Review “Scale-dependency in modeling nivo-glacial hydrological systems: the case of the Arolla basin, Switzerland” by Argentin et al.

This study presents a modelling exercise for the small Arolla basin in Switzerland (26 km2), with the aim of finding out how model parameters vary for nested and neighboring catchments and if parameters are thus spatially transferable for a semi-distributed/semi-lumped hydrological model. The calibration of the hydrological model is done for three different melt models, two different objective functions (NSE and KGE), and with or without considering debris cover on the glaciers. The many results show that parameters are transferable, and that similar parameters can thus be used to simulate streamflow along a river network (up- and downstream). For the temperature index melt model of Hock, that includes potential solar radiation, parameters are more similar across the basins when compared to the other two melt models that use less spatial information.

Overall, I found this a very interesting study with many different aspects that were looked at, a well written methodology section and a good presentation of the results and the discussion. However, I have a few points that require some further attention, which mainly relate to the framing of the study and clarity of the results.

1. Introduction – a) when reading the introduction the first time, I was a bit confused by the reasoning of why parameter transferability may be difficult in glacierized catchments and the later following explanations of the different melt models. At first, I thought that the study would focus on the different storage and routing parameters, but it turned out that the study focuses rather on the melt modelling (catchment-wide melt contribution). Although this becomes clear towards the end of the introduction, I think it should be mentioned earlier on, with an explanation of why this focus was chosen. b) What is also missing in the introduction is a discussion of studies that use glacier mass balance or snow related data to calibrate models. In such cases, melt parameters are calibrated independent of catchment size and the problems outlined here are not (less) applicable, especially if these measurements are available at large scale (remote sensing data). This is an important consideration for the framing of this study. c) And last, I think that the comparison between calibrating the model with NSE or KGE as objective function should be already mentioned as background material in the introduction. It would be good if it becomes clear how that fits too into the story of modelling glacierized catchments.

1. Although section 4.4 is very interesting, I found the formulation and presentation a bit weak at the moment. It would help if there was already a discussion on NSE and KGE and its different sensitivities in the introduction. Furthermore, the section mixes discussion with results, although a discussion section is following. And third, I do not understand why the neighboring catchments were not included too in the analyses of Figure 12?
2. Section 4.6 is supposed to give some insights into the physical meaningfulness of the transferred parameters, but does not discuss any of them. After reading this section I was not sure what message to take from it, besides that catchments with higher glacier cover show higher discharges later in the season. However, this is not related to the different weather patterns suggested in the lines before. Maybe this section could be tied in with the section where figure 12 is discussed?
3. Overparameterization – one of the conclusions of the study is that including debris cover in the calculations likely leads to overparameterization and therefore a less good fit when transferring parameters from one catchment to the other. While this may well be the case, I found the reasoning not always strong, as for example some of the melt models use more parameters (ATI) than including debris cover in the TI or HTI model. Without testing the removal of more parameters (even simpler models) and seeing when the model reaches some state of overparameterization, these conclusions are quite speculative. Maybe the authors could better argue why they choose that overparameterization might be occurring, rather than the debris melt being too spatially variable due to variable thickness?
4. In the last part of the discussion (5.3) I found the discussion on catchment sizes and transferability of parameters hard to follow (L412-L426). It seems to start with explaining that there is no converging of parameters for all melt models in small catchments, and that there is no improvement for the HTI model compared to the TI model, to then conclude that the HTI model parameters for catchments smaller than 7 km2 are good transferable. Please check the reasoning here and clarify. More on a general note, I was missing some discussion on the implications of the results presented in this study. For example, do the results hold for this specific set-up, or for this catchment size (26 km2 is still rather small), or can we expect similar transferability effects in larger catchments? And would the results also apply to parameters other than melt related parameters?

