CN111487477B - Thunderstorm cloud point charge positioning data complementation method based on atmospheric electric field instrument array group - Google Patents

Thunderstorm cloud point charge positioning data complementation method based on atmospheric electric field instrument array group Download PDF

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CN111487477B
CN111487477B CN202010448671.XA CN202010448671A CN111487477B CN 111487477 B CN111487477 B CN 111487477B CN 202010448671 A CN202010448671 A CN 202010448671A CN 111487477 B CN111487477 B CN 111487477B
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CN111487477A (en
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行鸿彦
杨旭
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Nanjing University of Information Science and Technology
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    • G01—MEASURING; TESTING
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    • G01R29/08—Measuring electromagnetic field characteristics
    • G01R29/0807—Measuring electromagnetic field characteristics characterised by the application
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    • G01R29/0842—Measurements related to lightning, e.g. measuring electric disturbances, warning systems
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Abstract

The invention discloses a thunderstorm cloud point charge positioning data complementation method based on an atmospheric electric field instrument array group, which comprises the following specific steps: firstly, an electric field component measurement model of an atmospheric electric field instrument is established, and azimuth parameters of electric charges of a thunderstorm cloud point are defined. According to the mirror image method principle, the charge coordinates of the thunderstorm cloud points are obtained by using a potential distribution formula. The positioning parameters include the distance from the electric field instrument to the thunderstorm cloud in addition to the horizontal deflection angle and the elevation angle. The method comprises the steps of establishing an atmospheric electric field instrument array group by taking a main electric field instrument as a reference, providing a thunderstorm cloud point charge positioning data complementation method based on the atmospheric electric field instrument array group, carrying out complementation processing on data measured by each electric field instrument, and obtaining the thunderstorm cloud point charge position again, thereby effectively solving the problem that the accuracy and the stability of the thunderstorm cloud point charge positioning are adversely affected due to data loss or distortion. The result shows that the method can accurately reflect the position of the charge of the thunderstorm cloud point and has a good positioning effect.

Description

Thunderstorm cloud point charge positioning data complementation method based on atmospheric electric field instrument array group
Technical Field
The invention relates to the technical field of thunderstorm cloud detection, in particular to a thunderstorm cloud point charge positioning data complementation method based on an atmospheric electric field instrument array group.
Background
Thunderstorm clouds are rain clouds generated after a certain intensity, and thunder is generated by charge accumulation in the thunderstorm clouds. With the development of social modernization, the effects of static induction and the like caused by lightning cause immeasurable loss to social economy. The large current and strong electromagnetic radiation generated in the lightning discharge process can damage ground forests, buildings, power electronic equipment, communication systems and the like, and even endanger personal safety. Therefore, an effective thunderstorm cloud detection method will help to reduce lightning hazards.
In the meteorological field, monitoring the atmospheric electric field in real time is one of important means for researching thunderstorm cloud distribution and lightning early warning. Therefore, the horizontal component and the vertical component of the atmospheric electric field are simultaneously observed by using the three-dimensional atmospheric electric field instrument, and more comprehensive charge azimuth information of the thunderstorm cloud point can be obtained. Research shows that researchers have realized real-time measurement of electric field components, but if the problem of data loss possibly caused by the complexity of the actual environment is considered, the actual application effect of the existing method needs to be further verified. The problem that the charge positioning performance of a thunderstorm cloud point is easily affected by data loss exists in the prior art.
Disclosure of Invention
The technical problem to be solved by the invention is to overcome the defects of the prior art and provide a thunderstorm cloud point charge positioning data complementation method based on an atmospheric electric field instrument array group.
The invention adopts the following technical scheme for solving the technical problems:
the invention provides a thunderstorm cloud point charge positioning data complementation method based on an atmospheric electric field instrument array group, which comprises the following steps:
step 1, establishing a main atmospheric electric field instrument model, wherein: the position N1(0,0,0) of the main atmospheric electric field instrument N1 is used as a coordinate origin, the south-righting direction is used as an X-axis positive half shaft, the east-righting direction is used as a Y-axis positive half shaft, and a three-dimensional rectangular coordinate system is established;
