SPACE WEATHER FORECASTING

Abstract

A method of forecasting transport of a region of plasma density enhancement within a polar region is provided. The method comprises: providing a convection model for predicting electrostatic potential distribution within the polar region over time; determining the total electron content distribution within the polar region; and determining whether reconnection is occurring. If reconnection is determined to be occurring, the method comprises: identifying a region of plasma density enhancement using the total electron content distribution; and calculating a velocity of at least a portion of the plasma density enhancement using the convection model, such that transport of a region of plasma density enhancement over time can be forecast.

Claims

1. A method of forecasting transport of a region of plasma density enhancement within a polar region; the method comprising: providing a convection model for predicting electrostatic potential distribution within the polar region over time; determining the total electron content distribution within the polar region; and determining whether reconnection is occurring; if reconnection is determined to be occurring, identifying a region of plasma density enhancement using the total electron content distribution; and calculating a velocity of at least a portion of the plasma density enhancement using the convection model, such that transport of a region of plasma density enhancement over time can be forecast.

2. The method according to claim 1, wherein the method comprises providing an output indicating where the plasma density enhancement will be over time.

3. The method according to claim 1, wherein the convection model comprises an Expanding Contracting Polar Cap paradigm.

4. The method according to claim 1, wherein the total electron content distribution is obtained from a reference table that provides an approximation to the total electron content at any given day and/or any given location in the polar region.

5. The method according to claim 4, wherein the reference table is formed using historical measured data.

6. The method according to claim 1, wherein the method comprises measuring the interplanetary magnetic field (IMF) to determine whether reconnection is occurring.

7. The method according to claim 1, wherein the method comprises determining that reconnection is occurring when the IMF z-component, B.sub.Z, is negative.

8. The method according to claim 1, wherein the method comprises determining the plasma density of the region of plasma density enhancement over time.

9. The method according to claim 1, wherein the method comprises determining the density gradients at the edge of the region of plasma density enhancement over time.

10. The method according to claim 1, wherein the method comprises determining a time and/or location that the plasma density enhancement will impact an auroral oval.

11. The method according to claim 10, wherein the method comprises determining the location of the auroral oval.

12. The method according to claim 1, wherein the method comprises determining if and/or when the region of plasma density enhancement will be in the field of view of a Global Navigation Satellite Systems (GNSS) receiver.

13. The method according to claim 1, wherein the method comprises, upon identifying a region of plasma density enhancement once reconnection has been determined, adding one or more tracer particles to a point of the convection model, and wherein the step of calculating the velocity of at least one portion of the plasma density enhancement comprises calculating the velocity at each one or more tracer particle over time.

14. The method according to claim 1, wherein the information from the method is provided in a form that can be accessed via a computer application and/or a website.

15. A system for forecasting transport of a region of plasma density enhancement within a polar region, the system comprising: a convection model for predicting electrostatic potential distribution within the polar region over time.

16. The system as claimed in claim 15 further comprising a data processing apparatus with a convection model for predicting electrostatic potential distribution within the polar region over time, wherein the data processing apparatus is configured to forecast transport of a region of plasma density enhancement within a polar region.

17. The system as claimed in claim 15, the system comprising a memory with total electron content distribution data stored thereon.

18. The system as claimed in claim 15, wherein the system is configured to receive data to allow the determinations to be made.

19. The system as claimed in claim 15, the system comprising one or more processors adapted to forecast transport of a region of plasma density enhancement within a polar region.

20. A computer program comprising instructions which, when the program is executed by a computer, cause the computer to perform operations, including to forecast transport of a region of plasma density enhancement within a polar region.

Description

[0093] A preferred embodiment of the present invention will now be described by way of example only with reference to the accompanying drawings, in which:

[0094] FIG. 1 is a flow chart.

[0095] The flow chart of FIG. 1 illustrates a method 100 of forecasting transport of a region of plasma density enhancement (such as a polar cap patch) within/across a polar region. This is useful because plasma density enhancement may disturb or interrupt Global Navigation Satellite Systems (GNSS). Thus, the forecast of the transport of a region of plasma density enhancement within/across a polar region may be used to improve the reliability of outputs from GNSS.

[0096] The method comprises at least five main steps. These steps include a step 102 of providing a convection model, a step 104 of determining the total electron content distribution, a step 106 of determining whether reconnection is occurring, a step 108 of identifying the region of plasma density enhancement and a step 110 of calculating a velocity of at least a portion of the plasma density enhancement.

