CN116451507B - Typhoon track path simulation method based on non-uniform grid division - Google Patents

Typhoon track path simulation method based on non-uniform grid division Download PDF

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CN116451507B
CN116451507B CN202310692302.9A CN202310692302A CN116451507B CN 116451507 B CN116451507 B CN 116451507B CN 202310692302 A CN202310692302 A CN 202310692302A CN 116451507 B CN116451507 B CN 116451507B
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CN116451507A (en
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王乃玉
黄秀兵
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Zhejiang University ZJU
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Abstract

The invention discloses a typhoon track path simulation method based on non-uniform grid division, which comprises the following steps: s1, acquiring tropical cyclone data, and preprocessing the tropical cyclone data; s2, dividing a research area into non-uniform grids, wherein the non-uniform grids refer to grids with incomplete equal sizes; and step S3, simulating a typhoon track through an empirical full-path model based on the non-uniform grids divided in the step S2. According to the invention, a non-uniform grid division method is adopted, the region with dense typhoons is finely divided, the resolution of dividing grids is improved, and meanwhile, each grid can be ensured to have enough historical data for parameter fitting, so that the simulated typhoon track path is ensured to be more accurate and close to the actual typhoon track.

Description

Typhoon track path simulation method based on non-uniform grid division
Technical Field
The invention relates to the technical field of typhoon path simulation, in particular to a typhoon track path simulation method based on non-uniform grid division.
Background
Typhoon disasters are one of common natural disasters, and seriously threaten the life and property safety of coastal areas. Strong winds can destroy house buildings and public facilities, and heavy rainfall accompanied by typhoons can cause flooding and urban inland inundation. Knowing the trajectory of typhoons is very important to reduce the disaster loss of typhoons.
The Vickery et al propose an empirical full path as a common typhoon track simulation method, which divides a research area into uniform grids, wherein the uniform grids refer to dividing the research area into a plurality of grids with identical sizes, and carrying out linear fitting on historical track data in each grid to obtain linear equation parameters. And substituting equation parameters, and adopting a linear equation to simulate the typhoon traveling speed, the typhoon traveling direction and the typhoon central air pressure. However, the grid division resolution of the method is low, and each grid cannot be guaranteed to provide enough history number for linear fitting, so that the accuracy of the simulated typhoon track path is not high.
Disclosure of Invention
The invention provides a typhoon track path simulation method based on non-uniform grid division in order to overcome the defects of the technology.
The technical scheme adopted for overcoming the technical problems is as follows:
a typhoon track path simulation method based on non-uniform grid division comprises the following steps:
s1, acquiring tropical cyclone data, and preprocessing the tropical cyclone data;
s2, dividing a research area into non-uniform grids, wherein the non-uniform grids refer to grids with incomplete equal sizes;
and step S3, simulating a typhoon track through an empirical full-path model based on the non-uniform grids divided in the step S2.
Further, the step S1 specifically includes:
s1.1, downloading tropical cyclone data of a preset year from a public website;
and step S1.2, deleting cyclones with the period number smaller than or equal to 10 in the tropical cyclone data downloaded in the step S1.1, wherein the period interval is 6 hours.
Further, step S2 specifically includes:
step S2.1, setting the research area as；
Step S2.2, assumeDivided into->Regions of equal size->、/>、/>Wherein->Is an integer and->The value range of (2) is +.>；
Step S2.3, judging、/>、/>Whether the number of data in the data storage unit is smaller than a preset threshold value: if yes, thenWill not be divided; if no, then->Is divided into->Regions of equal size->、/>、/>The method comprises the steps of carrying out a first treatment on the surface of the The method comprises the steps that a preset threshold is used for ensuring that enough data are available for fitting parameters in an empirical full-path model formula when the empirical full-path model simulates a typhoon track;
step S2.4, for、/>、/>The number of data in the region is smaller than the preset threshold value, and the parameters of the linear equation in the region are adopted as +.>Fitting the data in the step (a); for->、/>、/>And (3) respectively repeating the steps S2.2-S2.3 for each area with the data number larger than or equal to the preset threshold value until the area cannot be divided continuously or the size of the divided area is smaller than the preset minimum size.
Further, for areas with more focuses on typhoons, the sample points are more, and grid division is dense; for the area with little typhoon occurrence and little attention, the sample points are few, and the grid division is sparse.