the coordinate of the thunderstorm cloud point charge M1 measured by N1 is M1 (x)1,y1,z1) The projection of M1 on the X-Y plane is M1' (X)1,y10), distances from M1 to X-axis, Y-axis and Z-axis of N1 are respectively X1、y1、z1(ii) a The sum of the height of the main atmospheric electric field instrument and the altitude of the main atmospheric electric field instrument is h 1; the horizontal deflection angle and the elevation angle of the charge of the thunderstorm cloud point measured by N1 are respectively represented as alpha 1 and beta 1; the distance from M1 to N1 measured by N1 is r1, and the electric field intensity of the thunderstorm cloud point charge measured by N1 is E1;
step 2, based on the coordinate system established in the step 1, the thunderstorm cloud is regarded as a point charge q1, and the potential distribution of the thunderstorm cloud point charge M1 at the main atmospheric electric field instrument N1 is obtained
Figure BDA0002506728550000026
Figure BDA0002506728550000021
Wherein q1' is the mirror charge of the point charge q1,ε1is the dielectric constant of air, epsilon2The dielectric constant of the ground where the main atmospheric electric field instrument N1 is located;
the electric field strength E1 is subjected to orthogonal decomposition to obtain:
E1＝Ex1+Ey1+Ez1；
wherein E isx1、Ey1、Ez1Respectively measuring electric field intensity components of the thunderstorm cloud point charges in the X-axis direction, the Y-axis direction and the Z-axis direction for N1, wherein every two electric field intensity components are mutually vertical;
potential distribution in X, Y, Z-axis directions
Figure BDA0002506728550000027
Derivation is performed, so that the spherical coordinates (r1, α 1, β 1) of the thunderstorm cloud point charge M1 are obtained as follows:
Figure BDA0002506728550000022
intermediate variables
Figure BDA0002506728550000023
Intermediate variables
Figure BDA0002506728550000024
Combining the spherical coordinates (r1, alpha 1 and beta 1) of the thunderstorm cloud point charge M1, and obtaining the rectangular coordinates (x) of the thunderstorm cloud point charge M1 according to the vector relation of the main atmospheric electric field instrument model1,y1,z1) Comprises the following steps:
Figure BDA0002506728550000025
step 3, establishing an atmospheric electric field instrument array group model based on the coordinate system established in the step 1, wherein the altitude of the first sub-atmospheric electric field instrument N2 and the altitude of the second sub-atmospheric electric field instrument N3 are the same as the altitude of the second sub-atmospheric electric field instrument N1; n2 is located at the position (x)N2,yN20), the distances from N2 to the X-axis, Y-axis and Z-axis of N1 are X respectivelyN2、y N20; position N3In the position (x)N3,yN30), the distances from N3 to the X-axis, Y-axis and Z-axis of N1 are X respectivelyN3、yN3、0；
At this time, [ E ] is definedx2,Ey2,Ez2]Value of atmospheric electric field measured for N2, Ex2、Ey2、Ez2Respectively measuring electric field intensity components in X-axis, Y-axis and Z-axis directions for N2; [ E ]x3,Ey3,Ez3]Value of atmospheric electric field measured for N3, Ex3、Ey3、Ez3Respectively measuring electric field intensity components in X-axis, Y-axis and Z-axis directions for N3;
the coordinate of the charge M1 of the thunderstorm cloud point measured by N1 is (x)1,y1,z1) Using [ E ] in the same manner as in step 2x2,Ey2,Ez2]、[Ex3,Ey3,Ez3]The coordinates of the thunderstorm cloud point charge M1 directly measured by N2 and N3 are respectively (X)2,Y2,Z2)、(X3,Y3,Z3) Namely: the distances from M1 to the X axis, the Y axis and the Z axis of N2 measured by N2 are respectively X2、Y2、Z2(ii) a The distances from M1 to the X axis, the Y axis and the Z axis of N3 measured by N3 are respectively X3、Y3、Z3(ii) a Then, from the observation angle of N1, the coordinates of the thunderstorm cloud point charge M1 indirectly measured by N2 and N3 are respectively (x)2,y2,z2)、(x3,y3,z3) The following are:
Figure BDA0002506728550000031
wherein the distances from M1 to the X axis, Y axis and Z axis of N1 measured from N2 are X2、y2、z2(ii) a The distances from M1 to the X axis, the Y axis and the Z axis of N1 measured by N3 are respectively X3、y3、z3；
Expanding N2 and N3 outwards on an X0Y plane by taking the coordinate system established in the step 1 as a reference, and jointly positioning a thunderstorm cloud point charge M1; presetting a deviation rate threshold value P%(ii) a After the data measured by each electric field instrument are subjected to complementary processing, the charge coordinates (X, Y, Z) and the horizontal deflection angle of the thunderstorm cloud point are obtained again
Figure BDA0002506728550000039
And the expression of the elevation angle theta is as follows; x, Y, Z are the distances retrieved from M1 to the X, Y and Z axes of N1, respectively;
in the first case: for (x)i,yi,zi) And i is 1,2 and 3, when the deviation rate of each axis data measured by N1, N2 and N3 is less than P%, performing complementary processing on each axis data, and obtaining the charge positions of the thunderstorm cloud points:
when in use
Figure BDA0002506728550000032
When the temperature of the water is higher than the set temperature,
Figure BDA0002506728550000033
in the second case: for (x)i,yi,zi)，i＝1,2,3：
When the deviation rate of the data of each axis measured by N1 and N2 is more than P%, and the deviation rate of the data of each axis measured by N1 and N3 is less than P%, the following expression is obtained after the data complementation method is used for processing:
when in use
Figure BDA0002506728550000034
Or
Figure BDA0002506728550000035
Or
Figure BDA0002506728550000036
And is
Figure BDA0002506728550000037
Figure BDA0002506728550000038
When the temperature of the water is higher than the set temperature,
Figure BDA0002506728550000041
