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Ionospheric high frequency wave propagation using different IRI hmF2 and foF2 models
Journal Pre-proof Ionospheric high frequency wave propagation using different IRI hmF2 and foF2 models Mariano Fagre, Bruno S. Zossi, Jaroslav Chum, Erdal Yiğit, Ana G. Elias PII:
S1364-6826(19)30410-9
DOI:
https://doi.org/10.1016/j.jastp.2019.105141
Reference:
ATP 105141
To appear in:
Journal of Atmospheric and Solar-Terrestrial Physics
Received Date: 5 April 2019 Revised Date:
26 July 2019
Accepted Date: 29 August 2019
Please cite this article as: Fagre, M., Zossi, B.S., Chum, J., Yiğit, E., Elias, A.G., Ionospheric high frequency wave propagation using different IRI hmF2 and foF2 models Journal of Atmospheric and Solar-Terrestrial Physics, https://doi.org/10.1016/j.jastp.2019.105141. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
Ionospheric high frequency wave propagation using different IRI hmF2 and foF2 models Mariano Fagre1,2, Bruno S. Zossi3,4, Jaroslav Chum5, Erdal Yiğit6, and Ana G. Elias3,4 1
Consejo Nacional de Investigaciones Científicas y Técnicas, CONICET, Argentina. Laboratorio de Telecomunicaciones, Departamento de Electricidad, Electrónica y Computación, Facultad de Ciencias Exactas y Tecnología, Universidad Nacional de Tucuman, Argentina 3 Laboratorio de Física de la Atmosfera, Departamento de Física, Facultad de Ciencias Exactas y Tecnología, Universidad Nacional de Tucuman, Argentina 4 INFINOA (CONICET-UNT), Tucuman, Argentina 5 Institute of Atmospheric Physics, Prague, Czech Republic 6 Space Weather Laboratory, Department of Physics and Astronomy, George Mason University, USA
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Corresponding author: Ana G. Elias E-mail: [email protected] Laboratorio de Física de la Atmosfera - Departamento de Física Facultad de Ciencias Exactas y Tecnología Universidad Nacional de Tucuman Av. Independencia 1800 4000 Tucuman - Argentina Highlights • Ray tracing is used to study HF wave propagation for different IRI setting options • Ground range values vary appreciably with the choice of hmF2 and foF2 models • The effect of neglecting Earth’s magnetic field is in general smaller Abstract High frequency (HF) electromagnetic wave propagation is commonly used in long-distance communications and detection. The ionosphere is a highly variable medium affecting this propagation. However, mean climatological conditions are useful in order to determine a “base level” for the design and operation of systems using HF waves that propagate in the ionosphere. Important variables that determine these conditions are the ionosphere peak height, hmF2, and F2 critical frequency, foF2. In the present work the effect of different hmF2 and foF2 model options in IRI-2016 and its spatial variability are analyzed through the analysis of the ground range and reflection height of HF ray paths using a numerical ray tracing method. The model options are M(3000)F2, AMTB and SDMF2 for hmF2, and URSI and CCIR for foF2. We perform this study for a quiet day, April 26 at 12 LT, and solar activity maximum conditions. Ground range and reflection height variation between values obtained with the different model options are on average not greater than ~40%, but can be higher for a Pedersen ray case. These variations are in general much stronger than those obtained when Earth’s magnetic field is neglected in ray path assessments. However, while the magnetic field effect is of “physical” origin that has always the same sign, the effect of changing a model used for certain parameter’s estimation depends on the model performance which may vary with location and time. Keywords: Ray tracing; IRI model; Pedersen ray 1
1. Introduction High frequency (HF) electromagnetic waves between 3 and 30 MHz, also called radio frequency waves, are used mainly in long distance communication, detection and surveillance. It has always been a challenge to establish radio links and exact positions with radar systems using these waves traveling through and reflecting in the ionosphere due to the theoretical complexity of electromagnetic wave propagation through the ionospheric plasma that is embedded in the Earth’s magnetic field. The ray tracing technique is a powerful tool that is commonly employed to estimate the ray path between the transmitter and a long-range target. This technique helps to determine the exact path of radio waves if the ionospheric electron density profile along the propagation path is known with good precision, which is seldom the case since ionospheric measurements are not continuously available along the extended ray. Usually they are obtained from ionospheric modeling or a combination of measurements and modeling. Ray tracing can be performed analytically if simple ionospheric and terrestrial magnetic field models are considered, however this approach provides low accuracy. Alternatively, ray tracing can be assessed by numerical integration of the equations of electromagnetic wave propagation through a magnetized plasma and thus any ionospheric model or measured profiles can be used, including a realistic terrestrial magnetic field and absorption effects. A numerical ray tracing technique that has been widely used is that by Jones and Stephenson (1975) who calculated ray paths and associated quantities in three-dimensional space using spherical-polar coordinates. The presence of an ambient magnetic field increases the complexity of plasma dynamics and electromagnetic wave propagation. In addition, not only the field intensity enters the propagation equation, but also the angle between the ray and field vector. These conditions indeed apply to Earth’s ionosphere, which is a partially ionized plasma embedded in a complex intrinsic magnetic field. An ionospheric model that is commonly used for radio propagation studies and by ray tracing algorithms is the International Reference Ionosphere (IRI) (Bilitza et al., 2017), which is a semiempirical model based on available measurements of ionospheric characteristics. The last IRI version was introduced in 2016, and among the improvements over previous versions there are two new models for the height of the F2 peak electron density, hmF2. In older versions of IRI, hmF2 was based on the close correlation with the propagation factor M(3000)F2 (Shimazaki, 1955; Bilitza and Eyfrig, 1978; Bilitza et al., 1979; Dudeney, 1983) which in turn is based on the Consultative Committee on International Radio (CCIR) model (CCIR, 1967). Many studies highlighted some limitations of this approach for hmF2 (Bilitza, 1985; Adeniyi et al., 2003; Lee and Reinisch, 2006; Brum et al., 2011; Magdaleno et al., 2011; Araujo-Pradere et al., 2013; Ezquer et al., 2014). Adeniyi et al. (2003) pointed out that there are three main error sources: (1) the scarce data volume available at the time of the model development; (2) the limitations to reproduce small-scale features in the diurnal variation because of the chosen functional representation (harmonics of up to order 4 only); and (3) the uncertainty introduced with the formula describing the relationship between hmF2 and M(3000)F2.
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Because of these limitations of IRI hmF2 model a purely ionosonde based modeling was developed by Magdaleno et al. (2011) and Altadill et al. (2013). Additionally, Shubin et al. (2013) presented an hmF2 model based on radio occultation data from COSMIC (Constellation Observing System for Meteorology, Ionosphere and Climate), GRACE (Gravity Recovery and Climate Experiment), and CHAMP (Challenging Mini-Satellite Payload for Geophysical Research and Application). The last two models have been selected for inclusion in the 2016 version of the IRI model. Another parameter which plays an important role in HF radio propagations is the F2 layer critical frequency, foF2. The options provided by IRI for foF2 model are CCIR and URSI (Union RadioScientifique Internationale). There are many papers which compare the IRI performance using CCIR or URSI (Bertoni et al., 2006; Brum et al., 2011; Adebesin et al., 2014; Brown et al., 2018; Liu et al., 2019). Adebesin et al. (2014) found that in general, the URSI option presents better agreement with observed data than the CCIR option, especially during daytime, suggesting an improvement in the URSI option of IRI-2012 version over IRI-2007. In the present work the spatial variation of the ground range R and reflection height hR of a ray path at mid and low latitudes are analyzed in order to assess the effects of using the new hmF2 models incorporated by IRI with respect to the traditional one based on M(3000)F2, and also the effects of the two foF2 model options. These effects are compared to those produced by neglecting Earth’s magnetic field. There are several works, which analyze ray tracing in the ionosphere considering geomagnetic field effects (e.g., Kelso, 1968; Rao, 1969; Bennett et al., 1991; Tsai et al., 2010; Dao et al., 2016), but the effect of the different IRI options on a global scale has yet not been studied. IRI model parameters, such as hmF2 and foF2, as well as the configuration of the magnetic field have an important physical effect on the ray propagation process. Here we specifically focus on R and hR. It should be noted that the state of the ionosphere and hence the ionospheric model used influences also precision of Global Navigation Satellite Systems (GNSS) (Hoque & Jakowski, 2008, Petrie et al., 2011; Banville et al., 2017; Hadas et al., 2017). The structure of the paper is as follows: In section 2 we outline the methodology of our study, which includes the description of ray tracing approach, the IRI model options considered and the calculation set up, followed by the results in section 3. The discussion and conclusions are presented in section 4.
