Ground GNSS Atmospheric Sensing - GNSS Remote Sensing: Theory, Methods and Applications - page 42

Fig. 3.6 Distribution of ZTD
with the altitude (above the
global mean sea level)

2800

GPS observation
Empirical formula fitting

2600

2400

2200

2000

1800

1600

1400

0 1000 2000 3000 4000

Altitude (m)

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 ) :

h
15:5

log 10 P 5- (3.7)

where P is the pressure in Pascals and h is the height in km. Based on the Eq.
( 3.7 ), ZHD can be expressed as 2.28 * 10 (5 h /15.5) . As the ZHD accounts for 90 %
of ZTD, we can further deduce the approximate ZTD at all GPS sites as an empirical
formula:

ZTD D 2:28 10 .5h=15:5/ =0:9 (3.8)

where the units of ZTD and h are in millimeters, respectively. Comparing GPS-
derived ZTD with the empirical formula estimations (Fig. 3.6 ), it has shown a good
consistency.

3.3.2 Multi-Scale ZTD Variations

To fit the time series, a model with a linear trend and a seasonal component for ZTD
has been used. This model is described by the following function (Feng et al. 1978 ):

h c k sin .2 .t t 0 / =p k C ' k / i

X

2

ZTD t D a C bt C C " t (3.9)

kD1