when the deviation rate of the data of each axis measured by N1 and N3 is more than P%, and the deviation rate of the data of each axis measured by N1 and N2 is less than P%, the following expression is obtained after the data are processed by a data complementation method:
when in use
Figure BDA0002506728550000042
Or
Figure BDA0002506728550000043
Or
Figure BDA0002506728550000044
And is
Figure BDA0002506728550000045
Figure BDA0002506728550000046
When the temperature of the water is higher than the set temperature,
Figure BDA0002506728550000047
in the third case: for (x)i,yi,zi) When the deviation rate of any axis data measured between any two electric field instruments of N1, N2 and N3 is greater than P%, resetting the charge positioning data of the thunderstorm cloud point to zero, wherein the corresponding expression is as follows:
when in use
Figure BDA0002506728550000048
Or
Figure BDA0002506728550000049
Or
Figure BDA00025067285500000410
And is
Figure BDA00025067285500000411
Or
Figure BDA00025067285500000412
Or
Figure BDA00025067285500000413
When the temperature of the water is higher than the set temperature,
Figure BDA00025067285500000414
in a fourth case: for (x)i,yi,zi) When the deviation ratio of each axis data measured between N2 and N3 is less than P%, and the deviation ratio of each axis data measured between N2 and N3 and N1 is more than P%, the following expression is obtained after processing by a data complementation method:
when in use
Figure BDA00025067285500000415
And is
Figure BDA00025067285500000416
Or
Figure BDA00025067285500000417
Or
Figure BDA00025067285500000418
When the temperature of the water is higher than the set temperature,
Figure BDA0002506728550000051
as a further optimization scheme of the thunderstorm cloud point charge positioning data complementation method based on the atmospheric electric field instrument array group, in step 2, a specific method for obtaining spherical coordinates (r1, α 1, β 1) of the thunderstorm cloud point charge M1 is as follows:
the electric field intensity E1 is a three-dimensional vector, and is obtained by orthogonally decomposing E1:
E1＝Ex1+Ey1+Ez1 (1)
wherein E isx1、Ey1、Ez1The electric field intensity components of the charge of the thunderstorm cloud point in the X-axis direction, the Y-axis direction and the Z-axis direction are respectively measured by N1, and the two components are mutually perpendicular.
Potential distribution in X, Y, Z-axis directions
Figure BDA0002506728550000052
And (3) carrying out derivation:
Figure BDA0002506728550000053
z 12 orders of magnitude higher than h1, then:
z1≈z1-h1≈z1+h1 (3)
based on the main atmospheric electric field instrument model, the distance r1 from M1 to N1 is:
Figure BDA0002506728550000054
by using the formulas (3) and (4), the formula (2) is changed to:
Figure BDA0002506728550000055
in the formula (5), intermediate variables
Figure BDA0002506728550000056
Intermediate variables
Figure BDA0002506728550000057
According to the formula (5), the spherical coordinates (r1, α 1, β 1) of the thunderstorm cloud point charge M1 are obtained as follows:
Figure BDA0002506728550000061
as a further optimization scheme of the thunderstorm cloud point charge positioning data complementation method based on the atmospheric electric field instrument array group, X2、Y2、Z2Are respectively as
Figure BDA0002506728550000062
Wherein r2 is the distance from M1 to N2 measured by N2, alpha 2 is the horizontal deflection angle of the charge of the thunderstorm cloud point measured by N2, and beta 2 is the elevation angle of the charge of the thunderstorm cloud point measured by N2.
As a further optimization scheme of the thunderstorm cloud point charge positioning data complementation method based on the atmospheric electric field instrument array group, X3、Y3、Z3Respectively as follows:
Figure BDA0002506728550000063
wherein r3 is the distance from M1 to N3 measured by N3, alpha 3 is the horizontal deflection angle of the charge of the thunderstorm cloud point measured by N3, and beta 3 is the elevation angle of the charge of the thunderstorm cloud point measured by N3.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
(1) firstly, establishing a single atmospheric electric field measurement model based on a three-dimensional atmospheric electric field instrument, and deducing a thunderstorm cloud point charge coordinate calculation formula of a main electric field instrument according to a mirror image method theory; an electric field instrument array group model is built around a main electric field instrument on an X0Y plane, and a thunderstorm cloud point charge positioning data complementation method is provided;
(2) the method not only can utilize the array group to measure the thunderstorm cloud point charge azimuth data to carry out complementary processing on the thunderstorm cloud point charge azimuth data and obtain the point charge position again, but also can effectively solve the problem of positioning data loss.
Drawings
FIG. 1 is a model of a main atmospheric electric field instrument.
FIG. 2 is an atmospheric electric field instrument array cluster model.
FIG. 3 is a relationship curve of the distance from the charge of the cloud point of the thunderstorm to the electric field instrument, the measurement error of the electric field component and the distance measurement error.
FIG. 4 is a graph showing the relationship between the distance from the charge of the cloud point of the thunderstorm to the electric field instrument, the elevation angle and the measurement error of the horizontal deflection angle.
FIG. 5 is a graph showing the relationship between the distance from the cloud point charge of the thunderstorm to the electric field instrument, the elevation angle and the measurement error of the elevation angle.
FIG. 6 is a plot of the site distribution of an actual atmospheric E-field instrument array cluster.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in detail with reference to the accompanying drawings and specific embodiments.
