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mapping function is smaller than the wet mapping function. Exceptions are mapping
functions for observations at very low elevation angles where the geometric bending
effect, which is attributed to the hydrostatic mapping function, is increasing consider-
ably. Thus, the mapping functions are a measure for the thickness of the atmosphere
compared to the Earth radius (Niell et al. 2001 ). If the thickness of the atmosphere
gets smaller, it appears to be flatter, and the mapping function approaches 1
/
sin
(
e
)
.
Assuming a flat and evenly stratified atmosphere the mapping function is 1
.
For higher elevation angles (>20 elevation) these mapping functions are sufficiently
accurate. Marini ( 1972 ) showed that the dependence on the elevation angle of the
mapping functions for any horizontally stratified atmosphere can be described with
continued fractions, when a , b , c , etc. are constants (Eq. 120 ). For verification Marini
( 1972 ) used standard atmosphere data but no real weather data.
/
sin
(
e
)
1
mf
(
e
) =
.
(120)
a
sin
(
e
) +
b
sin
(
e
) +
c
sin
(
e
) +
sin
(
e
) + ...
This concept was first used in a model for the refraction of the hydrostatic atmosphere
(Marini and Murray 1973 ) which has since then been applied in the analysis of geo-
detic and astrometric VLBI observations for a long time. The zenith delay corre-
sponds to that by Saastamoinen ( 1972b ), and the mapping functions are represented
by a continued fraction form with two coefficients a and b . The first mapping func-
tions for space geodetic applications with different coefficients for the hydrostatic
and wet parts were published by Chao ( 1974 ) who replaced the second sin
(
e
)
by
tan
to get unity in zenith direction.
Davis et al. ( 1985 ) developed the mapping function CfA2.2 for the hydrosta-
tic delays down to 5 elevation; it is based on the approach by Chao ( 1974 )but
extended by an additional constant c . Based on ray-tracing through various standard
atmospheres with elevation angles between 5 and 90 , the coefficients a , b , and c
were determined as functions of pressure, water vapor pressure, and temperature
at the Earth surface, and from vertical temperature gradients and the height of the
troposphere. Herring ( 1992 ) developed coefficients for the mapping function MTT
(MIT Temperature) as functions of latitude, height, and the temperature at the site.
Unlike Davis et al. ( 1985 ) he did not use standard atmospheres but radiosonde data.
The MTTmapping functions are based on a slightly changed continued fraction form
which is widely accepted nowadays
(
e
)
a
1
+
b
1
+
1
+
c
mf
(
e
) =
.
(121)
a
sin
(
e
) +
b
sin
(
e
) +
sin
(
e
) +
c
 
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