CN113971350A - Wind speed field fitting gap filling method and device and medium - Google Patents

Wind speed field fitting gap filling method and device and medium Download PDF

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CN113971350A
CN113971350A CN202111578591.7A CN202111578591A CN113971350A CN 113971350 A CN113971350 A CN 113971350A CN 202111578591 A CN202111578591 A CN 202111578591A CN 113971350 A CN113971350 A CN 113971350A
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wind speed
cyclone
field
speed field
dimensional
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CN113971350B (en
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李静
王海江
徐自励
刘涛
彭祯珍
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Chengdu University of Information Technology
Second Research Institute of CAAC
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Second Research Institute of CAAC
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/95—Radar or analogous systems specially adapted for specific applications for meteorological use
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/08—Fluids
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
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    • Y02A90/10—Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation

Abstract

The invention discloses a fitting and gap filling method, a fitting and gap filling device and a fitting and gap filling medium for a wind speed field. The method comprises the steps of constructing a two-dimensional cyclone vector field basis function, then obtaining an objective function of a wind speed field based on superposition fitting of the two-dimensional cyclone basis function, determining the search direction of optimal parameters, finally establishing an ordinary differential equation of parameter search, seeking the optimal parameters through numerical solution of the ordinary differential equation, and then bringing the parameters into a two-dimensional cyclone basis function superposition equation to obtain the fitted and filled two-dimensional wind speed field. The invention also provides a wind speed field fitting and gap filling device and a medium. The method can directly make up for the two-dimensional vector wind speed field obtained by inversion, namely, make up for the lack area with more complex speed change by stacking the basis functions of the constructed two-dimensional cyclone vector field, thereby achieving the effect of filling up the wind speed field with high accuracy.

Description

Wind speed field fitting gap filling method and device and medium
Technical Field
The invention relates to the technical field of weather prediction, in particular to a wind speed field fitting vacancy filling method, a wind speed field fitting vacancy filling device and a wind speed field fitting vacancy filling medium.
Background
In weather forecast, the basic structure and development trend of the wind field need to be known to a certain extent, so that complete and accurate wind field information is particularly necessary. The Doppler weather radar has higher space-time resolution, completes one-time volume scanning within a few minutes, and can acquire high-precision meteorological target detection data, so that the acquisition of the large-range wind field information at present mainly depends on the detection data of the Doppler weather radar.
The essence of the doppler weather radar detecting information of a wide range of wind fields is to measure air targets, such as cloud and rain particles, based on the doppler effect to obtain the radial velocity of the particles. Therefore, the doppler weather radar can measure the radial velocity of the target only in the region containing the cloud and rain particles, and if there are no particles such as cloud and rain in the radar detection range, a lack-of-measurement region (as shown in fig. 1) will appear in the radar echo range, which affects the acquisition of the complete wind field of the target region. Therefore, fitting and blind-filling are performed on the wind field area with the missing speed by combining various numerical methods according to the detected data around the wind field missing area so as to obtain complete wind field information of the interested area.
The method for filling wind speed data is usually function fitting, but the existing function fitting method is mostly used for scalar data, and for wind speed filling, the existing fitting method is mainly used for filling radial speed, or respectively fitting and filling horizontal wind speed and vertical wind speed. At present, the method for directly fitting the two-dimensional vector wind field is less, for example, the method for interpolating the information of the low elevation layer through the information of the high elevation layer does not consider the condition that the changes of different elevation layers are inconsistent, once the changes of the speed field information of the high elevation layer and the low elevation layer are too large, the method is not applicable any more, and if the speed field information of the high elevation layer is missing, the method can not be applicable, so the method has certain limitation. In addition, an iteration method based on VAD (Velocity adaptive Display) technology is used for filling the area with the lack of the measured Doppler Velocity, the method has the defects in some areas, the calculated horizontal divergence is obviously influenced, and a reasonable filling scheme needs to be designed to fill the area with the lack of the measured radial Velocity. In addition, the method needs to assume that divergence and speed are uniformly changed, so the method can only fill up a Doppler radial speed field with more uniform data loss, and for a speed field with more complicated change, the method has larger error and poorer effect.
Generally, the existing methods can only fill in the doppler radial velocity field, and when the velocity field changes rapidly, the filling effect is not good. The invention discloses a two-dimensional wind speed field fitting and filling method based on vector field mode fitting.
