CN107229825A - A kind of tropical cyclone complete trails analogy method assessed towards calamity source - Google Patents
A kind of tropical cyclone complete trails analogy method assessed towards calamity source Download PDFInfo
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Abstract
A kind of tropical cyclone complete trails analogy method assessed towards calamity source, its specific steps include：The first step, it is established that initial point model, including sampling generation simulation tropical cyclone year frequency and generation start point information；Second step, sets up traveling model, simulates the translational speed of tropical cyclone and towards forming Tropical Cyclone Route；3rd step, sets up strength model, including ocean surface strength development model and land Strength degradation model, and select corresponding strength model according to the longitude and latitude of subsequent point in Tropical Cyclone Route；4th step, path simulation product test carries out statistical result inspection and Statistical Analysis to the Tropical Cyclone Route and intensity large sample generated at random；5th step, sets up Typhoon Wind Field engineering model and boundary layer model, includes the demarcation of wind-field model key parameter, and calculating simulation point typhoon wind speed carries out typhoon risk Disaster Assessment.The present invention can realize that the accurate reliable, computational efficiency of the assessment that becomes more meticulous, result is high, applied widely.
Description
Technical field
The invention belongs to engineering structure wind resistance design field, more particularly to a kind of heat assessed towards calamity source
Band cyclone complete trails analogy method.
Background technology
Typhoon is a classification of tropical cyclone.On meteorology, defined by World Meteorological Organization：Boiling pot
Sustained wind velocity reaches that 12 grades (i.e. 32.7 meters per second or more) are referred to as hurricane (hurricane), and the title of hurricane is used in Beijing University
The West and Eastern Pacific；And the nearly adopted word that northwest Pacific is used is typhoon (typhoon).On TaiWan, China, Japan and other places,
The tropical cyclone of more than 17.2 meters per second of Ze Jiang centers sustained wind velocity is all referred to as typhoon.The typhoon of one mature, by its knot
Structure and the weather brought, are divided into typhoon eye, whirlwind rain belt, the peripheral part of strong wind area three, are outwards arranged from center in concentric circles
Row.Typhoon eye is located at center of typhoon, about 5~10 kilometers of diameter.Down draft prevailing in typhoon eye, therefore weather eyeball is bright, wind is put down
Wave is quiet.It is whirlwind rain belt on the outside of typhoon eye, strong convergence ascending air prevailing, forms dense cloud layer here, occurs mad
Storm rain, wind-force is usually the worst region of weather in typhoon more than 12 grades.Outwards be again peripheral strong wind area, wind speed to
Outer to reduce, wind-force is generally more than 6 grades.Typhoon, which passes by, usually brings rough weather, causes sea billow, serious to threaten
Coastal engineering structure safety.
According to statistics, it is 9 that the tropical cyclone of China's southeastern coast is logged in per annual to include typhoon and the number of Super Typhoon
It is individual, and increase tendency is presented in intensity.With developing rapidly for coastal area economy, the rapid increase of population and site coverage,
More and more wind sensitive structure such as high-rise buildings, it is big build across stadium, Loads of Long-span Bridges etc., work caused by typhoon
Journey accident is of common occurrence.Therefore, in view of the massive losses that typhoon disaster is likely to result in, engineering structure wind resistance is designed with must
Consider that typhoon is acted on.But, current average wind and fluctuating wind characteristic part of the code for structural design on wind load both at home and abroad
The statistics achievement of the good state wind in ward is all based on, clear stipulaties are not made to Typhoon Wind Field, this is due to that determination is a certain
Return period corresponding Maximum wind speed and designed wind load at least need the observational data of engineering ground decades, and Typhoon Wind Field
There is the features such as yardstick is small, frequency is low, data acquisition difficulty is big relative to good state wind, cause current near-earth typhoon measured data
It is still inadequate, it is impossible to which that accurate calibration is made to typhoon climate pattern.Therefore, platform is carried out for the design of coastal civil infrastructure
Disaster caused by a windstorm does harm to risk assessment and the reasonable estimation of return period typhoon wind load must be based on limited meteorological data, by reasonable
Numerical simulation means realize.
In engineering design field, predominantly it is based on towards the tropical cyclone method for numerical simulation that calamity source is assessed single
The tropical cyclone measured data of passing by of website or local area, Digital calculation modelling is passed through using typhoon wind-field model
Typhoon wind speed, is comprised the following steps that：(1) a range of typhoon record that passes by is extracted using simulation circule method, and carries out data
Pretreatment；(2) statistics obtains the probabilistic model of each typhoon key parameter at simulation point；(3) the probability mould according to key parameter
Type carries out random sampling, one group of typhoon key parameter is obtained, with reference to typhoon wind-field model, the typhoon wind speed of calculating simulation point；
(4) walked in repetition, obtain the THE MAXIMUM WIND SPEED OF TYPHOON sequence of simulation point, (different reoccurrence is calculated for typhoon disaster risk assessment
Corresponding Maximum wind speed or determination typhoon wind profile parameter etc.).It is above-mentioned based on single website or local area
Numerical Simulation of Typhoon method operating procedure is few, and computational efficiency is high, but needs statistics to obtain mould there is also limitation simultaneously
Intend the probabilistic model of each typhoon key parameter at point.But, the tropical gas in some regional such as Zhejiang Province of coastal area of southeastern China
Rotation event population sample is considerably less, and the typhoon record that passes by obtained using simulation circule method screening is not enough to set up in the region
The probabilistic model of typhoon key parameter.
The content of the invention
The present invention, which proposes one kind, can realize that the accurate reliable, computational efficiency of the assessment that becomes more meticulous, result is high, applied widely
Towards calamity source assess tropical cyclone complete trails analogy method.
The technical solution adopted by the present invention is：
A kind of tropical cyclone complete trails analogy method assessed towards calamity source, its specific steps include：
The first step, it is established that initial point model, including the year frequency of sampling generation simulation tropical cyclone are originated with generation
Point information；
Second step, sets up traveling model, simulates the translational speed of tropical cyclone and towards forming Tropical Cyclone Route；
3rd step, sets up strength model, including ocean surface strength development model and land Strength degradation model, and according to heat
Longitude and latitude with subsequent point in trajectory of cyclone selects corresponding strength model；
4th step, path simulation product test is counted to the Tropical Cyclone Route and intensity large sample generated at random
Product test and Statistical Analysis；
5th step, sets up Typhoon Wind Field engineering model and boundary layer model, includes the demarcation of wind-field model key parameter,
Calculating simulation point typhoon wind speed, carries out typhoon risk Disaster Assessment.
Further, Estimating The Model Coefficients, and generation of sampling are carried out to year frequency using negative binomial distribution in the first step
Simulate the year frequency of tropical cyclone.According to the history tropical cyclone year frequency data characteristicses in northwest Pacific region,
Estimating The Model Coefficients, and the year frequency for generation simulation tropical cyclone of sampling are carried out to year frequency.Mainly have negative at present
Two kinds of models of bi-distribution and Poisson distribution are fitted the year frequency probability distribution of tropical cyclone.Georgiou is to black west
The typhoon that brother gulf and Atlantic Ocean seashore are met with is studied, and compares negative binomial distribution and Poisson distribution and typhoon year occurs
The fitting degree of rate model, finds the incidence for the typhoon sequence that negative binomial distribution can be preferably on analog sea, and Poisson
The incidence of the distribution energy more preferably typhoon sequence that simulation bank occurs, because the mobile route climate parameter of typhoon
Influence is larger, and the generation of typhoon is not affected by these factors.Therefore, in complete trails simulation, originating from ocean surface
Typhoon year frequency is preferably simulated with negative binomial distribution.
