This paper about lake level modelling presents an interesting case study with a clearly presented methodology that could readily be transposed to similar cases with little in situ data. The method is overall well presented and the implications for the case study nicely discussed and summarized in the conclusion; the literature review in the introduction is well written; it remains perhaps a little unclear how relevant / important similar case studies are: is a comparable modelling of lake systems a common problem? would most lake systems not be rather different, with numerous hillslopes connected to the lake that require an actual rainfall-runoff modelling part to account for surface inflow? It would perhaps be interesting to check what cited literature refers to similar low land lake systems (without surface water inflow) and which ones to more mountainous / alpine lake systems.

Detailed comments:

- the  balance equations are not well presented; they are a mixture between actual water balance equations and their numerical implementation; please check all units and make sure all quantities have the same units in all equations; do not mix fluxes (in units of volume or mm per unit time) with storage

- "in this study we used a lowpass filter over the lake level data, with a cutoff frequency at 20 days to help with the visualization of the analysis." I would not be able to reproduce the filtering with only this information; filtering comes again later, can you give more indications? is it always clear in the results if the shown data filtered or not?

- does the system not have surface water in- and outflow? this is not clear in the methods part;  it becomes clear in the case study section but this is unusual for most hydrologists, could be made clearer

- results: there are details that belong to the methods section, in particular the applied filter to remove the annual signal  requires more details; as is, this part is not reproducible; how does the signal look like after the annual signal removal?  the part on estimating optimal memory should have a reference

- testing memory length up to 250 days does not seem to make a lot of sense a priori; why could the system have such a a long memory? what explains the decrease of the metric after 100 days in figure 3?

- results, line 333: an actual equation of the numerical scheme would be preciser (with correct time steps)

- line 344: from figure 4, I get that there is too much water in the system, thus line 345 should read that an additional groundwater outflow is required? perhaps I misread the text here, please check

- line 386: how  do you standardize?  the daily  time series, how? how can you standardize a time series with many zeros such as precip)?

- line 400: the process description is as if we had a very simple system with a single groundwater system directly connected to the lake; is this the case? very unusual for most hydrologists, for a catchment of 33 km2.

Basically, I find the paper interesting and also agree with the conclusions. There are a couple of good ideas, but also a few technical aspects that should be critically discussed in the revised version of the manuscript. I also do not entirely agree with the strict separation between simple balance models and complex process-based hydrological models. And that the process-based model is the better choice if sufficient data is available. It always depends... If the components of a simple water balance have been robustly determined (which can often be a lot of work and requires a lot of data) this is not per se less good than a complex process-based hydrological model (with its very own weaknesses and uncertainties such as non-unique solutions etc.).

Line-specific comments:

Line 13: Why „indirectly“?

Line 38: Here you start to explain what you want to do in this study. I would rather put this at the end of the introduction.

Line 38: Citation style… only the year should be in brackets. This also applies to various other places in the manuscript.

Line 47: Not clear to me what is meant by “higher resolution models of the catchment”

Line 51-52: I do not agree with this statement. These handful of hydrological variables/flows are often quite difficult to determine/estimate. Therefore, I would not consider this a typical application in data-scarce regions. As I understand it, process-based models are more likely to be used in data-scarce areas to bridge the gaps of data scarcity (e.g. using standard parameter sets or those from comparable catchments + meteorological forcing data, which is usually quite accessible) – I am not very strict with my opinion here - it should rather be understood as a counter-argument.

Line 100: Should be “used”.

Line 102: What do you mean by "efficient"? I find the word somewhat unsuitable here and would rather write something like "easy to use".

Line 121: Maybe add something like “cannot yet be set up with the required level of confidence”.

Line 136: “physics” is a somewhat controversial term in this regard, I would just write “process-based”.

Line 149 and line 152: What do you mean with “we propose”? If this is part of your study, just delete “propose”. If you propose this for future research (based on the findings of your study), it rather belongs to a conclusion section.

Line 162: Why have you used ERA5 data and not data from the DWD weather station in Potsdam. This data should at least be compared to each other (for validation of the ERA5 dataset). Yes, ERA5 provides actET (as various other products as well), however, how reliable is that? In my experience, not very reliable… At best, this should be compared with the nearest station data (lysimeter) or at least discussed critically (perhaps this is not so relevant because the statistical analysis does not require very precise data… anyway requires some discussion for my taste).

Line 183: Which catchment area you are talking about? Relevant would be the groundwater catchment (right?), however, I worry that the surface catchment area is meant here. In the case of a relatively flat relief (and low hydraulic gradients) and also the fairly strong influence of groundwater extraction, it is quite likely that the subsurface and surface catchment areas differ.  

Line 201: “lake level changes are linearly related to storage changes” In general, I think this assumption is far too simplistic. I don't think this oversimplification is necessary either, as only a bathymetric model would be needed to represent this correctly. A quick Google search shows that such a bathymetric model exists and is accessible.

Line 209: The application of the strong oversimplification, mentioned in the previous comment, quite likely has a systematic impact/error on the estimation of dF and thus the identification of tipping points (e.g., presumed tipping points might actually be related to lake bed morphology).

With regard to the two previous comments, you could possibly also argue that in your particular case the water level decrease only takes place in a relatively small range and therefore such a linear assumption is not completely wrong... (but should be checked with the bathymetric model)

Line 228: Delete the word “same” or replace it by “respective”.

Line 239: I not really get why filtering helps neural networks? Such a statement should be explained.

Line 278: What exactly do you mean with “civil engineering information”? Please, specify.

Line 300-306: This belongs to the results section.

Line 308-310: These lines are superficial.

Line 324: Isn't that actually a pretty vague result? Couldn't it be that the memory size might not be larger, e.g. 100 days? How would the model results change if a different memory size were assumed?

Line 325: “One might link this time to the catchment size, as the distance travelled by the groundwater flow.” I would also delete this sentence. (It’s not a good style to assume that that the reader doesn’t know the very obvious fact that this is caused by pressure transmission…)

Line 415-427 and Figure 8: How representative are the selected time periods in 2006 and 2016? Is it valid to draw general conclusions from them (they could simply be singular phenomena…)? Either this should be well argued in the text or average values could simply be used as in Figure 9.

Line 444: Instead of “since 2015”, you should provide the exact time period, i.e. “between 2015 and XXX”. This also applies to later cases in the text, e.g. line 451.

Line 461: Why only 4%? Even if one takes 50% as the average (which could definitely be regarded as the upper limit), the influence would only be marginal.

Line 487: “some of the relevant information is only available on one side of the lake” Would be good to be a bit more specific, i.e. which information is missing on which side.

Figure 10: Why you took 2010 as a baseline? And is a baseline necessary? For Figure 10b you could also just sum up the anomalies (e.g. as deviation from the mean) starting at zero. And why are the cumulative anomalies going down when the NDVI increases (and are above the reference/baseline value)? – if I misunderstood something, it should be better explained…

Line 504-505: Basically, you are saying that an increase of 10% in NDVI causes an increase of 5-15% in ET. Do you have any reference for this or at least indications for this assumption?  

Line 508: One of the "However" is too many.

Line 512-521: I agree to the hypothesis that the evolution of groundwater levels at a regional scale has an impact (although it doesn’t explain the tipping point). However, doesn't that somewhat contradict your model assumption that your subsurface catchment corresponds to your surface catchment?

Line 540-541: Good point! But, again, it somehow contradicts your model assumption as described in the previous comment.  

Line 546-570: This is rather a summary of your results than a conclusion of your study. I would more focus on pros and cons of your study (maybe also some of my comments/critics can be discussed here).