Disclosure of Invention
The invention discloses a wind speed field fitting vacancy supplementing method, a device and a medium, aiming at the defects of the existing implementation method, the method can directly perform vacancy supplementing on a two-dimensional vector wind speed field obtained by inversion, namely, a vacancy measuring area with more complex change of speed is supplemented by stacking constructed two-dimensional cyclone vector field basis functions, and the high-accuracy wind speed field filling effect is achieved.
The specific technical scheme of the invention is as follows:
a fitting filling method for a wind speed field comprises the following steps:
constructing a two-dimensional cyclone vector field basis function on a plane according to the following formula (1):
Figure 979962DEST_PATH_IMAGE001
formula (1)
Wherein the content of the first and second substances,
Figure 959419DEST_PATH_IMAGE002
a position vector representing an arbitrary point on the plane,
Figure 598211DEST_PATH_IMAGE003
is the normal unit vector of the plane,
Figure 790158DEST_PATH_IMAGE004
which represents a cross-product operation of the vector,
Figure 338951DEST_PATH_IMAGE005
is the intensity of the cyclone, to represent the direction of rotation,
Figure 456686DEST_PATH_IMAGE006
is the scale of the cyclone to represent the acting radius of the cyclone,
Figure 582774DEST_PATH_IMAGE007
is a position vector of the center of the cyclone and consists of two coordinate parameters
Figure 250515DEST_PATH_IMAGE008
It is determined that,
Figure 716132DEST_PATH_IMAGE009
and
Figure 771813DEST_PATH_IMAGE010
unit vectors in horizontal and vertical directions, respectively;
will be provided withKAnd (3) superposing the basis functions of the two-dimensional cyclone vector fields to obtain a superposed vector field as shown in the following formula (2):
Figure 621082DEST_PATH_IMAGE011
formula (2)
Wherein the content of the first and second substances,
Figure 92515DEST_PATH_IMAGE012
respectively representKThe strength of the cyclone base is high,
Figure 412638DEST_PATH_IMAGE013
respectively representKThe size range of the base of each cyclone,
Figure 435957DEST_PATH_IMAGE014
respectively represent the centers of K cyclone bases;
according to the actual wind speed field
Figure 412004DEST_PATH_IMAGE015
Approximating the actual wind speed field with the vector field described by the equation (2)
Figure 483865DEST_PATH_IMAGE015
An objective function shown in the following formula (4) is obtained:
Figure 490785DEST_PATH_IMAGE016
formula (4)
Obtaining 4K parameters according to the minimum requirement condition of the objective function
Figure 622689DEST_PATH_IMAGE017
The objective function minimum requirement condition is that partial derivatives of each parameter thereof are required to be 0, which is described by the following formula (5):
Figure 820452DEST_PATH_IMAGE018
formula (5)
Establishing an optimal search direction based on the formula (5) is shown as the following formula (6):
Figure 758321DEST_PATH_IMAGE019
formula (6)
Wherein D is a negative gradient;
based on the equation (6), an ordinary differential equation shown in the following equation (7) is determined:
Figure 53036DEST_PATH_IMAGE020
formula (7)
Solving the ordinary differential equation to obtain an iterative equation of the optimal parameters of the two-dimensional cyclone basis function superposition fitting wind speed field shown in the following formula (9):
Figure 559104DEST_PATH_IMAGE021
formula (9)
Wherein the content of the first and second substances,
Figure 807945DEST_PATH_IMAGE022
iteratively updating step size factors for the parameters;
according to a set of parameter initial values
Figure 549505DEST_PATH_IMAGE023
And an iteration termination condition, wherein the optimal parameter of the wind speed field is fitted based on the superposition of the two-dimensional cyclone basis functions is found based on an iteration equation of the optimal parameter of the wind speed field fitted by the superposition of the two-dimensional cyclone basis functions, and the optimal parameter is substituted into the vector field after the superposition to obtain the two-dimensional wind speed field after fitting and filling.