Further, in step S3, the empirical full path model uses the following formula:
（1）
（2）
wherein,and->Respectively in typhoonsLongitude and latitude of the location of the heart; />And->Residual errors of the formula (1) and the formula (2), respectively; />And->Typhoons are in +.>Time and->The advancing angle at the moment, the angle value is from-180 degrees to 180 degrees in the clockwise direction, and the angle value in the north direction is set to be 0 degree; />Is->Time to->The change amount of the typhoon advancing angle at the moment; />Is in->The speed of travel at the moment; />Is->Time to->Time of day travel speed selfThe amount of change in log; />、/>、/>、/>、/>Is the coefficient of formula (1); />、/>、/>、/>、/>、Is the coefficient of formula (2).
The step S3 specifically comprises the following steps:
step S3.1, for each grid divided in step S2, the coefficients are respectively mapped by the formula (1) and the formula (2)、/>、/>、/>、/>And->、/>、/>、/>、/>、/>Fitting, wherein a random sampling consistency algorithm RANSAC in robust linear regression is adopted in the fitting method;
step S3.2, residual error to equation (1)And residual error of formula (2)>Adopts->Fitting the distribution;
and S3.3, selecting an initial state of the simulated typhoon, wherein the initial state comprises an initial position of the typhoon, an initial traveling angle of the typhoon and an initial traveling speed of the typhoon, and substituting the initial position, the initial traveling angle and the initial traveling speed of the typhoon into the formula (1) and the formula (2) to obtain a simulated typhoon track, wherein the initial position of the typhoon refers to the longitude and the latitude of the position of the typhoon center at the initial time.
Further, the random sample consensus algorithm RANSAC in step S3.1 is specifically as follows:
1) Randomly selecting a plurality of sample points from all sample points in the grid, and performing linear regression on the selected plurality of sample points;
2) Judging whether the sample points in the step 1) are points in the empirical full-path model or not in all the sample points in the grid;
3) If the proportion of the sample points in the empirical full path model reaches a set threshold value, adopting a least square method to linearly fit the points meeting the empirical full path model again, otherwise, repeating the steps 1) and 2);
the calculation formula of the least square method is as follows:
（3）
in the formula (3), the amino acid sequence of the compound,、/>、/>are all matrix, and are filled with->For matrix->Transpose of->For matrix->Inverse matrix of>In the form of a matrix of coefficients of an empirical full path model formula, < >>In the form of a matrix of independent variables for all sample points within the grid, +.>In the form of a matrix of dependent variables for all sample points within the grid.
The beneficial effects of the invention are as follows:
1. according to the invention, a non-uniform grid division method is adopted, the region with dense typhoons is finely divided, the resolution of dividing grids is improved, and meanwhile, each grid can be ensured to have enough historical data for parameter fitting, so that the simulated typhoon track path is ensured to be more accurate and close to the actual typhoon track.
2. In the parameter fitting, a part of the grid is data-shared, as in step S2.4When->When the number of data in the sub-area of (a) is smaller than a preset threshold value, area +.>Is given to the sub-region, which ensures that in the region +.>In dividing the subregion, even region->A large amount of sample data is gathered in a certain subarea, and the subarea can be still divided into smaller subareas; if the data cannot be shared, when +>When the number of data in the sub-area of (a) is smaller than the threshold value, the area +.>Cannot be divided.
3. Robust linear regression is adopted for parameter fitting in the grid, and influence of outliers on fitting results in the linear regression process is reduced.
Drawings
Fig. 1 is a schematic diagram of grid division of typhoon data according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of grid division of eastward typhoon data according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of grid division of the typhoon data in the west direction according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of a part of a historical typhoon track according to an embodiment of the present invention.
Fig. 5 is a schematic diagram of a partially simulated typhoon track according to an embodiment of the present invention.
Detailed Description
The invention will now be described in further detail with reference to the drawings and the specific examples, which are given by way of illustration only and are not intended to limit the scope of the invention, in order to facilitate a better understanding of the invention to those skilled in the art.
The method for simulating the typhoon track path based on the non-uniform grid division in the embodiment comprises the following steps:
s1, acquiring tropical cyclone data, and preprocessing the tropical cyclone data;
s2, dividing a research area into non-uniform grids, wherein the non-uniform grids refer to grids with incomplete equal sizes;
and step S3, simulating a typhoon track through an empirical full-path model based on the non-uniform grids divided in the step S2.
In order that the above-described aspects may be better understood, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings, in which exemplary embodiments of the present invention are shown, it should be understood that the present invention may be embodied in various forms and is not limited to the embodiments described herein. These embodiments are provided so that this disclosure will be thorough and complete.
