Ground GNSS Atmospheric Sensing - GNSS Remote Sensing: Theory, Methods and Applications - page 39

3.2.2.4 Global Mapping Function

The global mapping function (GMF) is similar to NMF, whose input parameters
are day of year, latitude, longitude and height. The GMF is an empirical mapping
function with input arguments are only the day of year and the site location, which
is consistent with VMF1. Expressions for the coefficients a h and a w were derived
from 3 years of ECMWF data and the coefficients b and c are taken from the VMF1
(Boehm et al. 2006 ).

3.3 ZTD Estimate and Variations

3.3.1 ZTD Estimates from IGS Observations

The quantity observed by the GPS receiver is the interferometric phase measurement
of the distance from the GPS satellites to the receiver. The processing software must
resolve or model the orbital parameters of the satellites, solve for the transmitter and
receiver positions, account for ionospheric delays, solve for phase cycle ambiguities
and the clock drifts in addition to solving for the tropospheric delay parameters of
interest. This requires the same type of GPS data processing software as that which
is used for high precision geodetic measurements. We use the GAMIT software
(King and Bock 1999 ), which solves for the ZTD and other parameters using a
constrained batch least squares inversion procedure. In addition, this study uses
the newly IGS recommended strategies to calculate ZTD time series with temporal
resolution of 2 h from 1994 to 2006.
The GAMIT software parameterizes ZTD as a stochastic variation from the
Saastamoinen model (Saastamoinen 1972 ), with piecewise linear interpolation
in between solution epochs. GAMIT is very flexible in that it allows apriori
constraints of varying degrees of uncertainty. The variation from the hydrostatic
delay is constrained to be a Gauss-Markov process with a specified power density of

2cm/ p ho u r , referred to below as the “zenith tropospheric parameter constraint”.
We designed a 12-h sliding window strategy in order to process the shortest data
segment possible without degrading the accuracy of ZTD estimates. The Gauss-
Markov process provides an implicit constraint on the ZTD estimate at a given
epoch from observations at proceeding and following epochs, which means that
the accuracy is expected to be lower at the beginning and end of each window.
We therefore extract ZTD estimates from the middle 4 h of the window and then
move the window forward by 4 h. Finally, the ZTD time series from 1994 to 2006
are obtained at globally distributed 150 IGS sites with temporal resolution of 2 h
(Fig. 3.2 ). Figure 3.3 shows the uncertainties for the ZTD solutions at 150 sites as a
histogram. It can see that the mean uncertainty of ZTD is about 3 mm.
The mean ZTD values at all GPS sites are shown in Fig. 3.4 as a color map.
It has noted that lower ZTD values are found at the areas of Tibet (Asia), Andes