CN113848374A - Ultra-long distance lightning intensity inversion algorithm considering influence of curvature radius of earth - Google Patents
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Abstract
The application relates to an ultra-long distance lightning intensity inversion algorithm considering the influence of the curvature radius of the earth, which is characterized in that firstly, lightning signals with different distances from an observation point are normalized to a preset distance according to the propagation rule of a lightning electromagnetic field along the surface of the earth; if the distance from the lightning signal to the observation point is more than 200km, the electric field amplitude E of the lightning signal is measuredPEAKThe attenuation law exhibited with the increase of the observation distance d is set as d‑1.32(ii) a If the distance from the lightning signal to the observation point is less than 200km, the electric field amplitude E of the lightning signal is measuredPEAKThe attenuation law exhibited with the increase of the observation distance d is set as d‑1(ii) a When thunder occurs, acquiring a magnetic field intensity peak value of the thunder at an observation point; and inverting the current peak value of the lightning according to the magnetic field intensity peak value. The lightning current peak value estimation model established by the algorithm provides technical support for business applications such as lightning detection, early warning and forecasting of disastrous weather and the like.
Description
Technical Field
The application relates to the technical field of lightning electromagnetic wave transmission and lightning detection, in particular to an ultra-long distance lightning intensity inversion algorithm considering the influence of the curvature radius of the earth.
Background
In the global scope, hundreds of lightning strikes occur every second, and electromagnetic waves with frequencies from extremely low frequency to ultrahigh frequency are released when frequent lightning strikes occur. In actual work, researchers can detect lightning radiation corresponding to different wave bands by using different detecting instruments, and further determine parameters such as spatial positions of lightning discharge and discharge parameters. However, because electromagnetic waves of different frequency bands are affected by factors such as soil conductivity, topography with high and low surface and earth ionosphere dielectric medium in the transmission process, the electromagnetic waves are attenuated in different degrees on different scales in the transmission process, unnecessary errors are brought to the time, position, intensity, polarity, charge, energy and the like for telemetering the discharge parameters of thunder and lightning by using the electromagnetic field characteristics of thunder and lightning radiation, and then great uncertainty is brought to the inversion of the discharge parameters of thunder and lightning, the determination of the intensity of the ground lightning and the position of a landing point and the like.
On the one hand in the local area (from 10)3Rice to 104Meters), which is typically the detection range of a ground-based lightning location net. When a lightning electromagnetic field propagates along the ground surface, due to the influence of the limitation of ground conductivity and the fluctuation characteristics of the ground, the electromagnetic radiation energy of a High Frequency (HF) frequency band can be quickly attenuated, so that the influence is brought to the remote measurement of the discharge parameters of the lightning by utilizing the electromagnetic field characteristics of the lightning radiation. Whether the errors can be quantitatively analyzed or not is judged, so that the conventional lightning positioning algorithm is revised in the application of mountainous regions, and the errors of a lightning monitoring system are revisedAnd the research of the positioning and quantifying algorithm is particularly important.
On the other hand in the global region (from 10)5Rice to 106Meters), the Very Low Frequency (VLF) (3-30kHz) and low frequency (ELF) (30-300kHz) signals of lightning strike-back propagate along the earth's surface with limited conductivity in the medium distance range of 100-2000km, subject to the propagation process, and the observed signals have significant attenuation and distortion. In a medium distance range within 1500km, the assumption of the earth spherical surface as a two-dimensional flat surface brings obvious errors, and the influence of the curved surface on the earth surface should be considered. In order to calculate the condition that the lightning return-strike electromagnetic field is transmitted along the limited conductivity earth surface of the earth curved surface, Shao et al in 2009 make corrections on the basis of a calculation formula provided by Wait et al, and the Shao et al use a Newton iteration method to solve the highly oscillatory Airy function to obtain a solution with higher accuracy, but the iteration process is very complex and time-consuming.