In a second aspect, the invention further provides a wind speed field fitting filling device, which comprises a wind speed field feature extraction module, a two-dimensional cyclone vector field basis function construction module, a two-dimensional cyclone vector field basis function superposition module and a wind speed field approximation optimization module. The wind speed field characteristic extraction module is used for extracting characteristics of an actual wind speed field to obtain initial values of the wind speed field about strength, scale and central position parameters, the two-dimensional cyclone vector field basis function construction module is used for constructing a single two-dimensional cyclone vector field basis function, the two-dimensional cyclone vector field basis function superposition module is used for superposing a plurality of two-dimensional cyclone vector field basis functions according to the wind speed field characteristics extracted by the wind speed field characteristic extraction, the wind speed field approximation optimization module is used for approximating the constructed wind speed field by using the actual wind speed field, the optimized parameters are solved, the optimized parameters are fed back to the two-dimensional cyclone vector field basis function construction module, the solution process is continuously iterated and optimized, iteration is stopped when error setting conditions are met, and the optimally fitted and filled two-dimensional wind speed field is obtained. The interrelationship of the modules is as follows: firstly, an actual wind speed field is input into a wind speed field characteristic extraction module to obtain initial values of wind speed field parameters, such as strength, central value and scale range parameters. And then, inputting the initial parameter values into a two-dimensional cyclone vector field basis function construction module, and iterating to obtain K two-dimensional cyclone vector field basis functions. And then, superposing the K two-dimensional cyclone vector field basis functions by using a two-dimensional cyclone vector field basis function superposition module to obtain a constructed wind speed field, and approximating the constructed wind speed field by using an actual wind speed field, namely solving the optimized parameters by using an actual wind speed field approximation optimization module. And finally, feeding the optimized parameters back to the two-dimensional cyclone vector field basis function construction module, continuously iterating the optimization solving process, and stopping iteration when error conditions are met to obtain the two-dimensional wind speed field which is optimally fitted and filled.
In a third aspect, the present invention also provides a computer-readable storage medium having stored thereon computer-readable instructions which, when executed by a processor of a computer, cause the computer to perform a computing method according to any of the embodiments of the present invention.
The invention has the beneficial effects that: the method can directly make up for the two-dimensional vector wind speed field obtained by inversion, and make up for the lack measurement area with more complex speed change by stacking the basis functions of the constructed two-dimensional cyclone vector field, thereby achieving the effect of filling up the wind speed field with high accuracy.
Drawings
In order to more clearly illustrate the detailed description of the invention or the technical solutions in the prior art, the drawings that are needed in the detailed description of the invention or the prior art will be briefly described below. Throughout the drawings, like elements or portions are generally identified by like reference numerals. In the drawings, elements or portions are not necessarily drawn to scale.
Fig. 1 shows a schematic diagram of a lack area of a wind speed field according to an embodiment of the present invention (in the diagram, (r) -sixth is the lack area).
FIG. 2 shows a vector distribution plot of a basis function of a cyclone vector field according to an embodiment of the present invention.
Fig. 3 shows a field vector distribution diagram after superposition of three basis functions according to an embodiment of the invention.
FIG. 4 shows a wind velocity field with a missing region according to an embodiment of the invention
Figure 698726DEST_PATH_IMAGE024
Schematic representation.
FIG. 5 shows a wind velocity field filling a defect area according to an embodiment of the invention
Figure 375695DEST_PATH_IMAGE025
Schematic representation.
FIG. 6 shows a logic block diagram of a specific embodiment of the wind speed field fitting gap filling apparatus of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely below, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The method of the present invention will now be further described with reference to the accompanying drawings.
Example 1
The embodiment 1 of the invention provides a wind speed field fitting and gap filling method. The method takes input data obtained by Doppler weather radar detection as an example, and starts with the construction of a two-dimensional cyclone vector field basis function on a plane according to the following formula (1):
Figure 610368DEST_PATH_IMAGE026
formula (1)
Wherein the content of the first and second substances,
Figure 388574DEST_PATH_IMAGE027
a position vector representing an arbitrary point on the plane,
Figure 657882DEST_PATH_IMAGE028
is the normal unit vector of the plane,
Figure 505752DEST_PATH_IMAGE029
which represents a cross-product operation of the vector,
Figure 227720DEST_PATH_IMAGE030
is the intensity of the cyclone, to represent the direction of rotation,
Figure 45504DEST_PATH_IMAGE031
is the scale of the cyclone to represent the acting radius of the cyclone,
Figure 841421DEST_PATH_IMAGE032
is a position vector of the center of the cyclone and consists of two coordinate parameters
Figure 423975DEST_PATH_IMAGE033
It is determined that,
Figure 429977DEST_PATH_IMAGE034
and
Figure 192396DEST_PATH_IMAGE035
unit vectors in horizontal and vertical directions, respectively.
