The authors present a method to improve the estimation of catchment-average effective precipitation from the ERA5 product by utilizing the information contained in stream flow data and a regional LSTM model. 

To validate this interesting approach the authors model the runoff using this catchment-average effective precipitation as forcing and compare it to the runoff in the CAMELS data set. Averaged over all catchments contained in the CAMELS data set this approach improves the modelled runoff compared to using only ERA5 precipitation estimates as forcing.

The paper is well written and has a reasonable length. However, I think the authors could address the topic of “scale” more in depth. This starts at describing the used data sets in more detail, especially by mentioning their spatial and temporal resolution. Furthermore, the selection of the out-of-sample data sets as “proof-of-concept” is restricted to very small-scale basins. It is especially at this scale that daily ERA5 precipitation will most likely not perform well as forcing for a hydrological model due to its coarse spatial resolution.

The authors state that the LSTM model is estimating catchment-average precipitation amounts. This implies that the introduced approach might not perform equally well for differently-sized basins, when the runoff dynamics shift from surface-runoff to baseflow dominated basins. In my opinion the authors should elaborate more on this topic.

The study is interesting and introduces a promising approach which is why I recommend its publication in NHESS after addressing the the attached comments.

See attached PDF for details with specific comments and technical corrections.

This paper illustrates “doing hydrology backwards” by developing an LSTM model to predict precipitation based on reanalysis products, given meteorological inputs and the added input of catchment discharge.  The authors show that a model given discharge does a better job at predicting precipitation, indicating that discharge encodes significant information about recent precipitation beyond other meteorological forcings.  They also find that while the LSTM underestimates precipitation totals relative to the ERA5 training dataset, it better reproduces events that are poorly captured by ERA5.

This is a very interesting paper and appropriate for this journal.  It effectively shows that a machine learning approach can be used to improve uncertain precipitation forcings, especially for short time-scale events that are not well represented in reanalysis.  With this, I have several comments listed below that could improve and clarify some aspects.  As a note, I see some of these may overlap with the first reviewer who also made good points and authors have already responded.

General comments:

This study poses that an LSTM model that is trained to reproduce ERA5 precip can actually estimate precip better than the ERA5 product itself.  This is based on the input of “future” discharge, which encodes observed precipitation events that are not typically well captured by ERA5.  In this way, the LSTM could deviate from the ERA5 because (a) ERA5 is not capturing precip as it actually occurred or (b) the LSTM is not performing well.  Unless I am mistaken it seems hard to disentangle these, and the observation gage-based “E-OBS” product seems important here and could be better described.  For example, Figure 2 shows that the LSTM “with discharge” better replicates ERA5 precipitation than the LSTM “without” – and it is assumed that this better replication is a good thing.  Meanwhile later figures illustrate differences in ERA5, LSTM, and E-OBS regarding specific events, but the LSTM “without” discharge is dropped.  In general, it seems useful if E-OBS, ERA5, and both LSTM estimates could be compared up front to more clearly establish differences between them, i.e. what is currently done just between the LSTM models and ERA5 in Figure 2.  As far as E-OBS, a few more details on that data might be beneficial especially in the events selected for Figure 5 and associated discussion.  For example, what is the proximity of a gage to the specific study catchments?

I can imagine that this method might be more effective for smaller catchments, and less effective for very large catchments where the effect of P on Q is more lagged and smoothed.  For a very large catchment, estimating a single time-series of P based on Q seems like it would be trying to “average” multiple ERA-5 or gage-based grid cells.  Some details on the spatial characteristics of the study catchments might be useful here, especially relative to the scale of gridded precipitation forcing.  For example, is there any meaningful trend in model behavior (for any model) with catchment area, or are all study catchments relatively smaller in scale than any precipitation input that would be used? 

With all the different models and products, a table or two might be useful – for example listing the properties of precipitation datasets, models and references, flow data.  This could be linked to Figure 1 which gives the flow of the study.

Figures: figure captions could all be expanded or improved.  For example, Figure 1needs a more descriptive caption that addresses the content of each panel and the connections.  As it is, it does not really describe the flow of the study and could be a lot more useful to the reader.  Otherwise, figures with (a), (b) (c) should be more clearly labeled as such in the captions, and figures like Figure 7 with no panels should not have any references to panels (a), (b), (c), etc.  It is also a bit hard to compare the spatial images in Figure 3 because of the grey shading in the top 2 figures but not in the E-OBS panels (so it would be nice if the same masking could be applied to all of these maps).   Finally in figures and text it should be made specific that when “LSTM” is mentioned in text or a caption that it is specified as one model or the other (“with” or “without” discharge).

