TROPOSPHERE AND IONOSPHERE - GPS Satellite Surveying - page 199

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TABLE 6.2 Coefficients for Niell's Wet Mapping Function

· 10 4 · 10 3 · 10 2 ϕ a b c

15 5.8021897 1.4275268 4.3472961

30 5.6794847 1.5138625 4.6729510

45 5.8118019 1.4572752 4.3908931

60 5.9727542 1.5007428 4.4626982

75 6.1641693 1.7599082 5.4736038

where DOY denotes the day of year and DOY 0 is 28 or 211 for stations in the Southern
or Northern Hemisphere, respectively. When computing the wet mapping function,
the height-dependent second term in (6.22) is dropped and the coefficients of Table
6.2 apply.
The Niell function enjoys such popularity because it is accurate, is independent
of surface meteorology, and requires only site location and time of year as input.
The Niell model assumes azimuthal symmetry. However, efforts have been reported
in Niell (2000) and Rocken et al. (2001) to improve the mapping function for low
elevation angles by incorporating temperature, pressure, and humidity profiles for a
specific location and time period.

[19

Lin
—
1 ——
No
*PgE

6.2.3 Horizontal Gradient Model

[19

As has been mentioned, the variability of the water vapor is of much concern in
ac curate GPS applications. The water vapor exists mostly in the lower 5 km of
th e troposphere. Its distribution may show an azimuthal dependency primarily due
to terrain and wind effects. One could attempt to model the lateral water vapor
re fractivity by the gradient method.
Assume that a point is parameterized in the local geodetic coordinate system
sp ecified by the northing, easting, and up coordinates, w [ neu ] T . See Section

2. 3.5 for the exact definition of this coordinate system. The refractive index at height
u above the station can be expanded as

=

∂N wv
∂n

∂N wv
∂e

∂N wv
∂u

N wv ( w ) = N wv (w = 0 ) + n + e + u (6.24)

Next we solve (2.91) for the distance s and substitute it in (2.89) and (2.90) and then
substitute the resulting expressions for northing n and easting e into (6.24), giving

u ∂N wv
∂n

(6.25)

∂N wv
∂u

1
tan

u ∂N wv
∂e

N wv ( w ) = N wv, 0 (w = 0 ) + u + cos α + sin α

β

The zenith delay is obtained by integrating along the vertical from the station to the
end of the effective troposphere,