Further, the tropical cyclone start point information based on history calculates the information needed for complete trails simulation in the first step：
Translational speed, direction, ocean surface temperature, the relative intensity of position, and then each simulation typhoon is determined by random sampling
Start point information.
Further, the translational speed and direction of Vickery paths forecast of regression model subsequent point are used in second step：
V is translational speed, △ lnv=lnv in formulai+1-lnvi；θ is direction, △ θ=θi+1-θi；ψ latitudes；λ longitudes； εv
And εθTo meet the zero-mean Disturbance of normal distribution；Regression coefficient ai, biIt is only relevant with geographic area, northwest is peaceful
Oceanic province domain is divided into some grids, collects the history Tropical Cyclone Route information in each grid, and distinguish direction eastwards and to
Western direction, coefficient ai, biIt can be obtained by the history tropical cyclone information regression analysis of each grid.
Further, the longitude and latitude of subsequent point in Tropical Cyclone Route is judged in the 3rd step, if subsequent point is position
In land, then land Strength degradation model is selected, if subsequent point is to be located at ocean surface, select ocean surface strength development model.
Further, ocean surface strength development model is, according to ocean surface intensity regression model, to predict next on ocean surface in the 3rd step
The relative intensity of point, so that it is determined that central pressure：
I is relative intensity in formula；T is ocean surface temperature；εITo meet the zero-mean Disturbance of normal distribution, coefficient ci
It can be obtained by the history tropical cyclone information regression analysis of each grid.The present invention considers ocean surface temperature, stratosphere
The such environmental effects such as temperature, relative humidity, relative intensity is converted to by central pressure.
Further, land Strength degradation model, using intensity regression model is logged in, simulates Tropical Cyclone Landing in the 3rd step
Strength retrogression afterwards：
△ p (t)=△ p0exp(-mt) (3)
△ p in formula0Central gas pressure difference during to log in；△ p (t) are the central gas pressure difference after logging in t hours；M=m0+
m1△p0+εm, Coefficient m0、m1With Disturbance εmRegression analysis can be changed by the draught head of history Landing Tropical Cyclone to obtain
Arrive.The present invention, which considers, logs in the influence of the factors such as duration, tropical cyclone intensity size and roughness of ground surface, sets up
Log in the strength retrogression after intensity regression model, simulation Tropical Cyclone Landing.
Further, it is path and intensity and the history tropical cyclone for contrasting stochastic simulation that analog result, which is examined, in the 4th step
Difference between data, quantitatively portrays the precision of analog result.
Further, the Statistical Analysis in the 4th step is that coastal area of southeastern China coastline is divided into some coast stations
Point, then count being simulated in the range of each seashore point 250km and history in the average annual frequency of tropical cyclone, translational speed, court
To and central gas pressure difference result difference, can reflect to a certain extent tropical cyclone complete trails simulation spatial distribution
Effect.
Further, used in the 5th step for entering typhoon track and intensity sample in the range of simulation point 250km
The typhoon wind speed of Yan Meng wind-field models calculating simulation points, is comprised the following steps that：
(1) demarcation of typhoon wind-field model key parameter
Using Vickery empirical models estimation maximum wind speed radius RmaxWith Holland air pressure sectional parameters B：
Draught head centered on △ p in formula；ψ is latitude；fc=2 × 7.273 × 10-5sinψ；And εBTo meet normal state
The zero-mean Disturbance of distribution；
(2) pressure model is set up
Using Holland pressure models：
P=p0+△pexp[-(Rmax/r)B] (6)
In formula, it away from center of typhoon radial distance is sea level pressure at r that P, which is,；RmaxFor maximum wind speed radius；B is gas
Press sectional parameter；
According to formula (6), barometric gradient expression formula is：
(3) equilibrium establishment equation
Navier-Stokes equations under the conditions of neutral atmosphere are：
In formula, V is the movement velocity of air micelle, and V is considered as gradient velocity V by Yan Meng wind-field modelsgRubbed with earth's surface
Wipe wind speed V ' two parts vector superposed, i.e. V=Vg+V’；F is Coriolis parameters；F is boundary layer friction power；
Due to radial direction blast gradient in PBL of typhoon with height change very little, then ignore friction more than boundary layer
Power, formula (8) can be decomposed into gradient layer and boundary layer two parts, respectively such as formula (9) and formula (10)：
With reference toAndFormula (9) and formula (10) can abbreviation be further：
In the two-dimentional polar coordinates moved with center of typhoon, breakdown (9) is obtained radially and tangentially：
In formula, VθgAnd VrgIt is gradient velocity tangentially and radially respectively；cr=-VTCos (θ-β '), cθ=-VT sin(θ-
β′)；ρ is atmospheric density, takes 1.2kg/m3；θ is due east direction and simulation point and center of typhoon line angle, to revolve counterclockwise
Switch to just；β ' is the angle in due east direction and Typhoon Tracks direction, using rotate counterclockwise as just；
In upper atmosphere environment, it is contemplated that VrgFar smaller than Vθg, ignore first two in formula (13), can obtain
Vθg；Due to VrgIt is worth very little, approximately takes 0 can still meet the accuracy of wind speed simulation, thus, develop and the parsing of gradient velocity
Formula, is shown below：
In near-earth boundary layer, the tangentially and radially component V ' of earth's surface wind friction velocityθAnd V 'rLess than corresponding gradient velocity
Component, therefore these components can be assumed that the first derivative of similarly less than corresponding gradient velocity component to θ first derivative；In
It is that formula (10) can make linearisation and decompose, and be shown below：
The boundary condition of upper atmosphere and adjacent ground surface is respectively formula (17) and formula (18)：
V′|z′→∞=0 (17)
Calculate starting point to be taken as at z=h+10 i.e. z '=0, it is considered to which after boundary condition, formula (16) can be solved to：
V "=Dexp [- (1+i) λ z '] (19)
In formula, the multiple constant D=D of boundary layer earth's surface1+i D2, dimensionless group ξ shown in introduction-type (20) and with dimension ginseng
Number λ, can finally derive the analytic expression of earth's surface wind friction velocity, as shown in formula (21)：
D1And D2It can be calculated as follows：
In formula, CdFor resistance coefficient；kmFor dynamic viscosity, 100m is taken2/s；K is Karman constants, takes 0.4；Average roughness
Cell height h=Az0 0.86, survey to obtain A=11.4；Zero-plane displacement d=0.75h；z10It is set in average roughness unit h high
At 10m；z0To consider that landform and roughness of ground surface influence " the equivalent roughness length " introduced；
(4) calculation process
Yan Meng typhoon wind-field models calculate earth's surface wind speed flow be：By formula (15) first in two-dimentional polar coordinates
Calculate gradient velocity, then take gradient velocity as the initial value of earth's surface wind speed, substitute into successively analytic formula (22), (20) and
(21) earth's surface wind friction velocity is tried to achieve, new earth's surface wind speed is obtained by gradient velocity and the superposition of earth's surface wind friction velocity, by repeatedly changing
Generation, until convergence；
(5) typhoon Its Extreme Value Wind Prediction and calamity source are assessed
Obtained by numerical simulation after typhoon Maximum wind speed sequence, it is necessary to be entered with extreme value probability Distribution Model to the sequence
Row fitting, and then predict return period Maximum wind speed.Conventional extreme value probability distribution have extremum I distributing (i.e. Gumbel distributions),
Extreme value II types are distributed (i.e. Fr é chet distributions) and the distribution of extreme value type III., should be preferred when the typhoon sample of simulation is enough
Experience is distributed.
