ANALYSIS OF WAVEFORM RETRACKING METHODS IN ANTARCTIC ICE SHEET BASED ON CRYOSAT-2 DATA

Satellite altimetry plays an important role in many geoscientific and environmental studies of Antarctic ice sheet. The ranging accuracy is degenerated near coasts or over nonocean surfaces, due to waveform contamination. A postprocess technique, known as waveform retracking, can be used to retrack the corrupt waveform and in turn improve the ranging accuracy. In 2010, the CryoSat-2 satellite was launched with the Synthetic aperture Interferometric Radar ALtimeter (SIRAL) onboard. Satellite altimetry waveform retracking methods are discussed in the paper. Six retracking methods including the OCOG method, the threshold method with 10%, 25% and 50% threshold level, the linear and exponential 5-β parametric methods are used to retrack CryoSat-2 waveform over the transect from Zhongshan Station to Dome A. The results show that the threshold retracker performs best with the consideration of waveform retracking success rate and RMS of retracking distance corrections. The linear 5-β parametric retracker gives best waveform retracking precision, but cannot make full use of the waveform data.


INTRODUCTION
Satellite altimetry is used to detect the earth and its variation precisely and periodically on a large scale.The satellite altimetry data are widely used to study the earth gravity field model, mean sea level, oceanic tidal model and seabed topography.In Polar Regions, satellite altimetry has proven to be a valuable tool for many geoscientific and environmental studies.It can, for example, be used for ice sheet mapping and mass balance study (Bamber et al. 2009, Zhang et al. 2015, Li et al. 2016).It is also used to detect sea ice changes in polar areas (Yuan et al. 2016).
However, the echo waveforms of altimetry impulse are often contaminated by the coastal terrain, islands, oceanic tide, geophysical conditions and hardware delay over nonocean areas.This kind of waveform is so irregular that the distance between the altimetry satellite and its nadir point cannot be precisely estimated from the waveforms.In order to calculate precise distances, the middle point of waveform leading edge should be repositioned, then the distance correction should be reestimated by comparing the retracked middle point of leading edge and the pregiven gate, which is called the waveform retracking technique of radar satellite altimetry.and 50% threshold level respectively, the linear and exponential 5-β parametric method to the CryoSat-2 return waveforms over the transect from Zhongshan Station to Dome A.

WAVEFORM RETRACKING TECHNIQUE
Methods of waveform retracking can be classified into two categories: one is based on functional fit and the other based on statistics.

OCOG algorithm
In 1986, between the threshold level and the leading edge.The threshold method is a statistical method and not of physical characteristics.The method can give more precise retracking gate than OCOG.The corresponding equations are as follows: where () yi is the power of i th gate; N y is the average power of former 5 gates; L T is the threshold level; A is the amplitude; k is the k th gate whose power is more than L T ; ret n is the middle point of leading edge.

β parametric fitting algorithm
The β parametric fitting algorithm was firstly put forward by Martin et al. in 1983  The 5-β parametric method is mainly used to process the complex waveform returned from the single reflecting surface, shown in Figure 2. If the waveform is present like a spike, the 5-β parametric algorithm may be non-convergent in the iterative procedure and cannot give the right results.The linear 5-β parametric equation is: Where () yt is the sampling power at time t; 1  is the thermal noise of returned waveform; 2  is the returned impulse power for leading edge; 3  is the middle point of leading edge which is the half power from the received power to the maximum power and used to calculate the difference to the pregiven gate and get the retracking distance correction; 4  is the risetime parameter; 5  is the slope of ramping edge; () Pz is the error function; () Qt is a linear function to fit the gradual attenuation echo wave in the ramping edge.
The exponential 5-β parametric equation is: The 5 parameters

Retracking distance correction
After retracking waveforms, the middle point of leading edge can be determined.According to the pregiven gate and the light velocity, the retracking distance correction where k t is the time interval for one gate; c is the light velocity, c=299792458 m/s; ret n is the middle point of leading edge; and tr n is the pregiven gate.

DATA AND METHOD
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLII-2/W7, 2017 ISPRS Geospatial Week 2017, 18-22 September 2017, Wuhan, China

CryoSat-2 data and study areas
The
from the National Aeronautics and Space Administration, USA (NASA).The method uses a relevant parametric function to fit the altimetry waveform based on the Brown mean impulse echo model.Β parameters can be estimated by the iterative calculation based on good initial values with the least squares adjustment or the maximum likelihood estimator.

iFigure 2 .
Figure 2. Schematic diagram of 5-β parameter method CryoSat-2 satellite was launched on April 8, 2010, carrying a new developed altimeter operating in Ku-band.The SIRAL instrument samples the surface every 300 m along track using three different measurement modes, LRM, SAR and SARIn.The low resolution mode (LRM) is used over oceans and the flat interior of the ice sheets.LRM is similar to the operation of conventional pulsewidth-limited altimeters.In the synthetic aperture (SAR) and synthetic aperture interferometric (SARIn) modes, SIRAL samples the surface with a higher pulse repletion frequency (18 181 Hz) than in LRM (1970 Hz).SARIn measures the steep areas at the margins of the ice sheet and ice caps, whereas the SAR mode is used over sea ice to reveal ice free-board by distinguishing leads and ice flows.In this study, we use the CryoSat-2 L1B product provided by ESA, which contains the precise orbit of the satellite, the back-scattered radar waveforms, the tracker range and the coherence and phase difference for SARIn mode.The product also contains additional information, such as geophysical and tidal corrections and quality flags.

Figure 3
Figure 3 shows the study areas with CryoSat-2 ground tracks over the transect from Zhongshan Station to Dome 3% and 22.1% with the two 5-β parametric fitting methods.The success rates for the other retracking methods are all 100%.The RMSs from the two 5-β parametric methods are low, which indicates that the two methods can give good retracking results.The RMS for threshold method is the minimum when the threshold is 50%.Figure 4 is the histograms of retracking results for LRM waveforms, the gray line indicates the onboard tracking point.The retracking results from the two 5-β parametric methods and the threshold method with 50% threshold level are close to normal distribution.

Figure 4 .
Figure 4. Histograms of retracking results for LRM waveforms, the gray line indicates the pregiven gate.

Figure 5 .
Figure 5. Histograms of retracking results for SARIn waveforms, the gray line indicates the pregiven gate.
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLII-2/W7, 2017 ISPRS Geospatial Week 2017, 18-22 September 2017, Wuhan, China evaluate waveform retracking methods in Antarctic by retracking the CryoSat-2 waveforms.We applied six retracking algorithms including the Off Center of Gravity (OCOG), the threshold retracking method with 10%, 25% The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLII-2/W7, 2017 ISPRS Geospatial Week 2017, 18-22 September 2017, Wuhan, China be determined based on the amplitude and the maximum waveform power calculated with OCOG.The retracked point can be obtained to linearly interpolate the neighboring samples close to the intersecting threshold

Table 1 .
Statistics of waveform retracking results