The invention provides a thunderstorm cloud point charge positioning data complementation method based on an atmospheric electric field instrument array group, which comprises the following steps:
establishing a main atmospheric electric field instrument model, which specifically comprises the following steps:
as shown in fig. 1, a three-dimensional rectangular coordinate system is established with a position N1(0,0,0) of the main atmospheric electric field instrument as an origin of coordinates, a south-positive direction as an X-axis positive half axis, and an east-positive direction as a Y-axis positive half axis; the coordinate of the charge of the thunderstorm cloud point measured by N1 is M1 (x)1,y1,z1) The projection of M1 on the X-Y plane is M1' (X)1,y10), distances from M1 to X-axis, Y-axis and Z-axis of N1 are respectively X1、y1、z1. The sum of the height of the main atmospheric electric field instrument and the altitude of the main atmospheric electric field instrument is h 1. The horizontal declination and elevation of the charge of the cloud point of the thunderstorm are denoted as α 1 and β 1, respectively. The distance from M1 to N1 is r1, and the electric field intensity of the thunderstorm cloud point charge measured by N1 is E1.
Secondly, the thunderstorm cloud is regarded as a point charge q1, and the potential distribution of the thunderstorm cloud point charge M1 at the main atmospheric electric field instrument N1 is obtained
Figure BDA0002506728550000071
Comprises the following steps:
Figure BDA0002506728550000072
in the formula (1), q1' is the mirror charge of the point charge q1,. epsilon1Is the dielectric constant of air, epsilon2Is the dielectric constant of the ground on which the atmospheric electric field instrument N is located.
The electric field intensity E1 is a three-dimensional vector, and is obtained by orthogonally decomposing E1:
E1＝Ex1+Ey1+Ez1 (2)
in the formula (2), Ex1、Ey1、Ez1The electric field intensity components of the thunderstorm cloud point charges in the X-axis direction, the Y-axis direction and the Z-axis direction are respectively measured by N1, and two components are mutually perpendicular.
Potential distribution in X, Y, Z-axis directions
Figure BDA0002506728550000073
And (3) carrying out derivation:
Figure BDA0002506728550000081
in general, z1Typically 2 orders of magnitude higher than h1, then:
z1≈z1-h1≈z1+h1 (4)
based on the main atmospheric electric field instrument model, the distance r1 from M1 to N1 is:
Figure BDA0002506728550000082
by using the formula (4) and the formula (5), the formula (3) is changed to:
Figure BDA0002506728550000083
in the formula (6), intermediate variables
Figure BDA0002506728550000084
According to the formula (6), the spherical coordinates (r1, α 1, β 1) of the thunderstorm cloud point charge M1 are obtained as follows:
Figure BDA0002506728550000085
combining the spherical coordinates (r1, alpha 1 and beta 1) of the thunderstorm cloud point charge M1, and obtaining the rectangular coordinates (x) of the thunderstorm cloud point charge M1 according to the vector relation of the main atmospheric electric field instrument model1,y1,z1) Comprises the following steps:
Figure BDA0002506728550000086
providing a thunderstorm cloud point charge positioning data complementation method based on an atmospheric electric field instrument array group, which specifically comprises the following steps:
establishing an atmospheric electric field instrument array group model shown in fig. 2, and establishing the atmospheric electric field instrument array group model based on the coordinate system established in the step 1, wherein the altitude of the first sub-atmospheric electric field instrument N2 and the altitude of the second sub-atmospheric electric field instrument N3 are the same as the altitude of the first sub-atmospheric electric field instrument N1; n2 is located at the position (x)N2,yN20), the distances from N2 to the X-axis, Y-axis and Z-axis of N1 are X respectivelyN2、y N20; n3 is located at the position (x)N3,yN30), the distances from N3 to the X-axis, Y-axis and Z-axis of N1 are X respectivelyN3、yN3、0；
At this time, [ E ] is definedx2,Ey2,Ez2]Value of atmospheric electric field measured for N2, Ex2、Ey2、Ez2Respectively measuring electric field intensity components in X-axis, Y-axis and Z-axis directions for N2; [ E ]x3,Ey3,Ez3]Value of atmospheric electric field measured for N3, Ex3、Ey3、Ez3Respectively measuring electric field intensity components in X-axis, Y-axis and Z-axis directions for N3;
the coordinate of the charge M1 of the thunderstorm cloud point measured by N1 is (x)1,y1,z1) Using [ E ] in the same manner as in step 2x2,Ey2,Ez2]、[Ex3,Ey3,Ez3]The coordinates of the thunderstorm cloud point charge M1 directly measured by N2 and N3 are respectively (X)2,Y2,Z2)、(X3,Y3,Z3) Namely: the distances from M1 to the X axis, the Y axis and the Z axis of N2 measured by N2 are respectively X2、Y2、Z2(ii) a The distances from M1 to the X axis, the Y axis and the Z axis of N3 measured by N3 are respectively X3、Y3、Z3(ii) a Then, from the observation angle of N1, the coordinates of the thunderstorm cloud point charge M1 indirectly measured by N2 and N3 are respectively (x)2,y2,z2)、(x3,y3,z3) The following are:
Figure BDA0002506728550000091
wherein the distances from M1 to the X axis, Y axis and Z axis of N1 measured from N2 are X2、y2、z2(ii) a The distances from M1 to the X axis, the Y axis and the Z axis of N1 measured by N3 are respectively X3、y3、z3；
Figure BDA0002506728550000092
Wherein r2 is the distance from M1 to N2 measured by N2, alpha 2 is the horizontal deflection angle of the charge of the thunderstorm cloud point measured by N2, and beta 2 is the elevation angle of the charge of the thunderstorm cloud point measured by N2.