Further, first the longitude and latitude of subsequent point in Tropical Cyclone Route is judged before the 5th step, when simulation point
The 5th step is carried out when being less than 250km away from boiling pot beeline, when simulation point is big away from boiling pot beeline
Judge whether tropical cyclone travel path meets end condition when 250km, meet end condition and then terminate, be unsatisfactory for then after
Continuous second step.
Beneficial effect：A kind of tropical cyclone complete trails mould based on whole northwest Pacific marine site provided by the present invention
Plan method can overcome the problem of regional area history tropical cyclone sample is not enough, to the torrid zone in whole northwest Pacific region
Cyclone generation, travel path, direct of travel, ocean surface strength development and log in strength retrogression and carry out stochastic simulation, generation is a large amount of
Meet the Tropical Cyclone Route and intensity chance event sample set of historical sample feature, Area In The Coast of Southeast China is carried out accordingly
Typhoon disaster risk quantifies the assessment that becomes more meticulous, and more accurate reliable result will be obtained, so as to efficiently solve partial zones
The problem of domain historical sample is not enough, is that the assessment that becomes more meticulous that quantifies of calamity source is laid a good foundation.This method computational efficiency is high,
Extend to other regions and carry out hurricane disaster risk-assessment.
Brief description of the drawings
Fig. 1 is techniqueflow chart of the invention.
Fig. 2 is history tropical cyclone year frequency Annual variations figure.
Fig. 3 is history tropical cyclone year frequency probability distribution graph.
Fig. 4 is history tropical cyclone starting point spatial distribution map.
Fig. 5 a are traveling model regression coefficient a1Spatial distribution map：(left side) westwards direction；(right side) direction eastwards.
Fig. 5 b are traveling model regression coefficient a2Spatial distribution map：(left side) westwards direction；(right side) direction eastwards.
Fig. 5 c are traveling model regression coefficient a3Spatial distribution map：(left side) westwards direction；(right side) direction eastwards.
Fig. 5 d are traveling model regression coefficient εvSpatial distribution map：(left side) westwards direction；(right side) direction eastwards.
Fig. 6 a are compared for the CMA historical paths in the range of influence Zhejiang Province coastal waters 100km with simulaed path.
Fig. 6 b are compared for the CMA historical paths in the range of influence Fujian Province coastal waters 100km with simulaed path.
Fig. 6 c are compared for the CMA historical paths in the range of influence Guangdong Province coastal waters 100km with simulaed path.
Fig. 7 is the spatial distribution map of seashore website.
Fig. 8 a are that Annual occurence rate of the CMA historical paths with simulaed path in each website is contrasted.
Fig. 8 b are that direction of the CMA historical paths with simulaed path in each website is contrasted.
Fig. 8 c are that translational speed of the CMA historical paths with simulaed path in each website is contrasted.
Fig. 8 d are that central gas pressure difference of the CMA historical paths with simulaed path in each website is contrasted.
Fig. 9 is the schematic diagram that wind-field model is activated during tropical cyclone complete trails is simulated.
Figure 10 is Shenzhen area typhoon year Maximum wind speed sequence.
Figure 11 is Shenzhen area typhoon year Maximum wind speed experience distribution map.
Embodiment
The present invention is further described with reference to specific embodiment, but does not limit the invention to these
Embodiment.One skilled in the art would recognize that present invention encompasses potentially included in Claims scope
All alternatives, improvement project and equivalents.
Referring to Fig. 1, a kind of tropical cyclone complete trails analogy method assessed towards calamity source, its specific steps includes：
The first step, it is established that initial point model, including the year frequency of sampling generation simulation tropical cyclone are originated with generation
Point information；It is specific that Estimating The Model Coefficients, and the tropical gas of generation simulation of sampling are carried out to year frequency using negative binomial distribution
The year frequency of rotation.According to the history tropical cyclone year frequency data characteristicses in northwest Pacific region, year occurs secondary
Number carries out Estimating The Model Coefficients, and the year frequency for generation simulation tropical cyclone of sampling.At present mainly have negative binomial distribution and
Two kinds of models of Poisson distribution are fitted the year frequency probability distribution of tropical cyclone.Georgiou is to the Gulf of Mexico and great Xi
The typhoon that foreign seashore is met with is studied, and compares the plan of negative binomial distribution and Poisson distribution to typhoon Annual occurence rate model
Conjunction degree, finds the incidence for the typhoon sequence that negative binomial distribution can be preferably on analog sea, and Poisson distribution can be more preferably
The incidence for the typhoon sequence that simulation bank occurs, because the mobile route climate parameter influence of typhoon is larger,
And the generation of typhoon is not affected by these factors.Therefore, in complete trails simulation, occur originating from the typhoon year on ocean surface
Number of times is preferably simulated with negative binomial distribution.
Tropical cyclone start point information based on history calculates the information needed for complete trails simulation：Translational speed, direction,
Ocean surface temperature, the relative intensity of position, and then each start point information for simulating typhoon is determined by random sampling.
Second step, sets up traveling model, simulates the translational speed of tropical cyclone and towards forming Tropical Cyclone Route；Adopt
With the translational speed and direction of Vickery paths forecast of regression model subsequent point：
V is translational speed, △ lnv=lnv in formulai+1-lnvi；θ is direction, △ θ=θi+1-θi；ψ latitudes；λ longitudes； εv
And εθTo meet the zero-mean Disturbance of normal distribution；Regression coefficient ai, biIt is only relevant with geographic area, northwest is peaceful
Oceanic province domain is divided into some grids, collects the history Tropical Cyclone Route information in each grid, and distinguish direction eastwards and to
Western direction, coefficient ai, biIt can be obtained by the history tropical cyclone information regression analysis of each grid.
3rd step, sets up strength model, including ocean surface strength development model and land Strength degradation model, and according to heat
Longitude and latitude with subsequent point in trajectory of cyclone selects corresponding strength model, specifically to the warp of subsequent point in Tropical Cyclone Route
Latitude is judged, if subsequent point is to be located at land, selects land Strength degradation model, if subsequent point is to be located at ocean
Face, then select ocean surface strength development model.
Consider the such environmental effects such as ocean surface temperature, Stratosphere Temperature, relative humidity, central pressure is converted to
Relative intensity.Strength development model in ocean surface predicts the relative intensity of subsequent point on ocean surface according to ocean surface intensity regression model, from
And determine central pressure：
I is relative intensity in formula；T is ocean surface temperature；εITo meet the zero-mean Disturbance of normal distribution, coefficient ci
It can be obtained by the history tropical cyclone information regression analysis of each grid.
Consider and log in the influence of the factors such as duration, tropical cyclone intensity size and roughness of ground surface, land is strong
Degree attenuation model is to set up to log in intensity regression model, the strength retrogression after simulation Tropical Cyclone Landing：
△ p (t)=△ p0exp(-mt) (3)
△ p in formula0Central gas pressure difference during to log in；△ p (t) are the central gas pressure difference after logging in t hours；M=m0+
m1△p0+εm, Coefficient m0、m1With Disturbance εmRegression analysis can be changed by the draught head of history Landing Tropical Cyclone to obtain
Arrive.
