Feldbauer et al. present a timely and very interesting study related to the uncertainty of physical lake models. Given the critical role of the studied models in climate impact analysis, such as ISIMIP, this research provides important implications for a better assessment of global change in lakes and reservoirs. The manuscript is with high quality of presentation and rigorous scientific inquiry. Only some clarifications and extended discussions are needed before it can be accepted for publication.

One limitation of the current approach, which simultaneously assesses three types of uncertainties in lake models (i.e., input uncertainty, parameter uncertainty, and structural uncertainty), should be further discussed. Due to the interactions among these uncertainties, it is challenging for this multi-objective approach to fully resolve specific uncertainties. As admitted in the manuscript, the uncertainty of the three input-related scaling factors may hide the uncertainty of model-specific parameters and process descriptions. Consequently, the method obscures the investigation of an optimal model for specific lake types and an optimal algorithm for specific lake processes. Notably, for global lake modeling, we hope that as climate data become more accurate with time, the uncertainty of global lake simulations will be reduced. We also hope that lake models can achieve consistent global simulations without lake-specific calibrations. Despite the great values of the current paper, it falls short in addressing these issues. Conversely, I would encourage the authors to conduct a future study which uses observed atmospheric forcings to exclude the uncertainty in input data and ensure the good model performance achieved for right reasons. There are some existing studies following the recommended approach, such as Guseva et al. (2020) and Guo et al. (2021). But their values are limited due to either focusing on only one lake or testing only one lake model.

Guo, M., Zhuang, Q., Yao, H., Golub, M., Leung, L. R., & Tan, Z. (2021). Intercomparison of thermal regime algorithms in 1-D lake models. Water Resources Research, 57, e2020WR028776. https://doi. org/10.1029/2020WR028776

Guseva, S., Bleninger, T., Jöhnk, K., Polli, B. A., Tan, Z., Thiery, W., ... & Stepanenko, V. (2020). Multimodel simulation of vertical gas transfer in a temperate lake. Hydrology and Earth System Sciences, 24(2), 697-715.

I suggest the authors to avoid the use of "hydrodynamic lake models" to describe the studied models. To me, hydrodynamic models refer to numerical models that solve the transport of both mass and momentum. The authors can use "physical lake models", "thermodynamic lake models", or just "lake models". 

In the methodology, one area that needs clarification is what procedure the authors have adopted to ensure appropriate initial conditions for simulations. It can be particularly important for the modeling of deep lakes.

Minor comments:

L55: also Zhuang et al. (2023). Zhuang, Q., Guo, M., Melack, J. M., Lan, X., Tan, Z., Oh, Y., & Leung, L. R. (2023). Current and future global lake methane emissions: A process-based modeling analysis. Journal of Geophysical Research: Biogeosciences, 128, e2022JG007137. https://doi. org/10.1029/2022JG007137

L181: gets absorbed

L202: How does the metric δ differ from the Sobol's total-order index?

L212: What is "SA"?

L226-227: I suggest moving Figure 3 upward to Section 2.2

L232: Figure S5 is introduced prior to that of Figure S4.

Figure 5: It is surprising to see that S1 is larger than δ in many cases. To my experience, the first-order sensitivity should be smaller than the total-order sensitivity.

L306: remove "a"

L407: potentially  

General comments

One-dimensional physical lake models are a widely used tool in simulations of lakes and reservoirs for diverse goals like now-casting, forecasting, or to compute mixing for use biogeochemistry. Although many different models exist and several of them are very widely used, to my knowledge no consistent comparison between them exists until now on a wide range of lakes. In general, research about the link between lake types, model parameters and uncertainty is not widespread and I think this manuscript is a good contribution to fill this gap. The manuscript is well organized and written with only few spelling mistakes. However, I think that there is a problem with one of the calibrated parameters of GOTM and not enough details on the observational data.

Specific comments:

The observational data used to calibrate the 73 lake models is of great importance, but very few details are given in this publication. I would find it useful to a small paragraph about time and depth resolution of the observational data and whether any weighting was done to compute performance metrics (lines 196 – 198). Is there a minimum requirement of observations to be included to the 73 lakes? In addition, I would welcome a Figure giving some information about depth and time resolution of measurements in the supporting information.

Is there a reason the GSWP3-W5E5 reanalysis dataset was chosen? Could you explain this in 1 – 2 sentences? Also a bit related, is there any chance of going to hourly instead of daily resolution? As far as I understand from the discussion this might solve some of the problems (wind speed effect on mixing is cubic). If yes, it would be interesting to mention this in the discussion/conclusion.

I would find it interesting to have the silhouette plot of the cluster analysis in the supporting information.

The authors discuss the fact that k_min of GOTM seems to be the most sensitive of the lake-specific calibration parameters. The range of k_min used in this study is 1.5e^-7 to 1e^-5, which is rather high values compared to a default value of 1e^-8 in the GOTM manual. In addition, typical values of ~1e^-6 are reported for TKE in the hypolimnion of lakes (e.g. Wüest and Lorke, 2003). I see a major problem if k_min is set too high: it could, together with high values for the scaling of shortwave radiation, offset a low value for the scaling of wind speed. There is evidence of this in Figure 7, where the calibrated parameters for GOTM are consistently low (wind speed) or high (shortwave) compared to the other models. The calibrated value of k_min always seems to be well above 1e^-6 (Figure S8), so on the order of typically observed values for TKE (Wüest and Lorke, 2003). The authors discuss the potential interactions between k_min and wind scaling on one hand (lines 341 – 345), and shortwave scaling and wind scaling on the other hand (lines 365 – 369) but not the potential interaction between all 3. In regard of this, I would like to ask the authors to motivate their choice of the range of k_min and to check its influence on the wind and shortwave scaling parameters. I see two ways to do this:

• Compute second/third order Sobol indices for the concerned parameters
• Redo some of the simulations with k_min = 1e-8

I understand that the interaction calculation shows that this suggested parameter interaction is not driving variance but the correlation could still be strong among these 3 parameters. There is also no obvious reason why wind and shortwave scaling should be so different for similar models like Simstrat and GOTM. I could be wrong but to me it seems like k_min in GOTM is playing the role of the seiche in Simstrat.

The authors seem to imply that larger lakes should generally have a larger value for wind scaling and vice versa for small lakes (lines 349 – 351). However, if true this effect should be visible in the calibrated wind scaling parameters, no?

Technical comments:

Title: maybe “hydrodynamic” or “physical” lake models instead of just lake models

Line 6: The following sentence is a bit too unspecific to me: “The models performance and parameter sensitivity showed a relation to the lake characteristics and model structure.”

Line 39 - 40: Maybe mention that although important for shallow lakes, the biogeochemical components are not discussed in this manuscript.

Line 64: Make clear that Table S1 of the current manuscript is meant and not Table S1 of Golub et al. (2022)

Line 82: delete “and” before “the 1D turbulence-based models GOTM”

Line 99: “comma” after “Equation 1”

Equation 3: Shouldn’t it be h < z < D_lake?

Equation 5: Please check whether term 1 is really negative.

Line 220: This sentence is not clear to me. Did the authors intend to say “between best and worst performing model”?

Line 263: “were” instead of “was”

Line 269: “Lake clusters” instead of “lake cluster”

Line 357: “better” instead of “more”