Figure BDA0002506728550000093
Wherein r3 is the distance from M1 to N3 measured by N3, alpha 3 is the horizontal deflection angle of the charge of the thunderstorm cloud point measured by N3, and beta 3 is the elevation angle of the charge of the thunderstorm cloud point measured by N3.
Based on the coordinate system shown in fig. 1, the thunderstorm cloud point charges M1 are jointly located by spreading N2 and N3 outwards on an X0Y plane. The charge positioning data of the thunderstorm cloud points measured by each electric field instrument may have data loss or distortion. For this possibility, a deviation rate threshold value P% is set in advance in order to more intuitively represent the data complementation method.
After the data measured by each electric field instrument are subjected to complementary processing, the charge coordinates (X, Y, Z) and the horizontal deflection angle of the thunderstorm cloud point are obtained again
Figure BDA00025067285500001014
And the expression for the elevation angle θ is as follows: (the distances of the recovered M1 from the X-axis, Y-axis and Z-axis of N1 are X, Y, Z respectively)
1) For (x)i,yi,zi) And i is 1,2 and 3, when the deviation rate of each axis data measured by N1, N2 and N3 is less than P%, performing complementary processing on each axis data, and obtaining the charge positions of the thunderstorm cloud points:
when in use
Figure BDA0002506728550000101
When the temperature of the water is higher than the set temperature,
Figure BDA0002506728550000102
2) for (x)i,yi,zi) I is 1,2, 3: when the deviation rate of the data of each axis measured by N1 and N2 is more than P%, and the deviation rate of the data of each axis measured by N1 and N3 is less than P%, the following expression is obtained after the data complementation method is used for processing:
when in use
Figure BDA0002506728550000103
Or
Figure BDA0002506728550000104
Or
Figure BDA0002506728550000105
And is
Figure BDA0002506728550000106
Figure BDA0002506728550000107
When the temperature of the water is higher than the set temperature,
Figure BDA0002506728550000108
when the deviation rate of the data of each axis measured by N1 and N3 is more than P%, and the deviation rate of the data of each axis measured by N1 and N2 is less than P%, the following expression is obtained after the data are processed by a data complementation method:
when in use
Figure BDA0002506728550000109
Or
Figure BDA00025067285500001010
Or
Figure BDA00025067285500001011
And is
Figure BDA00025067285500001012
Figure BDA00025067285500001013
When the temperature of the water is higher than the set temperature,
Figure BDA0002506728550000111
3) for (x)i,yi,zi) When the deviation rate of any axis data measured between any two electric field instruments of N1, N2 and N3 is greater than P%, resetting the charge positioning data of the thunderstorm cloud point to zero, wherein the corresponding expression is as follows:
when in use
Figure BDA0002506728550000112
Or
Figure BDA0002506728550000113
Or
Figure BDA0002506728550000114
And is
Figure BDA0002506728550000115
Or
Figure BDA0002506728550000116
Or
Figure BDA0002506728550000117
When the temperature of the water is higher than the set temperature,
Figure BDA0002506728550000118
4) for (x)i,yi,zi) When the deviation ratio of each axis data measured between N2 and N3 is less than P%, and the deviation ratio of each axis data measured between N2 and N3 and N1 is more than P%, the following expression is obtained after processing by a data complementation method:
when in use
Figure BDA0002506728550000119
And is
Figure BDA00025067285500001110
Or
Figure BDA00025067285500001111
Or
Figure BDA00025067285500001112
When the temperature of the water is higher than the set temperature,
Figure BDA00025067285500001113
according to the method of the embodiment, the performance analysis of the method for complementing the charge positioning data of the thunderstorm cloud points based on the atmospheric electric field instrument array group in the aspects of ranging and direction finding is carried out as follows:
combining the air charge electric field distribution and the thunderstorm cloud charge structure principle, the standard deviation of the electric field component measurement can be set as
Figure BDA00025067285500001114
1. Thunderstorm cloud point charge positioning ranging and direction finding performance analysis
Based on the indirect measurement error theory, measuring errors from electric field components
Figure BDA00025067285500001115
Causing measurement errors in the distance r1, horizontal declination angle alpha 1, and elevation angle beta 1
Figure BDA00025067285500001116
Comprises the following steps:
Figure BDA0002506728550000121
2. thunderstorm cloud point charge positioning and ranging performance analysis
Using equation (13), the distance r1 was investigated, and the electric field component measurement error was
Figure BDA0002506728550000122
And distance measurement error
Figure BDA0002506728550000123
The simulation results are shown in FIG. 3. In FIG. 3, the range error
Figure BDA0002506728550000124
Measured error due to distance r1 and electric field component
Figure BDA0002506728550000125
And is greatly affected by the former. Error in range finding
Figure BDA0002506728550000126
Both with distance r1 and electric field measurement error
Figure BDA0002506728550000127
Is increased. When error occurs
Figure BDA0002506728550000128
At 0 to 1kV/m, range error
Figure BDA0002506728550000129
Almost independent of the variation of the distance r1, the error is less than 0.06 km. In addition, when there is an error
Figure BDA00025067285500001210
When the voltage is more than 1kV/m, the distance measurement error
Figure BDA00025067285500001211
Increases sharply with increasing distance r1, conforming to the characteristics of a cubic function. In particular, when the distance r1 is greater than 1km, the ranging error
Figure BDA00025067285500001212
The linear increase with the increase of the distance r1 can reach 0.12km at most. In summary, the ranging error
Figure BDA00025067285500001213
Less than 0.12km, which fully embodies the stability of the ranging performance of the data complementation method.