[0097] The steps do not necessarily need to be performed in the order shown in the flow chart. For example, the step 104 of determining the total electron content distribution may be performed after the step 106 of determining whether reconnection is occurring.

[0098] The convection model provided in step 102 is for predicting electrostatic potential distribution within the polar region over time. Thus the convection model may be for predicting the driving forces behind plasma transport.

[0099] The convection model may comprise the Expanding Contracting Polar Cap paradigm. The ECPC model may comprise the ECPC model as presented by Freeman, M. P. in 2003 in A unified model of the response of ionospheric convection to changes in the interplanetary magnetic field. Journal of Geophysical Research—Space Physics, 108 (A1). doi: 10.1029/2002ja009385.

[0100] The Expanding Contracting Polar Cap paradigm (e.g. that presented by Freeman in 2003) may be modified to include a nightside merging gap. This convection model may comprise one or more of the following features.

[0101] The model used in the method may assume that the magnetic field in the high-latitude ionosphere is stationary. This may be reasonable for the timescales considered in the forecast, which may for example be hours. Accepting stationarity, the relationship between the irrotational electrostatic potential Φ and the associated electric field E may be given by:

E=−∇Φ  (1)

[0102] The current in the polar cap region may be considered as perpendicular to the magnetic field, J⊥. The relationship to the electric field may be given by:

J⊥=Σ.sub.PE+Σ.sub.H{circumflex over (B)}×E  (2)

[0103] where {circumflex over (B)} is the unit vector of the magnetic field and Σ.sub.P and Σ.sub.H are the height-integrated Pedersen and Hall conductivites, respectively.

[0104] Uniform conductivity in the polar cap and return flow region may be assumed. This may imply that the field aligned currents are restricted to the boundaries between regions. There are no field aligned currents into or out of the ionosphere polar cap, so the divergence of the perpendicular current may be taken as zero (i.e. ∇.Math.J.sub.⊥=0).

[0105] Taking the divergence on both sides of equation (2) and substituting for E by equation (1) may reduce the current problem to that of solving Laplace's equation in the polar cap and on the polar cap boundary which may be:

∇.sup.2Φ=0  (3)

[0106] It may be assumed that there is no spatial gradient in the Pedersen and Hall conductivities. It may also be assumed that the ionosphere is a thin, spherical shell, such that equation (3) has two variables, colatitude λ and local time θ. The coordinate system may be oriented such that θ=0 at local midnight, θ=π/2 at 06 magnetic local time (MLT) and θ=π at magnetic local noon. Laplace's equation (3) may then be written as:

[00001]$\begin{array}{cc}{\nabla }^2\Phi =\frac{{\partial }^2\Phi }{\partial x^2}+\frac{{\partial }^2\Phi }{\partial {\theta }^2}=0& \left(4\right)\end{array}$

[0107] This includes the substitution x=ln{tan(λ/2)}. The convection model may assume that the polar cap boundary coincides with the open/closed field line boundary, and that it is circular and centred on the Earth's geomagnetic pole.

[0108] It may be assumed that all magnetic reconnection takes place in merging gaps of half-width Θ=π/6, i.e. Θ.sub.N=Θ.sub.D=π/6. The corresponding lengths may be I.sub.D=2Θ.sub.DR.sub.E sin(λ.sub.1) and I.sub.N=2Θ.sub.NR.sub.E sin(λ.sub.1) where R.sub.E is the Earth's radius and λ.sub.1 is the colatitude of the polar cap boundary. The gaps may be centred at θ=0 for the nightside gap and θ=π for the dayside gap. The remainder of the polar cap boundary may be considered adiaroic, i.e. there is no plasma flow across the boundary.

[0109] The model may define three regions separated by boundaries located at x.sub.1 and x.sub.2. Latitudes x>x1 may be defined as the polar cap, and the x.sub.1 may be the open/closed field line boundary. Latitudes x.sub.1>x>x.sub.2 may make up the return flow region, such that x.sub.2 may be the equatorward limit of the convection pattern. This may be referred as the Heppner-Maynard boundary. Latitude equatorward of x.sub.2 have zero current in this model.