FIG. 2 shows a vector distribution plot of a basis function of a cyclone vector field according to an embodiment of the present invention. As shown in FIG. 2, it is specifically depicted as having a center at [ 00 ]]Intensity a =60, scale
Figure 170717DEST_PATH_IMAGE031
A vector profile of a cyclone vector field basis function of = 30. As can be understood, the cyclone vector field basis function has abundant wind speed field structural characteristics, and can better represent the characteristics of the cyclone from the central part along the radius; in the far-end area away from the center, the rotation characteristic is weaker and weaker, and the vector fields of all local areas are approximately parallel, so that the characteristic of a uniform wind speed field can be well represented; in addition, the central position, the intensity and the spread range of the basic function of the cyclone vector field can be determined by the four parameters, namely
Figure 219444DEST_PATH_IMAGE036
、
Figure 408680DEST_PATH_IMAGE037
、
Figure 709212DEST_PATH_IMAGE038
、
Figure 604356DEST_PATH_IMAGE039
To control, such a cyclone vector field basis function thus has flexibility in wind speed field description.
Then will beKAnd (3) superposing the basis functions of the two-dimensional cyclone vector fields to obtain a superposed vector field as shown in the following formula (2):
Figure 761667DEST_PATH_IMAGE040
formula (2)
Wherein the content of the first and second substances,
Figure 883207DEST_PATH_IMAGE041
respectively representKThe strength of the cyclone base is high,
Figure 49746DEST_PATH_IMAGE042
respectively representKThe size range of the base of each cyclone,
Figure 35282DEST_PATH_IMAGE043
respectively representing the centers of the K cyclone bases.
In some embodiments, three of the two-dimensional cyclone vector field basis functions are added to obtain a vector field after addition as shown in the following formula (3):
Figure 566758DEST_PATH_IMAGE044
formula (3)
Wherein the content of the first and second substances,
Figure 972331DEST_PATH_IMAGE045
respectively shows the strength of the three cyclone bases,
Figure 4878DEST_PATH_IMAGE046
respectively represent the scale ranges of three cyclone bases,
Figure 484401DEST_PATH_IMAGE047
respectively, the centers of the three cyclone bases.
Exemplary, embodiments of the invention specify parameters
Figure 249095DEST_PATH_IMAGE048
After the specific value of (3), a field vector distribution diagram obtained after the superposition of the three basis functions is obtained, as shown in fig. 3. With reference to fig. 2, it can be seen that a two-dimensional wind speed field with a rich variation trend can be synthesized by superimposing different basis functions of 3 cyclone vector fields. It can be understood that when a plurality of two-dimensional cyclone vector field basis functions are superposed, compared with a single two-dimensional cyclone vector field basis function, a two-dimensional wind speed field with richer tendency can be obtained. The embodiment of the invention is only an example, and the number of the superimposed base functions of the specific two-dimensional cyclone vector field is not limited.
Then according to the actual wind speed field
Figure 702816DEST_PATH_IMAGE049
Approximating the actual wind speed field with the vector field described by the equation (2)
Figure 211158DEST_PATH_IMAGE049
An objective function shown in the following formula (4) is obtained:
Figure 810767DEST_PATH_IMAGE050
equation (4).
Specifically, let the actual wind speed field be
Figure 746362DEST_PATH_IMAGE051
，
Figure 188844DEST_PATH_IMAGE052
Is a position vector. Vector field described by equation (2)
Figure 736763DEST_PATH_IMAGE053
To approximate it. Wherein
Figure 456457DEST_PATH_IMAGE054
Is that
Figure 359691DEST_PATH_IMAGE055
And (4) determining the undetermined parameters. For the actual wind speed field
Figure 227153DEST_PATH_IMAGE051
Assuming it is already in the precipitation zone with cloud rain particles
Figure 14980DEST_PATH_IMAGE056
A known point
Figure 651498DEST_PATH_IMAGE057
On which the wind vector value is measured
Figure 230028DEST_PATH_IMAGE058
Then, then
Figure 256889DEST_PATH_IMAGE059
To pair
Figure 707462DEST_PATH_IMAGE060
The best approximation is by finding the parameters
Figure 464066DEST_PATH_IMAGE061
Is optimized to minimize the sum of squares of the approximation errors, which sum of squares of the errors
Figure 584468DEST_PATH_IMAGE062
I.e. an objective function, which is in fact an objective function in the least squares sense.