Specifically, the method for simulating the typhoon track path based on non-uniform grid division according to the embodiment comprises the following steps:
and S1, acquiring tropical cyclone data, and preprocessing the tropical cyclone data.
Further, the step S1 specifically includes:
step S1.1, downloading tropical cyclone data of a preset year from a public website, wherein the tropical cyclone data of 1949 to 2021 is downloaded from a tropical cyclone data center of Meteorological office of a certain country as an example;
step S1.2, deleting the cyclone with shorter duration in the tropical cyclone data downloaded in step S1.1, because the weak influence of the cyclone with shorter duration is small. In this embodiment, the number of cyclones with a period of 10 hours or less is deleted, where the period interval is 6 hours, that is, the number of cyclones with a period of 60 hours or less in the tropical cyclone data downloaded in step S1.1 is deleted.
And S2, dividing the research area into non-uniform grids, wherein the non-uniform grids refer to grids with not-completely equal sizes.
In this embodiment, the biggest innovation is to grid the study area unevenly. Specifically, step S2 includes:
step S2.1, setting the research area as。
Step S2.2, assumeDivided into->Regions of equal size->、/>、/>Wherein->Is an integer and->The value range of (2) is +.>。
Step S2.3, judging、/>、/>Whether the number of data in the data storage unit is smaller than a preset threshold value: if yes, thenWill not be divided; if no, then->Is divided into->Regions of equal size->、/>、/>The method comprises the steps of carrying out a first treatment on the surface of the The preset threshold is used for ensuring that enough data is needed to fit parameters in an empirical full-path model formula when the empirical full-path model simulates a typhoon track.
Step S2.4, for、/>、/>The number of data in the region is smaller than the preset threshold value, and the parameters of the linear equation in the region are adopted as +.>Fitting the data in the step (a); for->、/>、/>And (3) respectively repeating the steps S2.2-S2.3 for each area with the data number larger than or equal to the preset threshold value until the area cannot be divided continuously or the size of the divided area is smaller than the preset minimum size.
For better understanding the method of dividing the non-uniform grid described in step S2, the following will be describedFor example, thenI.e.)>Divided into 4 equal-sized regions +.>、/>、/>、/>The specific implementation process is as follows:
(1) SelectingTaking the investigation regionIn the present embodiment, a region is exemplified, and +.>Aliquoting into->A basic unit due to->Here will->Aliquoting into->A basic unit->The size of each basic unit is calculated according to the following dividing standard, namely, the size of each basic unit is ensured to be larger than a preset minimum size, and the size of the sub-units divided by the basic unit is smaller than the minimum size; each basic cell size is the smallest size of the last divided grid area, and the grid may be composed of a plurality of basic cells or one basic cell. In the present embodiment byTaking 6 as an example, i.e. will +.>Aliquoting into->The individual basic units can be seen from fig. 1, 2, 3, 4 and 5. In fig. 1 to 5, the abscissa represents the east longitude and the ordinate represents the north latitude; HAX indicated by an arrow represents a coastline; the horizontal lines and the vertical lines represent the lines of the division grid, as seen in the direction of the diagrams of fig. 1 to 5.
(2) For the investigation regionIs included in the starting unit parameters of +.>、/>And->Wherein->Whether the area represented by the finger unit can be divided, < >>The size of the region represented by the finger cell, +.>Refers to the range of data used by the region represented by the cell.
(3) For a pair ofDividing into 4 equal-sized regions +.>、/>、/> Let the upper left corner beThe upper right corner is->The lower left corner is->The lower right corner is->. Judging->、/>、/>、/>Whether the number of the medium data is smaller than a preset threshold value or not:
if yes, thenWithout dividing, ->Start unit parameter->The state becomes +.>Cannot be divided;
if not, for the data number smaller than the preset threshold value, toFor example, then ∈ ->Initial unit value parameter of (2)Representation->Can not divide->Representing the size of the grid as +.>，/>The data representing use includes a range ofThe method comprises the steps of carrying out a first treatment on the surface of the For data number greater than or equal to preset threshold value, in +.>For example, then->The initial cell value parameter of +.>Representation ofCan divide and/or block>Representing the size of the grid as +.>，/>The data representing the use includes a range +.>。
(4) Parameters for the starting cells of the gridThe state being a divisible region, as in step (3)>Dividing the grid, repeating the step (2) and the step (3) until the grid does not meet the dividing condition or the grid size is a single cell size, wherein the minimum grid size is +.>(latitude x longitude). Generally, historical typhoon track data is divided into east-west directions, coefficients of a formula (1) and a formula (2) are fitted respectively, grid division is also divided according to the east-west direction data, fig. 1 is a schematic diagram of grid division of typhoon data according to an embodiment of the present invention, fig. 2 is a schematic diagram of grid division of east-west direction typhoon data according to an embodiment of the present invention, and fig. 3 is a schematic diagram of grid division of west-west direction typhoon data according to an embodiment of the present invention.
