## 2 Methodology for C/V of Radar Altimeters
### Satellite Estimate of the Water Height  
Altimetry for estimating the water-level variations over lakes and rivers now has a long history, since the launch of T/P in 1992, and is widely documented [6; 7; 24; 25]. Here, we briefly recall the key equation and the constitutive parameters. The lake water height above the ellipsoid (H) is given by Equation (1):  
\[\mathrm{H}=\mathrm{Alt}-\mathrm{R}-\mathrm{DTC}-\mathrm{WTC}-\mathrm{IC}- \mathrm{ET}-\mathrm{PT}-\mathrm{LT}-\mathrm{SSB}-\mathrm{IB} \tag{1}\]  
Alt (Altitude of the satellite) is given by the GDRs downloaded, in our study, from the CTOH (Centre de Topographie des Oceans et de l'Hydrosphere). The products used for both Sentinel-3A and Jason-3 were the ones generated by the ground segment of each mission. We used the GDR-D version for Jason-3 and the ESA Land_IPF_06.07_V1.5 version for Sentinel-3A. For the range R, we have used the 20 Hz LRM (Low Resolution Mode) with Jason-3, and SAR (Synthetic Aperture Radar) with Sentinel-3A. The DTC is directly proportional to the atmospheric pressure [26] and it is given by the GDRs. At the altitude of Lake Issykkul, DTC was about \(-1.9\) m, with a variation of few centimeters, depending on atmospheric conditions. In previous studies [9; 10; 11] we have shown that for C/V purpose, over Lake Issykkul, it is recommended to use in situ data for the calculation of DTC. Since the distribution of atmospheric pressure over the lake Issykkul was very homogeneous, we simply used the atmospheric pressure, at the Cholpon Ata station (Figure 2). For the WTC (Wet Tropospheric Correction), it has been often pointed out that the correction using radiometer is highly erroneous over continental water or coastal regions, due to land contamination, up to a distance of 20 to 30 km from the coastline ([9; 10; 11; 16; 27]). Therefore, apart from the very large lakes, the WTC used in continental water comes directly from a model based on climate gridded data sets--multi-layer water vapor and temperature fields [26]. It has been estimated that the models used for WTC, in the GDRs of past missions, generated an StD of several centimeters, on the water-level estimation [9; 10; 11; 27]. However, recent models, based on the ECMWF reanalysis, have significantly reduced the errors in the determination of WTC [27; 28], by up to 1 cm. WTC varies spatially and temporally and can reach several decimeters. WTC cannot be estimated with ground measurements only, as soundings are required. For C/V application where we expected to reduce, as much as possible, the sources of uncertainties in the calculation of the altimeter's absolute biases, we estimated an alternate WTC correction (hereafter WTC in-situ), by the Total Path Delay, using the GINS processing and the GPS data from a permanent receiver installed in 2012, in Kara Oi (Figure 2). WTC was simply given by the difference between the TPD and the DTC, derived from the in-situ met stations. For IC, bi-frequency and model are provided. The presence of charged particles in the high atmosphere, also named ionosphere, causes refraction of the radio signal emitted by the altimeter that must be taken into account. It is proportional to the Total Electronic Content (TEC), in this layer of the atmosphere and inversely proportional to the square of the frequency. With Jason-3 and Sentinel-3A, it could, therefore, be calculated from the Ku and C bands, using a combination of ranges in both bands, allowing the elimination of the TEC in the expression of the correction. For altimeters in the Ku band, the IC (Ionospheric Correction) ranged from a few millimeters to a few centimeters. However, it has been shown that over lakes, this correction could be erroneous, due to land contamination once the measurement was done close to the shoreline [29]. Therefore, it could be preferable to use the IC derived from the Global Ionospheric Maps (GIM), inferred from the GNSS worldwide network [30]. In [PERSON] et al. [9], we examined the StD of difference between the bi-frequential IC and the GIM model over Lake Issykkul.