2. Methodology 2.1 HF signal ray tracing model The propagation of HF electromagnetic waves in the ionosphere is a rather complex process because the ionosphere is an inhomogeneous and time-varying magnetized plasma (Davies, 1965). In fact, the presence of a strong intrinsic magnetic field makes the ionosphere an anisotropic medium that results in the double refraction of an incident electromagnetic, which is decomposed into ordinary and extraordinary modes. Additional magnetic field effects on the 3
refraction of an incident electromagnetic wave are that the direction of energy flow differs from that of the wave propagation. A valid approximation for the propagation of HF signals in the ionosphere is to assume a cold magnetoplasma where only electrons need to be taken into account. In this case the refractive index n is given by the Appleton-Hartree equation (Ratcliffe, 1962), that is, = 1 −
±
(1)
with
= =
= " =
' = () " = =
#
#
#
(2) sin "
cos "
(3) (4) (5)
where fo is the plasma frequency, f the incident electromagnetic wave frequency, N the electron number density, e the electron charge, m the electron mass, ε0 the permittivity of vacuum, B the magnetic field intensity, T stands for transverse and L for longitudinal, and θ corresponds to the angle between the direction of the wave propagation and the magnetic field vector. The upper sign in the denominator of Equation (1) refers to the ordinary component and the lower sign to the extraordinary. Considering that the extraordinary wave suffers higher absorption, and that useful sky wave propagation usually takes place through the ordinary wave, only the latter will be considered for simplicity. It should be noted that the absorption mainly takes place in the D layer and it is roughly proportional to the square of the inverse wave frequency (e.g., Chum et al., 2018). Thus, during the night when the D layer practically disappears, both modes might propagate over substantial distances. Various numerical ray tracing programs have been developed to determine the propagation of HF electromagnetic wave through the ionosphere. Among them, Azzarone et al. (2012) developed a software that is freely available and allows ionospheric ray tracing in a geocentric spherical coordinate system, taking into account a dipolar geomagnetic field. However, since we consider the current magnetic field with its multipolar contributions, the 3D ray tracing original code developed in the work by Jones and Stephenson (1975) was adjusted to include the International Geomagnetic Reference Field 12th Generation (IGRF-12) model (Thébault et al., 2015). This ray tracing is based on Hamilton's equations of geometrical optics given by Haselgrove (1955) in spherical coordinates. The Hamiltonian used here is given by
4
,-,/,0,12 ,13 ,14 = ∗ 67 8
9
:
;<- + − ?
(6)
where n is given by Equation (1), c is the speed of light in free space, r, θ, and ϕ are the spherical polar coordinates of a point on the ray path, and kr, kθ and kϕ are the spherical components of the HF wave vector of frequency ω=2πf. Hamilton’s equations, which consist in a set of six partial differential equations, are @@A
@/ @A
@0 @A
BC
= B1
BC
= - B1
@12
=
@A
@13 @A
@13 @A
(7)
2
3
(8) BC
-DEF/ B14
=−
BC B-
= G− =
-
+
BC B/
-DEF0
(9) @/ @A
−
G−
BC
B0
+ <0 "
@@A
@0 @A
(10)
+ <0 H() "
− <0 sin"
@@A
@0 @A
I
− <0 H() "
(11) @/ @A
I
(12)
where the quantity τ is the HF wave group path, ct, and the independent variable of the Hamiltonian. 2.2 Interpolation method and integration For the ray tracing technique here implemented continuous first derivatives are needed. Since N is not calculated at each step but obtained from a grid, an interpolation method is required. In order to guarantee derivative’s continuity when considering the actual magnetic field a method proposed by Akyildiz (1994) was used. It consists of a parametric curve fitting, which is cubic in each direction and is known as smooth-jointed interpolation. For simplicity, we will explain the one dimensional case. For a set of no ordered data points in order to interpolate a curve between two of them, we consider first the parabola which is determined by these two data points plus another one located to their left. Then, with a similar procedure a second parabola is obtained for the same two data points, but using as the third point one located on their right. The final arc that connects the two initial data points is given by the convex combination of these two parabolas. Thereby, the arc that connects two successive points will finally be determined by four points: the two points of interest, the point that precedes them and the point following them. Since in our code the interpolation is cubic (in the three directions), each interpolated point requires the use of 64 nearby points. One of the main advantage of this procedure is that is tighter than a spline interpolation because is more immune to overshoot problems between points, yet still provides continuity through the first derivative, something essential for a correct operation of the ray tracing.
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Hamilton’s equations given in Equations (6) to (12) are integrated using a Fortran subroutine which computes the numerical solutions of the system of six simultaneous first-order differential equations over a specified interval with given initial conditions applying the Adams-Moulton procedure (Moulton, 1926; Lastman, 1964). This is a multi-step method that requires a selfstarter, in this case a fourth order Runge-Kutta method, together with a predictor given by Adams-Bashforth formula (Bashforth and Adams, 1883).
2.3 Model of hmF2 and foF2 Previous versions to the current IRI 2016, estimate hmF2 in terms of M(3000)F2 through the following relationship (Bilitza et al., 1979): ℎKL2 =
NO
PQOOO R∆P
− 176
(13)
where ∆M is given by ×Y
W ∆V = Z[ Z\
+ ]Q
] = 0.00232 6 + 0.222
] = 1.2 − 0.0116 7 aW / .c
]Q = 0.096 ] = 1 −
aW e
aW
eO
eO
7 ∅
/ gOO
(14) (15) (17) (18) (16)
with R12 the 12-month running mean sunspot number and φ the dip latitude. M(3000)F2 is obtained from CCIR numerical maps usually recommended for calculations over continents or the URSI which provides a better fit over the sea. This hmF2 model appears as BSE-1979, after its authors Bilitza, Sheikh, and Eyfrig (Bilitza et al., 1979). M(3000)F2 will use CCIR or URSI coefficients depending on the choice made for foF2. However, this is not important in our case due to the variations in hmF2 between M(3000)F2 with CCIR and with URSI is less than 2%. As mentioned before, IRI-2016 introduced two new models for hmF2. One of the options is the AMTB model which is based on data from 26 digisonde stations from the Global Ionosphere Radio Observatory (GIRO) network for the period 1998–2006. For the spherical harmonics analysis to be feasible the global data coverage was filled out with fictitious data points (Altadill et al., 2013) and is called as AMTP2013 in IRI-2016. The other option is SDMF2 model which is based on radio occultation data from CHAMP of period 2001–2008 (~300,000 values), GRACE of period 2007–2011 (~100,000 values) and COSMIC of period 2006–2012 (~3,500,000 values), and with hmF2 data from 62 digisondes from the Digital Ionogram Data Base for the period 1987–2012. 6
The three models use spherical harmonics to describe global variations, but AMTB and SDMF2 model hmF2 directly and no longer uses M(3000)F2. Large discrepancies are found in hmF2 values between the models reaching ~50 km or more (Bilitza, 2018). IRI recommends, as a first choice, AMTB model since it presents the lowest error estimates for ionosonde measurements. Regarding foF2, IRI provides two different models. One of them is given by the CCIR maps which are based on monthly median values obtained by the worldwide network of ionosondes (about 150 stations) during years 1954 to 1958, based on around 10,000 station-months of data (Bilitza et al.,2017). This method follows a numerical mapping procedure developed by Jones and Gallet (1962, 1965). Another available option is the URSI set of model coefficients where the numerical mapping method is the same as for the previous model, based on a Fourier analysis of the monthly median diurnal variation of foF2 observed by the worldwide network of ionosondes, and on spherical Legendre functions of each Fourier coefficient, for each month and two solar activity levels. However, URSI foF2 model represents an improvement of the CCIR foF2 model due to data gap filling method used where ionosonde measurements do not exist or are sparse, as is the case of the Southern Hemisphere or above the oceans, before applying the spherical harmonics mapping procedure (Rush et al., 1983, 1984). Fox and McNamara (1988) established the final URSI coefficients for the combined data base of Rush's values and about 45,000 monthly ionosonde data (from about 180 stations worldwide).
