Ionized layer advancing type disturbance short wave propagation effect numerical calculation method based on wide-angle parabolic equation

Abstract

The invention discloses an ionosphere advancing type disturbance short wave propagation effect numerical calculation method based on a wide-angle parabolic equation. The method comprises the following steps of 1, background ionosphere generation, 2, TID model establishment, 3, TID refraction index calculation, 4, parabolic equation wide-angle approximation, 5, step-by-step Fourier numerical solution and 6, path propagation loss calculation. According to the calculation method disclosed by the invention, refraction, diffraction and interference effects during short-wave forward propagation during ionosphere TID are considered, the short-wave coverage range can be calculated, short-wave field intensity distribution and path propagation loss can also be calculated, and the calculation method is superior to a traditional short-wave ray tracing algorithm.

Description

Technical Field

[0001] The invention belongs to the field of ionospheric radio wave propagation, and particularly relates to a numerical calculation method for ionospheric traveling disturbance shortwave propagation effect based on wide-angle parabolic equation in the field. Background Art

[0002] Traveling ionospheric disturbance (TID) is a common form of ionospheric disturbance, which is widely present in the ionosphere. TID is manifested as a wave-like uneven structure, which is usually represented by parameters such as characteristic wavelength, speed and period. TID can be divided into three categories according to wavelength: small scale (less than 100km), medium scale (100-1000km) and large scale (greater than 1000km). The ionospheric electron density disturbance caused by TID will change the shortwave propagation characteristics, seriously affecting the prediction accuracy of the optimal operating frequency of the shortwave communication system, as well as the calculation accuracy of the coordinate registration of the skywave over-the-horizon radar.

[0003] At present, ray tracing technology is generally used to study the shortwave propagation effect of the background ionosphere, that is, using the ray theory approximation, ignoring the diffraction (diffraction) and interference effects caused by inhomogeneous structures, and only considering the refraction effect of radio waves. Shortwave ray tracing can give the ray path of shortwave between the ionosphere and the sea surface, but it cannot numerically calculate the distribution of radio wave field intensity and path propagation loss. When there are small and medium-scale inhomogeneous structures in the ionosphere, the shortwave ray theory that only considers the refraction effect is no longer applicable. For long-distance shortwave propagation, the Fresnel scale is about 10km. Therefore, when small and medium-scale TID occurs, in addition to refraction, the diffraction and interference effects of shortwave propagation cannot be ignored. On the other hand, numerical calculation methods that strictly solve wave equations, such as the finite difference time domain (FDTD) method, can accurately evaluate the shortwave propagation effect when inhomogeneous bodies occur. However, this numerical method requires high spatial sampling, that is, 10-20 calculation units need to be divided within one wavelength, and cannot be applied to shortwave propagation calculations in large-area scenarios. The parabolic equation derived from the forward scattering approximation of the wave equation can calculate the effects of refraction, diffraction, etc. when the radio wave propagates forward under the condition of inhomogeneous medium structure. It has been widely used in large-area scene calculations such as underwater sound wave propagation and beyond-horizon microwave propagation in the troposphere. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a numerical calculation method for the short-wave propagation effect of the ionospheric traveling disturbance based on the wide-angle parabolic equation.

[0005] The present invention adopts the following technical solution:

[0006] A numerical calculation method for the shortwave propagation effect of ionospheric traveling disturbance based on wide-angle parabolic equation, the improvement of which is that it comprises the following steps:

[0007] Step 1, background ionosphere generation:

[0008] Using the International Reference Ionosphere Model IRI, set parameters and obtain the background ionospheric electron density distribution N0, that is, the background ionospheric electron density distribution N0 under undisturbed conditions;

[0009] Step 2, TID model establishment:

[0010] The TID model is:

[0011] N=N0(1+Δ)

[0012] In the above formula, N is the total electron density when TID occurs; △ is the disturbance term;

[0013]

[0014] In the above formula, δ is the TID amplitude; z is the height from the ground; z0 is the height of the maximum disturbance amplitude; H is the elevation; t is the propagation time; t0 is the initial time; T is the period; x is the horizontal distance; λ x is the horizontal wavelength; λ z is the vertical wavelength;

[0015] Step 3, TID refractive index calculation:

[0016] The ionospheric radio refraction index n is:

[0017]

[0018] In the above formula, is the plasma frequency, f is the incident wave frequency, Z = υ e / 2πf, the collision frequency of electrons is υ e =υ en +υ ei , en is the collision frequency between electrons and neutral gas, υ ei is the collision frequency between electrons and ions; i is an imaginary unit;

[0019] υ en and ei They are:

[0020]

