## 2 Data Description
### Two-Step Waveform Retracking  
Waveform retracking is an effective tool for improving marine gravity recovery by using waveform-oriented algorithms developed either on fitting functions or empirical statistics. The two-step waveform retracker with a two-step fitting procedure that took into account the correlation between the waveform parameters for calculating two-way arrival time and significant wave height (SWH) was proven to be applicable for most conventional radar altimeters. During the first step, the waveforms were fitted by a three-parameter Brown model (arrival time, rise time and amplitude) with invariable constants describing thermal noise and antenna mis-pointing angles. The rise time parameter was then smoothed along track, before retracking the waveforms a second time using a two-parameter Brown model (arrival time and amplitude) with the rise time being fixed to the smoothed value. Either the former three parameters or the latter two parameters will be solved during the weighted least squaring procedure, while the constants (\(\alpha\) and P0) for describing antenna mis-pointing angles and thermal noise are critical before the model fitting procedure. A previous study of ours indicated that the two-step waveform retracker was also effective for HY-2A Ku-band waveforms and reduced the noise level by a factor of 1.6 [24]. Similar analyses about selecting suitable parameters for the HY-2B, HY-2C and HY-2D two-step waveform retracker are not discussed in this study as they would be repetitive. Instead, we checked whether the parameters needed to be adjusted for the other HY-2 missions. First, \(\alpha\) is the most crucial parameter for fitting the waveform shapes and its optimal value can be iteratively determined by considering the misfit standard deviation values between a normalized and modeled waveform. Based on randomly selected sample passes from the four HY-2 missions (HY-2A C0001P4632, HY-2B C0003P0003, HY-2C C0001P0251, HY-2D C0010P0001), the best-fit \(\alpha\) values were 0.0105, 0.0100, 0.0092 and 0.0100, respectively. According to the similar background noise level and the maximum power level of echoes between HY-2A and the other missions, we inherited the constant P0 value (5500) and a threshold value of 0.015, which provided an initial estimate of unknown arrival time t0 to accelerate the iterative process in model fitting [24]. Certain criteria had to be met to indicate a failed model fitting. A maximum of 10 times was required to suspend the iterative process if these criteria were not met. The editing threshold was established by constructing histograms of amplitude, chi-square misfits and SWH versus standard deviation of the arrival time parameter. For the four HY-2 missions, valid results had model amplitudes between 50,000 and 65,000, while the chi-squared misfit measurement could not exceed 800. Moreover, we removed waveforms having an SWH outside of a range of 0-10 m to exclude observations over extremely unusual sea state conditions. Considering the robustness of the statistical waveform retracking strategy, the estimated results by selected threshold value of 0.015 will also be adopted as a backup once the model fitting procedure failure happens. To evaluate the performance of two-step waveform retracking, we performed a statistical analysis on the retracked data for the four HY-2 missions. The noise was estimated as the standard deviation of the SSH with respect to the mean difference from the EGM2008 \begin{table}
\begin{tabular}{c c c} \hline \hline
**Contrastive Parameters** & **HY-2A** & **HY-2B, HY-2C and HY-2D** \\ \hline Dry troposphere correction & ECMWF & NCEP \\ Wet troposphere correction & ECMWF & NCEP \\ Ionospheric correction & Dual-frequency & GIM \\ Sea state bias & NSOAS empirical solution & NSOAS empirical solution \\ Ocean tide & GOT00.2 & GOT4.10c \\ Solid earth tide & Cartwright and Tayler tables & Cartwright and Tayler tables \\ Pole tide & Wahr [25] & Wahr [25] \\ Inverted barometer correction & NCEP & NCEP \\ \hline \hline \end{tabular}
\end{table}