As the present embodiment, preferably, for an area where typhoons occur with much attention, there are many sample points and grid division is dense; for the area with little typhoon occurrence and little attention, the sample points are few, and the grid division is sparse. Therefore, the grid division is refined as much as possible while enough sample data are ensured in each grid area, and the accurate simulation of typhoon tracks is facilitated.
Step S3, simulating a typhoon track through an empirical full-path model based on the non-uniform grids divided in the step S2, wherein the empirical full-path model adopts the following formula:
（1）
（2）
wherein,and->Longitude and latitude of the location of typhoon center；/>And->Residual errors of the formula (1) and the formula (2), respectively; />And->Typhoons are in +.>Time and->The advancing angle at the moment, the angle value is from-180 degrees to 180 degrees in the clockwise direction, and the angle value in the north direction is set to be 0 degree; />Is->Time to->The change amount of the typhoon advancing angle at the moment; />Is in->The speed of travel at the moment; />Is->Time to->Natural logarithmic change of time of day travel speedAn amount of; />、/>、/>、/>、/>Is the coefficient of formula (1); />、/>、/>、/>、/>、Is the coefficient of formula (2).
In this embodiment, step S3 specifically includes:
step S3.1, for each grid divided in step S2, the coefficients are respectively mapped by the formula (1) and the formula (2)、/>、/>、/>、/>And->、/>、/>、/>、/>、/>Fitting is carried out, and a random sampling consistency algorithm RANSAC in robust linear regression is adopted in the fitting method. In this embodiment, the calculation by the random sample consensus algorithm RANSAC is specifically as follows:
1) Randomly selecting a plurality of sample points from all sample points in a grid, taking 6-15 sample points as an example in the embodiment, and performing linear regression on the 6-15 sample points;
2) Judging whether the sample points in the step 1) are points in the empirical full-path model or not in all the sample points in the grid;
3) If the proportion of the sample points in the empirical full path model reaches a set threshold value, adopting a least square method to linearly fit the points meeting the empirical full path model again, otherwise, repeating the steps 1) and 2);
the calculation formula of the least square method is as follows:
（3）
in the formula (3), the amino acid sequence of the compound,、/>、/>are all matrix, and are filled with->For matrix->Transpose of->For matrix->Inverse matrix of>In the form of a matrix of coefficients of an empirical full path model formula, < >>In the form of a matrix of independent variables for all sample points within the grid, +.>In the form of a matrix of dependent variables for all sample points within the grid. Taking formula (1) as an example, +.>Is->、、/>、/>、/>In matrix form,/->For all sample points within the grid +.>、/>、/>、/>In matrix form,/->For all sample points within the grid +.>。
Step S3.2, residual error to equation (1)And residual error of formula (2)>Adopts->The distribution was fitted.
And S3.3, selecting an initial state of the simulated typhoon, wherein the initial state comprises an initial position of the typhoon, an initial traveling angle of the typhoon and an initial traveling speed of the typhoon, and substituting the initial position, the initial traveling angle and the initial traveling speed of the typhoon into the formula (1) and the formula (2) to obtain a simulated typhoon track, wherein the initial position of the typhoon refers to the longitude and the latitude of the position of the typhoon center at the initial time. Fig. 4 shows a schematic view of a part of a historical typhoon track, fig. 5 shows a schematic view of a part of a simulated typhoon track, and other non-horizontal lines and non-vertical lines represent typhoon tracks except for the coastline HAX as seen from the schematic directions of fig. 4 and 5. As can be seen from a comparison between fig. 4 and fig. 5, the typhoon track simulated in this embodiment has consistency with the historical typhoon track, so that it can be proved that the typhoon track path simulated by the method described in this embodiment has high accuracy.
The foregoing has described only the basic principles and preferred embodiments of the present invention, and many variations and modifications will be apparent to those skilled in the art in light of the above description, which variations and modifications are intended to be included within the scope of the present invention.