4th step, path simulation product test is counted to the Tropical Cyclone Route and intensity large sample generated at random
Product test and Statistical Analysis；It is path and intensity and the history for contrasting stochastic simulation that specific analog result, which is examined,
Difference between tropical cyclone data, quantitatively portrays the precision of analog result.
Statistical Analysis is that coastal area of southeastern China coastline is divided into some seashore websites, then counts each sea
It is being simulated in the range of bank point 250km and history in the average annual frequency of tropical cyclone, translational speed, direction and central gas pressure difference
Result difference, can reflect to a certain extent tropical cyclone complete trails simulation spatial distribution effect.
5th step, sets up Typhoon Wind Field engineering model and boundary layer model, includes the demarcation of wind-field model key parameter,
Calculating simulation point typhoon wind speed, carries out typhoon risk Disaster Assessment.Before this will be first to subsequent point in Tropical Cyclone Route
Longitude and latitude is judged, the 5th step is carried out when simulation point is less than 250km away from boiling pot beeline, when simulation point
Judge whether tropical cyclone travel path meets end condition when being more than 250km away from boiling pot beeline, meet eventually
Only condition then terminates, and is unsatisfactory for, and continues second step.
For entering typhoon track and intensity sample in the range of simulation point 250km, using Yan Meng wind-field models
The typhoon wind speed of calculating simulation point, is comprised the following steps that：
(1) demarcation of typhoon wind-field model key parameter
Using Vickery empirical models estimation maximum wind speed radius RmaxWith Holland air pressure sectional parameters B：
Draught head centered on △ p in formula；ψ is latitude；fc=2 × 7.273 × 10-5sinψ；And εBTo meet normal state
The zero-mean Disturbance of distribution；
(2) pressure model is set up
Using Holland pressure models：
P=p0+△pexp[-(Rmax/r)B] (6)
In formula, it away from center of typhoon radial distance is sea level pressure at r that P, which is,；RmaxFor maximum wind speed radius；B is gas
Press sectional parameter；
According to formula (6), barometric gradient expression formula is：
(3) equilibrium establishment equation
Navier-Stokes equations under the conditions of neutral atmosphere are：
In formula, V is the movement velocity of air micelle, and V is considered as gradient velocity V by Yan Meng wind-field modelsgRubbed with earth's surface
Wipe wind speed V ' two parts vector superposed, i.e. V=Vg+V’；F is Coriolis parameters；F is boundary layer friction power；
Due to radial direction blast gradient in PBL of typhoon with height change very little, then ignore friction more than boundary layer
Power, formula (8) can be decomposed into gradient layer and boundary layer two parts, respectively such as formula (9) and formula (10)：
With reference toAndFormula (9) and formula (10) can abbreviation be further：
In the two-dimentional polar coordinates moved with center of typhoon, breakdown (9) is obtained radially and tangentially：
In formula, VθgAnd VrgIt is gradient velocity tangentially and radially respectively；cr=-VTCos (θ-β '), cθ=-VT sin(θ-
β′)；ρ is atmospheric density, takes 1.2kg/m3；θ is due east direction and simulation point and center of typhoon line angle, to revolve counterclockwise
Switch to just；β ' is the angle in due east direction and Typhoon Tracks direction, using rotate counterclockwise as just；
In upper atmosphere environment, it is contemplated that VrgFar smaller than Vθg, ignore first two in formula (13), can obtain
Vθg；Due to VrgIt is worth very little, approximately takes 0 can still meet the accuracy of wind speed simulation, thus, develop and the parsing of gradient velocity
Formula, is shown below：
In near-earth boundary layer, the tangentially and radially component V ' of earth's surface wind friction velocityθAnd V 'rLess than corresponding gradient velocity
Component, therefore these components can be assumed that the first derivative of similarly less than corresponding gradient velocity component to θ first derivative；In
It is that formula (10) can make linearisation and decompose, and be shown below：
The boundary condition of upper atmosphere and adjacent ground surface is respectively formula (17) and formula (18)：
V′|z′→∞=0 (17)
Calculate starting point to be taken as at z=h+10 i.e. z '=0, it is considered to which after boundary condition, formula (16) can be solved to：
V "=Dexp [- (1+i) λ z '] (19)
In formula, the multiple constant D=D of boundary layer earth's surface1+i D2, dimensionless group ξ shown in introduction-type (20) and with dimension ginseng
Number λ, can finally derive the analytic expression of earth's surface wind friction velocity, as shown in formula (21)：
D1And D2It can be calculated as follows：
In formula, CdFor resistance coefficient；kmFor dynamic viscosity, 100m is taken2/s；K is Karman constants, takes 0.4；Average roughness
Cell height h=Az0 0.86, survey to obtain A=11.4；Zero-plane displacement d=0.75h；z10It is set in average roughness unit h high
At 10m；z0To consider that landform and roughness of ground surface influence " the equivalent roughness length " introduced；
(4) calculation process
Yan Meng typhoon wind-field models calculate earth's surface wind speed flow be：By formula (15) first in two-dimentional polar coordinates
Calculate gradient velocity, then take gradient velocity as the initial value of earth's surface wind speed, substitute into successively analytic formula (22), (20) and
(21) earth's surface wind friction velocity is tried to achieve, new earth's surface wind speed is obtained by gradient velocity and the superposition of earth's surface wind friction velocity, by repeatedly changing
Generation, until convergence；
(5) typhoon Its Extreme Value Wind Prediction and calamity source are assessed
Obtained by numerical simulation after typhoon Maximum wind speed sequence, it is necessary to be entered with extreme value probability Distribution Model to the sequence
Row fitting, and then predict return period Maximum wind speed.Conventional extreme value probability distribution have extremum I distributing (i.e. Gumbel distributions),
Extreme value II types are distributed (i.e. Fr é chet distributions) and the distribution of extreme value type III., should be preferred when the typhoon sample of simulation is enough
Experience is distributed.
In order to more clearly from illustrate above-mentioned steps, now introduced by taking the typhoon disaster risk assessment of Shenzhen area as an example
The embodiment of this patent, it is specific as follows：
(1) starting point model is set up
Fig. 2 show -2015 years 1949 history heat for counting and obtaining based on CMA tropical cyclone optimal paths data set
Band cyclone year frequency Annual variations figure.Average annual frequency of the tropical cyclone in northwest Pacific region is 32.6, just
Root 6.78.As seen from Figure 2, in northwest Pacific region, the tropical cyclone year frequency is presented necessarily before 1970s
Ascendant trend, and downward trend is obvious after the seventies.
Fig. 3 show the year frequency probability distribution graph for being fitted and obtaining using negative binomial distribution.Obtained based on fitting
Distributed model parameter, can obtain the year frequency for simulating typhoon by random sampling.
Fig. 4 is the spatial distribution map of history tropical cyclone starting point, it can be seen that the tropical gas in northwest Pacific region
Rotation is mainly generated between 5 degree to 30 degree of north latitude, and about 17% tropical cyclone is created on the South Sea of China.Based on history
Start point information calculate complete trails simulation needed for information：It is translational speed, direction, the ocean surface temperature of position, relatively strong
Degree etc., and then each start point information for simulating typhoon can be determined by random sampling.