Detailed comments

• L2 (abstract) “and streamflow generation factors” – should this be “on streamflow ….”?
• L8 “streamflow patterns” – what is meant here with patterns?
• L11 “and model performance” – I found the wording a bit confusing, would model performance metrics work here?
• L16 “the long-, intermediate, and short-term storage capacities of alpine glaciers are impacted” – without context of what these storages are, I think the sentence does not add much
• L21 would “leading to critical changes in streamflow regimes” not fit better here?
• L29 – L34 – maybe it would help to also add that the category of “lumped” models here, do not include a “real” spatial location, and that is the reason why they are calibrated at the outlet (as the functioning of the whole system)
• L62 what is a “parameter bias”?
• L66, possibly use another symbol for degree day factor, as “a” is often also used for albedo
• L74 what is meant with “correlation of aspects?”
• L133-135 possibly add that the discharge data were normalized with the same maximum values? Otherwise biases between simulations and observations will not be visible
• L161 “along with baseflow from melt and rainfall” – what is meant here? The outflow from the groundwater/slow reservoir?
• L163 – “fed into (to – remove) two lumped parallel reservoirs” – can you briefly describe what these reservoirs represent?
• L193 “night time” – at what temporal scale is Ipot calculated?
• L202 “downscaling” – how was this done?
• L211 “but an inequality is added” – can this be described in a more elaborative way? How much is it, and to which parameters is it applied? Are estimates of debris thickness known to assure it has a lower melting effect instead of an increasing effect?
• L250 “more robust yearly signatures” – this sounds like stable flow, while what is meant here is that it is more variable flow, right?
• L261 “Fig 14” – consider moving this figure earlier in the paper, as figures need to be called in order
• L263 “With the TI model” – this sentence is confusing as it is contradictory with the previous one but does not indicate so
• In Section 4.5, what is the difference between reason i and reason iii?
• L369 “here close linked”, add “is”
• L371-372 “Longer in-stream flow paths lead hereby to a stronger dampening effect of hillslope- and glacier scale runoff variability” – Could the mechanisms behind this be explained here? Does it relate to more sub-surface storage and other streamflow components to compensate the glacier runoff variability?
• L379, here I think there should not be a new paragraph starting
• L384 “Thus” – could this be elaborated? E.g., since the KGE includes different aspects, xxx

Figures:

• Figure 1, in figure a, the legend seems to have other colors than in the map, for b) the aspect legend looks strange with the black background and the arrows at the bottom. For c) the figure would look more clean if the labels were in the figure and not overlapping (try with arrows or other symbols), for d) how come that discharge is available from 1971? But the figure says something else? I think it would be better to have points in Figure d, as the area or glacier cover fraction in between the observed years is uncertain. I found that the references to the “GLAMOS” inventory comes later in the text, but it would be good to already have a proper reference from the start, or alternatively referring to a table with all the input data.
• Figure 2 – Can BI be added to the timeseries as this is the one that is mainly used in the paper? Also, it would be good if the line thickness was thinner so that one can actually see the daily variations
• Figure 4 – a solid line would be better to see the differences
• Figure 5 – what does the distribution of parameters represent here? Are these all parameters of the 10000 simulations?
• Figure 3, Figure 7, Figure 13 – it may be helpful to not only add the names of the catchments, but also a label for nested or neighboring catchment
• Figure 5 – can the units also be provided of the different parameters?
• Figure 12 the “relative difference” units are not very clear. Maybe “relative difference” can be explained in the caption, as well as “relative performance change”, is it a fraction of the original one (i.e. calibration run /BI characteristic?). And how was the over/underestimation assessed?
• L446 “when focusing on attenuation of discharge trend offsets” – what is referred to here? This comes new in the conclusion and hasn’t been explained before, at least not using these wordings

The paper “Scale-dependency in modeling nivo-glacial hydrological systems: the case of the Arolla basin, Switzerland” investigates the transferability of parameters of a semi-lumped hydrological model within nested catchments in a high Alpine environment. It specifically explores the role of including physiographic information by implementing temperature-index models with decreasing simplicity for modelling snow and glacier melt. The authors conclude that including the effect of solar radiation in melt modelling increases the transferability of parameters, while including the effect of debris coverage of glaciers reduces parameter transferability.