Then, 4K parameters are obtained according to the minimum requirement condition of the objective function
Figure 692102DEST_PATH_IMAGE063
The objective function minimum requirement condition is that partial derivatives of each parameter thereof are required to be 0, which is described by the following formula (5):
Figure 385514DEST_PATH_IMAGE064
formula (5)
Based on the formula (5), it is found that about 4K parameters
Figure 793361DEST_PATH_IMAGE065
The direct solution of the nonlinear equation system cannot be solved, and only numerical methods are used, that is, the numerical method is used to gradually search the optimal solution of the parameters, and the searching direction (i.e. the direction of the parameter change) is towards the objective function
Figure 678141DEST_PATH_IMAGE066
The opposite direction to the gradient of the parameter (which may also be referred to as the negative gradient direction), and the gradient direction is the partial derivative term on the left of the equation set in equation (5), becauseThis optimal solution search direction is shown as the following equation (6):
Figure 679595DEST_PATH_IMAGE067
formula (6)
Wherein D is a negative gradient;
based on the equation (6), an ordinary differential equation shown in the following equation (7) is determined:
Figure 675232DEST_PATH_IMAGE068
formula (7)
Finally, solving the ordinary differential equation to obtain an iterative equation of the optimal parameters of the two-dimensional cyclone basis function superposition fitting wind speed field shown in the following formula (9):
Figure 436122DEST_PATH_IMAGE069
formula (9)
Wherein the content of the first and second substances,
Figure 163906DEST_PATH_IMAGE070
iteratively updating step size factors for the parameters;
according to a set of parameter initial values
Figure 714973DEST_PATH_IMAGE071
And an iteration termination condition, wherein the optimal parameter of the wind speed field is fitted based on the superposition of the two-dimensional cyclone basis functions is found based on an iteration equation of the optimal parameter of the wind speed field fitted by the superposition of the two-dimensional cyclone basis functions, and the optimal parameter is substituted into the vector field after the superposition to obtain the two-dimensional wind speed field after fitting and filling.
Equation (7) is an initial value problem of a differential equation, the solution of which is a function of the initial point (initial parameter vector)
Figure 311040DEST_PATH_IMAGE072
Starting pointIntegral hyperbola of
Figure 631163DEST_PATH_IMAGE073
. Since the direction of this integral hyperbola is the objective function
Figure 795428DEST_PATH_IMAGE074
In the opposite direction, so that along this integral hyperbola, the function value
Figure 69676DEST_PATH_IMAGE074
Only decrease and not increase.
Therefore, in the embodiment of the present invention, the ordinary differential equation is solved by the following steps:
solving the formula (7) by using a numerical method, and approximating the differential on the left side of the formula (7) by using a difference to obtain the following formula (8):
Figure 203855DEST_PATH_IMAGE075
formula (8)
And (5) finishing the formula (8) to obtain the formula (9).
In the following, example 1 of the present invention will be described with a more complex actual wind speed field
Figure 581746DEST_PATH_IMAGE076
For example, as shown in fig. 4, the two-dimensional wind speed field is obtained by detecting and inverting multiple doppler radars in the precipitation process, and the wind speed field contains uniform wind, shear wind and vortex wind, and has some lack of measurement areas, which is suitable for verifying the method provided by the embodiment of the present invention.
