mn>
<mfrac>
<mrow>
<mi>n</mi>
<mo>+</mo>
<msub>
<mi>&lambda;</mi>
<mn>4</mn>
</msub>
<mo>+</mo>
<mn>1</mn>
</mrow>
<msub>
<mi>m</mi>
<mn>2</mn>
</msub>
</mfrac>
</msubsup>
</mrow>
</mfrac>
<mi>&Gamma;</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mi>m</mi>
<mo>+</mo>
<msub>
<mi>&lambda;</mi>
<mn>4</mn>
</msub>
<mo>+</mo>
<mn>1</mn>
</mrow>
<msub>
<mi>m</mi>
<mn>1</mn>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mi>&Gamma;</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mi>n</mi>
<mo>+</mo>
<msub>
<mi>&lambda;</mi>
<mn>4</mn>
</msub>
<mo>+</mo>
<mn>1</mn>
</mrow>
<msub>
<mi>m</mi>
<mn>2</mn>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula：M, n are arbitrary parameter；
(7) by the reckoning of step (1)-step (6), it can obtain answering on each factor of typhoon is associated with wave height, water level
Close distribution pattern：
F (x, y)=F0(x, y)+ε (x, y)-P (0,0,0),
In formula：ε (x, y) is error term, wherein m, n,
R span is nonnegative integer, and (m, n, r) is a kind of discrete distribution, remembers p { (m, n, r)=(i, j, k) }=pijk
I, j, k=0,1 ..., ∑ pijk=1；
(8) reckoning of step (1)-(7) is based on, intensity of typhoon, typhoon hair can be further associated by below equation
The calculating of the Design Wave value of the raw beeline of the frequency and center of typhoon away from observation station：
<mrow>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>&infin;</mi>
</munderover>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>&infin;</mi>
</munderover>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>&infin;</mi>
</munderover>
<mi>i</mi>
<mi>j</mi>
<mi>k</mi>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
<mo>)</mo>
</mrow>
<msubsup>
<mo>&Integral;</mo>
<mrow>
<mo>-</mo>
<mi>&infin;</mi>
</mrow>
<mi>z</mi>
</msubsup>
<msubsup>
<mo>&Integral;</mo>
<mrow>
<mo>-</mo>
<mi>&infin;</mi>
</mrow>
<mi>y</mi>
</msubsup>
<msubsup>
<mo>&Integral;</mo>
<mrow>
<mo>-</mo>
<mi>&infin;</mi>
</mrow>
<mi>x</mi>
</msubsup>
<msubsup>
<mi>G</mi>
<mn>1</mn>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>u</mi>
<mo>,</mo>
<mi>v</mi>
<mo>,</mo>
<mi>w</mi>
</mrow>
<mo>)</mo>
</mrow>
<mi>d</mi>
<mi>u</mi>
<mi>d</mi>
<mi>v</mi>
<mi>d</mi>
<mi>w</mi>
<mo>+</mo>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mrow>
<mn>0</mn>
<mo>,</mo>
<mn>0</mn>
<mo>,</mo>
<mn>0</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
2. the Design Wave projectional technique according to claim 1 for embodying the influence of the factor of typhoon three, it is characterised in that：I, j
Mixed moment can show that therefore by calculating i, j each rank square can calculate i, j joint probabilities point by measured data estimation
Parameter lambda in cloth function1、λ4、m1、m2、λ2、λ3Value.
3. the Design Wave projectional technique according to claim 1 for embodying the influence of the factor of typhoon three, it is characterised in that：Step
(2) the discrete division number range of barometric minimum grade is near the center of typhoon in：1019-1006；1005-991；990-
975；974-957；956-938；Totally 6 grades of ＜=937, unit is hundred handkerchiefs, or needed according to research will be certain near center of typhoon
In the range of barometric minimum carry out discrete level division on demand.
4. the Design Wave projectional technique according to claim 1 for embodying the influence of the factor of typhoon three, it is characterised in that：Typhoon
Beeline away from observation station is represented using plane rectangular coordinate, and the implementation represented using coastal area of china typhoon track by plane rectangular coordinate
Standard is divided to research area.
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| CN108009127A (en) * | 2017-09-12 | 2018-05-08 | 陈柏宇 | The analysis method that a kind of typhoon characterization factor influences sea wave height |
| CN108021786A (en) * | 2017-12-18 | 2018-05-11 | 中国海洋大学 | A kind of coastal more ground storm tide joint nature strength analysis method |
| CN108196314A (en) * | 2017-12-22 | 2018-06-22 | 南京大学 | A kind of northwest Pacific ring-type typhoon automatic recognition system |
| CN111766642A (en) * | 2020-06-16 | 2020-10-13 | 中国气象科学研究院 | Login tropical cyclone precipitation forecasting system |
| CN111898089A (en) * | 2020-06-16 | 2020-11-06 | 中国海洋大学 | Method for determining effective wave height and water increasing joint probability of typhoon-influenced sea area |
| CN112445856A (en) * | 2020-12-01 | 2021-03-05 | 海南长光卫星信息技术有限公司 | Sea surface height influence correlation analysis method and device |
| CN114386294A (en) * | 2022-03-23 | 2022-04-22 | 北京弘象科技有限公司 | Typhoon environment model generation method and device |
| CN116523125A (en) * | 2023-04-13 | 2023-08-01 | 宁波市气象台 | Wave height forecasting method based on sea surface wind speed forecasting |
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Cited By (12)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN108009127A (en) * | 2017-09-12 | 2018-05-08 | 陈柏宇 | The analysis method that a kind of typhoon characterization factor influences sea wave height |
| CN108021786A (en) * | 2017-12-18 | 2018-05-11 | 中国海洋大学 | A kind of coastal more ground storm tide joint nature strength analysis method |
| CN108021786B (en) * | 2017-12-18 | 2021-11-09 | 中国海洋大学 | Coastal multi-geowind storm surge combined natural intensity analysis method |
| CN108196314A (en) * | 2017-12-22 | 2018-06-22 | 南京大学 | A kind of northwest Pacific ring-type typhoon automatic recognition system |
| CN108196314B (en) * | 2017-12-22 | 2023-04-18 | 南京大学 | Automatic northwest Pacific annular typhoon identification system |
| CN111766642A (en) * | 2020-06-16 | 2020-10-13 | 中国气象科学研究院 | Login tropical cyclone precipitation forecasting system |
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| CN111898089B (en) * | 2020-06-16 | 2024-05-10 | 中国海洋大学 | Method for determining effective wave height and water increasing joint probability of typhoon affecting sea area |
| CN112445856A (en) * | 2020-12-01 | 2021-03-05 | 海南长光卫星信息技术有限公司 | Sea surface height influence correlation analysis method and device |
| CN114386294A (en) * | 2022-03-23 | 2022-04-22 | 北京弘象科技有限公司 | Typhoon environment model generation method and device |
| CN116523125A (en) * | 2023-04-13 | 2023-08-01 | 宁波市气象台 | Wave height forecasting method based on sea surface wind speed forecasting |
| CN116523125B (en) * | 2023-04-13 | 2023-10-20 | 宁波市气象台 | Wave height forecasting method based on sea surface wind speed forecasting |
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Application publication date: 20170829 |