[0110] The amount of open magnetic flux in the polar cap, F.sub.PC, may vary with the amount of dayside Φ.sub.D and nightside Φ.sub.N reconnection:

[00002]$\begin{array}{cc}\frac{{\mathrm{dF}}_{PC}}{\mathrm{dt}}={\Phi }_D-{\Phi }_N& \left(5\right)\end{array}$

[0111] For a dipolar magnetic field with strength B and a given polar cap flux, the polar cap boundary radius λ.sub.1 may be found from:

F.sub.PC=2πBR.sup.2.sub.E sin.sup.2(λ.sub.1)  (6)

[0112] Equations 5 and 6 may be used to find the location of the open/closed field line boundary for a given polar cap flux, and from its derivative, may be used to find the speed at which the boundary moves, v.sub.λ1:

[00003]$\begin{array}{cc}{v}_{{\lambda }_1}=\frac{{\Phi }_D-{\Phi }_N}{2\pi R_E^{2}B\sin \left(2{\lambda }_1\right)}& \left(7\right)\end{array}$

[0113] The electric field along the adiaroic portions of the boundary may be given by E=−V×B.

[0114] The electric field component parallel to the polar cap boundary around the circumference may be found from:

[00004]$\begin{array}{cc}{E}_{\theta }\left({\lambda }_1,\theta \right)=\{\begin{array}{cc}-v_{{\lambda }_1}{B}_r& \mathrm{if}{\theta }_N<.Math.\theta .Math.<\pi -{\theta }_D\\ -v_{{\lambda }_1}{B}_r+\frac{{\Phi }_D}{l_D}& \mathrm{if}.Math.\theta .Math.>\pi -{\theta }_D\\ -v_{{\lambda }_1}{B}_r-\frac{{\Phi }_N}{l_N}& \mathrm{if}.Math.\theta .Math.<\pi -{\theta }_N\end{array}& \left(8\right)\end{array}$

[0115] β.sub.r is the radial component of the Earth's magnetic field, such that B.sub.r=2B cos λ

[0116] The potential at the polar cap boundary x.sub.1 may be found by integrating the electric field around the boundary, Ee:

Φ.sub.λ.sub.1=−R sin λ.sub.1∫.sub.0.sup.θE.sub.θ(λ.sub.1,θ)dθ  (9)

[0117] Using the polar cap boundary, it may be possible to find the solution for the rest of the polar region by the following equation.

[00005]$\begin{array}{cc}\Phi \left(x,\theta \right)=\{\begin{array}{cc}\underset{m=1}{\overset{\infty }{.Math.}}{c}_m\exp m\left(x-x_1\right)\sin \left(m\theta \right)& \mathrm{if}x\le x_1\\ \underset{m=1}{\overset{\infty }{.Math.}}{c}_m\frac{\sinh m\left(x-x_2\right)}{\sinh m\left(x_1-x_2\right)}\sin \left(m\theta \right)& \mathrm{if}{x}_1<x\le x_2\\ 0& \mathrm{if}x>x_2\end{array}& \left(10\right)\end{array}$

[0118] c.sub.m may be the coefficients of a Fourier expansion of the potential at the polar cap boundary as follows:

[00006]$\begin{array}{cc}{c}_m=\frac{1}{m}{\int }_0^{2\pi }{\Phi }_{x_1}\left(\theta \right)\sin \left(m\theta \right)d\theta & \left(11\right)\end{array}$

[0119] m may be given a predetermined value. For example, m may be set as follows: m=1.20.

[0120] Solving equation (10) for each time step may allow calculation of the flow speed using V=E×B such that:

[00007]$\begin{array}{cc}{v}_{\lambda }=-\frac{E_{\theta }}{B_r},v_{\theta }=\frac{E_{\lambda }}{B_r}& \left(12\right)\end{array}$

[0121] The initial polar cap flux may be input to the model to define the boundary locations of different flow regimes. This may for example be 0.5 GWb. A time series of both the dayside and nightside reconnection rates may also be input.

[0122] This information may be measured in real time or based on data measured in real time and/or estimated based on historical data.

[0123] The model may also assume that the dayside reconnection is 10 kV higher in the growth phase of the storm, while nightside reconnection dominates in the expansion phase. This may simulate an expanding and contracting polar cap.

[0124] The method also comprises determining the total electron content distribution within the polar region (step 104), specifically within the ionosphere of the polar region. This may be achieved by using historical data of total electron content in the polar region over a previous solar cycle. This may provide an empirical model of the ionospheric total electron content distribution in the polar region.