[0021] In the above formula, n eis the total electron density after N0 plus the disturbance, [N2], [O2] and [O] are the concentrations of neutral nitrogen, oxygen and oxygen atoms respectively, T e is the electron temperature;

[0022] Step 4, wide angle approximation of the parabolic equation:

[0023] The wave equation approximates the forward propagation one-way parabolic equation:

[0024]

[0025] In the above formula, u(x,z) is the wave amplitude function, k0 is the incident wave number, k0=2Πf / c, c is the speed of light constant, and Q is the differential operator, which is defined as:

[0026]

[0027] Using the Feit-Fleck approximation, the differential operator Q is expanded to obtain the Feit-Fleck type wide-angle parabolic equation:

[0028]

[0029] Step 5, step-by-step Fourier numerical solution:

[0030] The numerical solution to the Feit-Fleck type wide-angle parabolic equation is:

[0031]

[0032] In the above formula, Im represents the imaginary part of the refractive index n, Re represents the real part of the refractive index n, △x is the step length in the x-axis direction, p=k0sin(θ) is the angular spectrum domain variable, θ is the angle between the electromagnetic wave and the horizontal direction, is the inverse Fourier transform, is the inverse Fourier transform, the ground is approximately the surface of an ideal conductor, and under horizontal polarization conditions, u(x,0)=0;

[0033] Step 6, path propagation loss calculation:

[0034] The Gaussian beam radiation source is equivalent to an omnidirectional radiation source. Assuming that there is no system loss and considering the free space loss, the path propagation loss is:

[0035] L(x,z)=32.4+20lg(f)+20lg(x)+10lg(2π)-10lg(F 2 )

[0036] In the above formula, F is the propagation factor, and its relationship with the wave amplitude u(x,z) is:

[0037] F2 =x|u(x,z)| 2 λ

[0038] In the above formula, λ is the wavelength of the incident wave;

[0039] Assuming the transmitting source is a Gaussian beam, the initial field is:

[0040]

[0041] In the above formula, A is the normalization constant, β is the half-power Gaussian beamwidth, and z s is the beam height, and θ0 is the beam elevation angle.

[0042] Furthermore, in step 1, the parameters set include year, month, universal time, longitude, latitude and altitude.

[0043] Further, in step 2, δ = 0.3, T = 10 hours, t = 12 hours, t0 = 0 hours, H = 150 km, z0 = 250 km, z range is 0-500 km, x range is 0-3000 km, λ x =80km,λ z =60km.

[0044] Further, in step 3, f is set to 20 MHz.

[0045] Further, in step 5, Δx=1 km.

[0046] Further, in step 6, β = 5°, z s =5m,θ0=25°.

[0047] The beneficial effects of the present invention are:

[0048] For shortwave systems such as shortwave communications and skywave over-the-horizon radar, when TID occurs in the ionosphere, the effects of radio wave refraction, diffraction, and interference are significant, which seriously affects the working performance of the shortwave system. The calculation method disclosed in the present invention takes into account the refraction, diffraction, and interference effects of shortwave forward propagation during ionospheric TID. It can not only calculate the shortwave coverage range, but also calculate the shortwave field intensity distribution and path propagation loss, which is better than the traditional shortwave ray tracing algorithm. With the help of the parabolic equation step-by-step Fourier algorithm, the deficiency of geometric optics approximation that cannot calculate radio wave field intensity and propagation loss is overcome, and technical support can be provided for the design and operation of shortwave communications, radars and other systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a schematic diagram of the flow chart of the calculation method disclosed in the present invention;

[0050] Figure 2 It is the distribution map of small-scale TID electron density in the ionosphere;

[0051] Figure 3 It is the propagation loss distribution diagram of the Gaussian beam path with an elevation angle of 25°, a frequency of 20MHz, and a height of 5m. DETAILED DESCRIPTION

[0052] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0053] Embodiment 1, this embodiment discloses a numerical calculation method for the shortwave propagation effect of the ionospheric traveling disturbance based on the wide-angle parabolic equation. First, based on the ionospheric background model, the ionospheric TID model is established; secondly, the parabolic equation is processed by Feit-Fleck wide-angle approximation, and the step-by-step Fourier algorithm is used to calculate the radio wave field intensity distribution; finally, the free space loss and propagation factor are calculated to obtain the shortwave path propagation loss. Figure 1 As shown, the specific steps include:

[0054] Step 1, background ionosphere generation:

[0055] Using the International Reference Ionosphere Model IRI, input the year, month, universal time, longitude, latitude and altitude parameters to obtain the background ionospheric electron density distribution N0, that is, the background ionospheric electron density distribution N0 under undisturbed conditions;

[0056] Take April 17, 2014, the universal time is 4 o'clock (i.e. 12 o'clock Beijing time), the longitude is 110°, the latitude is 40°-65°, and the altitude is 0-500km.