General comments

The paper by Manoj et al. describes a method to estimate catchment scale precipitation from streamflow records using a machine learning approach. The paper is well-written, and its objective is highly significant in the context of hydrological sciences, where precipitation data remain scarce and critical to improve water resources modelling. Using streamflow as a predictor to estimate rainfall is not new, but it makes perfect sense as streamflow reflects recent rainfall history. The LSTM model is perfectly justified for this task, considering the high level of performance reached by this type of machine learning approach. We particularly appreciated exploring a large sample of catchments, which reinforces the author’s conclusions. We were also impressed with the final validation exercise using different hydrological models.

Overall, this paper contains many valuable elements and a tremendous amount of work. However, it suffers from two fundamental flaws requiring a major revision before its acceptance for publication:

• Comment #1: The fundamental aim of the paper stated in the introduction is to generate better precipitation estimates compared to currently available reanalysis products such as ERA5-Land. The authors are clear about the issues of reanalysis products in various parts of the manuscript. For example, related to a particular flood event, they indicate: “Our previous work (Manoj J et al., 2024) indicated that ERA5 Land could not accurately replicate the characteristics of the convective storm that caused this annual flood event” (line 240). Consequently, we do not see the point in training an LSTM using ERA5-Land precipitation as a target. The best we can expect from this approach is to generate rainfall series identical to ERA5-Land precipitation, which is known to be problematic.
  
  Furthermore, any performance comparison between LSTM outputs (trained on ERA5-Land precip) and original ERA5-Land precip using an independent dataset as a reference (E-OBS in this case) are logically flawed: the LSTM was not trained to reproduce anything else than ERA5, so any perceived “improvement” between its outputs and ERA5-Land precip when simulating an independent dataset (E-OBS in this case) is due to chance.
  
   
  
  Fortunately, the solution to this problem is simple: instead of ERA5-Land, the authors could set the LSTM training target to rainfall observation (i.e. E-OBS). The comparison between LSTM and ERA5-Land would become meaningful and clarify if precipitation estimation can be improved compared to using ERA5-land.
  
  
  
  
• Comment #2: When training their LSTM, the author used the mean catchment rainfall as a predictor (Pmean, see line 138). In other words, they use some of the predictand data as a static predictor. This is a major flaw in a regression setup: it gives the LSTM model a distinct advantage over an operational situation where, obviously, the mean catchment rainfall is not known. Here again, the solution to this issue is straightforward: remove this predictor from the list of static predictors.

Aside from these two fundamental problems, we also have a few general comments:

• Comment #3: some aspects of the method lack clarity. We got a bit lost in all the cases considered by the authors at the end of the manuscript. We suggest clarifying several elements using summary tables in the method section (and not later in the paper):
  • the list of all LSTM configurations tested with their inputs (including lagged inputs) and their outputs,
  • the list of all performance metrics,
  • the list of all test cases including the number of catchments, the forcings (if using hydrological models) and the outputs tested.
    
    
    
    
• Comment #3: The LSTM model was trained on mean squared error, emphasising large rainfall values. We recommend testing other configurations where training is done on transformed values, e.g. square roots and log transform, to check if certain rainfall metrics can be improved further.
  
  
  
  

Detailed comments

• Comment #4: Line 68, “we conjecture that the catchment-average precipitation can be inversely identified”: this problem is still numerically ill-posed due to catchment memory. We suggest rephrasing to “we conjecture that streamflow data can reduce the uncertainty associated with this process by providing valuable information on recent rainfall history”.
• Comment #5: Line 115, “The Caravan dataset uses the ERA5 Land as meteorological forcing”: it would be useful to remind that this is far from satisfactory as ERA5 is known to have important limitations when simulating rainfall.
• Comment #6: Line 185, “model “with_discharge” outperforms the model “without_discharge” not only on average but also concerning the best-performing catchments.”: It would also be useful to show the distribution of pairwise NSE differences. This would answer the question: “How many catchments reach better NSE when using streamflow predictors?”.
• Comment #7: Figure 3: This map is a bit confusing because for LSTM and ERA5-Land, the data generated by the authors is in the form of points (i.e. catchment average), not surfaces. Please update the map accordingly.
• Comment #8, Line 204 “preserves spatial gradients”: what do the authors mean by “preserve”? Please clarify. It is hard to assess spatial patterns from maps as small as Figure 3. We suggest an additional metric and a figure to clarify this point.
• Comment #9, source code: please list software requirements in the source code. This includes the list of software packages required and their versions. If the authors are using Anaconda, it can be done by adding to their repository a conda environment configuration file, also referred as “yml” file (conda contributors, 2025), which lists all Python package and their version.

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References

conda contributors. (2025, February 13). Managing environments—Conda 25.1.2.dev38 documentation. https://docs.conda.io/projects/conda/en/latest/user-guide/tasks/manage-environments.html