3. Thunderstorm cloud point charge positioning direction-finding performance analysis
The direction finding performance simulation results shown in fig. 4 and 5 were obtained from equation (13). In FIG. 3, as distance r1 and elevation angle β 1 increase, horizontal declination measurement error
Figure BDA00025067285500001214
And will increase accordingly. In particular, when the distance r1 is between 0 and 1km, the measurement error
Figure BDA00025067285500001215
Hardly influenced by the change of the elevation angle beta 1, and hardly influenced by the error
Figure BDA00025067285500001216
Less than 0.5 degrees. But when the distance r1 is between 1 and 2km, the error is
Figure BDA00025067285500001217
Will increase exponentially with the increase of the elevation angle beta 1, and the error will increase exponentially
Figure BDA00025067285500001218
Will reach 1.9 degrees. Likewise, in FIG. 4, the elevation measurement error
Figure BDA00025067285500001219
Increasing slowly with increasing distance r1 and elevation angle β 1. However, when the distance r1 is in the range of 1 to 2km, the error increases with the elevation angle β 1
Figure BDA00025067285500001220
Slowly rises to 0.16 degrees in a parabolic fashion.
In the actual measurement experiment, the main atmospheric electric field instrument of the Nanjing university of information engineering test station is installed in the institute of electronics and information engineering, the distance between the electric field instrument and the average sea level is about 28 meters, and the positive half shafts of the X axis and the Y axis respectively point to the south and the east. Meanwhile, a first sub-atmospheric electric field instrument N2 and a second sub-atmospheric electric field instrument N3 for forming an array group are respectively installed at the Binjiang station and the Pancheng station, as shown in fig. 6.
In FIG. 6, the coordinates of N2 and N3 are (0, -1,0) and (-1,1,0), respectively, in km. P% was selected as 20% as the deviation ratio of the interaxial data, and the following two sets of experiments were performed.
1. Cloudy day experiment
The measurement data (unit: kV/m) of the three-dimensional atmospheric electric field instrument array group at 06 minutes on day 10 of 4/9 in 2019 are shown in Table 1.
TABLE 06 points of experimental data for 4, 9, 10, 12019 years
Figure BDA0002506728550000131
In table 1, the relationship between three-dimensional electric field components measured from a single electric field apparatus cannot be directly seen. It is difficult to judge whether there is data loss only from the values of the horizontal component and the vertical component. Therefore, it is difficult to further obtain the position of the charge of the cloud point of the thunderstorm. It is noted that the vertical electric field component is larger than the horizontal electric field component, and therefore, the existence of a thunderstorm cloud over the site of the main electric field instrument can be preliminarily predicted.
As shown in table 1, the problem reflected by the measured data of the array group is consistent with the formula (8) and the corresponding description, which indicates that the measured data of 06 minutes at 10 hours of each electric field instrument is normal. After the data complementation method is introduced, the actually measured data is processed by using the formula (8). The charge coordinates of the thunderstorm cloud point are (0.094, -0.138,0.513) (unit: km) based on the atmospheric electric field instrument array group. This indicates that the point charge is 55.74 degrees south partial west and is about 539 meters from the master station. In particular, the point charge elevation angle is large, reaching 71.97 degrees, which indicates that thunderstorm cloud exists in the area above the main atmospheric electric field instrument, and further verifies the previous hypothesis.
2. Sunny day experiment
The measurement data (unit: kV/m) of the three-dimensional atmospheric electric field instrument array group at 20 hours, 22 months, 22 days and 43 minutes in 2019 are shown in Table 2.
TABLE 22019 Experimental data for 4 month, 22 day, 20 hours, 43 points
Figure BDA0002506728550000132
Also, in table 2, it is difficult to judge whether there is data loss according to only the values of the horizontal component and the vertical component. Therefore, it is difficult to further obtain the position of the charge of the cloud point of the thunderstorm. In general, the three-dimensional atmospheric electric field component values are small. However, the electric field instrument measures that the vertical electric field component has a larger value exceeding 1kv/m, and the existence of the thunderstorm cloud can be guessed before introducing the data complementation method.
As shown in table 2, the problem reflected by the measured data of the array group is in accordance with the expression (11) and the corresponding description, which indicates that the data measured by each electric field instrument at time 20 and time 43 is lost. After a data complementation method is introduced, the actually measured data is processed by using a formula (11), and the charge coordinates of the thunderstorm cloud point are (0,0, 0). At this time, it can be judged that the thunderstorm cloud does not appear over the master station. For the previous misguess, the main reason is that the single electric field instrument is difficult to judge the authenticity of the charge coordinates of the thunderstorm cloud points. Although the values are relatively large, in the case of sunny weather, the deviation is likely due to other electric field disturbances, not the weather itself.
