A numerical calculation method for the shortwave propagation effect of ionospheric traveling disturbances based on wide-angle parabolic equation

Abstract

The present invention discloses a numerical calculation method for the shortwave propagation effect of ionospheric traveling disturbances based on wide-angle parabolic equations, comprising the following steps: Step 1: Generating a background ionosphere; Step 2: Establishing a TID model; Step 3: Calculating the TID refractive index; Step 4: Wide-angle approximation of the parabolic equation; Step 5: Step-by-step Fourier numerical solution; and Step 6: Calculating path propagation loss. 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 calculate not only the shortwave coverage range but also the shortwave field intensity distribution and path propagation loss, outperforming traditional shortwave ray tracing algorithms.

Description

Technical Field

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

[0002] Traveling ionospheric disturbances (TIDs) are a common form of ionospheric disturbance, widespread in the ionosphere. TIDs manifest as wavelike, nonuniform structures, often characterized by parameters such as characteristic wavelength, velocity, and period. TIDs can be categorized by wavelength: small-scale (less than 100 km), medium-scale (100–1000 km), and large-scale (greater than 1000 km). The ionospheric electron density disturbances caused by TIDs alter shortwave propagation characteristics, severely impacting the accuracy of optimal operating frequency predictions for shortwave communication systems and the accuracy of coordinate registration calculations for skywave over-the-horizon radars.

[0003] Currently, ray tracing techniques are generally used to study the effects of shortwave propagation in the background ionosphere. This approach employs a ray theory approximation, ignoring effects such as diffraction and interference caused by inhomogeneities, and only considering the effects of radio wave refraction. Shortwave ray tracing can provide the shortwave ray paths between the ionosphere and the sea surface, but it cannot numerically calculate the radio wave field intensity distribution and path propagation losses. When small and medium-scale inhomogeneities exist in the ionosphere, shortwave ray theory, which only considers refraction, is no longer applicable. For long-distance shortwave propagation, the Fresnel scale is on the order of 10 km. Therefore, when small and medium-scale TIDs occur, in addition to refraction, shortwave propagation diffraction and interference effects cannot be ignored. On the other hand, numerical methods that rigorously solve wave equations, such as the finite difference time domain (FDTD) method, can accurately assess the effects of shortwave propagation when inhomogeneities occur. However, this numerical method requires high spatial sampling, requiring 10-20 computational units within a wavelength, making it unsuitable for shortwave propagation calculations over large areas. The parabolic equation derived from the forward scattering approximation of the wave equation can calculate the effects of refraction, diffraction, etc. when radio waves propagate forward under conditions of inhomogeneous medium structure. It has been widely used in large-area scenario calculations such as underwater sound wave propagation and beyond-the-horizon microwave propagation in the tropospheric region. Summary of the Invention

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

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

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

[0007] Step 1, background ionosphere generation:

[0008] Using the International Reference Ionosphere Model (IRI), we set parameters to 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 perturbation term;

[0013]

[0014] In the above formula, δ is the TID amplitude; z is the height above 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 refractive 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 ,υ en is the collision frequency between electrons and neutral gas, υ ei is the collision frequency between electrons and ions; i is the 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 perturbation, [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 forward propagation one-way parabolic equation is approximated by the wave 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 of 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, and 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, and under horizontal polarization conditions, u(x,0)=0;

[0033] Step 6: Calculate the path propagation loss:

[0034] Equivalently treating the Gaussian beam radiation source as an omnidirectional radiation source, assuming no system loss, and considering 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] Furthermore, 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] Furthermore, in step 3, f is set to 20 MHz.

[0045] Furthermore, in step 5, Δx=1 km.

[0046] Furthermore, 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, radio wave refraction, diffraction, and interference effects are significant, seriously affecting the performance of shortwave systems. The calculation method disclosed in this invention takes into account the refraction, diffraction, and interference effects of shortwave forward propagation during ionospheric TID. This method can calculate not only the shortwave coverage range, but also the shortwave field intensity distribution and path propagation loss, outperforming traditional shortwave ray tracing algorithms. By leveraging the parabolic equation split-step Fourier algorithm, this method overcomes the inability of geometric optics approximations to calculate radio wave field intensity and propagation loss, providing technical support for the design and operation of systems such as shortwave communications and radar. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a schematic diagram of the flow 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 This is the propagation loss distribution diagram of the Gaussian beam path with an elevation angle of 25°, a frequency of 20 MHz, and a height of 5 m. DETAILED DESCRIPTION

[0052] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to 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] Example 1. This example discloses a numerical calculation method for the shortwave propagation effect of ionospheric traveling disturbances based on a wide-angle parabolic equation. First, an ionospheric TID model is established based on the ionospheric background model. Second, the parabolic equation is subjected to Feit-Fleck wide-angle approximation processing, and the split-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), we 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, 4:00 UTC (i.e. 12:00 Beijing time), longitude 110°, latitude 40°-65°, and altitude 0-500km.

[0057] Step 2: TID model establishment:

[0058] Based on the background model, the electron density distribution of ionospheric TID is obtained by assuming that the spatial distribution of TID has Gaussian and cosine forms and setting characteristic parameters.

[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 perturbation term;

[0062]

[0063] In the above formula, δ is the TID amplitude; z is the height above 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 refractive 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 ,υ en is the collision frequency between electrons and neutral gas, υ ei is the collision frequency between electrons and ions; i is the 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 perturbation, [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, and 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, the 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 an ideal conductor surface, and under horizontal polarization conditions, u(x,0)=0;

[0085] Step 6: Calculate the path propagation loss:

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

[0087] Equivalently treating the Gaussian beam radiation source as an omnidirectional radiation source, assuming no system loss, and considering 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 This is the propagation loss distribution diagram of the Gaussian beam path with an elevation angle of 25°, a frequency of 20 MHz, and a height of 5 m.

[0096] In summary, the calculation method disclosed in this paper, by numerically solving the parabolic equation under the wave equation forward scattering approximation, is particularly suitable for calculating shortwave field strength and propagation loss in the presence of small and medium-scale inhomogeneous structures in the ionosphere. This method is of great significance for the research of applied 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), we set parameters to 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 perturbation term; In the above formula, δ is the TID amplitude; z is the height above 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; Step 3, TID refractive index calculation: The ionospheric radio refractive 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 ,υ en is the collision frequency between electrons and neutral gas, υ ei is the collision frequency between electrons and ions; i is the imaginary unit; υ en and ei They are: In the above formula, n e is the total electron density after N0 plus the perturbation, [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 forward propagation one-way parabolic equation is approximated by the wave 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 of 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, and 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, and under horizontal polarization conditions, u(x,0)=0; Step 6: Calculate the path propagation loss: Equivalently treating the Gaussian beam radiation source as an omnidirectional radiation source, assuming no system loss, and considering 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 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 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 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 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 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°.

Images