GNSS Atmospheric and Ionospheric Sounding – Methods and Results - Global Navigation Satellite Systems: Signal,Theory and Applications - page 362

cycle ambiguities and the clock drifts in addition to solving for the tropospheric delay
parameters of interest. 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 recommended strategies (Byun et al. 2005) to calculate
ZTD time series with temporal resolution of 2 hours 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 a priori 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 2 cm / hour , referred to below as the “zenith tropospheric parameter
constraint”. We designed a 12-hour sliding window strategy in order to process the shortest
data segment possible without degrading the accuracy of ZTD estimates. The ZTD estimates
are extracted from the middle 4 hours of the window and then move the window forward
by 4 hours. Finally, the ZTD time series from 1994 to 2006 are obtained at globally
distributed 150 IGS sites with temporal resolution of 2 hours. For example, Figure 2 shows
the times series of zenith total delay (ZTD) (upper) at TOW2 station, Australia.

2.3 Global mean zenith tropospheric delay

The ZTD consists of the hydrostatic delay (ZHD) and wet delay (ZWD). The ZHD can be
well calculated from surface meteorological data, ranging 1.5-2.6 meters, which accounts for
90% of ZTD. It derives from the relationship with hydrostatic equilibrium approximation for
the atmosphere. Under hydrostatic equilibrium, the change in pressure with height is
related to total density at the height h above the mean sea level by

dp = − ρ ()() hghdh (3)

where ρ () and g(h) h are the density and gravity at the height h. It can be further deduced as

ZHD=kp0 (4)

where k is constant (2.28 mm/hPa) and p 0 is the pressure at height h 0 (Davis et al. 1985). It
shows that the ZHD is proportional to the atmospheric pressure at the site. The ZWD is
highly variable due possibly to varying climate, relating to the temperature and water
vapour. The mean ZTD values at all GPS sites are shown in Figure 3 as a color map. It has
noted that lower ZTD values are found at the areas of Tibet (Asia), Andes Mountain (South
America), Northeast Pacific and higher latitudes (Antarctica and Arctic), and the higher
ZTD values are concentrated at the areas of middle-low latitudes. In addition, the ZTD
values decrease with increasing altitude, which is due to the atmospheric pressure
variations with the height increase. Atmospheric pressure is the pressure above any area in
the Earth's atmosphere caused by the weight of air. Air masses are affected by the general
atmospheric pressure within the mass, creating areas of high pressure (anti-cyclones) and
low pressure (depressions). Low pressure areas have less atmospheric mass above their
locations, whereas high pressure areas have more atmospheric mass above their locations.
As elevation increases, there are exponentially, fewer and fewer air molecules. Therefore,
atmospheric pressure decreases with increasing altitude at a decreasing rate. The following
relationship is a first-order approximation to the height (http://www.chemistrydaily.com/
chemistry/Atmospheric_pressure):