(2) set up and advance and strength model
Using Vickery traveling model and strength model simulate the translational speed of tropical cyclone subsequent point, direction and in
Motive pressure, model regression coefficient ai, bi, ciIt is only relevant with geographic area.Northwest Pacific region division is spent into net into 2 degree * 2
Lattice, wherein in 105E-130E, 15N-35N region divisions spend grid into 1 degree * 1.Based on CMA tropical cyclone optimal path data
Collection collects the history Tropical Cyclone Route information in each grid, and distinguishes direction eastwards and westwards direction, coefficient ai, bi, ci
It can be obtained by the history tropical cyclone information regression analysis in each grid.Fig. 5 (a-d) is respectively model regression coefficient
a1、a2、a3、εvSpatial distribution map.
Simulate the Tropical Cyclone Route random sample of 67 years, with CMA 67 years history Tropical Cyclone Routes (1949-
2015) contrasted, Fig. 6 (a-c) is respectively to influence Zhejiang Province, Fujian Province, the CMA in the range of the 100km of Guangdong Province coastal waters to go through
Compared figure with simulaed path spatial trend in history path.It can qualitatively judge simulaed path with CMA historical paths in sky from figure
Between in trend substantially close to.As latitude increases, the direction of tropical cyclone is gradually converted into direction eastwards from direction westwards.
(3) path simulation product test
Coastal area of southeastern China coastline is divided into 25 websites, adjacent sites spacing 100km, Fig. 7 compile for seashore website
Number S1-S25 spatial distribution map.The Tropical Cyclone Route random sample of 100000 years is simulated, Fig. 8 (a-d) show 25
The key parameter contrast of CMA historical paths and simulaed path in the range of seashore website 250km.As can be seen that simulaed path exists
Typhoon key parameter in each site-bound of coastline and the key parameter corresponding to CMA historical path coincide substantially, can
To verify the validity of tropical cyclone complete trails analogy method.
(4) Yan Meng typhoon wind-field models are set up
Fig. 9 show the schematic diagram that typhoon wind-field model is activated in the simulation of tropical cyclone complete trails.It is assumed that when certain torrid zone
When beeline of the cyclone center away from simulation point is less than 250km, simulation point is activated wind field by this tropical cyclones influence
Model is used for risk Disaster Assessment.Figure 10 is that obtained Shenzhen area typhoon year is calculated using Yan Meng typhoon wind-field models
Maximum wind speed sequence, Figure 11 is corresponding probability distribution graph, because typhoon Maximum wind speed sample is enough, so using experience
Distribution.Table 1 gives the typhoon Maximum wind speed of Shenzhen area under 10/50/100 year return period, and corresponding with Chinese load code
Design wind speed contrasted.As can be seen from Table 1, under 10 years and 50 year return period, according to setting that load code is provided
Meter wind speed is partial to risk.
Typhoon Maximum wind speed under the Shenzhen area different reoccurrence of table 1
Claims (10)
1. a kind of tropical cyclone complete trails analogy method assessed towards calamity source, its specific steps include：
The first step, it is established that initial point model, including the year frequency for generation simulation tropical cyclone of sampling are believed with generation starting point
Breath；
Second step, sets up traveling model, simulates the translational speed of tropical cyclone and towards forming Tropical Cyclone Route；
3rd step, sets up strength model, including ocean surface strength development model and land Strength degradation model, and according to tropical cyclone
The longitude and latitude of subsequent point selects corresponding strength model in path；
4th step, path simulation product test carries out statistical result to the Tropical Cyclone Route and intensity large sample generated at random
Examine and Statistical Analysis；
5th step, sets up Typhoon Wind Field engineering model and boundary layer model, includes the demarcation of wind-field model key parameter, calculates mould
Intend point typhoon wind speed, carry out typhoon risk Disaster Assessment.
2. a kind of tropical cyclone complete trails analogy method assessed towards calamity source according to claim 1, its feature
It is：Estimating The Model Coefficients, and the tropical gas of generation simulation of sampling are carried out to year frequency using negative binomial distribution in the first step
The year frequency of rotation；Tropical cyclone start point information based on history calculates the information needed for complete trails simulation：Translational speed,
Direction, ocean surface temperature, the relative intensity of position, and then determine that the starting point of each simulation typhoon is believed by random sampling
Breath.
3. a kind of tropical cyclone complete trails analogy method assessed towards calamity source according to claim 1, its feature
It is：The translational speed and direction of Vickery paths forecast of regression model subsequent point are used in second step：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>&Delta;</mi>
<mi>ln</mi>
<mi> </mi>
<mi>v</mi>
<mo>=</mo>
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<mi>a</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>2</mn>
</msub>
<mi>ln</mi>
<mi> </mi>
<msub>
<mi>v</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>3</mn>
</msub>
<msub>
<mi>&theta;</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>4</mn>
</msub>
<mi>&psi;</mi>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>5</mn>
</msub>
<mi>&lambda;</mi>
<mo>+</mo>
<msub>
<mi>&epsiv;</mi>
<mi>v</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>&Delta;</mi>
<mi>&theta;</mi>
<mo>=</mo>
<msub>
<mi>b</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mi>b</mi>
<mn>2</mn>
</msub>
<msub>
<mi>v</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<msub>
<mi>b</mi>
<mn>3</mn>
</msub>
<msub>
<mi>&theta;</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<msub>
<mi>b</mi>
<mn>4</mn>
</msub>
<mi>&psi;</mi>
<mo>+</mo>
<msub>
<mi>b</mi>
<mn>5</mn>
</msub>
<mi>&lambda;</mi>
<mo>+</mo>
<msub>
<mi>b</mi>
<mn>6</mn>
</msub>
<msub>
<mi>&theta;</mi>
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</mrow>
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<msub>
<mi>&epsiv;</mi>
<mi>&theta;</mi>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
V is translational speed, △ lnv=lnv in formulai+1-lnvi；θ is direction, △ θ=θi+1-θi；ψ latitudes；λ longitudes；εvAnd εθFor
Meet the zero-mean Disturbance of normal distribution；Regression coefficient ai, biIt is only relevant with geographic area, by northwest Pacific region
It is divided into some grids, collects the history Tropical Cyclone Route information in each grid, and distinguishes direction eastwards and westwards direction,
Coefficient ai, biIt can be obtained by the history tropical cyclone information regression analysis of each grid.
4. a kind of tropical cyclone complete trails analogy method assessed towards calamity source according to claim 1, its feature
It is：The longitude and latitude of subsequent point in Tropical Cyclone Route is judged in 3rd step, if subsequent point is to be located at land, selected
Land Strength degradation model is selected, if subsequent point is to be located at ocean surface, ocean surface strength development model is selected.
5. a kind of tropical cyclone complete trails analogy method assessed towards calamity source according to claim 4, its feature
It is：Ocean surface strength development model is that according to ocean surface intensity regression model, subsequent point is relatively strong on prediction ocean surface in 3rd step
Degree, so that it is determined that central pressure：
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<mi>c</mi>
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<mi>i</mi>
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</mrow>
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<mi>I</mi>
</msub>
<mo>-</mo>
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<mrow>
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</mrow>
</mrow>
I is relative intensity in formula；T is ocean surface temperature；εITo meet the zero-mean Disturbance of normal distribution, coefficient ciCan be with
Obtained by the history tropical cyclone information regression analysis of each grid.