Subsequently, Hou et al propose a new approximation method to calculate the propagation conditions of the medium-distance lightning strike-back low-frequency and very-low-frequency electromagnetic waves within 1500km, and verify the correctness of the text approximation algorithm under different surface conductivities by using a Newton iteration method proposed by Shao (Shao and Jacobson,2009), and the verification result shows that the electric field amplitude and wave head time calculated by the text approximation algorithm are very accurate. When the surface conductivity is more than 0.01S/m, the conductivity factor has little influence on the amplitude of the medium-distance lightning strike-back low-frequency and very-low-frequency radiation fields, but the earth curved surface has obvious influence on the propagation of the medium-distance electromagnetic fields. For example, under the influence of the earth curved surface, the amplitude of the lightning strike-back low-frequency and very-low-frequency radiation electromagnetic field at 1500km is only 30% -40% of the flat ground surface condition, and the amplitude of the lightning strike-back low-frequency and very-low-frequency radiation electromagnetic field at 500km is only 75% -80% of the flat ground surface condition. For flat ground, the electric field amplitude Epeak(V/m) a gain d at a horizontal distance d (km) range-1.32. Therefore, in the transmission of the medium-distance lightning strike-back low-frequency radiation field of hundreds to thousands of kilometers, more attenuation is generated due to the influence of the earth curved surface, and if the attenuation influence of the earth curved surface on the amplitude of the lightning strike-back electric field is not considered, the attenuation is calculated to be more than the real attenuationThe magnitude of the electric field is small.
In summary, the lightning electromagnetic radiation almost covers the whole electromagnetic spectrum, and because the propagation characteristics of electromagnetic waves in different frequency bands along the earth surface (ground waves for short) are different, the higher the frequency band is, the greater the attenuation is. When the distance is close, the propagation of ground waves along the earth's surface depends mainly on the influence of the unevenness of the surface and the ground conductivity, but when the distance exceeds several hundred kilometers, the influence of the curvature of the earth on the propagation of ground waves is greater. Therefore, how to establish a corresponding lightning current peak value estimation method for lightning electromagnetic field characteristics of different distance ranges is very important.
Disclosure of Invention
The application provides an ultra-long distance lightning intensity inversion algorithm considering the influence of the curvature radius of the earth, and aims to solve the problem that the traditional method cannot obtain accurate long-distance lightning electromagnetic field characteristics.
The technical scheme adopted by the application for solving the technical problems is as follows:
an ultra-long distance lightning intensity inversion algorithm considering the influence of the curvature radius of the earth comprises the following steps:
normalizing the lightning signals at different distances from the observation point to a preset distance according to the propagation rule of the lightning electromagnetic field along the earth surface;
if the distance between the lightning signal and the observation point is more than 200km, the electric field amplitude E of the lightning signal is measuredPEAKThe attenuation law exhibited with the increase of the observation distance d is set as d-1.32Wherein the electric field amplitude EPEAKThe unit of (a) is V/m, and the unit of the observation distance d is km;
if the distance between the lightning signal and the observation point is less than 200km, the electric field amplitude E of the lightning signal is measuredPEAKThe attenuation law exhibited with the increase of the observation distance d is set as d-1Wherein the electric field amplitude EPEAKThe unit of (a) is V/m, and the unit of the observation distance d is km;
when thunder occurs, acquiring a magnetic field intensity peak value of the thunder at the observation point position;
and inverting the current peak value of the lightning according to the magnetic field intensity peak value.
Further, the inverting the peak current value of the lightning according to the peak magnetic field strength value comprises:
if the distance between the lightning and the observation point is more than 200km, the current peak value of the lightning is determined according to a formula
Ip＝12.63327+4.51341×Bp
Is obtained by calculation of formula IpDenotes the current intensity in kA, BpDenotes the magnetic induction in nT.
Further, the inverting the peak current value of the lightning according to the peak magnetic field strength value comprises:
if the distance between the lightning and the observation point is less than 200km, the current peak value of the lightning is determined according to a formula
Ip＝13.99819+5.32947×Bp
Is obtained by calculation of formula IpDenotes the current intensity in kA, BpDenotes the magnetic induction in nT.
Further, the method for determining the attenuation of the electromagnetic field of the lightning along with the propagation distance comprises the following steps:
acquiring a vertical electric field intensity E at an observation distance d from the lightning, wherein the electric field intensity E is expressed as
E＝E0W
In the formula, E0The vertical electric field under the ideal conditions of infinite curvature radius of the earth and infinite conductivity is represented, and W represents an attenuation factor considering the influence of the curvature radius of the earth and the conductivity of the soil;
calculating the attenuation factor W, expressed as
W＝WσWρ
In the formula, WσDenotes the influence factor of the conductivity, WρRepresenting the influence factor of the earth curvature.
