General comment:

In the submitted manuscript, Abhervé et al present a study that deals with the estimation of hydraulic conductivity at the catchments scale. Solving the groundwater flow equation for R/K (R: long term recharge, K: catchment-scale hydraulic conductivity), the authors try to find most realistic values of K for 24 catchments in north-western France with different geologies, for which they compare simulated stream network extent with independently derived stream network maps. As a measure of similarity, they use the difference of the averaged over- and under-estimated stream network lengths. The results show that estimated K values cluster by the geologies of the 24 catchments with increasing estimated Ks towards more permeable rock types (Limestone). Sensitivity analysis shows that the resolution of the available DEM for estimating K is much less important than the stream map product to calculate most suitable K estimate.

Overall, the topic of the study and the produced results are of great value for the hydrological community and beyond since K estimates are usually available on much smaller scales (points to contributing areas of wells during pumping tests). The presented approach would provide K estimates at a scale most useful to be transferred into prediction models. However, I see two major weaknesses that need to be addressed until this work can be considered for publication:

1. There is a lack of reference to proceeding studies and methods to estimate K both in the introduction and the (very short) discussion. Although the authors estimate K at the catchments scale, they should provide more information about existing approaches to estimate K (e.g. well cores, pumping tests, model calibration) and for which scale they are applicable. There should also be more information on previous work trying to up-scale this information for large-scale modelling. Hartmann and Moosdorf are mentioned but no information about their upscaling approach and the range of K values they obtained. Also, there is some recent work on earth-tides and their usability for K estimation on larger scales. There is also need for mentioning typical ranges of K for different lithologies found by different studies or provided by established text books (e.g., Freeze & Cherry).
2. There is a lack comparison to K values obtained by different approaches and studies. The authors relate their results to the works of Stoll and Weiler (2010) and Lou et al. (2010), who used very similar methods. But I would expect more comparison and discussion to independently derived K values, ideally for some of the test sites but at least to typical ranges provided in text books (e.g. Freeze & Cherry) or the values provided from up-scaled map like the one of Hartmann and Moosdorf (note that there are more recent versions of the global permeability map available). Generally, the values found here seem to be quite similar compared to the differences of several orders of magnitude for different geologies mentioned in Freeze & Cherry or even in Stoll and Weiler (2010).

For those reasons, and for the more specific comments in the following, I recommend major revisions.

Specific comments:

1. The introductions provides the motivation of the study and moves quickly to methodological aspects (LL 46 and following). Please move methodological parts to the methods section and provide a more detailed review of the state of the art of K estimation ide3ntifying the research gap addressed by this study.
2. Equation (1) describes anisotropic conditions (different Ks in the directions of x, y and z), while K estimates of this study assume isotropic conditions (no specification of K direction). Please simplify Eq (1) or clarify why the more complex version of the equation is shown here. Also, shouldn’t W have the unit [L T^-1] and not [T^-1] as indicated in L 114?
3. I am not sure if the performance metric J, as specified in Eq (2) will give you the best estimation of K of a given catchment. Since real geological systems are always heterogeneous and anisotropic, a best estimate of a catchment’s K might give you a small over-estimation and a larger under-estimation of stream lengths, while J would find its optimum when both lengths are the same. Why did you not choose a metric that minimizes both over- and underestimation?
4. Subsection 3.1 provide new methods Eqs (3-5), which should be moved to the methods section.
5. The Discussion section is much too short and it should be separated from the conclusions. Please discuss here your assumptions and resulting uncertainty, compare to more other studies (not just Stoll & Weiler and Lou et al.), and explain under which conditions and how the approach can be applied at other catchments and the limits of transferability.

The authors present a methodology for estimating a catchment-scale effective hydraulic conductivity by matching the surface expression of a 3D groundwater model and an estimate of the stream network.

This is a valuable contribution, and very interesting. I expect there will be more work in this area in the coming years. I have one major issue that I believe the authors should address, and only a few minor concerns. My recommendation of major revisions reflects only the one major issue I mention below. Otherwise only minor revisions are needed.

## Major issue

- I strongly recommend that the paper be changed to characterize the approach as providing estimates of the transmissivity, not the conductivity. I realize the authors may not welcome this suggestion, and will likely be tempted to argue that the difference is trivial and not worth the effort to modify so many figures and text. I would urge them to consider the recommendation seriously though.

