Geophysical Research Letters
Supporting Information for
Coastal sea level from inland CryoSat-2 Interferometric SAR altimetry
Adili Abulaitijiang, Ole Baltazar Andersen and Lars Stenseng
DTU Space, Technical University of Denmark, Lyngby, Copenhagen, Denmark
Contents of this file
Text S1 to S4
Figure S1 to S3
Introduction
The document provides the supplementary information for processing L1b SARIn
altimetry products(Text S1), simplified projection and transformation of off-nadir distance
to latitude and longitude correction components(Text S2), a short description of
remaining (unprocessed) land acquisitions present in Figure 4a and also Figure 5(Text
S3) and the potential roll bias remaining in the Level-1b data which we used for our
computations(Text S4).
Figure S1 shows the projection geometry which sets up the equations in Text S2; Figure
S2 is an additional figure to support the statements in Text S3, which shows the along
track backscatter and the window delay parameter; Figure S3 shows the (a) spatial and
(b) temporal distribution of Envisat and CryoSat-2 data. The CryoSat-2 data is along track
averaged to produce 1Hz estimations and a retracker offset of 2.2m is removed.
Text S1. Concerning off-nadir range correction and Equations in Section 2
The detailed technical descriptions and derivations off-nadir range correction as part of
SARIn data processing can be found in the recent paper by Armitage and
Davidson[2014](citation can be found in submitted manuscript). In the submitted
manuscript, we briefly outlined the finalized expressions (Eq.1 and Eq.2) for the flat
surface geometry shown in Figure 1b.
Text S2. Geometric projection of off-nadir distance
Based on the across track off-nadir distance, we can determine the location of the
scattering target with the nadir latitude and longitude (Bnadir , Lnadir ) information provided
in L1b data. This requires a transformation from distance measurement (unit:m) to
latitude and longitude correction terms δlat and δlon (unit: degree) on the sphere.
As shown in Figure S1, the nominal orbit inclination angle i = 92°,
δlat = η ∙ (d ∙ sin(i − 90°))/R earth
δlon = η ∙ (d ∙ cos(i − 90°))/r
where η is the geometric factor to correct for the earth curvature(same as Eq.1), d is
the off nadir distance, R earth is the mean radius of the earth, r is the radius of parallel
corresponding to satellite nadir latitude Bnadir and given by
r = R earth ∙ cos(Bnadir )
The final latitude and longitude for the scatterer is given by
B = Bnadir + δlat
L = Lnadir + δlon
One should be careful with units in the derivations. The orbit inclination is 92° on the
equator. But the off-nadir distance is always in the across track direction, so the small
projection angle (i − 90°), should be derived from the satellite heading at the local
satellite nadir.
Text S3. Remaining inland acquisitions in Figure 4a
However, in Figure 4a and Figure 5, there are still some inland acquisitions we cannot
handle. These are the points around latitude 73.55. When the satellite moves further
away from the coast, tracking window will continuously adjust the window-delay to locate
the peaky signal in the waveform. However, when the distance is large enough, the
tracking system will lose the bright "peaky" signal from the fjords and significantly adjust
window-delay to locate a seemingly peaky segment in the returned echoes. Such
variation in the along track window-delay is presented here (Figure S2(b)). Waveforms
and corresponding phase measurements in this segment are noisy and backscatter
parameters are close to zero (Figure S2(a)). Therefore, we do not trust in these inland
points and only focus on observations achieved before and after the window-delay jump.
Text S4. Remaining roll bias in the data
The known biases in Level-1b products are reported by ESA and can be obtained from
the link : https://wiki.services.eoportal.org/tiki-download_wiki_attachment.php?attId=2699.
1
As stated in the document, in Baseline B, the L1b products are already corrected for the
known roll bias of 0.1055°. In our processing, the off-nadir range corrections are
computed with an additional (residual) bias of 0.0126°(personal communication with
Marco Fornari), which is only a small fraction of the reported biases given in the ESA
report. The remaining roll bias did affect the off-nadir range correction with large phase
angles (relates to large across track distance) and could be an error source of large sea
level anomalies resulting from off-nadir ranging. Therefore, further investigation should
be carried out in the future.
Earth Rotation Axis
Flight
direction
lon
lat
Scatterser
d
r
Satellite
Nadir
Orbit Inclination(92o)
Equator
Rearth
Figure S1. Geometric projection and transformation of off-nadir distance to latitude and
longitude correction component
2
Backscatter[dB]
40
(a)
30
20
10
0
-3
4.913
x 10
win_delay [s]
(b)
4.912
4.911
4.91
4.909
73.35
73.45
73.55
73.65
73.75
Latitude
Figure S2. (a) backscatter coefficient (or received peak power[in Watts] of each
waveform) and (b) window delay of the exemplified track in Figure 2.
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Figure S3. (a)Distribution of 1Hz sea level anomalies for CryoSat-2 (filled circles) and
Envisat (filled square boxes) in the K. F. Joseph fjord and Moskusokse fjord.(b)Time
series of the 1Hz sea level anomaly estimations from 2002 to 2014. Red for Envisat and
blue for CryoSat-2. A retracker offset of 2.2m is removed for CryoSat-2. Unit:m
4