Further, the influence factor W of the conductivityσAnd the relational expression of the observation distance d for observing the lightning is as follows:
where erfc is the complementary error function and p ═ j ω d Δ2/(2c), ω is the angular frequency,
c is the speed of light and d is the distance between the source point and the observation point.
Further, the influence factor W of the curvature of the earthρExpressed as:
ts＝e-jπ/3(3πvs/2)2/3
vs＝s-3/4-0.00795/(s-3/4)，s＝1，2，···
wherein, the value of s is 0,1,2 …, and the larger the value of s is, the smaller the error of the result is,
is an arc angle between two points.
Further, the preset distance is 300 km.
The technical scheme provided by the application comprises the following beneficial technical effects:
according to the ultra-long distance lightning intensity inversion algorithm considering the influence of the curvature radius of the earth, firstly, according to the propagation rule of a lightning electromagnetic field along the surface of the earth, lightning signals at different distances from an observation point are normalized to a preset distance; if the distance of the lightning signal from the observation pointIf the amplitude is more than 200km, the electric field amplitude E of the lightning signal is measuredPEAKThe attenuation law exhibited with the increase of the observation distance d is set as d-1.32(ii) a If the distance from the lightning signal to the observation point is less than 200km, the electric field amplitude E of the lightning signal is measuredPEAKThe attenuation law exhibited with the increase of the observation distance d is set as d-1(ii) a When thunder occurs, acquiring a magnetic field intensity peak value of the thunder at an observation point; and inverting the current peak value of the lightning according to the magnetic field intensity peak value. The application provides the algorithm according to the propagation law of thunder and lightning electromagnetic field along the earth surface, with the thunder and lightning signal normalization of different distances to same distance of predetermineeing to this carries out the analysis to the thunder and lightning of different intensity, and then according to the current peak value of the magnetic field intensity peak inversion thunder and lightning of thunder and lightning. The lightning current peak value estimation model established by the algorithm provides technical support for business applications such as lightning detection, early warning and forecasting of disastrous weather and the like.
Drawings
FIG. 1 is a graph of the relationship between lightning electromagnetic field strength and propagation distance with consideration of the influence of the curvature of the earth provided by an embodiment of the present application;
FIG. 2 is a graph of lightning electric field strength versus distance of travel for a flat ground surface provided by an embodiment of the present application;
FIG. 3 is a diagram illustrating the attenuation law d between the peak value of the normalized magnetic field intensity and the peak value of the normalized current according to the method for considering the influence of the curvature of the earth provided by the embodiment of the present application-1.32The correlation of (2);
FIG. 4 is a graph showing the decay law d between the peak value of the normalized magnetic field intensity and the peak value of the normalized current without considering the influence of the curvature of the earth according to the embodiment of the present application-1The correlation of (2).
Detailed Description
For the purpose of describing and understanding the technical solutions of the present application, the technical solutions of the present application will be further described below with reference to the accompanying drawings and examples.
First, a conventional method for estimating a lightning current peak in a short distance will be described.
Cloud-ground lightning (short for ground lightning) is the most common type of lightning, with a discharge channel of between 4 and 10km, typically around 5 km. At the beginning of the ground flash process, there is a current pulse in the entire channel, starting from ground and traveling upward. Thus, the whole discharge channel is similar to a radiating antenna, and positive correlation exists between the lightning electromagnetic radiation fields in different distance ranges and the channel current. In general, the estimation of the earth-strike-back current peak is performed by using the measured vertical electric or magnetic fields at different distance positions and then by using the following formula.
In the formula, mu0Represents the magnetic permeability in vacuum, v represents the strike-back speed, t represents time, i represents the strike-back current intensity, and c represents the light speed; d represents an observation distance. Currently, the above two equations have been widely used for estimation of the snapback current peak. However, these two equations are obtained in an ideal case, assuming ideal conditions: first, the distribution of the ground bounce current along the channel satisfies the transmission line mode; second, the ground is assumed to be smooth and the conductivity is infinite. The actual situation is much more complex than the two assumptions above.
In the prior art, a set of lightning current peak value estimation methods is provided according to manual lightning strike observation data:
Ip＝1.5-0.037Epr (3)
in the formula IpRepresents the ground snapback current peak (in kA); epRepresenting the peak value of the radiated electric field (in kV/m) at d (in m) from the lightning path, EpIs positive; for normal lightning, EpIs negative.