2.4 Calculation setup Two ray tracing outputs were chosen for the present analysis: the ground range, R, that is the measure of the distance along the surface of Earth from the ray’s origin (a transmitter for instance) to the point where it again reaches Earth’s surface (a receiver or a target), and the reflection height, hR, that is the true vertical distance of the point in the ray path where the ray is reflected by the ionosphere. The electron density grid used by the ray tracing code is generated with the International IRI2016 (Bilitza et al., 2017) with a resolution of 2.5° x 2.5° in latitude and longitude, and 1 km in altitude. Earth’s magnetic field parameters are from IGRF-12 (Thebault et al., 2015). From the three IRI available options for the bottomside thickness parameter: ABT-2009, Bil-2000, and Gul-1987, we used the default and recommended one, that is ABT-2009. This option (Altadill et al., 2009) uses a large volume of ionosonde data to develop an improved representation of latitudinal and solar cycle variation of the bottomside ionosphere parameters, B0 and B1. The first corresponds to the height difference between hmF2 and the height where the electron density profile has dropped down to half the F peak value, and the second describes the bottomside profile shape. The global spatial structure of R and hR were assessed on a grid with 2.5° latitude and 5° longitude resolution between 45°S and 45°N latitude and 180°W and 180°E longitude, where each grid point corresponds to the transmitter location. Northward and Eastward wave propagation directions were considered with a fixed elevation angle, α = 20°, and a single frequency of 12.5 MHz, which are typical mean values for over the horizon radars, OTHR, 7
which use Earth’s ionosphere as a mirror to illuminate targets beyond the line-of-sight horizon. The date and time chosen for this study is April 26, 2000, at 12 LT. It represents a quiet day around equinox and solar activity maximum conditions, with F10.7=192 sfu, and Kp index less than 1. Calculation of HF propagation requires setting up electron density at the same UT moment in each point along the propagation path. However, we considered the same local time (12 LT) everywhere for simplicity. This allowed us to use a single grid for the whole globe and each ray tracing run. This simplification might be not exactly realistic for eastward propagation. The difference from real conditions is, however, negligible as the maximum obtained R values roughly correspond to 1-hour time difference for the Eastward propagation. Such a small time difference around noon is well within model uncertainties. In the case of Northward propagation, which is almost along a meridian, considering LT or UT makes no difference. In order to compare the dependence of R and hR on foF2 and hmF2 model choices in IRI, their values were calculated considering URSI and CCIR for foF2 and M(3000)F2, AMTB and SDMF2 for hmF2. The URSI and M(3000)F2 options were considered as baselines since these were the default settings of the previous IRI version, IRI-2012. 3. Results Figure 1 shows hmF2 for the zone here analyzed, between 45°S and 45°N, obtained with URSI option for foF2 and each of the three hmF2 models: M(3000)F2, AMTB and SDMF2. In all the cases hmF2 is maximum at the magnetic equator. Overall, the imprint of the magnetic field is clearly seen in the geographical variation of hmF2. Figure 2 presents hmF2 differences between AMTB and SDMF2 with respect to M(3000)F2. The greatest differences are observed at the EIA region, from the southern to the northern crest. In percentage terms, hmF2 differences do not exceed ~15-20%. R estimated using M(3000)F2 for eastward propagation is presented in Figure 3 together with the differences with respect to this model when AMTB and SDMF2 are used instead as the hmF2 model. Here, as expected, the differences are greatest at the EIA region, but in percentage terms the greatest differences reach ~40% in the case of AMTB, and ~100% in SDMF2 case. Note that the color scales are different in each plot. In the case of northward propagation (azimuth angle 0°), shown in Figure 4, the magnetic field effect is stronger due to a more field aligned ray path. At certain regions, the occurrence of Pedersen rays (rays that satisfy conditions for downward refraction critically and propagate substantial distances almost parallel to the Earth’s surface) greatly increases R. Since this is an unstable condition, very small environment changes make the ray to return to its normal condition, generating extremely big R differences when comparing two different but similar situations, as in our case. Under the conditions here analyzed, R values obtained with M(3000)F2 are enhanced around the magnetic equator in the Pacific Ocean close to South America and around Indonesia, and also at ~45°N. This creates differences of more than double at these regions, which look like peculiarities in Figure 4 around the magnetic equator and at ~45°N.
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Differences observed in hR are shown in Figure 5 for eastward propagation. The percentage differences observed are similar to R case, and the spatial pattern is almost exactly the same as that observed for R. In the northward case, presented in Figures 6(a)-(c), where hR for Pedersen rays is the same as for a “regular” ray, the spatial variation presents less peculiarities than Figures 4(a)-(c). Figure 7 shows foF2 obtained with URSI and CCIR options in IRI-2016, with M(3000)F2 for hmF2 model. As in the case of the different hmF2 models, the greatest differences appear at the EIA region, with percentage differences around 20%. And the same happens with R differences obtained when comparing R values obtained with each foF2 model, as can be seen in Figure 8. The percentage differences in this case do not exceed ~25%. For Northward propagation (not shown), as in the case of hmF2 model comparison, at certain regions the occurrence of Pedersen rays is propitiated which greatly increases R. The differences are similar to those shown in Figure 4(b). Differences in hR (not shown) present, as in the case a hmF2 model comparison, a behavior almost identical to R differences. 4. Discussion and conclusions We have studied the effect of different hmF2 and foF2 model options in IRI-2016 on R and hR of HF ray paths, using a numerical ray tracing method. IRI model options are M(3000)F2, AMTB and SDMF2 for hmF2, and URSI and CCIR for foF2. We have performed this study for a representative quiet day, April 26 at 12 LT, and solar activity maximum conditions. Our results indicate that the choice of ionospheric parameters in model settings may greatly affect the parameters determined for the ray path’s R and hR in the ray tracing code. How accurate these values are with respect to true values would depend on both, the accuracy of the ray tracing code and how realistic the modeled ionosphere is. Every numerical scheme has various numerical uncertainties. In particular, for numerical ray tracing one of the causes of loss of accuracy is the step size chosen to perform the ray trace. The numerical integration of the method implemented in this work has a built-in mechanism to check errors and adjust the integration step length accordingly. If the errors get larger than a maximum value (10-6 km for this case) the routine will decrease the step length in order to maintain the accuracy. On the other hand, if the accuracy is greater than required, the routine will increase the step length in order to reduce the computing cost. Another source of error in the estimation of the ray path propagation depends on whether or not Earth’s magnetic field is taken into account, since it modifies the value of the refractive index obtained from Equation (1), therefore producing changes in ray trajectories. However, we use the same ray tracing model consistently for all estimations. Using different IRI model settings, the different retrieved values for R and hR vary significantly from each other. The model choice for a given parameter in the ray tracing assessment affects R and hR in a sort of “random” way depending on the models performance. In particular, AMTB and SDMF2 hmF2 values at the magnetic equator are lower than M(3000)F2 hmF2 values, and higher towards the EIA crests, as can be noticed in Figure 2 and more clearly in Figure 9 which shows as an example hmF2 latitudinal variation at 300° (60°W). For a given foF2, decreasing hmF2 implies increasing the electron density at heights below hmF2 that means an increase also in the refractive index, and vice versa. R and hR should decrease or increase accordingly. Figures 3-6 show this behavior clearly: R and hR present lower values with respect to those obtained with 9