According to the above experimental results, the following conclusions are reached:
in order to reduce the negative influence of data loss on the positioning performance of the thunderstorm cloud point charge positioning process, a thunderstorm cloud point charge positioning data complementation method based on an atmospheric electric field instrument array group is provided. The method is applied to the thunderstorm cloud detection, and the limitation that observers can acquire the charge azimuth of the thunderstorm cloud point only when a single electric field instrument works normally is reduced. The result shows that compared with the data measured by a single electric field instrument, the method has better effect on the aspect of point charge positioning, and effectively enlarges the monitoring range of the thunderstorm area.
The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.

Claims (4)

1. A thunderstorm cloud point charge positioning data complementation method based on an atmospheric electric field instrument array group is characterized by comprising the following steps:
step 1, establishing a main atmospheric electric field instrument model, wherein: the position N1(0,0,0) of the main atmospheric electric field instrument N1 is used as a coordinate origin, the south-righting direction is used as an X-axis positive half shaft, the east-righting direction is used as a Y-axis positive half shaft, and a three-dimensional rectangular coordinate system is established;
the coordinate of the thunderstorm cloud point charge M1 measured by N1 is M1 (x)1,y1,z1) The projection of M1 on the X-Y plane is M1' (X)1,y10), distances from M1 to X-axis, Y-axis and Z-axis of N1 are respectively X1、y1、z1(ii) a The sum of the height of the main atmospheric electric field instrument and the altitude of the main atmospheric electric field instrument is h 1; the horizontal deflection angle and the elevation angle of the charge of the thunderstorm cloud point measured by N1 are respectively represented as alpha 1 and beta 1; the distance from M1 to N1 measured by N1 is r1, and the distance from N1 isThe electric field intensity of the cloud point charge is E1;
step 2, based on the coordinate system established in the step 1, the thunderstorm cloud is regarded as a point charge q1, and the potential distribution of the thunderstorm cloud point charge M1 at the main atmospheric electric field instrument N1 is obtained
Figure FDA0002506728540000011
Figure FDA0002506728540000012
Wherein q1' is the mirror charge of the point charge q1, ∈1Is the dielectric constant of air, epsilon2The dielectric constant of the ground where the main atmospheric electric field instrument N1 is located;
the electric field strength E1 is subjected to orthogonal decomposition to obtain:
E1＝Ex1+Ey1+Ez1；
wherein E isx1、Ey1、Ez1Respectively measuring electric field intensity components of the thunderstorm cloud point charges in the X-axis direction, the Y-axis direction and the Z-axis direction for N1, wherein every two electric field intensity components are mutually vertical;
potential distribution in X, Y, Z-axis directions
Figure FDA0002506728540000013
Derivation is performed, so that the spherical coordinates (r1, α 1, β 1) of the thunderstorm cloud point charge M1 are obtained as follows:
Figure FDA0002506728540000014
intermediate variables
Figure FDA0002506728540000015
Intermediate variables
Figure FDA0002506728540000016
Ball seat combined with thunderstorm cloud point charge M1And (r1, alpha 1 and beta 1) obtaining the rectangular coordinates (x) of the thunderstorm cloud point charge M1 according to the vector relation of the main atmospheric electric field instrument model1,y1,z1) Comprises the following steps:
Figure FDA0002506728540000021
step 3, establishing an atmospheric electric field instrument array group model based on the coordinate system established in the step 1, wherein the altitude of the first sub-atmospheric electric field instrument N2 and the altitude of the second sub-atmospheric electric field instrument N3 are the same as the altitude of the second sub-atmospheric electric field instrument N1; n2 is located at the position (x)N2,yN20), the distances from N2 to the X-axis, Y-axis and Z-axis of N1 are X respectivelyN2、yN20; n3 is located at the position (x)N3,yN30), the distances from N3 to the X-axis, Y-axis and Z-axis of N1 are X respectivelyN3、yN3、0；
At this time, [ E ] is definedx2,Ey2,Ez2]Value of atmospheric electric field measured for N2, Ex2、Ey2、Ez2Respectively measuring electric field intensity components in X-axis, Y-axis and Z-axis directions for N2; [ E ]x3,Ey3,Ez3]Value of atmospheric electric field measured for N3, Ex3、Ey3、Ez3Respectively measuring electric field intensity components in X-axis, Y-axis and Z-axis directions for N3;
the coordinate of the charge M1 of the thunderstorm cloud point measured by N1 is (x)1,y1,z1) Using [ E ] in the same manner as in step 2x2,Ey2,Ez2]、[Ex3,Ey3,Ez3]The coordinates of the thunderstorm cloud point charge M1 directly measured by N2 and N3 are respectively (X)2,Y2,Z2)、(X3,Y3,Z3) Namely: the distances from M1 to the X axis, the Y axis and the Z axis of N2 measured by N2 are respectively X2、Y2、Z2(ii) a The distances from M1 to the X axis, the Y axis and the Z axis of N3 measured by N3 are respectively X3、Y3、Z3(ii) a Then, from the observation angle of N1, the coordinates of the thunderstorm cloud point charge M1 indirectly measured by N2 and N3 are respectively (x)2,y2,z2)、(x3,y3,z3) The following are:
Figure FDA0002506728540000022
wherein the distances from M1 to the X axis, Y axis and Z axis of N1 measured from N2 are X2、y2、z2(ii) a The distances from M1 to the X axis, the Y axis and the Z axis of N1 measured by N3 are respectively X3、y3、z3；