The equations (1) and (2) are suitable for ideal ground surface conditions, such as sea surface or very close distance, and the striking-back speed v in the equation is between (1-3) × 108m/s, v are not fixed values, which brings difficulties to practical work. WhileThe formula (3) is a statistical regression relation obtained according to observation data, and a good snapback current peak value can be obtained by using the formula, but the formula is obtained based on special discharge of artificial lightning strike, and the application range of the formula is limited because the observation distance is only within 5 km.
In order to obtain the lightning intensity beyond the ultra-long distance (more than 200km), the inversion is still carried out by adopting the method at present due to the lack of a corresponding inversion algorithm, but the lightning intensity obtained by adopting the inversion is obviously wrong, because the influence of the curvature radius of the earth needs to be considered when the lightning intensity exceeds 200km, and the propagation of the lightning very low frequency signal is different from that of the flat ground.
In view of the above, the embodiment of the present application provides an ultra-long distance lightning intensity inversion algorithm considering the influence of the curvature radius of the earth.
Specifically, the vertical electric dipole source located on the smooth earth surface with spherical curved surface of the earth has a vertical electric field intensity E at the distance of the surrounding radius d as follows:
E＝E0W
in the formula, E0The vertical electric field under the ideal conditions of infinite curvature radius of the earth and infinite conductivity is represented, and W represents an attenuation factor considering the influence of the curvature radius of the earth and the conductivity of the soil.
In order to quickly iterate and reduce computer time consumption, the attenuation factors of the traditional algorithm are divided into curvature attenuation factors and conductivity attenuation factors, namely:
W＝WσWρ
in the formula, WσDenotes the influence factor of the conductivity, WρRepresenting the influence factor of the earth curvature.
Where erfc is the complementary error function and p ═ j ω d Δ2/(2c), ω is the angular frequency,
c is the speed of light and d is the distance between the source point and the observation point.
ts＝e-jπ/3(3πvs/2)2/3
vs＝s-3/4-0.00795/(s-3/4),s＝1,2,...
Wherein, the value of s is 0,1,2 …, and the larger the value of s is, the smaller the error of the result is,
is an arc angle between two points.
According to the three formulas, the influence factor W of the curvature of the earth can be obtainedρ。
Referring to fig. 1 and 2, fig. 1 is a relationship between a lightning electromagnetic field strength and a propagation distance considering an influence of an earth curvature provided by an embodiment of the present application, and fig. 2 is a relationship between a lightning electromagnetic field strength and a propagation distance of a flat ground provided by an embodiment of the present application. The propagation law of the lightning long-distance very low frequency signal under the influence of different soil conductivity and earth curvature is given in fig. 1. It can be seen that, considering the influence of the curvature of the earth, the propagation attenuation of the lightning remote very low frequency signal is obviously different from that of the flat ground, and the electric field amplitude EPEAK(V/m) shows a law of attenuation d with increasing observed distance d (km)-1.32This is significantly greater than the inverse distance relationship for flat ground given in fig. 2.
Therefore, referring to fig. 1 and 2, it can be seen that when the lightning occurrence distance is less than 200km, the propagation rule of the lightning very low frequency signal along the ground surface satisfies the inverse distance relationship, i.e., d-1(ii) a When the distance exceeds 200km, as shown in fig. 2, the influence of the curvature radius of the earth should be considered, and the attenuation law of the lightning very low frequency signal satisfies d-1.32The relationship (2) of (c).
In order to invert the lightning current peak value, the normalization processing of the ground wave peak values at different distances is firstly needed, because the electromagnetic radiation intensity is different due to different lightning occurrence positions. Therefore, the lightning signals of different distances need to be normalized to the same distance according to the propagation rule of the lightning electromagnetic field along the earth surface, so that the lightning with different intensities can be analyzed.
Therefore, referring to fig. 3, the normalized magnetic field intensity peak value and the current peak value considering the influence of the earth curvature provided for the embodiment of the present application are in accordance with the attenuation law d-1.32According to the attenuation rule of the lightning electromagnetic field shown in FIG. 3, the lightning radiation magnetic field signals at different distances are normalized to 300km, and then a remote lightning current peak value estimation method considering the influence of the earth curvature is obtained. As shown in fig. 3, it can be seen that the normalized magnetic field intensity peak value has a good linear correlation with the current peak value:
Ip＝12.63327+4.51341×Bp
in the formula IpDenotes the current intensity in kA, BpDenotes the magnetic induction in nT.