M(3000)F2 at the magnetic equator, and higher values towards the EIA crests. For a certain latitude region in the African sector, M(3000)F2 overestimates hmF2 with respect to the other models. This is also noticed in R and hR as an overestimation. A similar situation occurs with foF2, with an overestimation of URSI with respect to CCIR around the magnetic equator, and an underestimation towards the crests. There is also a special signature at the African sector, although not coincident with the hmF2 case. These differences are larger than the differences between including and neglecting the Earth’s magnetic field. For instance, Figures 3(d) and 4(d) show these difference in R using M(3000)F2 model for hmF2. In the case of eastward propagation, neglecting the magnetic field result in R values differing in at most ~60 km in certain regions, but mainly this difference do not exceeds ~20 km. This is an order of magnitude less than R difference observed when different hmF2 models are used. For northward propagation neglecting the magnetic field has a strongest effect due, not only to the stronger effect in the refractive index, but also to the occurrence of Pedersen rays. In the case of hR the effect of the magnetic field is smaller than in the case of R. In general, when the Earth’s magnetic field is neglected, the ionospheric refractive index decreases with respect to its value when this field is taken into account. The refractive index n for the case B=0 is smaller than refractive index for ordinary mode in the magnetized plasma. The smaller n, the lower hR as the oblique HF wave roughly reflects at the height at which the refractive index equals its horizontal component on the ground, if horizontal plasma gradients are much smaller than the vertical gradients. In the case of hR this is clearly noticed in Figures 5(d) and 6(d). In the case of R, the Pedersen ray occurrence blurs this condition. The effect of magnetic field on the refractive index is largest for the propagation along the magnetic field lines. Such situation occurs near the geomagnetic equator for rays propagating in meridian plane. The effect of magnetic field, together with significant changes of electron densities in meridian direction, is likely the main reason for the appearance of elongated structures along the geomagnetic equator in the EIA region in Figure 6(d) that displays differences of reflection heights hR between the case with geomagnetic field and the case B=0 for northward propagation. The amplitude of these structures in the image of hR differences is much smaller than the values of hR and is also smaller than the values of hR differences obtained for various models of electron densities. It should be noted that the elongated “wave” structures remain in Figure 6(d) even if the ray tracing was calculated on grid with higher (1o) spatial resolution. The magnetic field effect could be classified as of "physical" origin, which has the same sign independently of location and time. However, in Figures 3(d), 4(d) and 5(d) certain areas present positive R and hR differences between neglecting and considering the magnetic field. An explanation for this is that R and hR depend mainly on the ionization along the ray path: its amount and its distribution. For this reason, small changes in the structure of the ionosphere along the ray path may result in big R differences which cannot be deduced only from considering the inclusion of a magnetic field. Conversely, the effect of changing a model used for certain parameter’s estimation depends on the model performance which may vary with location and time. Acknowledgments This work was supported by Projects PIUNT E642 and PICT 2015-0511. Jaroslav Chum acknowledges the support under the grant 18-01969S by the Czech Science Foundation. The ray 10
tracing code and simulations are available from Mariano Fagre upon request ([email protected]). References Adebesin, B.O., Adekoya, B.J., Ikubanni, S.O., Adebiyi, S.J., Adebesin, O.A., Joshua, B.W., Olonade, K.O., 2014. Ionospheric foF2 morphology and response of F2 layer height over Jicamarca during different solar epochs and comparison with IRI-2012 model. J. Earth Syst. Sci. 123, 751–765. Adeniyi, J., Bilitza, D., Radicella, S., Willoughby, A., 2003. Equatorial F2-peak parameters in the IRI model. Adv. Space Res. 31(3), 507–512. https://doi.org/10.1016/S0273-1177(03)00039-5 Akyildiz, Y., 1994. Parametric curve fitting: An alternative to Lagrange interpolation and splines. Comput. Phys. 8, 722–729. Altadill, D., Torta, J.M., Blanch E., 2009. Proposal of new models of the bottom-sideB0 andB1parameters for IRI. Adv. Space Res., 43, 1825-1834. https://doi.org/10.1016/j.asr.2008.08.014 Altadill, D., Magdaleno, S., Torta, J.M., Blanch, E., 2013. Global empirical models of the density peak height and of the equivalent scale height for quiet conditions. Adv. Space Res. 52, 1756–1769. https://doi.org/10.1016/j.asr.2012.11.018 Araujo-Pradere, E.A., Buresova, D., Fuller-Rowell, D.J., Fuller-Rowell, T.J., 2013. Initial results of the evaluation of IRI hmF2 performance for minima 22–23 and 23–24. Adv. Space Res. 51, 630–638. https://doi.org/10.1016/j.asr.2012.02.010. Azzarone, A., Bianchi, C., Pezzopane, M., Pietrella, M., Scotto, C., Settimi, A., 2012. IONORT: A Windows software tool to calculate the HF ray tracing in the ionosphere. Computers & Geosciences 42, 57-63. https://doi.org/10.1016/j.cageo.2012.02.008. Banville, S., Sieradzki, R., Hoque, M., Wezka, K., Hadas, T., 2017. On the estimation of higherorder ionospheric effects in precise point positioning. GPS Solutions 21, 1817–1828. https://doi.org/10.1007/s10291-017-0655-0. Bashforth F., Adams J.C., 1883. An attempt to test the theories of capillary action by comparing the theoretical and measured forms of drops of fluid, with an explanation of the method of integration employed in constructing the tables which give the theoretical forms of such drops, Cambridge University Press, Cambridge. Bennett, J.A., Chen, J., Dyson, P.L., 1991. Analytic ray tracing for the study of HF magnetoionic radio propagation in the ionosphere. The Applied Computational Electromagnetics Society Journal 6, 192-210.
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Moulton, F.R., 1926. New Methods in Exterior Balistics, University of Chicago, Chicago. Petrie, E.J., Hernández-Pajares, M., Spalla, P., Moore, P., King, M.A., 2011. A Review of Higher Order Ionospheric Refraction Effects on Dual Frequency GPS. Surveys in Geophysics 32, 197–253. https://doi.org/10.1007/s10712-010-9105-z Rao, N.N., 1969. Bearing Deviation in High‐Frequency Transionospheric Propagation: 3. Ray Tracing Investigation of the Magnetoionic Effect. Radio Science 4(2), 153–161. https://doi.org/10.1029/RS004i002p00153. Ratcliffe, J.A., 1962. The magneto-ionic theory and its applications to the ionosphere, Cambridge University Press, London, UK. Rush, C.M., PoKempner, M., Anderson, D.N., Stewart, F.G., Perry, J., 1983. Improving Ionospheric Maps Using Theoretically Derived Values of foF2. Radio Sci. 18, 95, 1983. Rush, C.M., PoKempner, M., Anderson, D.N., Perry, J., Stewart, F.G., Reasoner, R. 1984. Maps of foF2 Derived from Observations and Theoretical Data, Radio Sci. 19, 1083. Shimazaki, T., 1955. World-wide daily variations in the height of the electron density of the ionospheric F2-layer. J. Radio Res. Lab. 2, 85–97. Shubin, V.N., 2015. Global median model of the F2-layer peak height based on ionospheric radio-occultation and ground-based digisonde observations. Adv. Space Res. 56, 916–928, https://doi.org/10.1016/j.asr.2015.05.029. Thébault, E., Finlay, C.C., Beggan, C., Alken, P., Aubert, J., et al., 2015. International Geomagnetic Reference Field: the 12th generation. Earth, Planets and Space 67, 79. https://doi.org/10.1186/s40623-015-0228-9. Tsai, L.C., Liu, C.H., Huang, J.Y., 2010. Three-dimensional numerical ray tracing on a phenomenological ionospheric model. Radio Science 45, RS5017. https://doi.org/10.1029/2010RS004359. Figures
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(a)
(b)
(c) Figure 1. Ionosphere F2 layer peak height hmF2 [km] obtained with each of the three optional models included in IRI-2016: (a) M(3000)F2, (b) AMTB, and (c) SDMF2. Values obtained for 26 April, 2000, 12 LT.
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(a)
(b) Figure 2. Difference in [km] of hmF2 values obtained with IRI-2016 (a) between AMTB and M(3000)F2 models, and (b) between SMD2 and M(3000)F2 models. Values obtained for 26 April, 2000, 12 LT.
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(d) Figure 3. (a) Ground range R [km] for an eastward propagating wave with 20° elevation angle and 12.5 MHz frequency, using URSI foF2 and M(3000)F2 model for hmF2. (b) Difference in R [km] between using AMTB and M(3000)F2 (c), and SDMF2 and M(3000)F2 as hmF2 models. (d) Difference in R [km] between neglecting and considering the Earth’s magnetic field, using in both cases M(3000)F2 model for hmF2. Values in all cases obtained for 26 April, 2000, 12 LT.
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(d) Figure 4. (a) Ground range R [km] for a northward propagating wave with 20° elevation angle and 12.5 MHz frequency, using URSI foF2 and M(3000)F2 model for hmF2. (b) Difference in R [km] between using AMTB and M(3000)F2 (c), and SMD2 and M(3000)F2 as hmF2 models. (d) Difference in R [km] between neglecting and considering the Earth’s magnetic field, using in both cases M(3000)F2 model for hmF2. Values in all cases obtained for 26 April, 2000, 12 LT.
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(d) Figure 5. (a) Reflection height hR [km] for a eastward propagating wave with 20° elevation angle and 12.5 MHz frequency, using the URSI foF2 and M(3000)F2 model for hmF2. (b) Difference in hR [km] between using AMTB and M(3000)F2 (c), and SMD2 and M(3000)F2 as hmF2 models. (d) Difference in hR [km] between neglecting and considering the Earth’s magnetic field, using in both cases M(3000)F2 model for hmF2. Values in all cases obtained for 26 April, 2000, 12 LT. 19
(a)
(b)
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(d) Figure 6. (a) Reflection height hR [km] for a northward propagating wave with 20° elevation angle and 12.5 MHz frequency, using URSI foF2 and the M(3000)F2 model for hmF2. (b) Difference in hR [km] between using AMTB and M(3000)F2 (c), and SMD2 and M(3000)F2 as hmF2 models. (d) Difference in hR [km] between neglecting and considering the Earth’s magnetic field, using in both cases M(3000)F2 model for hmF2. Values in all cases obtained for 26 April, 2000, 12 LT.