According to the formula (2), two-dimensional cyclone basis function superposition is carried out, in the embodiment of the invention, 3 two-dimensional cyclone basis function superposition is utilized to carry out fitting approximation on the wind speed field shown in the figure 4 so as to achieve the purpose of filling up the lack-of-measurement area, and the superposed wind speed field function is shown as the formula (10):
Figure 713650DEST_PATH_IMAGE077
formula (10)
There are 12 unknown parameters in the above equation:
Figure 301627DEST_PATH_IMAGE078
。
in fig. 4, there are 676 grid points, and 602 grid points with known wind velocity field, excluding points on the missing region, and the positions of these points are used
Figure 505792DEST_PATH_IMAGE079
And representing, the objective function of the superposition fitting approximation is as follows:
Figure 738190DEST_PATH_IMAGE081
formula (11)
The optimal parameter search iteration equation of this example is obtained according to equation (9):
Figure 40995DEST_PATH_IMAGE082
formula (12)
According to equation (12), the solution of the optimal parameters is performed by:
step 1, defining iteration stopping conditions
Figure 850689DEST_PATH_IMAGE083
I.e. objective function
Figure 467615DEST_PATH_IMAGE084
The iteration is stopped, setting in this example, as long as the optimal parameters are considered to have been found
Figure 616836DEST_PATH_IMAGE085
(ii) a Setting a search step size factor
Figure 654325DEST_PATH_IMAGE086
In this example is arranged
Figure 826680DEST_PATH_IMAGE087
。
Step 2, setting initial values of 12 parameters:
Figure 44035DEST_PATH_IMAGE088
。
step 3, solving the objective function at the value position of the current parameter
Figure 375659DEST_PATH_IMAGE089
For each parameter partial derivative, respectively
Figure 692371DEST_PATH_IMAGE090
、
Figure 414339DEST_PATH_IMAGE091
、
Figure 996237DEST_PATH_IMAGE092
、
Figure 120051DEST_PATH_IMAGE093
、
Figure 873243DEST_PATH_IMAGE094
、
Figure 144824DEST_PATH_IMAGE095
、
Figure 703982DEST_PATH_IMAGE096
、
Figure 619985DEST_PATH_IMAGE097
、
Figure 373440DEST_PATH_IMAGE098
、
Figure 866738DEST_PATH_IMAGE099
、
Figure 167269DEST_PATH_IMAGE100
、
Figure 96DEST_PATH_IMAGE101
。
Step 4, iterative calculation is carried out according to the formula (12) and parameters are updated
Figure 485304DEST_PATH_IMAGE102
。
And 5, repeating the step (3) and the step (4) until the iteration condition in the step (1) is reached.
The parameters of the last 3 cyclone basis functions are shown in table 1 below:
parameters of 3 cyclone basis functions found in Table 1
Figure 341265DEST_PATH_IMAGE103
These iteratively searched optimal parameters are substituted into the formula (10), and a fitted wind speed field is obtained as shown in fig. 5.
Comparing fig. 5 and fig. 4, it can be seen that the doppler weather radar wind speed field fitting filling method based on two-dimensional cyclone basis function superposition fitting has a good filling effect on the lack-of-measurement area, the continuity of the filling effect is good, and the visual inspection error between the grid points of the known wind speed field and the original wind speed field is small. To more accurately compare the errors of the fitted wind speed field and the original wind speed field, the average absolute errors of the horizontal wind speed and the vertical wind speed are calculated for the original wind speed field and the fitted wind speed field on the grid points of the known wind speed field, as shown in table 2 below.
TABLE 2 two-dimensional cyclone basis function overlay fitting error
Component of velocity Mean absolute error (m/s)
Horizontal velocityu 0.8323
Vertical velocityv 0.8136
As can be seen from Table 2, when the method provided by the embodiment of the invention fills up the lacking area, the average absolute error between the fitted wind speed field and the original wind speed field is less than 1m/s, and the error is small, which also indicates that the method is reasonable and reliable for filling up the lacking area.
