## 2 Methodology for C/V of Radar Altimeters
### Satellite Estimate of the Water Height
It ranged between 4 mm (Jason-2) to 1.1 cm (Jason-1). We obtained similar values with Jason-3 and Sentinel-3A--the RMS (Root Mean Square) of differences from the model or from the combination of the two instrumental frequencies was around 5 mm, once we were 10 km away from the coast. Therefore, we decided to use only the GIM model, in the calculation of the altimeter bias. The GIM model, according to the [PERSON] and [PERSON] [29] assessment, has improved performances by 1.5 cm of \(\sigma\), as compared to the bi-frequential IC (comparison done with in situ levels, from January 2008 to December 2009, over the Lake Ontario). For very big lakes, however, the use of a smoothed bi-frequency IC can provide slightly better performances than the GIM model [26], but in general, over lakes, the model is preferred due to land contamination. The Earth tide (ET) and Pole tide (PT) are provided by the GDRs. The ET was estimated from the model developed by [PERSON] and [PERSON] [31]. Lake Tide can reach centimetric level over the great lakes of North America [29] but does not exceed a magnitude of 2-3 mm, over Lake Issykkul [10]. The SSB and the IB (Inverse Barometer) corrections applied over oceans are usually not used over lakes. Both effects have very little impact on the lake surface and are, therefore, generally simply ignored when satellite altimetry is used over lakes, except for studies over very big lakes (see [PERSON] et al. [9] for more information). For this study, we selected the measurements collected when the lake was in calm weather conditions. This selection eliminated measurements potentially affected by an unknown SSB effect. Over continental waters, the radar echoes assembled into so-called waveforms in the LRM mode but did not conform to the [PERSON] model, for which the on-board tracking algorithm was adapted. Hence, alternate algorithms that are run during post-processing, and thus, are named retracking algorithms, were used. Among them, for lakes, the _Ice-1_ algorithm, based on a OCOG scheme was renowned to outperform the others [8]. In this study, we used the ranges derived from the _Ocean (SAMOSA)_ and the _Ice-1 (OCOG)_ retracking algorithms. Detailed information on the mathematics of each algorithm can be found in the handbook [32; 33]. For the Ocean retracker, it is supposed that the reflecting surface is isotropic. Over continental water the echo can, however, be extremely variable. It depends on the complexity of the topography and the backscatter characteristics of the surrounding terrain for small water bodies. Therefore, the analytical expression given in the _Ocean_ retracker is not valid, anymore, or present potential high source of errors, for the range estimation. For a large lake, _Ocean_ retracker is valid only when far from the shoreline. _Ice-1_ retracker determines the shape of the waveform in terms of its amplitude, width, and center of gravity, allowing calculating the leading-edge position (LEP) of the waveform, which is directly linked to the range. The _Ice-1_ has proven to be robust for non-Brownian waveforms, such as those generally registered over lakes and rivers. It is, therefore, often used in the application of satellite altimetry for hydrology studies. _Ocean_ is the algorithm dedicated to oceanography and it is the focus of many ongoing C/V studies in coastal and open-sea conditions. Thus, it will allow for comparing our results for the altimetry biases calculation over Lake Issykkul, with the ones published for ocean sites.