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(c) Figure 7. Critical F2 frequency foF2 [MHz] obtained with both optional models included in IRI2016: (a) URSI and (b) CCIR. (c) Difference in [MHz] of foF2 values obtained with IRI-2016 between CCIR and URSI models using M(3000)F2 model for hmF2. Values obtained for 26 April, 2000, 12 LT.
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(a)
(b) Figure 8. (a) Ground range R [km] for a eastward propagating wave with 20° elevation angle and 12.5 MHz frequency, using CCIR for foF2 and M(3000)F2 model for hmF2. (b) Difference in R [km] between using CCIR and URSI (lower panel).
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Figure 9. Ionosphere F2 layer peak height hmF2 [km] obtained with each of the three optional models included in IRI-2016: M(3000)F2 (black), AMTB (red), and SDMF2 (blue). Values obtained for 26 April, 2000, 12 LT, 300° (60°W).
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Ionospheric high frequency wave propagation using different IRI hmF2 and foF2 models Mariano Fagre, Bruno S. Zossi, Jaroslav Chum, Erdal Yiğit, and Ana G. Elias Highlights • Ray tracing is used to study HF wave propagation for different IRI setting options • Ground range values vary appreciably with the choice of hmF2 and foF2 models • The effect of neglecting the Earth’s magnetic field is in general smaller
S1364-6826(19)30410-9
DOI:
https://doi.org/10.1016/j.jastp.2019.105141
Reference:
ATP 105141
To appear in:
Journal of Atmospheric and Solar-Terrestrial Physics
Received Date: 5 April 2019 Revised Date:
26 July 2019
Accepted Date: 29 August 2019
Please cite this article as: Fagre, M., Zossi, B.S., Chum, J., Yiğit, E., Elias, A.G., Ionospheric high frequency wave propagation using different IRI hmF2 and foF2 models Journal of Atmospheric and Solar-Terrestrial Physics, https://doi.org/10.1016/j.jastp.2019.105141. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
Ionospheric high frequency wave propagation using different IRI hmF2 and foF2 models Mariano Fagre1,2, Bruno S. Zossi3,4, Jaroslav Chum5, Erdal Yiğit6, and Ana G. Elias3,4 1
Consejo Nacional de Investigaciones Científicas y Técnicas, CONICET, Argentina. Laboratorio de Telecomunicaciones, Departamento de Electricidad, Electrónica y Computación, Facultad de Ciencias Exactas y Tecnología, Universidad Nacional de Tucuman, Argentina 3 Laboratorio de Física de la Atmosfera, Departamento de Física, Facultad de Ciencias Exactas y Tecnología, Universidad Nacional de Tucuman, Argentina 4 INFINOA (CONICET-UNT), Tucuman, Argentina 5 Institute of Atmospheric Physics, Prague, Czech Republic 6 Space Weather Laboratory, Department of Physics and Astronomy, George Mason University, USA
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Corresponding author: Ana G. Elias E-mail: [email protected] Laboratorio de Física de la Atmosfera - Departamento de Física Facultad de Ciencias Exactas y Tecnología Universidad Nacional de Tucuman Av. Independencia 1800 4000 Tucuman - Argentina Highlights • Ray tracing is used to study HF wave propagation for different IRI setting options • Ground range values vary appreciably with the choice of hmF2 and foF2 models • The effect of neglecting Earth’s magnetic field is in general smaller Abstract High frequency (HF) electromagnetic wave propagation is commonly used in long-distance communications and detection. The ionosphere is a highly variable medium affecting this propagation. However, mean climatological conditions are useful in order to determine a “base level” for the design and operation of systems using HF waves that propagate in the ionosphere. Important variables that determine these conditions are the ionosphere peak height, hmF2, and F2 critical frequency, foF2. In the present work the effect of different hmF2 and foF2 model options in IRI-2016 and its spatial variability are analyzed through the analysis of the ground range and reflection height of HF ray paths using a numerical ray tracing method. The model options are M(3000)F2, AMTB and SDMF2 for hmF2, and URSI and CCIR for foF2. We perform this study for a quiet day, April 26 at 12 LT, and solar activity maximum conditions. Ground range and reflection height variation between values obtained with the different model options are on average not greater than ~40%, but can be higher for a Pedersen ray case. These variations are in general much stronger than those obtained when Earth’s magnetic field is neglected in ray path assessments. However, while the magnetic field effect is of “physical” origin that has always the same sign, the effect of changing a model used for certain parameter’s estimation depends on the model performance which may vary with location and time. Keywords: Ray tracing; IRI model; Pedersen ray 1
1. Introduction High frequency (HF) electromagnetic waves between 3 and 30 MHz, also called radio frequency waves, are used mainly in long distance communication, detection and surveillance. It has always been a challenge to establish radio links and exact positions with radar systems using these waves traveling through and reflecting in the ionosphere due to the theoretical complexity of electromagnetic wave propagation through the ionospheric plasma that is embedded in the Earth’s magnetic field. The ray tracing technique is a powerful tool that is commonly employed to estimate the ray path between the transmitter and a long-range target. This technique helps to determine the exact path of radio waves if the ionospheric electron density profile along the propagation path is known with good precision, which is seldom the case since ionospheric measurements are not continuously available along the extended ray. Usually they are obtained from ionospheric modeling or a combination of measurements and modeling. Ray tracing can be performed analytically if simple ionospheric and terrestrial magnetic field models are considered, however this approach provides low accuracy. Alternatively, ray tracing can be assessed by numerical integration of the equations of electromagnetic wave propagation through a magnetized plasma and thus any ionospheric model or measured profiles can be used, including a realistic terrestrial magnetic field and absorption effects. A numerical ray tracing technique that has been widely used is that by Jones and Stephenson (1975) who calculated ray paths and associated quantities in three-dimensional space using spherical-polar coordinates. The presence of an ambient magnetic field increases the complexity of plasma dynamics and electromagnetic wave propagation. In addition, not only the field intensity enters the propagation equation, but also the angle between the ray and field vector. These conditions indeed apply to Earth’s ionosphere, which is a partially ionized plasma embedded in a complex intrinsic magnetic field. An ionospheric model that is commonly used for radio propagation studies and by ray tracing algorithms is the International Reference Ionosphere (IRI) (Bilitza et al., 2017), which is a semiempirical model based on available measurements of ionospheric characteristics. The last IRI version was introduced in 2016, and among the improvements over previous versions there are two new models for the height of the F2 peak electron density, hmF2. In older versions of IRI, hmF2 was based on the close correlation with the propagation factor M(3000)F2 (Shimazaki, 1955; Bilitza and Eyfrig, 1978; Bilitza et al., 1979; Dudeney, 1983) which in turn is based on the Consultative Committee on International Radio (CCIR) model (CCIR, 1967). Many studies highlighted some limitations of this approach for hmF2 (Bilitza, 1985; Adeniyi et al., 2003; Lee and Reinisch, 2006; Brum et al., 2011; Magdaleno et al., 2011; Araujo-Pradere et al., 2013; Ezquer et al., 2014). Adeniyi et al. (2003) pointed out that there are three main error sources: (1) the scarce data volume available at the time of the model development; (2) the limitations to reproduce small-scale features in the diurnal variation because of the chosen functional representation (harmonics of up to order 4 only); and (3) the uncertainty introduced with the formula describing the relationship between hmF2 and M(3000)F2.
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Because of these limitations of IRI hmF2 model a purely ionosonde based modeling was developed by Magdaleno et al. (2011) and Altadill et al. (2013). Additionally, Shubin et al. (2013) presented an hmF2 model based on radio occultation data from COSMIC (Constellation Observing System for Meteorology, Ionosphere and Climate), GRACE (Gravity Recovery and Climate Experiment), and CHAMP (Challenging Mini-Satellite Payload for Geophysical Research and Application). The last two models have been selected for inclusion in the 2016 version of the IRI model. Another parameter which plays an important role in HF radio propagations is the F2 layer critical frequency, foF2. The options provided by IRI for foF2 model are CCIR and URSI (Union RadioScientifique Internationale). There are many papers which compare the IRI performance using CCIR or URSI (Bertoni et al., 2006; Brum et al., 2011; Adebesin et al., 2014; Brown et al., 2018; Liu et al., 2019). Adebesin et al. (2014) found that in general, the URSI option presents better agreement with observed data than the CCIR option, especially during daytime, suggesting an improvement in the URSI option of IRI-2012 version over IRI-2007. In the present work the spatial variation of the ground range R and reflection height hR of a ray path at mid and low latitudes are analyzed in order to assess the effects of using the new hmF2 models incorporated by IRI with respect to the traditional one based on M(3000)F2, and also the effects of the two foF2 model options. These effects are compared to those produced by neglecting Earth’s magnetic field. There are several works, which analyze ray tracing in the ionosphere considering geomagnetic field effects (e.g., Kelso, 1968; Rao, 1969; Bennett et al., 1991; Tsai et al., 2010; Dao et al., 2016), but the effect of the different IRI options on a global scale has yet not been studied. IRI model parameters, such as hmF2 and foF2, as well as the configuration of the magnetic field have an important physical effect on the ray propagation process. Here we specifically focus on R and hR. It should be noted that the state of the ionosphere and hence the ionospheric model used influences also precision of Global Navigation Satellite Systems (GNSS) (Hoque & Jakowski, 2008, Petrie et al., 2011; Banville et al., 2017; Hadas et al., 2017). The structure of the paper is as follows: In section 2 we outline the methodology of our study, which includes the description of ray tracing approach, the IRI model options considered and the calculation set up, followed by the results in section 3. The discussion and conclusions are presented in section 4.