[0125] As an example for the Northern polar region, this may be achieved using data from MIT's Haystack observatory, which provides TEC from the global GPS receiver network in 1° by 1° bins in the polar region every 5 minutes. To obtain a reference TEC distribution for the northern polar cap, TEC data has been obtained for 11 years 2007-2017, the duration of one solar cycle. The long-term variations between different solar cycles are not taken into account. This is achieved by taking magnetic latitudes from 60 degrees and northward, and dividing the polar cap into 30 bins in the latitudinal direction and 60 bins in the longitudinal direction. For each bin, the median over one month for each day of the solar cycle is taken. For example, for 15 Mar. 2014, the median TEC value from 28 Feb. to 30 Mar. 2014 was taken. Similarly, for 16 Mar. 2014, the median TEC value from 1 Mar. to 31 Mar. 2014 was taken. The result is a TEC distribution map for each day.

[0126] The rolling median smoothes out daily variations, while retaining the monthly, seasonal and yearly variations.

[0127] It has been found that the TEC concentration is always higher on the dayside, while simultaneously also varying more.

[0128] The method comprises step 106 of determining whether reconnection is occurring. This may be achieved by any known method but in the present example is achieved using satellite observations of the interplanetary magnetic field (IMF) at the first Lagrange point (L1). The determination may be performed (e.g. periodically or continuously) until it has been determined that reconnection is occurring.

[0129] Once reconnection is occurring (e.g. on the dayside and the nightside), the plasma in the ionosphere may be convected and thus the convection model is applicable to being able to predict the transport of a region of plasma density enhancement within the polar region.

[0130] Once reconnection has been determined to be occurring, the method may comprise step 108 of identifying a region of plasma density enhancement. This is done using the determined total electron content. For example, the region of plasma density enhancement may be achieved by retrieving data from the reference data formed from the historical data.

[0131] Once a region of plasma density enhancement has been identified the method comprises performing step 110 that involves calculating a velocity of at least a portion of the plasma density enhancement using the convection model, such that transport of a region of plasma density enhancement over time can be forecast.

[0132] The information may be output in the form of a simulation that illustrates the transport of a region of plasma density enhancement over time.

[0133] The method may comprise providing an output of where the plasma density enhancement will be over time. This information can be used to determine whether the plasma density enhancement will interfere with GNSS. If so, appropriate action can be taken so that unreliable outputs from the GNSS can be identified and ensured that it is not relied upon. This output may for example be a simulation.

[0134] Once a region of plasma density enhancement has been identified, the method may comprise putting one or more tracer particles in the convection model to indicate the location of the plasma density enhancement at the start of the convection. The velocity of each of these tracer particles may be determined overtime so as to allow modelling of the transport of the plasma density enhancement over time.

[0135] The method may additionally comprise quantifying the loss rate of a plasma density enhancement traversing the polar region. It may be assumed that the electron density is equal to the O+ density in the F region, and a thin ionosphere at 350 km altitude. Based on this the loss rate may be estimated to be β=10.sup.−5 s.sup.−1. The electron density of the plasma density enhancement over time is given by:

n(t)=n.sub.0 exp{−βt}  (13)

[0136] where n(t) is the electron density, β is the loss rate in s.sup.−1, t is time in seconds since plasma density enhancement generation, and no is the electron density at t=0 s. In the forecasting method, the plasma density enhancement density n(t) is calculated by using TEC at t=0 s, estimated from the determined total electron content distribution as n.sub.0, and loss rate β as explained above. Equation (13) may thus be used to give the plasma density enhancement density at every time step. This information may be input to the convection model.

[0137] The method may be used to predict when the plasma density enhancement arrives at the nightside auroral oval. This may be achieved by determining (e.g. measuring or estimating) the position of the nightside auroral oval and using the calculated velocity of at least a portion of the plasma density enhancement to forecast when the plasma density enhancement will reach the nightside auroral oval.

[0138] The convection model may also be used to calculate the shape and size of the plasma density enhancement over time.

[0139] The method has been validated by comparing the results from the forecasting method to observations from GPS TEC data from the MIT's Madrigal Database, convection data from SuperDARN radar network, and scintillation data from Svalbard for an event in the evening of 26 Sep. 2011, from 18:00 UT to 22:00 UT. The event was caused by a coronal mass ejection (CME) on 24 Sep. 2011 which impacted with the magnetosphere two days later, and caused auroral activity, patches in the polar cap and scintillations on GPS signals. In terms of geomagnetic indices, the storm resulted in Kp=6 from about 18-21 UT, corresponding to a geomagnetic storm level G2 in the National Oceanic and Atmospheric Administration (NOAA) classification system.

[0140] The results show that the method can be used to describe plasma density enhancement motion well, and can be used to predict scintillations of GPS signals in the polar region.