[0057] Step 2, TID model establishment:

[0058] Based on the background model, it is assumed that the spatial distribution of TID has Gaussian and cosine forms, and the characteristic parameters are set to obtain the electron density distribution of ionospheric TID.

[0059] The TID model is:

[0060] N=N0(1+Δ) (1)

[0061] In the above formula, N is the total electron density when TID occurs; △ is the disturbance term;

[0062]

[0063] In the above formula, δ is the TID amplitude; z is the height from the ground; z0 is the height of the maximum disturbance amplitude; H is the elevation; t is the propagation time; t0 is the initial time; T is the period; x is the horizontal distance; λx is the horizontal wavelength; λ z is the vertical wavelength; take δ = 0.3, T = 10 hours, t = 12 hours, t0 = 0 hours, H = 150 km, z0 = 250 km, z range is 0-500 km, x range is 0-3000 km, λ x =80km,λ z =60km.

[0064] Step 3, TID refractive index calculation:

[0065] Considering the collision between electrons and neutral components, the refractive index of ionospheric TID shortwave propagation is calculated.

[0066] Ignoring the influence of the geomagnetic field and considering the absorption effect, the ionospheric radio wave refraction index n is:

[0067]

[0068] In the above formula, is the plasma frequency, f is the incident wave frequency, f is 20MHz. Z = υ e / 2πf, the collision frequency of electrons is υ e =υ en +υ ei , en is the collision frequency between electrons and neutral gas, υ ei is the collision frequency between electrons and ions; i is an imaginary unit;

[0069] υ en and ei They are:

[0070]

[0071] In the above formula, n e is the total electron density after N0 plus the disturbance, [N2], [O2] and [O] are the concentrations of neutral nitrogen, oxygen and oxygen atoms respectively, T e is the electron temperature; the neutral component concentration and temperature are obtained from the MSIS model. Assume that the electron temperature T e Equal to the neutral component temperature.

[0072] Step 4, wide angle approximation of the parabolic equation:

[0073] Starting from the wave equation, the Feit-Fleck approximation is performed on the differential operator to obtain the wide-angle parabolic equation.

[0074] If the refractive index changes slowly in the x direction during the propagation of electromagnetic waves, the one-way parabolic equation for forward propagation can be approximated by the wave equation:

[0075]

[0076] In the above formula, u(x,z) is the wave amplitude function, k0 is the incident wave number, k0=2πf / c, c is the speed of light constant, and Q is the differential operator, which is defined as:

[0077]

[0078] Using the Feit-Fleck approximation, the differential operator Q is expanded to obtain the Feit-Fleck type wide-angle parabolic equation:

[0079]

[0080] Step 5, step-by-step Fourier numerical solution:

[0081] Based on the split-step Fourier algorithm, boundary conditions are set and the wave amplitude distribution is numerically solved.

[0082] Using the split-step Fourier algorithm and considering electron impact absorption, the numerical solution of equation (8) is:

[0083]

[0084] In the above formula, Im represents the imaginary part of the refractive index n, Re represents the real part of the refractive index n, △x is the step length in the x-axis direction, △x=1km, p=k0sin(θ) is the angular spectrum domain variable, θ is the angle between the electromagnetic wave and the horizontal direction, is the inverse Fourier transform, is the inverse Fourier transform, the ground is approximately the surface of an ideal conductor, and under horizontal polarization conditions, u(x,0)=0;

[0085] Step 6, path propagation loss calculation:

[0086] Set the initial field, consider the shortwave propagation free space loss and propagation factor, and calculate the shortwave path propagation loss.

[0087] The Gaussian beam radiation source is equivalent to an omnidirectional radiation source. Assuming that there is no system loss and considering the free space loss, the path propagation loss is:

[0088] L(x,z)=32.4+20lg(f)+20lg(x)+10lg(2π)-10lg(F 2 ) (10)

[0089] In the above formula, F is the propagation factor, and its relationship with the wave amplitude u(x,z) is:

[0090] F 2 =xu(x,z) 2 λ (11)

[0091] In the above formula, λ is the wavelength of the incident wave;

[0092] Assuming the transmitting source is a Gaussian beam, the initial field is:

[0093]

[0094] In the above formula, A is the normalization constant, β is the half-power Gaussian beamwidth, and z s is the beam height, θ0 is the beam elevation angle. Take β = 5°, z s =5m, θ0=25°. After determining the initial field, the regional shortwave path propagation loss can be numerically solved according to equations (9), (10) and (11).

[0095] Figure 2 It is the distribution map of small-scale TID electron density in the ionosphere; Figure 3 It is the propagation loss distribution diagram of the Gaussian beam path with an elevation angle of 25°, a frequency of 20MHz, and a height of 5m.