2. Methodology 2.1 HF signal ray tracing model The propagation of HF electromagnetic waves in the ionosphere is a rather complex process because the ionosphere is an inhomogeneous and time-varying magnetized plasma (Davies, 1965). In fact, the presence of a strong intrinsic magnetic field makes the ionosphere an anisotropic medium that results in the double refraction of an incident electromagnetic, which is decomposed into ordinary and extraordinary modes. Additional magnetic field effects on the 3
refraction of an incident electromagnetic wave are that the direction of energy flow differs from that of the wave propagation. A valid approximation for the propagation of HF signals in the ionosphere is to assume a cold magnetoplasma where only electrons need to be taken into account. In this case the refractive index n is given by the Appleton-Hartree equation (Ratcliffe, 1962), that is, = 1 −
±
(1)
with
= =
= " =
' = () " = =
#
#
#
(2) sin "
cos "
(3) (4) (5)
where fo is the plasma frequency, f the incident electromagnetic wave frequency, N the electron number density, e the electron charge, m the electron mass, ε0 the permittivity of vacuum, B the magnetic field intensity, T stands for transverse and L for longitudinal, and θ corresponds to the angle between the direction of the wave propagation and the magnetic field vector. The upper sign in the denominator of Equation (1) refers to the ordinary component and the lower sign to the extraordinary. Considering that the extraordinary wave suffers higher absorption, and that useful sky wave propagation usually takes place through the ordinary wave, only the latter will be considered for simplicity. It should be noted that the absorption mainly takes place in the D layer and it is roughly proportional to the square of the inverse wave frequency (e.g., Chum et al., 2018). Thus, during the night when the D layer practically disappears, both modes might propagate over substantial distances. Various numerical ray tracing programs have been developed to determine the propagation of HF electromagnetic wave through the ionosphere. Among them, Azzarone et al. (2012) developed a software that is freely available and allows ionospheric ray tracing in a geocentric spherical coordinate system, taking into account a dipolar geomagnetic field. However, since we consider the current magnetic field with its multipolar contributions, the 3D ray tracing original code developed in the work by Jones and Stephenson (1975) was adjusted to include the International Geomagnetic Reference Field 12th Generation (IGRF-12) model (Thébault et al., 2015). This ray tracing is based on Hamilton's equations of geometrical optics given by Haselgrove (1955) in spherical coordinates. The Hamiltonian used here is given by
4
,-,/,0,12 ,13 ,14 = ∗ 67 8
9
:
;<- + − ?
(6)
where n is given by Equation (1), c is the speed of light in free space, r, θ, and ϕ are the spherical polar coordinates of a point on the ray path, and kr, kθ and kϕ are the spherical components of the HF wave vector of frequency ω=2πf. Hamilton’s equations, which consist in a set of six partial differential equations, are @@A
@/ @A
@0 @A
BC
= B1
BC
= - B1
@12
=
@A
@13 @A
@13 @A
(7)
2
3
(8) BC
-DEF/ B14
=−
BC B-
= G− =
-
+
BC B/
-DEF0
(9) @/ @A
−
G−
BC
B0
+ <0 "
@@A
@0 @A
(10)
+ <0 H() "
− <0 sin"
@@A
@0 @A
I
− <0 H() "
(11) @/ @A
I
(12)
where the quantity τ is the HF wave group path, ct, and the independent variable of the Hamiltonian. 2.2 Interpolation method and integration For the ray tracing technique here implemented continuous first derivatives are needed. Since N is not calculated at each step but obtained from a grid, an interpolation method is required. In order to guarantee derivative’s continuity when considering the actual magnetic field a method proposed by Akyildiz (1994) was used. It consists of a parametric curve fitting, which is cubic in each direction and is known as smooth-jointed interpolation. For simplicity, we will explain the one dimensional case. For a set of no ordered data points in order to interpolate a curve between two of them, we consider first the parabola which is determined by these two data points plus another one located to their left. Then, with a similar procedure a second parabola is obtained for the same two data points, but using as the third point one located on their right. The final arc that connects the two initial data points is given by the convex combination of these two parabolas. Thereby, the arc that connects two successive points will finally be determined by four points: the two points of interest, the point that precedes them and the point following them. Since in our code the interpolation is cubic (in the three directions), each interpolated point requires the use of 64 nearby points. One of the main advantage of this procedure is that is tighter than a spline interpolation because is more immune to overshoot problems between points, yet still provides continuity through the first derivative, something essential for a correct operation of the ray tracing.
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Hamilton’s equations given in Equations (6) to (12) are integrated using a Fortran subroutine which computes the numerical solutions of the system of six simultaneous first-order differential equations over a specified interval with given initial conditions applying the Adams-Moulton procedure (Moulton, 1926; Lastman, 1964). This is a multi-step method that requires a selfstarter, in this case a fourth order Runge-Kutta method, together with a predictor given by Adams-Bashforth formula (Bashforth and Adams, 1883).
2.3 Model of hmF2 and foF2 Previous versions to the current IRI 2016, estimate hmF2 in terms of M(3000)F2 through the following relationship (Bilitza et al., 1979): ℎKL2 =
NO
PQOOO R∆P
− 176
(13)
where ∆M is given by ×Y
W ∆V = Z[ Z\
+ ]Q
] = 0.00232 6 + 0.222
] = 1.2 − 0.0116 7 aW / .c
]Q = 0.096 ] = 1 −
aW e
aW
eO
eO
7 ∅
/ gOO
(14) (15) (17) (18) (16)
with R12 the 12-month running mean sunspot number and φ the dip latitude. M(3000)F2 is obtained from CCIR numerical maps usually recommended for calculations over continents or the URSI which provides a better fit over the sea. This hmF2 model appears as BSE-1979, after its authors Bilitza, Sheikh, and Eyfrig (Bilitza et al., 1979). M(3000)F2 will use CCIR or URSI coefficients depending on the choice made for foF2. However, this is not important in our case due to the variations in hmF2 between M(3000)F2 with CCIR and with URSI is less than 2%. As mentioned before, IRI-2016 introduced two new models for hmF2. One of the options is the AMTB model which is based on data from 26 digisonde stations from the Global Ionosphere Radio Observatory (GIRO) network for the period 1998–2006. For the spherical harmonics analysis to be feasible the global data coverage was filled out with fictitious data points (Altadill et al., 2013) and is called as AMTP2013 in IRI-2016. The other option is SDMF2 model which is based on radio occultation data from CHAMP of period 2001–2008 (~300,000 values), GRACE of period 2007–2011 (~100,000 values) and COSMIC of period 2006–2012 (~3,500,000 values), and with hmF2 data from 62 digisondes from the Digital Ionogram Data Base for the period 1987–2012. 6
The three models use spherical harmonics to describe global variations, but AMTB and SDMF2 model hmF2 directly and no longer uses M(3000)F2. Large discrepancies are found in hmF2 values between the models reaching ~50 km or more (Bilitza, 2018). IRI recommends, as a first choice, AMTB model since it presents the lowest error estimates for ionosonde measurements. Regarding foF2, IRI provides two different models. One of them is given by the CCIR maps which are based on monthly median values obtained by the worldwide network of ionosondes (about 150 stations) during years 1954 to 1958, based on around 10,000 station-months of data (Bilitza et al.,2017). This method follows a numerical mapping procedure developed by Jones and Gallet (1962, 1965). Another available option is the URSI set of model coefficients where the numerical mapping method is the same as for the previous model, based on a Fourier analysis of the monthly median diurnal variation of foF2 observed by the worldwide network of ionosondes, and on spherical Legendre functions of each Fourier coefficient, for each month and two solar activity levels. However, URSI foF2 model represents an improvement of the CCIR foF2 model due to data gap filling method used where ionosonde measurements do not exist or are sparse, as is the case of the Southern Hemisphere or above the oceans, before applying the spherical harmonics mapping procedure (Rush et al., 1983, 1984). Fox and McNamara (1988) established the final URSI coefficients for the combined data base of Rush's values and about 45,000 monthly ionosonde data (from about 180 stations worldwide).