6. a kind of tropical cyclone complete trails analogy method assessed towards calamity source according to claim 4, its feature
It is：Land Strength degradation model is to utilize the intensity logged in after intensity regression model, simulation Tropical Cyclone Landing in 3rd step
Decay：
△ p (t)=△ p0exp(-mt) (3)
△ p in formula0Central gas pressure difference during to log in；△ p (t) are the central gas pressure difference after logging in t hours；M=m0+m1△p0
+εm, Coefficient m0、m1With Disturbance εmRegression analysis can be changed by the draught head of history Landing Tropical Cyclone to obtain.
7. a kind of tropical cyclone complete trails analogy method assessed towards calamity source according to claim 1, its feature
It is：In 4th step analog result examine be contrast stochastic simulation path and intensity and history tropical cyclone data between difference
It is different, quantitatively portray the precision of analog result.
8. a kind of tropical cyclone complete trails analogy method assessed towards calamity source according to claim 1, its feature
It is：Statistical Analysis in 4th step is that coastal area of southeastern China coastline is divided into some seashore websites, then counts every
It is being simulated in the range of one seashore point 250km and history in the average annual frequency of tropical cyclone, translational speed, direction and central gas
The result difference of pressure difference, can reflect the spatial distribution effect of tropical cyclone complete trails simulation to a certain extent.
9. a kind of tropical cyclone complete trails analogy method assessed towards calamity source according to one of claim 1~8,
It is characterized in that：For entering typhoon track and intensity sample in the range of simulation point 250km in 5th step, using Yan
The typhoon wind speed of Meng wind-field models calculating simulation point, is comprised the following steps that：
(1) demarcation of typhoon wind-field model key parameter
Using Vickery empirical models estimation maximum wind speed radius RmaxWith Holland air pressure sectional parameters B：
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<msub>
<mi>R</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
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<mn>3.015</mn>
<mo>-</mo>
<mn>6.291</mn>
<mo>&times;</mo>
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<mn>5</mn>
</mrow>
</msup>
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<mi>&Delta;p</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mn>0.0337</mn>
<mi>&psi;</mi>
<mo>+</mo>
<msub>
<mi>&epsiv;</mi>
<mrow>
<msub>
<mi>lnR</mi>
<mi>max</mi>
</msub>
</mrow>
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<mo>-</mo>
<mo>-</mo>
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<mo>(</mo>
<mn>4</mn>
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</mrow>
</mrow>
<mrow>
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<mn>1.833</mn>
<mo>-</mo>
<mn>0.326</mn>
<msqrt>
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<msub>
<mi>f</mi>
<mi>c</mi>
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</msub>
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</msub>
<mo>-</mo>
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<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
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</mrow>
</mrow>
Draught head centered on △ p in formula；ψ is latitude；fc=2 × 7.273 × 10-5sinψ；εlnRmaxAnd εBTo meet normal distribution
Zero-mean Disturbance；
(2) pressure model is set up
Using Holland pressure models：
P=p0+△pexp[-(Rmax/r)B] (6)
In formula, it away from center of typhoon radial distance is sea level pressure at r that P, which is,；RmaxFor maximum wind speed radius；B is air pressure section
Parameter；
According to formula (6), barometric gradient expression formula is：
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<mrow>
<mo>&part;</mo>
<mi>p</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>r</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
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<mi>&Delta;</mi>
<mi>p</mi>
<mo>&CenterDot;</mo>
<mi>B</mi>
</mrow>
<mi>r</mi>
</mfrac>
<msup>
<mrow>
<mo>(</mo>
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<mi>R</mi>
<mi>max</mi>
</msub>
<mi>r</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mi>B</mi>
</msup>
<mi>exp</mi>
<mo>&lsqb;</mo>
<mo>-</mo>
<msup>
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<mo>(</mo>
<msub>
<mi>R</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
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<mi>r</mi>
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</mrow>
<mi>B</mi>
</msup>
<mo>&rsqb;</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
(3) equilibrium establishment equation
Navier-Stokes equations under the conditions of neutral atmosphere are：
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>V</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>t</mi>
</mrow>
</mfrac>
<mo>+</mo>
<mi>V</mi>
<mo>&CenterDot;</mo>
<mo>&dtri;</mo>
<mi>V</mi>
<mo>=</mo>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mi>&rho;</mi>
</mfrac>
<mo>&dtri;</mo>
<mi>p</mi>
<mo>-</mo>
<mi>f</mi>
<mi>k</mi>
<mo>&times;</mo>
<mi>V</mi>
<mo>+</mo>
<mi>F</mi>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, V is the movement velocity of air micelle, and V is considered as gradient velocity V by Yan Meng wind-field modelsgWith earth's surface wind friction velocity
V ' two parts are vector superposed, i.e. V=Vg+V’；F is Coriolis parameters；F is boundary layer friction power；
Due to radial direction blast gradient in PBL of typhoon with height change very little, then ignore frictional force more than boundary layer, formula
(8) gradient layer and boundary layer two parts can be decomposed into, respectively such as formula (9) and formula (10)：
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>V</mi>
<mi>g</mi>
</msub>
</mrow>
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<mo>&part;</mo>
<mi>t</mi>
</mrow>
</mfrac>
<mo>+</mo>
<msub>
<mi>V</mi>
<mi>g</mi>
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<mo>&dtri;</mo>
<msub>
<mi>V</mi>
<mi>g</mi>
</msub>
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<mfrac>
<mn>1</mn>
<mi>&rho;</mi>
</mfrac>
<mo>&dtri;</mo>
<mi>p</mi>
<mo>-</mo>
<mi>f</mi>
<mi>k</mi>
<mo>&times;</mo>
<msub>
<mi>V</mi>
<mi>g</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
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<mo>)</mo>
</mrow>
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<mi>V</mi>
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</msup>
</mrow>
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</msup>
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</msup>
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<mi>g</mi>
</msub>
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<mi>V</mi>
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<mo>&dtri;</mo>
<msup>
<mi>V</mi>
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</msup>
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<mi>f</mi>
<mi>k</mi>
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<mi>F</mi>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
With reference toAndFormula (9) and formula (10) can abbreviation be further：
<mrow>
<mo>(</mo>
<msub>
<mi>V</mi>
<mi>g</mi>
</msub>
<mo>-</mo>
<mi>c</mi>
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<mo>&dtri;</mo>
<msub>
<mi>V</mi>
<mi>g</mi>
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<mfrac>