Example 2
The embodiment 2 of the invention provides a wind speed field fitting and gap filling device which comprises a wind speed field feature extraction module, a two-dimensional cyclone vector field basis function construction module, a two-dimensional cyclone vector field basis function superposition module and a wind speed field approximation optimization module. The wind speed field characteristic extraction module is used for extracting characteristics of an actual wind speed field to obtain initial values of the wind speed field about strength, scale and central position parameters, the two-dimensional cyclone vector field basis function construction module is used for constructing a single two-dimensional cyclone vector field basis function, the two-dimensional cyclone vector field basis function superposition module is used for superposing a plurality of two-dimensional cyclone vector field basis functions according to the characteristics extracted by the wind speed field, the wind speed field approximation optimization module is used for approximating the constructed wind speed field by using the actual wind speed field, the optimized parameters are solved, the optimized parameters are fed back to the two-dimensional cyclone vector field basis function construction module, the optimization solving process is continuously iterated, iteration is stopped when error setting conditions are met, and the optimally-fitted and filled two-dimensional wind speed field is obtained. The interrelationship of the modules is as follows: firstly, an actual wind speed field is input into a wind speed field characteristic extraction module to obtain initial values of wind speed field parameters, such as strength, central value and scale range parameters. And then, inputting the initial parameter values into a two-dimensional cyclone vector field basis function construction module, and iterating to obtain K two-dimensional cyclone vector field basis functions. And then, superposing the K two-dimensional cyclone vector field basis functions by using a two-dimensional cyclone vector field basis function superposition module to obtain a constructed wind speed field, and approximating the constructed wind speed field by using an actual wind speed field, namely solving the optimized parameters by using an actual wind speed field approximation optimization module. And finally, feeding the optimized parameters back to the two-dimensional cyclone vector field basis function construction module, continuously iterating the optimization solving process, and stopping iteration when error conditions are met to obtain the two-dimensional wind speed field which is optimally fitted and filled. Taking the input data detected by the doppler weather radar in the range of 1000 meters by 1000 meters as an example, as shown in fig. 6, 5 two-dimensional cyclone vector field basis functions are superimposed to form a two-dimensional fitting wind speed field according to the characteristics of the wind speed field. The wind speed field approximation optimization module optimizes parameters of each basis function through errors between actual wind speeds on limited grid points obtained by minimum Doppler weather radar detection and fitted wind speeds on the grid points, namely, the constructed fitted wind speed field is used for approximating a real wind speed field on the grid points with the detected wind speeds, the optimized parameters are solved, the optimized parameters are fed back to the two-dimensional cyclone vector field basis function construction module, the optimization solving process is continuously iterated, iteration is stopped when error setting conditions are met, and the two-dimensional wind speed field after optimal fitting filling is obtained.
The device effect provided by embodiment 2 of the present invention is consistent with the technical effect of the method as set forth above, and will not be described again here.
The above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit and scope of the present invention, and they should be construed as being included in the following claims and description.

Claims (5)

1. A wind speed field fitting filling method is characterized by comprising the following steps:
constructing a two-dimensional cyclone vector field basis function on a plane according to the following formula (1):
Figure 780563DEST_PATH_IMAGE001
formula (1)
Wherein the content of the first and second substances,
Figure 846739DEST_PATH_IMAGE002
a position vector representing an arbitrary point on the plane,
Figure 523577DEST_PATH_IMAGE003
is the normal unit vector of the plane,
Figure 850653DEST_PATH_IMAGE004
which represents a cross-product operation of the vector,
Figure 541528DEST_PATH_IMAGE005
is the intensity of the cyclone, to represent the direction of rotation,
Figure 403655DEST_PATH_IMAGE006
is the scale of the cyclone to represent the acting radius of the cyclone,
Figure 697233DEST_PATH_IMAGE007
is a position vector of the center of the cyclone and consists of two coordinate parameters
Figure 285341DEST_PATH_IMAGE008
It is determined that,
Figure 661964DEST_PATH_IMAGE009
and
Figure 765050DEST_PATH_IMAGE010
unit vectors in horizontal and vertical directions, respectively;
will be provided withKSuperposing the two-dimensional cyclone vector field basis functions to obtain a superposed vectorThe field is shown in equation (2) below:
Figure 596739DEST_PATH_IMAGE011
formula (2)
Wherein the content of the first and second substances,
Figure 554200DEST_PATH_IMAGE012
respectively representKThe strength of the cyclone base is high,
Figure 118036DEST_PATH_IMAGE013
respectively representKThe size range of the base of each cyclone,
Figure 770735DEST_PATH_IMAGE014
respectively represent the centers of K cyclone bases;
according to the actual wind speed field
Figure 593066DEST_PATH_IMAGE015
Approximating the actual wind speed field with the vector field described by the equation (2)
Figure 624607DEST_PATH_IMAGE015
An objective function shown in the following formula (4) is obtained:
Figure 877121DEST_PATH_IMAGE016
formula (4)
Obtaining 4K parameters according to the minimum requirement condition of the objective function
Figure 751536DEST_PATH_IMAGE017
The objective function minimum requirement condition is that partial derivatives of each parameter thereof are required to be 0, which is described by the following formula (5):
Figure 128291DEST_PATH_IMAGE018
formula (5)
Establishing an optimal search direction based on the formula (5) is shown as the following formula (6):
Figure 529185DEST_PATH_IMAGE019
formula (6)
Wherein D is a negative gradient;
based on the equation (6), an ordinary differential equation shown in the following equation (7) is determined:
Figure 700404DEST_PATH_IMAGE020
formula (7)
Solving the ordinary differential equation to obtain an iterative equation of the optimal parameters of the two-dimensional cyclone basis function superposition fitting wind speed field shown in the following formula (9):
Figure 327694DEST_PATH_IMAGE021
formula (9)
Wherein the content of the first and second substances,
Figure 429511DEST_PATH_IMAGE022
iteratively updating step size factors for the parameters;
according to a set of parameter initial values
Figure 825858DEST_PATH_IMAGE023
And an iteration termination condition, wherein the optimal parameter of the wind speed field is fitted based on the superposition of the two-dimensional cyclone basis functions is found based on an iteration equation of the optimal parameter of the wind speed field fitted by the superposition of the two-dimensional cyclone basis functions, and the optimal parameter is substituted into the vector field after the superposition to obtain the two-dimensional wind speed field after fitting and filling.
