Reply on RC2

included information on the lake volume uncertainty (see details below), expanded the description on the model used to calculate the water input in the lake basin, added an Appendix B to present all salt dilution experiments used to calculate the hydraulics and thermodynamics parameters. added information on the 2020 and 2021 lake drainage event and the role of the supra glacial channel in section Discussion, corrected all typography mistakes and followed the re-phrasing proposed.

with winter snow when the filling set in, meaning that the ice determining the actual lake bathymetry was protected from melt. Note that roughly half of the lake floor lies on ice (Figure 1.b), and is therefore affected by this ice-melt related uncertainty. To constrain the lake volume on 10 July 2019, we calculated the lake volume using the DEM acquired in September 2019 as an upper limit of uncertainty (1.59x10 6 m 3 ), and the lake volume using the DEM acquired in late August 2018 as a lower limit of uncertainty (1.38x10 6 m 3 ), both for the same lake level elevation corresponding to 10 July 2019. We took the average of the two volume to determine the maximum volume value, with the two extremas constituting the uncertainty range. (2) The used Swisstopo DEM is also affected by uncertainties. These are specified as +/-2m in the vertical at the pixel scale. We however can assume this pixel-based uncertainty to be spatially uncorrelated. Thus, the overall uncertainty in computed lake volume is reduced with sigma/√N, where sigma is the DEM pixel-based uncertainty for each pixel (+/-2m) and N the number of pixels (several thousands), resulting in an uncertainty of +-0.01 m. (3) The maximum lake level elevation, measured by differential GPS, is also affected by uncertainties. This uncertainty is estimated to be in the order of a few millimetres, and is thus negligible compared to (1).
In the revised version of the text, we will address the above points by adding the following paragraph: "The main uncertainty in our estimate of lake volume is the poorly constrained ice-surface melt occurring in the lake basin between late August 2018 (date of DEM acquisition) and July 2019. This results in bare-ice melting in autumn 2018, and in bare-ice melting due to heat transfer from water to glacier-ice before the lake drainage. Since these melt processes are not quantified in the lake basin, we constrained the lake volume using DEMs from August 2018 (1.38x10 6 m 3 ) and September 2019 (1.59x10 6 m 3 ) as a lower and upper bound, respectively. We determine the volume to be the average of the two bounds, i.e. 1.49 x10 6 m 3 +/-0.11 x10 6 m 3 . In the following the DEM from 2018 is considered to be the most suitable DEM for hydraulics calculations, because ice-melt between 28 August 2018 to 10 July 2019 is expected to be smaller than between 10 July 2019 to 3 September 2019. Authors: The measurement range of conductivity is [0-0.002] S/m. The accuracy is 2.5% of the range, so 5 x 10 -5 S/m. We added that to the text. RC2: L161: the stated uncertainty of the water level measurements is in the same range as the readings presented in Fig 5. Isn't this a major problem? how significant are the recorded variations?

Authors:
We made a mistake on the specifications of the pressure measurements. The standard deviation is actually 0.05% of the measurement range. The latter is 10 m in our case, resulting in an water level uncertainty of 5 mm, and not 0.2 m, as erroneously stated before. We modified the text accordingly.

RC2: L169: uncertainty (instead of error)?
Authors: Yes. Modification done. RC2: L170: please describe how you picture the formation of these melt-imprints and how this relates to diurnal discharge variations.

Authors:
We have a hypothesis that we formulated as follows: Revised text: "We suppose that the deeper incised sections of the melt-imprints form during the afternoon, when relatively high water temperature and discharge yield to significant melt on the channel walls. Conversely, decreasing discharge and water stage during the night yields to less side-way melt on the wall section which then emerges from the water, thus producing the less deeply incised sections of the melt-imprints." We think also that further research is needed to fully understand their formation.

RC2: L179/180: either 'salt dilution' or 'tracer dilution', 'salt tracer dilution' is redundant
Authors: We replaced "salt tracer dilution" by "salt dilution". RC2: L180: referring to this method is ambiguous, there exits more than one dilution method, (continuous vs instantaneous injection) Authors: We clarified it by mentioning "salt dilution" method instead of "salt trace dilution" (see comment above). We believe that this is now less ambiguous, since this specific salt dilution method that we use is explained in the book of Hubbard and Glasser.
Revised text: "Channel discharge Qi was measured using the salt dilution method (Hubbard and Glasser, 2005). We carried out 33 instantaneous salt injections at station P5 on 12 different days during the campaign." RC2: L188: …which was the case for all presented measurements. How do you know this?
Authors: When the sensors were not at the bottom of the channel, we could guess it from the water stage time series that were noisy and close to the atmospheric pressure. In that case we discarded the data. Certainty about the sensors being at the bottom also came from visual inspections, and thanks to the weight coupled with the sensors, which ensured that the water pressure corresponds to the maximum water stage. We added this information.
Revised text: "The measurements rely on the pressure transducer sinking to the bottom of the channel. This is ensured to be the case for all presented measurements, thanks to repeated visual inspection during field visits and because pressure transducers were weighted. When pressures transducers were not at the bottom of the channel, times series were noisy and close to the atmospheric pressure value, and we discarded the data."