The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part B7. Beijing 2008 
89 
As shown in Figure 1, to reduce water vapour effects on the 
interferograms, ZPDDM are inserted into the interferometric 
processing sequence after removal of topographic signals by 
use of a precise DEM such as that produced by the Space 
Shuttle Radar Topography Mission (SRTM) (Farr et al., 2007); 
The procedure used for InSAR water vapour correction has 
been successfully incorporated into the JPL/Caltech ROI PAC 
software by introducing two processing parameters: 
ACMMODEL and ACMISZPDDM. ACMMODEL can be 
set to NULL if no correction is applied; otherwise, the value 
ACM IS ZPDDM is used to distinguish the type of difference 
map(s) (currently, 0 = Slant Path Delay Difference Map 
(SPDDM), 1 = ZPDDM). 
After water vapour correction, atmospheric effects on the 
corrected interferograms are limited and their residuals can be 
considered as random noise, so that 
50*1 (x,r) = ZPDDM + 5<j)^ ual (x,r) can be cancelled out in 
Equation (1): 
solid triangles represent GPS stations where the agreements of 
InSAR-derived and GPS-derived range changes are within a 
1-sigma range both before and after correction, white squares 
with black borders imply improvement in their agreements after 
correction, and red solid circles indicate deterioration in their 
agreements after correction; (4) The circle and ovals in Figure 
2(b) are believed to represent regions with real deformation 
signals (see text). 
Figures 2(a) and 2(b) show the interferogram spanning the 
summer from 14 May 2005 to 27 August 2005 before and after 
MERIS water vapour correction respectively. This InSAR pair 
has a small baseline of c. 100 m, and the errors in the SRTM 
DEM (c. 7.0 m in North America (Farr et al., 2007)) might lead 
to a phase error of 0.49 rad (i.e. 0.22 cm in the satellite line of 
sight range changes), which can be considered negligible. The 
RMS of the unwrapped phase decreased from 1.95 rad before 
correction to 0.79 rad after applying the MERIS water vapour 
correction, indicating that the unwrapped phase was much 
flatter after correction. 
вф‘2 GO - £<C GO+c; GO+■sc’ GO 
■SCG0=« i *UG0- 2>MW ( 2 ) 
¿C" 1 GO=¿C GO+<SC“ GO 
where S<f>™T{x,r) represents corrected phase values and 
8^ (x,r) residual water vapour effects after correction. 
3.3 To what extent can water vapour effects be reduced 
using MERIS? 
-118*30’ —118"0Q' -117*30' -118*30' -118*00' -117*30' -117*00' 
35*30' 
35*00’ 
34*30' 
34*00' 
33*30' 
33'00’ 
35*30' 
35*00' 
34*30’ 
34*00' 
33*30' 
(mm) 
Figure 2. Interferogram (050514-050827) superimposed on a 
SRTM DEM. (a) Original interferogram; (b) Corrected 
interferogram using MERIS data. Note: (1) Grey within 
interferogram coverage implies areas with low coherence due to 
steep slopes and vegetation; (2) Negative values imply that the 
surface moves towards the satellite; (3) In Figure 2(b), black 
In order to validate the MERIS correction model, independent 
3D GPS-derived displacements provided by the Scripps Orbit 
and Permanent Array Center (SOPAC) (Nikolaidis, 2002) were 
compared with InSAR results in the satellite line of sight (LOS) 
direction, which showed that the RMS difference decreased 
from 9.9 mm before correction to 4.1 mm after the MERIS 
correction. 
It is clear in Figure 2(b) that some real geophysical signals were 
brought out after removing atmospheric water vapour signals: 
(1) The black dashed oval indicates seasonal surface subsidence 
in the Long Beach-Santa Ana basin (Argus et al., 2005; Bawden 
et al., 2001); (2) The white solid oval implies surface 
subsidence in Antelope Valley (Hoffmann and Zebker, 2003); 
(3) The black solid circle represents geophysical signals in San 
Bernardino (Lu and Danskin, 2001). 
This case study has two important implications: (1) Water 
vapour induced range changes in the LOS direction can be 
greater than 4 cm even in a desert region such as Southern 
California, and greater water vapour effects are expected in 
tropic regions; (2) coincident water vapour products are 
invaluable to assess and then reduce water vapour effects on 
InSAR measurements. This successful integration of MERIS 
and ASAR measurements not only contributes directly to the 
ENVISAT mission, but also will benefit space agencies’ plans 
to design and launch InSAR missions, because intensive 
investigation of the major error source of InSAR techniques 
will clearly identify necessary characteristics of future InSAR 
missions which will in turn aid their ability to better achieve 
space agencies’ science goals. 
4. INSAR TIME SERIES WITH WATER VAPOUR 
CORRECTION (INSAR TS + PWV) 
4.1 InSAR time series with water vapour correction 
Let t be a vector of SAR acquisition dates in chronological 
order. For a dataset containing N interferograms constructed 
from S acquisitions on different dates, assuming v kMl is the 
mean velocity between the time-adjacent (e.g. the kth and 
[k + \)th time) acquisition, the corrected phase can be written 
as: