## 2 Methodology for C/V of Radar Altimeters
### Instrumental Design of the Field Campaigns  
The instrumental design of the field campaigns was aimed at computing the height of the water surface, independent of that provided by the altimetry. It was based on a kinematic GPS survey of the lake height, along the different satellites tracks. A boat (28 m long, hence very stable) carried a GPS receiver at the bow, coupled with a microwave radar (named RLS in the following), and continuously measured the height of the GPS antenna, above the lake surface (Figure 3). The boat cruised along the altimeter tracks (Sentinel-3A and Jason-3 in the present study), when the satellite passed over the lake. The GNSS-based navigation system of the boat insured that we followed the theoretical track of the satellites, with a decameter precision. The RLS and the GPS systems were synchronized and they both provided their measurements every 30 s. Practically speaking, the 30 s measurements were obtained by averaging individual measurements at a much higher frequency (one measurement, every 0.5 s for the RLS and the GPS). This also allowed averaging the potential attitude pitch and the roll of the boat. However, due to the very calm weather conditions during all three of our campaigns, the noise in these measurements that could be provoked by wind and waves on the lake, was insignificant. We also installed a permanent GNSS station in the vicinity of the lake which enabled complementary estimates of the zenithal tropospheric corrections. Combined with the atmospheric pressure measured by a permanent weather station located on the shoreline of the lake, these allowed for separate determination of the wet and dry tropospheric delays that could be compared to the tropospheric corrections, distributed with the altimetry data, or used as the tropospheric corrections themselves. Figure 2: Last campaign done in July 2017 over Lake Issykkul—in red are the cruise tracks, in white are the Sentinel-3A tracks, and in black (dots) the Jason-3 track, over the lake. Numbers indicate the pass number of Sentinel-3A orbit ground track. The blue dots represent the Jason-3 track over the lake. The color scale represents the altitude of the land around the lake. The brown/black stars represent the weather stations. We identified that the three main sources of uncertainty in the C/V, over Lake Issykkul were coming from:  
* The weather conditions, including wind driven waves and Seiche effects. * The computation of the height of the GPS antenna, embarked on the boat. * The estimate of the distance between this antenna and the water surface during the cruise. The instrumental design is, thus, a source of uncertainty. From the first campaign in 2004 to the last six ones since 2014, we have tested different settings and performed different types of fieldwork and data processing. [PERSON] et al. (2015) showed that Seiche-induced errors could be avoided by cruising exactly at the same time as the pass of the altimeter and by using the GINS (Geodesie par Integrations Numeriques Simultanees) software in the Precise Point Positioning (PPP) mode ([PERSON], 2019) (see Section 2.3). Moreover, we scheduled the cruise in order to be in the middle of the lake at the very time the satellite overpassed the lake. This allowed us to eliminate any shoreline effect on the altimeter range. Instantaneous GPS antenna height above the lake surface was another question, which has been solved, since the campaign was done in July 2014, for the calculation of absolute bias of Saral/AltiKa (2016). In contrast to a former work and to avoid errors introduced by time-dependent variations of GPS antenna height, we now used an additional instrument. This instrument was a radar measuring the distance between its antenna and the lake surface, linked physically to the GPS antenna, in order to estimate instantaneous GPS height above the lake surface, when the boat is moving, from a slow to a high speed (see Section 2.3).