I have found numerous papers that estimate Faraday rotation (FR) using total electron content (TEC) measurements and an average value for the parallel component of Earth's magnetic field. I know it is better to use models like International Geomagnetic Reference Field (IGRF) or data when available, but I am curious how others feel about an average value for the magnetic field.
I was asked once during a presentation whether I should use a value closer to the satellite altitude (1000 km) rather than average value. The extensive literature supported the approach (using an average value), however a back of envelope calculation out of curiosity revealed a value weighted in favor of ground based measurements as opposed to space based measurements seemed more appropriate.
Any thoughts on how the parallel component of the magnetic field should be treated for estimation of ionospheric FR are welcomed in advance.
To the first order and second order, yes; however, their are a good number of papers out there on "higher order" ionospheric effects on GPS signals (as an example). I imagine that would be a good place for you to start.
Some example work: http://www.sciencedirect.com/science/article/pii/S0273117710001183
http://www.iers.org/SharedDocs/Publikationen/EN/IERS/Publications/tn/TechnNote36/tn36_132.pdf;jsessionid=D2372AF71AB1030C0EA33EBC1D3369BA.live2?__blob=publicationFile&v=1
Yes, i think the above answers are correct.. If i recall, the faraday effect -- the rotation
of the wave,, takes the integral along the line of sight, of the wave-- (integral of B. dl)
Thank you for the high quality replies and references thus far! Another paper I found following David's suggestion is [Hernandez-Pajares et al., 2007]:
Hernandez-Pajares, M., Juan, J. and Sanz, J.,2007. Second-order ionospheric term in GPS: Implementation and impact on geodetic estimates . Journal of Geophysical Research. 112, pp. 1-16.
Yes, FR (in rad) is calculated as \integral{N_e*B_par dl} multiplied by e^32c \epsilon_0 m^2 \omega^2.
where the Faraday rotation, is in radians, c = 3 e8 m/s is the speed of light, e = 1.602e-19, C is the elementary charge, m = 9.10910e-31 kg is the mass of an electron and \epsillon_0 = 8.854 e-12 C2^2/N m^2 is the vacuum permittivity. The magnetic field B_par is in nT.
Several authors [1-5] simplify the integral from \integral{N_e*B_par dl} to B_par_avg \integral{N_e*dl} where \integral{N_e*dl} is TEC.
[1] http://www.academia.edu/7565035/FARADAY_ROTATION_ESTIMATION_FROM_UNFOCUSSED_RAW_DATA_ANALYSIS_USING_ALOS_PALSAR_DATA
[2] https://books.google.ca/books?id=hfZnkqSPSeAC&pg=PA99&lpg=PA99&dq=faraday+rotation+TEC+average+magnetic+field&source=bl&ots=tqISJ8msrs&sig=mOknuk9FgRThiWCWfJc22g5dmvk&hl=en&sa=X&ved=0ahUKEwjvkt2z6IzLAhWjtYMKHYoTBDIQ6AEILDAC#v=onepage&q=faraday%20rotation%20TEC%20average%20magnetic%20field&f=false
[3] P. A. Wright, S. Quegan, N. S. Wheadon, and C. D. Hall, “Faraday rotation effects on L-band spaceborne data,” IEEE Trans. Geosci. Remote Sens., vol. 41, no. 12, pp. 2735–2744, Dec. 2003.
[4] https://books.google.ca/books?id=kxd6Ovryqf0C&pg=PA142&lpg=PA142&dq=faraday+rotation+TEC+average+magnetic+field&source=bl&ots=QSKEgXHh3q&sig=-lNufm8VYH5PekpYeZLVgPh_Lqk&hl=en&sa=X&ved=0ahUKEwjvkt2z6IzLAhWjtYMKHYoTBDIQ6AEILzAD#v=onepage&q=faraday%20rotation%20TEC%20average%20magnetic%20field&f=false
[5] http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.459.5824&rep=rep1&type=pdf
- Badges
- Science topic
- Similar topics
- Engineering
- Control Theory
- Control Systems
- Control Systems Engineering