Claims (6)

1. The typhoon track path simulation method based on non-uniform grid division is characterized by comprising the following steps:
s1, acquiring tropical cyclone data, and preprocessing the tropical cyclone data;
s2, dividing a research area into non-uniform grids, wherein the non-uniform grids refer to grids with incomplete equal sizes; the step S2 specifically comprises the following steps:
step S2.1, setting the research area as；
Step S2.2, assumeDivided into->Regions of equal size->、/>、/>Wherein->Is an integer and->The value range of (2) is +.>；
Step S2.3, judging、/>、/>Whether the number of data in the data storage unit is smaller than a preset threshold value: if yes, ->Will not be divided; if no, then->Is divided into->Regions of equal size->、/>、/>The method comprises the steps of carrying out a first treatment on the surface of the The method comprises the steps that a preset threshold is used for ensuring that enough data are available for fitting parameters in an empirical full-path model formula when the empirical full-path model simulates a typhoon track;
step S2.4 needleFor a pair of、/>、/>The number of data in the region is smaller than the preset threshold value, and the parameters of the linear equation in the region are adopted as +.>Fitting the data in the step (a); for->、/>、/>The method comprises the steps that S2.2-S2.3 are repeated for each area with the data number larger than or equal to a preset threshold value, until the area cannot be divided continuously or the size of the divided area is smaller than a preset minimum size;
and step S3, simulating a typhoon track through an empirical full-path model based on the non-uniform grids divided in the step S2.
2. The method for typhoon trajectory path simulation based on non-uniform grid division according to claim 1, wherein step S1 specifically comprises:
s1.1, downloading tropical cyclone data of a preset year from a public website;
and step S1.2, deleting cyclones with the period number smaller than or equal to 10 in the tropical cyclone data downloaded in the step S1.1, wherein the period interval is 6 hours.
3. The method for carrying out typhoon trajectory path simulation based on non-uniform grid division according to claim 1, wherein for areas where typhoons occur with more concerns, sample points are more and grid division is dense; for the area with little typhoon occurrence and little attention, the sample points are few, and the grid division is sparse.
4. The method for typhoon trajectory path simulation based on non-uniform grid partitioning according to claim 1, wherein in step S3, the empirical full path model uses the following formula:
（1）
（2）
wherein,and->Longitude and latitude of the location of the typhoon center respectively; />And->Residual errors of the formula (1) and the formula (2), respectively; />And->Typhoons are in +.>Time and->The angle of travel at the moment, the angle value is set from +.>To->Let the north direction angle value be +.>；/>Is->Time to->The change amount of the typhoon advancing angle at the moment; />Is in->The speed of travel at the moment; />Is->Time to->The change amount of the natural logarithm of the moment advancing speed; />、/>、/>、/>、/>Is the coefficient of formula (1); />、/>、/>、/>、/>、Is the coefficient of formula (2).
5. The method for typhoon trajectory path simulation based on non-uniform grid division according to claim 4, wherein step S3 specifically comprises:
step S3.1, for each grid divided in step S2, the coefficients are respectively mapped by the formula (1) and the formula (2)、/>、/>、/>、/>And->、/>、/>、/>、/>、/>Fitting, wherein a random sampling consistency algorithm RANSAC in robust linear regression is adopted in the fitting method;
step S3.2, residual error to equation (1)And residual error of formula (2)>Adopts->Fitting the distribution;
and S3.3, selecting an initial state of the simulated typhoon, wherein the initial state comprises an initial position of the typhoon, an initial traveling angle of the typhoon and an initial traveling speed of the typhoon, and substituting the initial position, the initial traveling angle and the initial traveling speed of the typhoon into the formula (1) and the formula (2) to obtain a simulated typhoon track, wherein the initial position of the typhoon refers to the longitude and the latitude of the position of the typhoon center at the initial time.
6. The method for typhoon trajectory path simulation based on non-uniform grid partitioning according to claim 5, wherein the random sampling consistency algorithm RANSAC in step S3.1 is specifically as follows:
1) Randomly selecting a plurality of sample points from all sample points in the grid, and performing linear regression on the selected plurality of sample points;
2) Judging whether the sample points in the step 1) are points in the empirical full-path model or not in all the sample points in the grid;
3) If the proportion of the sample points in the empirical full path model reaches a set threshold value, adopting a least square method to linearly fit the points meeting the empirical full path model again, otherwise, repeating the steps 1) and 2);
the calculation formula of the least square method is as follows:
（3）
in the formula (3), the amino acid sequence of the compound,、/>、/>are all matrix, and are filled with->For matrix->Transpose of->For matrix->Inverse matrix of>In the form of a matrix of coefficients of an empirical full path model formula, < >>In the form of a matrix of independent variables for all sample points within the grid, +.>In the form of a matrix of dependent variables for all sample points within the grid.
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