2.4 Calculation setup Two ray tracing outputs were chosen for the present analysis: the ground range, R, that is the measure of the distance along the surface of Earth from the ray’s origin (a transmitter for instance) to the point where it again reaches Earth’s surface (a receiver or a target), and the reflection height, hR, that is the true vertical distance of the point in the ray path where the ray is reflected by the ionosphere. The electron density grid used by the ray tracing code is generated with the International IRI2016 (Bilitza et al., 2017) with a resolution of 2.5° x 2.5° in latitude and longitude, and 1 km in altitude. Earth’s magnetic field parameters are from IGRF-12 (Thebault et al., 2015). From the three IRI available options for the bottomside thickness parameter: ABT-2009, Bil-2000, and Gul-1987, we used the default and recommended one, that is ABT-2009. This option (Altadill et al., 2009) uses a large volume of ionosonde data to develop an improved representation of latitudinal and solar cycle variation of the bottomside ionosphere parameters, B0 and B1. The first corresponds to the height difference between hmF2 and the height where the electron density profile has dropped down to half the F peak value, and the second describes the bottomside profile shape. The global spatial structure of R and hR were assessed on a grid with 2.5° latitude and 5° longitude resolution between 45°S and 45°N latitude and 180°W and 180°E longitude, where each grid point corresponds to the transmitter location. Northward and Eastward wave propagation directions were considered with a fixed elevation angle, α = 20°, and a single frequency of 12.5 MHz, which are typical mean values for over the horizon radars, OTHR, 7
which use Earth’s ionosphere as a mirror to illuminate targets beyond the line-of-sight horizon. The date and time chosen for this study is April 26, 2000, at 12 LT. It represents a quiet day around equinox and solar activity maximum conditions, with F10.7=192 sfu, and Kp index less than 1. Calculation of HF propagation requires setting up electron density at the same UT moment in each point along the propagation path. However, we considered the same local time (12 LT) everywhere for simplicity. This allowed us to use a single grid for the whole globe and each ray tracing run. This simplification might be not exactly realistic for eastward propagation. The difference from real conditions is, however, negligible as the maximum obtained R values roughly correspond to 1-hour time difference for the Eastward propagation. Such a small time difference around noon is well within model uncertainties. In the case of Northward propagation, which is almost along a meridian, considering LT or UT makes no difference. In order to compare the dependence of R and hR on foF2 and hmF2 model choices in IRI, their values were calculated considering URSI and CCIR for foF2 and M(3000)F2, AMTB and SDMF2 for hmF2. The URSI and M(3000)F2 options were considered as baselines since these were the default settings of the previous IRI version, IRI-2012. 3. Results Figure 1 shows hmF2 for the zone here analyzed, between 45°S and 45°N, obtained with URSI option for foF2 and each of the three hmF2 models: M(3000)F2, AMTB and SDMF2. In all the cases hmF2 is maximum at the magnetic equator. Overall, the imprint of the magnetic field is clearly seen in the geographical variation of hmF2. Figure 2 presents hmF2 differences between AMTB and SDMF2 with respect to M(3000)F2. The greatest differences are observed at the EIA region, from the southern to the northern crest. In percentage terms, hmF2 differences do not exceed ~15-20%. R estimated using M(3000)F2 for eastward propagation is presented in Figure 3 together with the differences with respect to this model when AMTB and SDMF2 are used instead as the hmF2 model. Here, as expected, the differences are greatest at the EIA region, but in percentage terms the greatest differences reach ~40% in the case of AMTB, and ~100% in SDMF2 case. Note that the color scales are different in each plot. In the case of northward propagation (azimuth angle 0°), shown in Figure 4, the magnetic field effect is stronger due to a more field aligned ray path. At certain regions, the occurrence of Pedersen rays (rays that satisfy conditions for downward refraction critically and propagate substantial distances almost parallel to the Earth’s surface) greatly increases R. Since this is an unstable condition, very small environment changes make the ray to return to its normal condition, generating extremely big R differences when comparing two different but similar situations, as in our case. Under the conditions here analyzed, R values obtained with M(3000)F2 are enhanced around the magnetic equator in the Pacific Ocean close to South America and around Indonesia, and also at ~45°N. This creates differences of more than double at these regions, which look like peculiarities in Figure 4 around the magnetic equator and at ~45°N.
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Differences observed in hR are shown in Figure 5 for eastward propagation. The percentage differences observed are similar to R case, and the spatial pattern is almost exactly the same as that observed for R. In the northward case, presented in Figures 6(a)-(c), where hR for Pedersen rays is the same as for a “regular” ray, the spatial variation presents less peculiarities than Figures 4(a)-(c). Figure 7 shows foF2 obtained with URSI and CCIR options in IRI-2016, with M(3000)F2 for hmF2 model. As in the case of the different hmF2 models, the greatest differences appear at the EIA region, with percentage differences around 20%. And the same happens with R differences obtained when comparing R values obtained with each foF2 model, as can be seen in Figure 8. The percentage differences in this case do not exceed ~25%. For Northward propagation (not shown), as in the case of hmF2 model comparison, at certain regions the occurrence of Pedersen rays is propitiated which greatly increases R. The differences are similar to those shown in Figure 4(b). Differences in hR (not shown) present, as in the case a hmF2 model comparison, a behavior almost identical to R differences. 4. Discussion and conclusions We have studied the effect of different hmF2 and foF2 model options in IRI-2016 on R and hR of HF ray paths, using a numerical ray tracing method. IRI model options are M(3000)F2, AMTB and SDMF2 for hmF2, and URSI and CCIR for foF2. We have performed this study for a representative quiet day, April 26 at 12 LT, and solar activity maximum conditions. Our results indicate that the choice of ionospheric parameters in model settings may greatly affect the parameters determined for the ray path’s R and hR in the ray tracing code. How accurate these values are with respect to true values would depend on both, the accuracy of the ray tracing code and how realistic the modeled ionosphere is. Every numerical scheme has various numerical uncertainties. In particular, for numerical ray tracing one of the causes of loss of accuracy is the step size chosen to perform the ray trace. The numerical integration of the method implemented in this work has a built-in mechanism to check errors and adjust the integration step length accordingly. If the errors get larger than a maximum value (10-6 km for this case) the routine will decrease the step length in order to maintain the accuracy. On the other hand, if the accuracy is greater than required, the routine will increase the step length in order to reduce the computing cost. Another source of error in the estimation of the ray path propagation depends on whether or not Earth’s magnetic field is taken into account, since it modifies the value of the refractive index obtained from Equation (1), therefore producing changes in ray trajectories. However, we use the same ray tracing model consistently for all estimations. Using different IRI model settings, the different retrieved values for R and hR vary significantly from each other. The model choice for a given parameter in the ray tracing assessment affects R and hR in a sort of “random” way depending on the models performance. In particular, AMTB and SDMF2 hmF2 values at the magnetic equator are lower than M(3000)F2 hmF2 values, and higher towards the EIA crests, as can be noticed in Figure 2 and more clearly in Figure 9 which shows as an example hmF2 latitudinal variation at 300° (60°W). For a given foF2, decreasing hmF2 implies increasing the electron density at heights below hmF2 that means an increase also in the refractive index, and vice versa. R and hR should decrease or increase accordingly. Figures 3-6 show this behavior clearly: R and hR present lower values with respect to those obtained with 9