Expanding N2 and N3 outwards on an X0Y plane by taking the coordinate system established in the step 1 as a reference, and jointly positioning a thunderstorm cloud point charge M1; presetting a deviation rate threshold value P%; after the data measured by each electric field instrument are subjected to complementary processing, the charge coordinates (X, Y, Z) and the horizontal deflection angle of the thunderstorm cloud point are obtained again
Figure FDA0002506728540000023
And the expression of the elevation angle theta is as follows; x, Y, Z are the distances retrieved from M1 to the X, Y and Z axes of N1, respectively;
in the first case: for (x)i,yi,zi) And i is 1,2 and 3, when the deviation rate of each axis data measured by N1, N2 and N3 is less than P%, performing complementary processing on each axis data, and obtaining the charge positions of the thunderstorm cloud points:
when in use
Figure FDA0002506728540000031
When the temperature of the water is higher than the set temperature,
Figure FDA0002506728540000032
in the second case: for (x)i,yi,zi)，i＝1,2,3：
When the deviation rate of the data of each axis measured by N1 and N2 is more than P%, and the deviation rate of the data of each axis measured by N1 and N3 is less than P%, the following expression is obtained after the data complementation method is used for processing:
when in use
Figure FDA0002506728540000033
Or
Figure FDA0002506728540000034
Or
Figure FDA0002506728540000035
And is
Figure FDA0002506728540000036
Figure FDA0002506728540000037
When the temperature of the water is higher than the set temperature,
Figure FDA0002506728540000038
when the deviation rate of the data of each axis measured by N1 and N3 is more than P%, and the deviation rate of the data of each axis measured by N1 and N2 is less than P%, the following expression is obtained after the data are processed by a data complementation method:
when in use
Figure FDA0002506728540000039
Or
Figure FDA00025067285400000310
Or
Figure FDA00025067285400000311
And is
Figure FDA00025067285400000312
Figure FDA00025067285400000313
When the temperature of the water is higher than the set temperature,
Figure FDA00025067285400000314
in the third case: for (x)i,yi,zi) When the deviation rate of any axis data measured between any two electric field instruments of N1, N2 and N3 is greater than P%, resetting the charge positioning data of the thunderstorm cloud point to zero, wherein the corresponding expression is as follows:
when in use
Figure FDA00025067285400000315
Or
Figure FDA00025067285400000316
Or
Figure FDA00025067285400000317
And is
Figure FDA00025067285400000318
Or
Figure FDA0002506728540000041
Or
Figure FDA0002506728540000042
When the temperature of the water is higher than the set temperature,
Figure FDA0002506728540000043
in a fourth case: for (x)i,yi,zi) When the deviation ratio of each axis data measured between N2 and N3 is less than P%, and the deviation ratio of each axis data measured between N2 and N3 and N1 is more than P%, the following expression is obtained after processing by a data complementation method:
when in use
Figure FDA0002506728540000044
And is
Figure FDA0002506728540000045
Or
Figure FDA0002506728540000046
Or
Figure FDA0002506728540000047
When the temperature of the water is higher than the set temperature,
Figure FDA0002506728540000048
2. the method as claimed in claim 1, wherein the specific method for obtaining the spherical coordinates (r1, α 1, β 1) of the electrical charge M1 of the thunderstorm cloud point in step 2 is as follows:
the electric field intensity E1 is a three-dimensional vector, and is obtained by orthogonally decomposing E1:
E1＝Ex1+Ey1+Ez1 (1)
wherein E isx1、Ey1、Ez1Respectively measuring electric field intensity components of the thunderstorm cloud point charges in the X-axis direction, the Y-axis direction and the Z-axis direction for N1, wherein every two electric field intensity components are mutually vertical;
potential distribution in X, Y, Z-axis directions
Figure FDA0002506728540000049
And (3) carrying out derivation:
Figure FDA0002506728540000051
z12 orders of magnitude higher than h1, then:
z1≈z1-h1≈z1+h1 (3)
based on the main atmospheric electric field instrument model, the distance r1 from M1 to N1 is:
Figure FDA0002506728540000052
by using the formulas (3) and (4), the formula (2) is changed to:
Figure FDA0002506728540000053
in the formula (5), intermediate variables
Figure FDA0002506728540000054
Intermediate variables
Figure FDA0002506728540000055
According to the formula (5), the spherical coordinates (r1, α 1, β 1) of the thunderstorm cloud point charge M1 are obtained as follows:
Figure FDA0002506728540000056
3. the method of claim 1, wherein X is X2、Y2、Z2Are respectively as
Figure FDA0002506728540000057
Wherein r2 is the distance from M1 to N2 measured by N2, alpha 2 is the horizontal deflection angle of the charge of the thunderstorm cloud point measured by N2, and beta 2 is the elevation angle of the charge of the thunderstorm cloud point measured by N2.
4. The atmospheric electric field instrument array group-based thunderstorm cloud point charge localization method according to claim 1Data complementation method, characterized in that X3、Y3、Z3Respectively as follows:
Figure FDA0002506728540000061
wherein r3 is the distance from M1 to N3 measured by N3, alpha 3 is the horizontal deflection angle of the charge of the thunderstorm cloud point measured by N3, and beta 3 is the elevation angle of the charge of the thunderstorm cloud point measured by N3.
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