<mn>1</mn>
<mi>&rho;</mi>
</mfrac>
<mo>&dtri;</mo>
<mi>p</mi>
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<mi>f</mi>
<mi>k</mi>
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<msub>
<mi>V</mi>
<mi>g</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
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<mrow>
<mo>(</mo>
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<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msup>
<mi>V</mi>
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</msup>
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<mo>&dtri;</mo>
<msup>
<mi>V</mi>
<mo>&prime;</mo>
</msup>
<mo>+</mo>
<msup>
<mi>V</mi>
<mo>&prime;</mo>
</msup>
<mo>&CenterDot;</mo>
<mo>&dtri;</mo>
<msub>
<mi>V</mi>
<mi>g</mi>
</msub>
<mo>+</mo>
<mi>V</mi>
<mo>&CenterDot;</mo>
<mo>&dtri;</mo>
<msup>
<mi>V</mi>
<mo>&prime;</mo>
</msup>
<mo>=</mo>
<mo>-</mo>
<mi>f</mi>
<mi>k</mi>
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<msup>
<mi>V</mi>
<mo>&prime;</mo>
</msup>
<mo>+</mo>
<mi>F</mi>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
In the two-dimentional polar coordinates moved with center of typhoon, breakdown (9) is obtained radially and tangentially：
<mrow>
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<msub>
<mi>V</mi>
<mrow>
<mi>r</mi>
<mi>g</mi>
</mrow>
</msub>
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<mi>c</mi>
<mi>r</mi>
</msub>
<mo>)</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>r</mi>
<mi>g</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>r</mi>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mi>&theta;</mi>
<mi>g</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>c</mi>
<mi>&theta;</mi>
</msub>
</mrow>
<mi>r</mi>
</mfrac>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>r</mi>
<mi>g</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>&theta;</mi>
</mrow>
</mfrac>
<mo>-</mo>
<mfrac>
<msubsup>
<mi>V</mi>
<mrow>
<mi>&theta;</mi>
<mi>g</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mi>r</mi>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mi>&theta;</mi>
<mi>g</mi>
</mrow>
</msub>
<msub>
<mi>c</mi>
<mi>&theta;</mi>
</msub>
</mrow>
<mi>r</mi>
</mfrac>
<mo>=</mo>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mi>&rho;</mi>
</mfrac>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>p</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>r</mi>
</mrow>
</mfrac>
<mo>+</mo>
<msub>
<mi>fV</mi>
<mrow>
<mi>&theta;</mi>
<mi>g</mi>
</mrow>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mo>(</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>r</mi>
<mi>g</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>c</mi>
<mi>r</mi>
</msub>
<mo>)</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>&theta;</mi>
<mi>g</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>r</mi>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mi>&theta;</mi>
<mi>g</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>c</mi>
<mi>&theta;</mi>
</msub>
</mrow>
<mi>r</mi>
</mfrac>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>&theta;</mi>
<mi>g</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>&theta;</mi>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mi>&theta;</mi>
<mi>g</mi>
</mrow>
</msub>
<msub>
<mi>V</mi>
<mrow>
<mi>r</mi>
<mi>g</mi>
</mrow>
</msub>
</mrow>
<mi>r</mi>
</mfrac>
<mo>-</mo>
<mfrac>
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mi>r</mi>
<mi>g</mi>
</mrow>
</msub>
<msub>
<mi>c</mi>
<mi>&theta;</mi>
</msub>
</mrow>
<mi>r</mi>
</mfrac>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>fV</mi>
<mrow>
<mi>r</mi>
<mi>g</mi>
</mrow>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>14</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, VθgAnd VrgIt is gradient velocity tangentially and radially respectively；cr=-VTCos (θ-β '), cθ=-VTsin(θ-β′)；ρ
It is atmospheric density, takes 1.2kg/m3；θ is due east direction and simulation point and center of typhoon line angle, using rotate counterclockwise as just；
β ' is the angle in due east direction and Typhoon Tracks direction, using rotate counterclockwise as just；
In upper atmosphere environment, it is contemplated that VrgFar smaller than Vθg, ignore first two in formula (13), V can be obtainedθg；Due to
VrgIt is worth very little, approximately takes 0 can still meet the accuracy of wind speed simulation, thus, developing the analytic expression of gradient velocity, such as following formula institute
Show：
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mi>&theta;</mi>
<mi>g</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>c</mi>
<mi>&theta;</mi>
</msub>
<mo>-</mo>
<mi>f</mi>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>c</mi>
<mi>&theta;</mi>
</msub>
<mo>-</mo>
<mi>f</mi>
<mi>r</mi>
</mrow>
<mn>2</mn>
</mfrac>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<mfrac>
<mi>r</mi>
<mi>&rho;</mi>
</mfrac>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>p</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>r</mi>
</mrow>
</mfrac>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>15</mn>
<mo>)</mo>
</mrow>
</mrow>
Vrg=0
In near-earth boundary layer, the tangentially and radially component V ' and V ' of earth's surface wind friction velocityrLess than corresponding gradient velocity component,
Therefore these components can be assumed that the first derivative of similarly less than corresponding gradient velocity component to θ first derivative；Then, formula
(10) linearisation can be made to decompose, be shown below：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mn>2</mn>
<msub>
<mi>V</mi>
<mrow>
<mi>&theta;</mi>
<mi>g</mi>
</mrow>
</msub>
</mrow>
<mi>r</mi>
</mfrac>
<mo>+</mo>
<mi>f</mi>
<mo>)</mo>
</mrow>
<msubsup>
<mi>V</mi>
<mi>&theta;</mi>
<mo>&prime;</mo>
</msubsup>
<mo>=</mo>
<msub>
<mi>k</mi>
<mi>m</mi>
</msub>
<mfrac>
<mrow>
<msup>
<mo>&part;</mo>
<mn>2</mn>
</msup>
<msubsup>
<mi>V</mi>
<mi>r</mi>
<mo>&prime;</mo>
</msubsup>
</mrow>
<mrow>
<mo>&part;</mo>
<msup>
<mi>z</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>&theta;</mi>
<mi>g</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>r</mi>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<msub>
<mi>V</mi>
<mrow>
<mi>&theta;</mi>
<mi>g</mi>
</mrow>
</msub>
<mi>r</mi>
</mfrac>
<mo>+</mo>
<mi>f</mi>
<mo>)</mo>
<msubsup>
<mi>V</mi>
<mi>r</mi>
<mo>&prime;</mo>
</msubsup>
<mo>=</mo>
<msub>
<mi>k</mi>
<mi>m</mi>
</msub>
<mfrac>
<mrow>
<msup>
<mo>&part;</mo>
<mn>2</mn>
</msup>
<msubsup>
<mi>V</mi>
<mi>&theta;</mi>
<mo>&prime;</mo>
</msubsup>
</mrow>
<mrow>
<mo>&part;</mo>
<msup>
<mi>z</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>16</mn>
<mo>)</mo>
</mrow>
</mrow>
The boundary condition of upper atmosphere and adjacent ground surface is respectively formula (17) and formula (18)：
V′|z′→∞=0 (17)
<mrow>
<msub>
<mi>&rho;k</mi>
<mi>m</mi>
</msub>
<mfrac>
<mrow>
<mo>&part;</mo>
<msup>
<mi>V</mi>
<mo>&prime;</mo>
</msup>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>z</mi>
</mrow>
</mfrac>
<msub>
<mo>|</mo>
<mrow>
<msup>
<mi>z</mi>
<mo>&prime;</mo>
</msup>
<mo>=</mo>
<mn>0</mn>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>&rho;C</mi>
<mi>d</mi>
</msub>
<mo>|</mo>
<msub>
<mi>V</mi>
<mi>s</mi>
</msub>
<mo>|</mo>
<msub>
<mi>V</mi>
<mi>s</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>18</mn>
<mo>)</mo>
</mrow>
</mrow>
Calculate starting point to be taken as at z=h+10 i.e. z '=0, it is considered to which after boundary condition, formula (16) can be solved to：
V "=Dexp [- (1+i) λ z '] (19)
