Ground GNSS Atmospheric Sensing - GNSS Remote Sensing: Theory, Methods and Applications - page 38

3.2.2.1 Herring Mapping Function

Marini ( 1972 ) developed the mapping function with a continued fraction and
Herring ( 1992 ) specified the Marini's function with three coefficients ( a , b , and
c ) depending on the latitude and height as well as surface temperature. This is the
first empirical mapping function related to the elevation angle. The wet component
and dry component of this mapping function can be expressed as,

a i

1 C

b i

1 C

1 C c i

m i .E/ D (3.5)

a i
sin EC

sin E C

b i
sin E

C c i

where subscript i stands for the dry and wet components of the mapping function and
the parameters a , b , and c are coefficients for the hydrostatic and wet components
of the atmosphere.

3.2.2.2 Niell Mapping Function

Niell ( 1996 ) developed the mapping function following the Herring's function with
the continued fraction (Eq. 3.5 ), i.e., Niell Mapping Function (NMF). The NMF is
an empirical function that was based on 1 year of radiosonde observations mostly
from the Northern Hemisphere. The coefficients of the dry component depend on
the day of the year, the latitude and height above sea level of the observing site, and
the coefficients of the wet component only depend on the latitude of the site (Niell
1996 ). The dry coefficients are defined as:
p d .'; t/ D p a v g .'/ p amp .'/ cos 2 t T 0
365:25

;

.p D a; b; c/ (3.6)

where p denotes the calculated coefficients of a, b, and c, ' is the latitude of the site,
t is the observing time in day-of-year (DOY), and T 0 is the adopted phase, p avg and
p amp are the mean value and the amplitude, respectively.

3.2.2.3 Vienna Mapping Functions 1 (VMF1)

The coefficients a h and a w were determined from a rigorous raytracing through
global grids of monthly mean profiles for pressure, temperature, and humidity from
the ECMWF (European Centre for Medium-Range Weather Forecasts) 40 years
reanalysis data (ERA40). The coefficients b h and c h were derived from 1 year of
ECMWF data in a least squares fit. Whereas b h is constant, c h depends on the
day of year and the latitude. Since the coefficient a w is sufficient to model the
dependence of the wet mapping function on latitude, b w and c w were taken from
the Niell mapping function (Niell 1996 )at45 ı latitude (Boehm and Schuh 2004 ).