solar cycle effects on gnss-derived ionospheric total electron content ...

where it is evident that the 2nd and the 4th terms are functions of the maximum electron density andfrequency, whereas the 3rd and 5th are a function of the maximum electron density, the Earth `smagnetic field strength and the frequency. However, Komjathy (1997) showed that the contributionof the 3rd, 4th and 5th terms to the error budget of the determination of the refractive index are 3, 5,and 6 orders of magnitude less than the second term when assuming Θ = 0, and the typical values12 -3for F2 layer maximum electron density ( N = 10 m ) and typical value for the Earth’s magnetic−5 -2field strength ( B 0= 5.0× 10 Wb.m ) respectively.When both collisions and the magnetic field are negligible, only the 1st and 2nd terms in equation(2.7) are considered. However, to enable calculating the phase refractive index of the ionosphere,appropriate for the carrier phase observations, we obtain:2.6.2 Group refractive indexAccording to Langley (1996), the group refractive index is defined as:nϕ40.3⋅N≅ 1 − .(2.8)2fdn= + . (2.9)ngn f dfBy invoking the value of phase refractive index n= n ϕin equation (2.8),dn dn g d ⎛ 40.3⋅N ⎞= = ⎜1 − ,2 ⎟df df df ⎝ f ⎠d ⎛ 1 ⎞40.3 N , df ⎝ f ⎠= − ⋅ ⎜ 2 ⎟and therefore the equation (2.9) takes the form:⎛ 1 ⎞2( 40.3 ) ,⎝ f ⎠= − ⋅ N ⎜ 3 ⎟(2.10)33