In formula, the multiple constant D=D of boundary layer earth's surface1+i D 2, dimensionless group ξ shown in introduction-type (20) and with dimensional parameters
λ, can finally derive the analytic expression of earth's surface wind friction velocity, as shown in formula (21)：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<mi>&xi;</mi>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>&theta;</mi>
<mi>g</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>r</mi>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<msub>
<mi>V</mi>
<mrow>
<mi>&theta;</mi>
<mi>g</mi>
</mrow>
</msub>
<mi>r</mi>
</mfrac>
<mo>+</mo>
<mi>f</mi>
<mo>)</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
<mo>/</mo>
<msup>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mfrac>
<msub>
<mi>V</mi>
<mrow>
<mi>&theta;</mi>
<mi>g</mi>
</mrow>
</msub>
<mi>r</mi>
</mfrac>
<mo>+</mo>
<mi>f</mi>
<mo>)</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>&lambda;</mi>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>&theta;</mi>
<mi>g</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>r</mi>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<msub>
<mi>V</mi>
<mrow>
<mi>&theta;</mi>
<mi>g</mi>
</mrow>
</msub>
<mi>r</mi>
</mfrac>
<mo>+</mo>
<mi>f</mi>
<mo>)</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>4</mn>
</mrow>
</msup>
<msup>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mfrac>
<msub>
<mi>V</mi>
<mrow>
<mi>&theta;</mi>
<mi>g</mi>
</mrow>
</msub>
<mi>r</mi>
</mfrac>
<mo>+</mo>
<mi>f</mi>
<mo>)</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>4</mn>
</mrow>
</msup>
<mo>/</mo>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<msub>
<mi>k</mi>
<mi>m</mi>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>20</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>V</mi>
<mi>&theta;</mi>
<mo>&prime;</mo>
</msubsup>
<mo>=</mo>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<msup>
<mi>&lambda;z</mi>
<mo>&prime;</mo>
</msup>
</mrow>
</msup>
<mrow>
<mo>&lsqb;</mo>
<mrow>
<msub>
<mi>D</mi>
<mn>1</mn>
</msub>
<mi>cos</mi>
<mrow>
<mo>(</mo>
<mrow>
<msup>
<mi>&lambda;z</mi>
<mo>&prime;</mo>
</msup>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>D</mi>
<mn>2</mn>
</msub>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<mrow>
<msup>
<mi>&lambda;z</mi>
<mo>&prime;</mo>
</msup>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>V</mi>
<mi>r</mi>
<mo>&prime;</mo>
</msubsup>
<mo>=</mo>
<mo>-</mo>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<msup>
<mi>&lambda;z</mi>
<mo>&prime;</mo>
</msup>
</mrow>
</msup>
<mi>&xi;</mi>
<mrow>
<mo>&lsqb;</mo>
<mrow>
<msub>
<mi>D</mi>
<mn>2</mn>
</msub>
<mi>cos</mi>
<mrow>
<mo>(</mo>
<mrow>
<msup>
<mi>&lambda;z</mi>
<mo>&prime;</mo>
</msup>
</mrow>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>D</mi>
<mn>1</mn>
</msub>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<mrow>
<msup>
<mi>&lambda;z</mi>
<mo>&prime;</mo>
</msup>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>21</mn>
<mo>)</mo>
</mrow>
</mrow>
3
D1And D2It can be calculated as follows：
<mrow>
<msub>
<mi>D</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<mo>-</mo>
<mfrac>
<mrow>
<mi>&chi;</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mi>&chi;</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>V</mi>
<mrow>
<mi>&theta;</mi>
<mi>g</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>&chi;V</mi>
<mrow>
<mi>r</mi>
<mi>g</mi>
</mrow>
</msub>
<mo>/</mo>
<mi>&xi;</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mi>&chi;</mi>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
</mrow>
<mrow>
<msub>
<mi>D</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>&chi;V</mi>
<mrow>
<mi>&theta;</mi>
<mi>g</mi>
</mrow>
</msub>
<mo>+</mo>
<mi>&chi;</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mi>&chi;</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>V</mi>
<mrow>
<mi>r</mi>
<mi>g</mi>
</mrow>
</msub>
<mo>/</mo>
<mi>&xi;</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mi>&chi;</mi>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>22</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>&chi;</mi>
<mo>=</mo>
<mfrac>
<msub>
<mi>C</mi>
<mi>d</mi>
</msub>
<mrow>
<msub>
<mi>k</mi>
<mi>m</mi>
</msub>
<mi>&lambda;</mi>
</mrow>
</mfrac>
<mo>|</mo>
<msub>
<mi>V</mi>
<mi>s</mi>
</msub>
<mo>|</mo>
<mo>=</mo>
<mfrac>
<msub>
<mi>C</mi>
<mi>d</mi>
</msub>
<mrow>
<msub>
<mi>k</mi>
<mi>m</mi>
</msub>
<mi>&lambda;</mi>
</mrow>
</mfrac>
<msqrt>
<mrow>
<msubsup>
<mi>V</mi>
<mrow>
<mi>&theta;</mi>
<mi>s</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>V</mi>
<mrow>
<mi>r</mi>
<mi>s</mi>
</mrow>
<mn>2</mn>
</msubsup>
</mrow>
</msqrt>
</mrow>
Cd=k2/{ln[(z10+h-d)/z0]}2
In formula, CdFor resistance coefficient；kmFor dynamic viscosity, 100m is taken2/s；K is Karman constants, takes 0.4；Average roughness unit
Height h=Az0 0.86, survey to obtain A=11.4；Zero-plane displacement d=0.75h；z10It is set at the high 10m of average roughness unit h；z0
To consider that landform and roughness of ground surface influence " the equivalent roughness length " introduced；
(4) calculation process
Yan Meng typhoon wind-field models calculate earth's surface wind speed flow be：Ladder is calculated by formula (15) first in two-dimentional polar coordinates
Wind speed is spent, then takes gradient velocity as the initial value of earth's surface wind speed, analytic formula (22), (20) and (21) is substituted into successively and is tried to achieve
Earth's surface wind friction velocity, obtains new earth's surface wind speed, by successive ignition, Zhi Daoshou by gradient velocity and the superposition of earth's surface wind friction velocity
Hold back；
(5) typhoon Its Extreme Value Wind Prediction and calamity source are assessed
Obtained by numerical simulation after typhoon Maximum wind speed sequence, it is necessary to be intended with extreme value probability Distribution Model the sequence
Close, and then predict return period Maximum wind speed.
10. a kind of tropical cyclone complete trails analogy method assessed towards calamity source according to claim 9, its feature
It is：First the longitude and latitude of subsequent point in Tropical Cyclone Route is judged before 5th step, when simulation point is away from tropical cyclone
Center beeline carries out the 5th step when being less than 250km, sentences when simulation point is more than 250km away from boiling pot beeline
Whether disconnected tropical cyclone travel path meets end condition, meets end condition and then terminates, be unsatisfactory for, continues second step.
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| CN108399507A (en) * | 2018-03-22 | 2018-08-14 | 中国气象局公共气象服务中心 | A kind of typhoon causes the appraisal procedure and device of calamity influence |
| CN108982904A (en) * | 2018-07-17 | 2018-12-11 | 中国人民解放军国防科技大学 | Typhoon Intensity Monitoring Method Based on MMV Fitting |
| CN110045439A (en) * | 2018-01-15 | 2019-07-23 | 钱维宏 | Numerical weather prediction model system based on atmospheric variable Transient Eddy equation group |
| CN110059423A (en) * | 2019-04-23 | 2019-07-26 | 中国人民解放军国防科技大学 | Tropical cyclone objective strength determination method based on multi-factor generalized linear model |
| CN110399625A (en) * | 2019-09-05 | 2019-11-01 | 重庆大学 | A kind of improved Typhoon Wind Field empirical model |
| WO2019222149A1 (en) * | 2018-05-16 | 2019-11-21 | University Of Hawaii | Systems and methods for determining maximum alert geography for a hazard |
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