Bernese GPS Software Version 5.0 - Bernese GNSS Software

11. Troposphere Modeling and Estimation
where
∆̺i k is the tropospheric path delay between station k and satellite i,
t is the observation time,
zi k , Aik are the zenith and azimuth of satellite i as observed from station k,
) is the slant delay according to an a priori model,
∆̺apr,k(zi k
∆h̺k(t), f(zi k ) is a (time-dependent) zenith path delay parameter and its mapping function,
and
∆n̺k(t), ∆e̺k(t) are the (time-dependent) horizontal north and east troposphere gradient
parameters.
The a priori zenith delay ∆̺apr may also be time dependent (for fixed z) if, e.g., measured
meteorological values are used for its computation. As mentioned above, the troposphere
path delay and the mapping function may depend on the site location and the day of the
year.
Note that the tropospheric delay from the a priori model may be computed while site-specific
ZPD and gradient parameters must be estimated during the processing. The following sections
provide more details on all three parts from Eqn. (11.14), the related programs, and
relevant options.
11.4.1 The A Priori Model
The Bernese GPS Software offers several a priori models and corresponding mapping functions
to take into account the tropospheric refraction. In Version 5.0 the following models
are available:
• the Saastamoinen model [Saastamoinen, 1973] as shown in Eqn. (11.11),
• the (dry and wet) Niell model [Niell, 1996], i.e., the Saastamoinen zenith path delay
together with the Niell mapping functions (recommended for GNSS data analysis with
low elevation cutoff angle),
• the modified Hopfield model [Goad and Goodman, 1974],
• the model based on formulae by Essen and Froome [Rothacher et al., 1986], and
• the Marini-Murray model [Marini and Murray, 1973] (which should only be used for
SLR-data processing).
The Niell model is implemented as a product of the Saastamoinen zenith delay and the
Niell mapping function. For some a priori models there is also the possibility to use only
the dry component (Saastamoinen, Hopfield, and Niell). This option is normally used when
estimating site-specific troposphere parameters. In this way the dry component is computed,
the wet component estimated, and for each component the correct mapping function (dry
and wet) may be applied.
A troposphere model in general includes implicitly a mapping function. Approximately the
slant delay may be written as a product of zenith path delay and mapping function:
∆̺ i k (z) ≃ ∆̺apr,k fapr(z i k ). (11.15)
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