Ground GNSS Ionosphere Sounding - GNSS Remote Sensing: Theory, Methods and Applications - page 67

Fig. 4.1 Geometry of GPS-TEC estimation

4.2.1 DCB Determination

From Eq. ( 4.8 ), it is easy to extract slant total electron content (STEC) from GNSS
dual-frequency observations as follow

f 1 2 f 1 2
40:3 .f 1 2 f 2 2 / P 4;sm cDCB j

cDCB i

STEC D (4.9)

where DCB's unit is the time. The earth's ionosphere ranges in altitude from 60 to
1,000 km. It is assumed that all electrons in the ionosphere are concentrated in a
thin shell at altitude H (see Fig. 4.1 ), so the STEC can be translated into the vertical
total electron content (VTEC) using the modified single-layer model (MSLM: http://
aiuws.unibe.ch/spec/ion.php#processing_description ) , namely

VTEC D MF. z /S TEC

D cos arcsin sin.˛ z /

R
R C H

MF (4.10)

where z is the satellite elevation angle, R is the earth's radius, and H is the attitude
of the ionosphere thin shell (normally the approximate peak height of the F2 layer).
R is set to 6,371 km. H and ˛ can be set by users. Here they are defaulted as
H D 506.7 km and ˛ D 0.9782 which are consistent with the values used by the
CODE group. An ionospheric spherical harmonic function is applied in the M_DCB
software. The VTEC, E (ˇ, s ) can be expressed as follows (Schaer 1999 ):

n max

X X

n

P nm .sin ˇ/.a nm cos ms C b nm sin ms/

E .ˇ; s/ D (4.11)

n D 0 m D 0