## 3 Calibration Methodologies & Dataset Used
### Transponder Calibration
This step includes the calibration of the Sentinel-3A Level-0 engineering SAR data products using its internal calibration files (e.g., CAL1 for the time delay in the range instrument correction, CAL2 to compensate distortions in the system transfer function on signal returns, etc.). 3. _Waveform retracking_. Used for determining the measured altimeter range. Slant ranges between the satellite and the transponder are computed by waveform retracking of the range compressed SAR data. An example of such a waveform is presented in Figure 8.  
The measured altimeter range is given as the difference between the gate number (bin number) of the peak (maximum) of each pulse and the reference gate number set on the altimeter, multiplied by the actual \"bin resolution\" (in theory about 3.125 ns for the Ku-band pulse duration). For example, for Sentinel-3 the tracking point is gate 44, i.e., bin index is 43 for Ku-band, or gate 46, i.e., bin index 45 for C-band, as measuring starts from bin index zero (index = 0). Nonetheless, the effective range resolution with which the actual range is to be determined by the altimeter is driven by the width of the point target response recorded with 3 dB, and included in its \"Autocal\" mode [23]. The measured altimeter distance \(R_{k}\) between the satellite and the transponder, is given by:  
\[R_{k}=R_{trc}+(B_{max}-B_{0})\times\frac{c\tau_{p}}{2}\]  
where \(R_{trc}\) is the altimeter distance from the satellite to the Earth's surface corrected for instrumental delays, such as Ultra Stable Oscillator frequency drift, internal path correction or Doppler correction (Called \"tracker range\"), \(B_{max}\) is the bin number of the maximum signal return by the transponder, \(B_{0}\) is the reference bin number, c is the speed of light, and \(\tau_{p}\) is the  
Figure 7: Flowchart of the transponder calibration developed for range and datation bias estimation of Sentinel-3A. pulse duration in seconds. The altimeter range bias is computed as measured minus theoretical altimeter range after corrections are applied. 4. _Corrections on the observed range._ The altimeter range \(R_{m}\), as reckoned in the previous step, is corrected for the following quantities: (a) troposphere and ionosphere delays caused by the atmosphere onto the altimeter's signal; (b) difference between the satellite's center of gravity and the altimeter's effective center of measurement; (c) drift of the Ultra Stable Oscillator in the altimeter; (d) internal delays of the associated instruments as the echo travels back and forth; (e) geophysical corrections (i.e., solid earth tides, etc.) at the transponder location; (f) Doppler correction from both altitude rate and velocity of the satellite. 5. _Theoretical Range Estimation._ The absolute Cartesian coordinates of the satellite \((x_{k},\ y_{k},\ z_{k})\) as well as of the transponder \((X_{0},\ Y_{0},\ Z_{0})\) are, respectively, given by the satellite's navigation files and by local geodetic surveys on the ground. Care should be taken to ensure that all coordinates refer to the same geodetic reference frame of coordinates and time. The theoretical range \(\rho_{k}\) is then calculated by the Euclidian distance between the satellite and the transponder: \[\rho_{k}=\sqrt{\left(x_{k}-X_{0}\right)^{2}+\left(y_{k}-Y_{0}\right)^{2}+\left( z_{k}-Z_{0}\right)^{2}}\]
6. _Range Bias Determination._ Given the measured \(R_{k}\) and the theoretical range \(\rho_{k}\) between the Sentinel-3A SRAL and the ground transponder, the range bias is estimated as \"\(Bias=Mean_{\{k\}}[R_{k}-\rho_{k}],\ k=1,\ 2,\ \cdots,N\)\", after corrections for time-tagging offsets (dotation) and Doppler-altitude slope are applied [20; 21; 23]. All in all, the Sentinel-3A level 0 products have been used as input in the custom-made software to derive the SRAL altimeter's absolute range bias. Overflights for Transponder Calibrations  
The ascending Pass No.14 of Sentinel-3A flies over the CDN1 transponder Cal/Val site at 20:00:12 UTC.