    - Firstly, the transmissivity is the physical property that most controls the surface drainage expression, not the conductivity. The results of Litwin et al 2022 (see in particular figure 4, and note that gamma is a dimensionless transmissivity, and Hi is better understood as related to K/R) show that under geomorphic equilibrium the drainage density is most closely related to the transmissivity, not merely the conductivity. The drainage network appears where the groundwater table needed to transmit water downslope just reaches the surface, so it is the depth-integrated conductivity that matters, i.e. the transmissivity. Because of this, the drainage network contains information about the transmissivity, not about the underlying conductivity. 

    - At present, the thickness is set to 30m in the model, which seems arbitrary and unjustified given the likely variability in permeable thickness across the region. One might reasonably ask whether changing this (to, say, 20m) would affect the estimates of K? It surely would. In fact, it would almost certainly result in an increase in the estimates of K by just enough so that the product of K and 20m would be the same as in the case where the depth was 30m (i.e. K would be about 50% larger for the 20 m case than it was for the 30 m case). In other words, I would guess that there is a roughly linear sensitivity of K to the choice of thickness. 

    - Such sensitivity will be an impediment to efforts to understand the results and make comparisons between studies. Conductivities from different studies will not be comparable if they are based on models with different assumed thicknesses.

    - However, if the authors reported that their model estimates transmissivity, they would likely find that those estimates are not so sensitive to the choice of thickness. Varying the thickness will likely not change the estimated transmissivity nearly as much. This will make the results more robust, and easier to compare with other future studies.

    - The approach presented here is important and will probably be taken up by others in the future. It would be in the long term best interests of the discipline that this important issue be clarified early on. I urge them to consider it.

## Minor issues

- It isn't clear to me why the recommendation of using lower resolution DEMs is justified. I understand that registration errors are enhanced with a high resolution DEM, but that doesn't seem like a problem that arises from the DEM itself. Wouldn't it be better to create a buffer around the stream network to account for uncertainty in its location? Furthermore, it is not clear why r_optim should be less than or equal to 2 "considering that the mismatch cannot exceed the resolution of two pixels" (Line 210). I don't follow the reasoning, and the restriction is clearly violated in the results. What is the purpose of normalizing by pixel size? Doing so will always result in a larger 'error' for high resolution DEMs. The larger values of r_optim for the 5m and 25m don't reveal a clear deficiency to me.

- The discussion of the errors from line 246 on is important and ought to be expanded. Consider:

    - The assertion that the differences "come essentially from the data" is confusing. It also seems inaccurate, since some of the errors are due to deficiencies in the model (where the assumption of a uniform K strays too far from reality, such as Site 8) and some are due to deficiencies in the data (where the mapped stream network does not adequately capture a more complex reality, such as site 18), and in some cases it is not immediately clear which is in error (Site 23 -- is the true stream in fact offset from the lowest point in the topography, or is there a registration error in the alignment of the stream location data with the DEM data?).

    - In the case of site 21 and 22 does 'non-reported subsurface flow' refer to a karst conduit (i.e. a channel, but underground) that is known to exist (i.e. data exists showing that it is there)? Or could the down-valley flow be through porous media with a higher K than other areas? One might argue that these are quite different sorts of errors. If the former, it suggests that improved accuracy would come from including conduit flow in the observed stream networks. If the latter, it suggests improved accuracy would come from allowing for spatial variability in the K-field of the model. It may not be possible to distinguish between these in practice.

- It might be worth discussing a geomorphic justification for the approach. For example the ideal stream network data is mapped extent of flowing streams, not merely the existence of a blue line on a topographic map, which are often based on purely geomorphic criteria (e.g. minimum upstream area). Further errors would occur where the surface drainage is not in geomorphic equilibrium (e.g. where relic channels remain from historical periods of erosion following deforestation, but they do not carry flow today). The authors should caution that incorrect results would arise from using stream network data that does not actually represent the extent of the flowing stream.

- Can the authors provide better justification for the performance criterion? Why this and not something else?

- Does the groundwater model include overland flow and reinfiltration? I.e. losing and gaining reaches?

- It is confusing that the description of the recharge rate estimation is included in section 2.1.5 and not in section 2.1.2 (where the estimated recharge rate is presumably used, unless I misunderstand)

- A uniform recharge rate is used -- this limitation of the method should be acknowledged. We know that riparian areas receive more recharge than uplands, and that evapotranspiration can be drawn from the groundwater.

- Line 203-204: I think D_os and D_so are switched here

- Figure 5: please expand the figure so that the horizontal error bars are not cut off.