Referring to fig. 4, the normalized magnetic field intensity peak value and the current peak value provided for the embodiment of the present application without considering the influence of the earth curvature are in accordance with the attenuation law d-1The correlation of (2). In contrast to FIG. 3, FIG. 4 further shows the attenuation law according to the reciprocal distance (d)-1) The normalized result shows that the normalized magnetic field intensity peak value and the current peak value have a good linear correlation relationship:
Ip＝13.99819+5.32947×Bp
in the formula IpDenotes the current intensity in kA, BpDenotes the magnetic induction in nT.
By comparing fig. 3 and 4, it can be seen that the propagation law of the long-distance lightning electromagnetic field signal exceeding 300km is very different from that of the flat ground. When the lightning current peak value inversion is carried out by utilizing the long-distance lightning magnetic field peak value signal, the influence of the curvature of the earth needs to be considered.
The lightning detection method and the lightning detection device have good reference value for development of lightning detection technology.
Claims (7)
1. An ultra-long distance lightning intensity inversion algorithm considering the influence of the curvature radius of the earth is characterized by comprising the following steps of:
normalizing the lightning signals at different distances from the observation point to a preset distance according to the propagation rule of the lightning electromagnetic field along the earth surface;
if the distance between the lightning signal and the observation point is more than 200km, the electric field amplitude E of the lightning signal is measuredPEAKThe attenuation law exhibited with the increase of the observation distance d is set as d-1.32Wherein the electric field amplitude EPEAKThe unit of (a) is V/m, and the unit of the observation distance d is km;
if the distance between the lightning signal and the observation point is less than 200km, the electric field amplitude E of the lightning signal is measuredPEAKThe attenuation law exhibited with the increase of the observation distance d is set as d-1Wherein the electric field amplitude EPEAKThe unit of (a) is V/m, and the unit of the observation distance d is km;
when thunder occurs, acquiring a magnetic field intensity peak value of the thunder at the observation point position;
and inverting the current peak value of the lightning according to the magnetic field intensity peak value.
2. The method of claim 1, wherein inverting the peak current value of the lightning according to the peak magnetic field strength comprises:
if the distance between the lightning and the observation point is more than 200km, the current peak value of the lightning is determined according to a formula
Ip＝12.63327+4.51341×Bp
Is obtained by calculation of formula IpDenotes the current intensity in kA, BpDenotes the magnetic induction in nT.
3. The method of claim 1, wherein inverting the peak current value of the lightning according to the peak magnetic field strength comprises:
if the distance between the lightning and the observation point is less than 200km, the current peak value of the lightning is determined according to a formula
Ip＝13.99819+5.32947×Bp
Is obtained by calculation of formula IpDenotes the current intensity in kA, BpDenotes the magnetic induction in nT.
4. The method of claim 1, wherein the method of determining the attenuation of the electromagnetic field of lightning with propagation distance comprises the steps of:
acquiring a vertical electric field intensity E at an observation distance d from the lightning, wherein the electric field intensity E is expressed as
E＝E0W
In the formula, E0The vertical electric field under the ideal conditions of infinite curvature radius of the earth and infinite conductivity is represented, and W represents an attenuation factor considering the influence of the curvature radius of the earth and the conductivity of the soil;
calculating the attenuation factor W, expressed as
W＝WσWρ
In the formula, WσDenotes the influence factor of the conductivity, WρRepresenting the influence factor of the earth curvature.
5. The method of claim 4, wherein the factor W of the conductivity is a factor of the lightning intensity inversionσAnd the relational expression of the observation distance d for observing the lightning is as follows:
where erfc is the complementary error function and p ═ j ω d Δ2/(2c), ω is the angular frequency,
c is the speed of light and d is the distance between the source point and the observation point.
6. The method of claim 4, wherein the factor W of the influence of the curvature of the earth is a factorρExpressed as:
ts＝e-jπ/3(3πvs/2)2/3
vs＝s-3/4-0.00795/(s-3/4)，s＝1，2，···
wherein, the value of s is 0,1,2 …, and the larger the value of s is, the smaller the error of the result is,
is an arc angle between two points.
7. The method of claim 1, wherein the predetermined distance is 300 km.
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