The paper is well written, and presents a comprehensive modelling study and analysis that is of potential interest to the community of lumped hydrological modellers. A few concerns, however, occurred to me while reading the draft. These are outlined below and should be addressed by the authors in a revised version before the paper can be published in HESS.

The largest concern in my opinion is that the role of precipitation input is hardly discussed. The authors are making quite some efforts to explore the role of physiography for differences in production of melt water, which arguably is a major source for river discharge in their study area. At the same time, the role of physiography for differences in precipitation (snow, rain) input to the studied catchments is not analysed or discussed. The authors explain that local station data is limited and gridded data is used for precipitation, but it would be interesting to know if and how the precipitation characteristics could also explain some of the differences  of the subcatchments. The focus here is on melt modelling, for which spatial differences in snow pack accumulation could be important. Similarly, also rainfall patterns could be important for shaping the discharge from different subcatchments, at least it appears that rainfall-runoff after depletion of snowpack produced some of the highest discharges in the observations (e.g., Figures 14 & E1).

I thus encourage the authors to add some analysis of the precipitation patterns, for example: Are there differences in precipitation input among the catchments? What about inter-annual variability? How do the gridded precipitation data compare to local info (at least two meteo stations are mentioned)? These issues should be discussed critically, especially if and how these relate to the parameter transferability between subcatchments.

Another doubt regards the bootstrapping approach the authors use as a benchmark. This is not critical for the evaluation of the paper, but perhaps some more explanation or even a revision would be possible. If I got it correctly, five years of observations were resampled in yearly blocks to obtain 100 benchmark series of discharge, such that each year is represented by a random choice of one of the other four years. Goodness-of-fit of observed and resampled series are calculated and averaged. The authors find that these benchmark values drop with decreasing size of subcatchments.

While I get the idea of providing a benchmark that preserves some of its characteristics like autocorrelation, It is not entirely clear to me what the assumptions behind this specific implementation of bootstrapping as a benchmark are. Would it not be problematic if the precipitation dynamics were different in different years? How similar are the resampled series to each other, given that only five yearly blocks were used? Why are 100 random combinations used, and not all possible combinations? Does it make a difference whether the series are averaged or the goodness-of-fit criteria are averaged? Could averaging the discharges for the same day of year provide an alternative and possibly more robust metric? What insights does the drop of benchmark metrics with catchment sizes provide for similarity of the subcatchments, for example regarding their interannual dynamics?

Further comments

Figure 1: a) Colors are not clear, especially for debris cover; the legend seems a bit oddly placed. Legend b) – it’s confusing that the extremes both represent "West" – please consider a cyclic colormap as an option. The shown meteo station appear to be unused in the analysis.

130-131: Does analysing the time lags between the hydrographs support your assumption?

Fig. 8: It appears as if the maximum discharge of 1.0 was never captured by the model. What are the reasons for this discrepancy?  

315-316: What about the spatial variations in precipitation? Can these also be highly variable?

372-375: I agree with that statement, but this directly invalidates your benchmarking approach, doesn’t it?  “In contrast, even simple meteorology-based hydrological models deliver much better results” – so what would be the best option in the end?

386: “As discussed previously” – maybe I missed it, but where was explained why simulated hydrographs should outperform NSE and match KGE?

399-404: If there were clear relationships of discharge and physiography - would taking them into account explicitly in your model solve a part of the transferability problem? This could hint at structural deficits of the model.

Figure E2 ff: Please revise the captions to include the info that these are modelled data.

Technical comments

117: Delete “capture”

296: “Fig 9t” – I do not get what “t” stands for.

587: Check Parajka et al. citation and link