M(3000)F2 at the magnetic equator, and higher values towards the EIA crests. For a certain latitude region in the African sector, M(3000)F2 overestimates hmF2 with respect to the other models. This is also noticed in R and hR as an overestimation. A similar situation occurs with foF2, with an overestimation of URSI with respect to CCIR around the magnetic equator, and an underestimation towards the crests. There is also a special signature at the African sector, although not coincident with the hmF2 case. These differences are larger than the differences between including and neglecting the Earth’s magnetic field. For instance, Figures 3(d) and 4(d) show these difference in R using M(3000)F2 model for hmF2. In the case of eastward propagation, neglecting the magnetic field result in R values differing in at most ~60 km in certain regions, but mainly this difference do not exceeds ~20 km. This is an order of magnitude less than R difference observed when different hmF2 models are used. For northward propagation neglecting the magnetic field has a strongest effect due, not only to the stronger effect in the refractive index, but also to the occurrence of Pedersen rays. In the case of hR the effect of the magnetic field is smaller than in the case of R. In general, when the Earth’s magnetic field is neglected, the ionospheric refractive index decreases with respect to its value when this field is taken into account. The refractive index n for the case B=0 is smaller than refractive index for ordinary mode in the magnetized plasma. The smaller n, the lower hR as the oblique HF wave roughly reflects at the height at which the refractive index equals its horizontal component on the ground, if horizontal plasma gradients are much smaller than the vertical gradients. In the case of hR this is clearly noticed in Figures 5(d) and 6(d). In the case of R, the Pedersen ray occurrence blurs this condition. The effect of magnetic field on the refractive index is largest for the propagation along the magnetic field lines. Such situation occurs near the geomagnetic equator for rays propagating in meridian plane. The effect of magnetic field, together with significant changes of electron densities in meridian direction, is likely the main reason for the appearance of elongated structures along the geomagnetic equator in the EIA region in Figure 6(d) that displays differences of reflection heights hR between the case with geomagnetic field and the case B=0 for northward propagation. The amplitude of these structures in the image of hR differences is much smaller than the values of hR and is also smaller than the values of hR differences obtained for various models of electron densities. It should be noted that the elongated “wave” structures remain in Figure 6(d) even if the ray tracing was calculated on grid with higher (1o) spatial resolution. The magnetic field effect could be classified as of "physical" origin, which has the same sign independently of location and time. However, in Figures 3(d), 4(d) and 5(d) certain areas present positive R and hR differences between neglecting and considering the magnetic field. An explanation for this is that R and hR depend mainly on the ionization along the ray path: its amount and its distribution. For this reason, small changes in the structure of the ionosphere along the ray path may result in big R differences which cannot be deduced only from considering the inclusion of a magnetic field. Conversely, the effect of changing a model used for certain parameter’s estimation depends on the model performance which may vary with location and time. Acknowledgments This work was supported by Projects PIUNT E642 and PICT 2015-0511. Jaroslav Chum acknowledges the support under the grant 18-01969S by the Czech Science Foundation. The ray 10
tracing code and simulations are available from Mariano Fagre upon request ([email protected]). References Adebesin, B.O., Adekoya, B.J., Ikubanni, S.O., Adebiyi, S.J., Adebesin, O.A., Joshua, B.W., Olonade, K.O., 2014. Ionospheric foF2 morphology and response of F2 layer height over Jicamarca during different solar epochs and comparison with IRI-2012 model. J. Earth Syst. Sci. 123, 751–765. Adeniyi, J., Bilitza, D., Radicella, S., Willoughby, A., 2003. Equatorial F2-peak parameters in the IRI model. Adv. Space Res. 31(3), 507–512. https://doi.org/10.1016/S0273-1177(03)00039-5 Akyildiz, Y., 1994. Parametric curve fitting: An alternative to Lagrange interpolation and splines. Comput. Phys. 8, 722–729. Altadill, D., Torta, J.M., Blanch E., 2009. Proposal of new models of the bottom-sideB0 andB1parameters for IRI. Adv. Space Res., 43, 1825-1834. https://doi.org/10.1016/j.asr.2008.08.014 Altadill, D., Magdaleno, S., Torta, J.M., Blanch, E., 2013. Global empirical models of the density peak height and of the equivalent scale height for quiet conditions. Adv. Space Res. 52, 1756–1769. https://doi.org/10.1016/j.asr.2012.11.018 Araujo-Pradere, E.A., Buresova, D., Fuller-Rowell, D.J., Fuller-Rowell, T.J., 2013. Initial results of the evaluation of IRI hmF2 performance for minima 22–23 and 23–24. Adv. Space Res. 51, 630–638. https://doi.org/10.1016/j.asr.2012.02.010. Azzarone, A., Bianchi, C., Pezzopane, M., Pietrella, M., Scotto, C., Settimi, A., 2012. IONORT: A Windows software tool to calculate the HF ray tracing in the ionosphere. Computers & Geosciences 42, 57-63. https://doi.org/10.1016/j.cageo.2012.02.008. Banville, S., Sieradzki, R., Hoque, M., Wezka, K., Hadas, T., 2017. On the estimation of higherorder ionospheric effects in precise point positioning. GPS Solutions 21, 1817–1828. https://doi.org/10.1007/s10291-017-0655-0. Bashforth F., Adams J.C., 1883. An attempt to test the theories of capillary action by comparing the theoretical and measured forms of drops of fluid, with an explanation of the method of integration employed in constructing the tables which give the theoretical forms of such drops, Cambridge University Press, Cambridge. Bennett, J.A., Chen, J., Dyson, P.L., 1991. Analytic ray tracing for the study of HF magnetoionic radio propagation in the ionosphere. The Applied Computational Electromagnetics Society Journal 6, 192-210.
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(c) Figure 1. Ionosphere F2 layer peak height hmF2 [km] obtained with each of the three optional models included in IRI-2016: (a) M(3000)F2, (b) AMTB, and (c) SDMF2. Values obtained for 26 April, 2000, 12 LT.
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(b) Figure 2. Difference in [km] of hmF2 values obtained with IRI-2016 (a) between AMTB and M(3000)F2 models, and (b) between SMD2 and M(3000)F2 models. Values obtained for 26 April, 2000, 12 LT.
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(d) Figure 3. (a) Ground range R [km] for an eastward propagating wave with 20° elevation angle and 12.5 MHz frequency, using URSI foF2 and M(3000)F2 model for hmF2. (b) Difference in R [km] between using AMTB and M(3000)F2 (c), and SDMF2 and M(3000)F2 as hmF2 models. (d) Difference in R [km] between neglecting and considering the Earth’s magnetic field, using in both cases M(3000)F2 model for hmF2. Values in all cases obtained for 26 April, 2000, 12 LT.
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(d) Figure 4. (a) Ground range R [km] for a northward propagating wave with 20° elevation angle and 12.5 MHz frequency, using URSI foF2 and M(3000)F2 model for hmF2. (b) Difference in R [km] between using AMTB and M(3000)F2 (c), and SMD2 and M(3000)F2 as hmF2 models. (d) Difference in R [km] between neglecting and considering the Earth’s magnetic field, using in both cases M(3000)F2 model for hmF2. Values in all cases obtained for 26 April, 2000, 12 LT.
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(d) Figure 5. (a) Reflection height hR [km] for a eastward propagating wave with 20° elevation angle and 12.5 MHz frequency, using the URSI foF2 and M(3000)F2 model for hmF2. (b) Difference in hR [km] between using AMTB and M(3000)F2 (c), and SMD2 and M(3000)F2 as hmF2 models. (d) Difference in hR [km] between neglecting and considering the Earth’s magnetic field, using in both cases M(3000)F2 model for hmF2. Values in all cases obtained for 26 April, 2000, 12 LT. 19
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(d) Figure 6. (a) Reflection height hR [km] for a northward propagating wave with 20° elevation angle and 12.5 MHz frequency, using URSI foF2 and the M(3000)F2 model for hmF2. (b) Difference in hR [km] between using AMTB and M(3000)F2 (c), and SMD2 and M(3000)F2 as hmF2 models. (d) Difference in hR [km] between neglecting and considering the Earth’s magnetic field, using in both cases M(3000)F2 model for hmF2. Values in all cases obtained for 26 April, 2000, 12 LT.
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(c) Figure 7. Critical F2 frequency foF2 [MHz] obtained with both optional models included in IRI2016: (a) URSI and (b) CCIR. (c) Difference in [MHz] of foF2 values obtained with IRI-2016 between CCIR and URSI models using M(3000)F2 model for hmF2. Values obtained for 26 April, 2000, 12 LT.
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(a)
(b) Figure 8. (a) Ground range R [km] for a eastward propagating wave with 20° elevation angle and 12.5 MHz frequency, using CCIR for foF2 and M(3000)F2 model for hmF2. (b) Difference in R [km] between using CCIR and URSI (lower panel).
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Figure 9. Ionosphere F2 layer peak height hmF2 [km] obtained with each of the three optional models included in IRI-2016: M(3000)F2 (black), AMTB (red), and SDMF2 (blue). Values obtained for 26 April, 2000, 12 LT, 300° (60°W).
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Ionospheric high frequency wave propagation using different IRI hmF2 and foF2 models Mariano Fagre, Bruno S. Zossi, Jaroslav Chum, Erdal Yiğit, and Ana G. Elias Highlights • Ray tracing is used to study HF wave propagation for different IRI setting options • Ground range values vary appreciably with the choice of hmF2 and foF2 models • The effect of neglecting the Earth’s magnetic field is in general smaller