2. The method according to claim 1, wherein three said two-dimensional cyclone vector field basis functions are superimposed to obtain a superimposed vector field as shown in the following formula (3):
Figure 902398DEST_PATH_IMAGE024
formula (3)
Wherein the content of the first and second substances,
Figure 938356DEST_PATH_IMAGE025
respectively shows the strength of the three cyclone bases,
Figure 329017DEST_PATH_IMAGE026
respectively represent the scale ranges of three cyclone bases,
Figure 498312DEST_PATH_IMAGE027
respectively, the centers of the three cyclone bases.
3. The method of claim 1, wherein the ordinary differential equation is solved by:
solving the formula (7) by using a numerical method, and approximating the differential on the left side of the formula (7) by using a difference to obtain the following formula (8):
Figure 339229DEST_PATH_IMAGE028
formula (8)
And (5) finishing the formula (8) to obtain the formula (9).
4. A wind speed field fitting filling device is characterized by comprising
Wind speed field feature extraction module, two-dimensional cyclone vector field basis function construction module and two-dimensional cyclone vector field basis function
The system comprises a number superposition module and a wind speed field approximation optimization module;
the wind speed field feature extraction module is used for extracting features of an actual wind speed field to obtain a wind speed field gate
Initial values for intensity, scale, and center position;
the two-dimensional cyclone vector field basis function construction module is used for constructing a single two-dimensional cyclone vector field basis
A function;
the two-dimensional cyclone vector field basis function superposition module is used for extracting the obtained wind speed according to the characteristics of the wind speed field
The field characteristics are used for superposing a plurality of two-dimensional cyclone vector field basis functions;
the wind speed field approximation optimization module is used for approximating the constructed wind speed field by using the actual wind speed field to obtain
Solving the optimized parameters, and feeding the optimized parameters back to the two-dimensional cyclone vector field basis function construction module continuously
An iterative optimization solving process, wherein iteration is stopped when an error setting condition is met, and the best fit after filling is obtained
A two-dimensional wind speed field;
the connection relation is constructed by the following modules:
inputting the actual wind speed field into a wind speed field characteristic extraction module to obtain an initial value of a wind speed field parameter, wherein the wind speed field parameter is a wind speed field parameter
The speed field parameters comprise intensity, central bit value and scale range;
inputting the initial parameter values into a two-dimensional cyclone vector field basis function construction module, and obtaining K cyclone vector field basis function construction modules after iteration
A two-dimensional cyclone vector field basis function;
the K two-dimensional cyclone vector field basis functions are subjected to the two-dimensional cyclone vector field basis function superposition module
Superposing to obtain a constructed wind speed field, and approaching the constructed wind speed field by using the actual wind speed field so as to pass the actual wind speed field
The interstagy wind speed field approximation optimization module is used for solving the optimized parameters;
feeding the optimized parameters back to the two-dimensional cyclone vector field basis function construction module, and continuously iterating and optimizing to solve
And stopping iteration when the error setting condition is met, and obtaining the two-dimensional wind speed field after the best fitting and filling.
5. A computer-readable storage medium having computer-readable instructions stored thereon, which, when executed by a processor of a computer, cause the computer to perform the computing method of any one of claims 1-3.
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