[0096] In summary, the calculation method disclosed in the present invention is particularly suitable for calculating the shortwave field intensity and propagation loss when there are small and medium-scale inhomogeneous structures in the ionosphere by numerically solving the parabolic equation under the approximate condition of the wave equation forward scattering. It is of great significance to the research on application technologies such as shortwave communication link design and skywave over-the-horizon radar positioning.

Claims

1. A numerical calculation method for the shortwave propagation effect of ionospheric traveling disturbance based on wide-angle parabolic equation, characterized in that: The steps include: Step 1, background ionosphere generation: Using the International Reference Ionosphere Model IRI, set parameters and obtain the background ionospheric electron density distribution N0, that is, the background ionospheric electron density distribution N0 under undisturbed conditions; Step 2, TID model establishment: The TID model is: N=N0(1+Δ) In the above formula, N is the total electron density when TID occurs; △ is the disturbance term; In the above formula, δ is the TID amplitude; z is the height from the ground; z0 is the height of the maximum disturbance amplitude; H is the elevation; t is the propagation time; t0 is the initial time; T is the period; x is the horizontal distance; λ x is the horizontal wavelength; z is the vertical wavelength; Step 3, TID refractive index calculation: The ionospheric radio refraction index n is: In the above formula, is the plasma frequency, f is the incident wave frequency, Z = υ e / 2πf, the collision frequency of electrons is υ e =υ en +υ ei , en is the collision frequency between electrons and neutral gas, υ ei is the collision frequency between electrons and ions; i is an imaginary unit; υ en and ei They are: In the above formula, n e is the total electron density after N0 plus the disturbance, [N2], [O2] and [O] are the concentrations of neutral nitrogen, oxygen and oxygen atoms respectively, T e is the electron temperature; Step 4, wide angle approximation of the parabolic equation: The wave equation approximates the forward propagation one-way parabolic equation: In the above formula, u(x,z) is the wave amplitude function, k0 is the incident wave number, k0=2πf / c, c is the speed of light constant, and Q is the differential operator, which is defined as: Using the Feit-Fleck approximation, the differential operator Q is expanded to obtain the Feit-Fleck type wide-angle parabolic equation: Step 5, step-by-step Fourier numerical solution: The numerical solution to the Feit-Fleck type wide-angle parabolic equation is: In the above formula, Im represents the imaginary part of the refractive index n, Re represents the real part of the refractive index n, △x is the step length in the x-axis direction, p=k0sin(θ) is the angular spectrum domain variable, θ is the angle between the electromagnetic wave and the horizontal direction, is the inverse Fourier transform, is the inverse Fourier transform, the ground is approximately an ideal conductor surface, under horizontal polarization conditions, u(x,0)=0; Step 6, path propagation loss calculation: The Gaussian beam radiation source is equivalent to an omnidirectional radiation source. Assuming that there is no system loss and considering the free space loss, the path propagation loss is: L(x,z)=32.4+20lg(f)+20lg(x)+10lg(2π)-10lg(F 2 ) In the above formula, F is the propagation factor, and its relationship with the wave amplitude u(x,z) is: F 2 =x|u(x,z)| 2 λ In the above formula, λ is the wavelength of the incident wave; Assuming the transmitting source is a Gaussian beam, the initial field is: In the above formula, A is the normalization constant, β is the half-power Gaussian beamwidth, and z s is the beam height, and θ0 is the beam elevation angle.

2. The numerical calculation method for the shortwave propagation effect of the ionospheric traveling disturbance based on the wide-angle parabolic equation according to claim 1 is characterized by: In step 1, the parameters to be set include year, month, universal time, longitude, latitude, and altitude.

3. The numerical calculation method for the shortwave propagation effect of the ionospheric traveling disturbance based on the wide-angle parabolic equation according to claim 1 is characterized by: In step 2, δ = 0.3, T = 10 hours, t = 12 hours, t0 = 0 hours, H = 150 km, z0 = 250 km, z range is 0-500 km, x range is 0-3000 km, λ x =80km,λ z =60km.

4. The numerical calculation method for the shortwave propagation effect of the ionospheric traveling disturbance based on the wide-angle parabolic equation according to claim 1 is characterized by: In step 3, f is set to 20 MHz.

5. The numerical calculation method for the shortwave propagation effect of the ionospheric traveling disturbance based on the wide-angle parabolic equation according to claim 1 is characterized by: In step 5, Δx=1 km.

6. The numerical calculation method for the shortwave propagation effect of the ionospheric traveling disturbance based on the wide-angle parabolic equation according to claim 1 is characterized by: In step 6, β = 5°, z s =5m,θ0=25°.

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