This revised manuscript shows improvements over the previous one. The authors have addressed some (but not all) of the issues in the previous manuscript by removing the use of the young water fraction and have instead focused on investigating the uncertainties associated with the SAS function modeling. This study reiterates a common concern about the uncertainty of SAS models when trace data sets are limited.
The authors considered the uncertainties arising from temporal interpolation and spatial interpolation of the rainfall tracer data, as well as the uncertainty arising from the predetermined formula describing the SAS function. Although investigating the model uncertainty arising from the temporal interpolation has been previously addressed, as acknowledged by the authors (e.g., Buzacott et al., 2020), it seems that the incorporation of spatial rainfall tracer data (in addition to the consideration of the predetermined shape of the SAS function) could offer a novel contribution.
The authors concluded that the temporal interpolation method affects the result significantly (L511-512), while the spatial interpolation method did not substantially affect the uncertainty (L516-519). (Note that the line number in this document is based on the track-change document.)
However, there are several study designs that I find unconvincing and thus I recommend a major revision. Please refer to my comments below. There may be something I'm missing, and if so, I think it would be relatively easy for the authors to respond to my comments.
1. Temporal interpolation: On the use of the sinusoidal function
The purpose behind using the sinusoidal function in the SAS function model remains unclear. While I comprehend that the authors aimed to demonstrate the model's sensitivity to the choice of temporal interpolation method, it seems apparent that the sinusoidal function could not capture the observed input tracer signal well. Consequently, it is unclear why this particular method, which misses many features in data, was used with the SAS function model. Once this question arose, I found it challenging to follow the manuscript smoothly. In the previous manuscript, I speculated that, by using the sinusoidal function, the authors want to develop an argument related to the young water fraction (which utilizes the sinusoidal function), but this issue becomes apparent after the removal of the young water fraction from the manuscript.
Although the sinusoidal function has been utilized in TTD modeling, e.g., when estimating the young water fraction, its application there is to focus on capturing only dominant features like seasonality. Note that, for the estimation of young water fraction, the outflow tracer time series is also approximated using the sinusoidal function. I am unsure if capturing only seasonality is a valuable practice in the SAS function modeling. Also, I am not sure about the meaning of uncertainty when the input tracer data that only approximates the seasonality is used to model the outflow tracer data that contain more detailed features.
Buzacott et al. (2020) employed a sophisticated temporal interpolation method in the SAS function modeling, namely the Generalised Additive Model (GAM), to perform gap-filling and estimate the uncertainty of the gap-filled data. They subsequently explored how this estimated input uncertainty propagated through the SAS model. I believe that this approach provided more informative insights compared to utilizing multiple methods that include the uncommon practice of fitting the sinusoidal function in the SAS function modeling.
If the authors still intend to present the results using the sinusoidal function, it is essential for them to provide a compelling argument justifying the necessity of using the sinusoidal function over other methods that have been applied for the gap-filling, despite the concerns and points I have raised earlier. Without that, I worry that others could argue that the presented large uncertainty (or the significant differences in the median transit time, e.g., L511-512) is just because the temporal interpolation method utilizing the sinusoidal function was poorly performing.
2. Spatial Interpolation: Conclusion regarding the use of spatial rainfall tracer data
Despite having rainfall data from multiple locations, the authors have chosen to only present results for two cases: 1) the SAS model result using the data collected around the outlet, and 2) the result obtained by using spatially interpolating values based on data collected at 24 locations using kriging. The decision to focus solely on these two rainfall tracer time series is unfortunate and appears to underutilize the full potential of the dataset.
It remains unclear whether the authors would reach the same conclusion when utilizing other rainfall time series collected at different locations (for their ‘raw’ case). Consequently, it is unclear what meaningful insights can be gleaned from the presented results. What was the reasoning behind exploring the two cases (e.g., for the ‘raw’ case, why is the location close to the catchment outlet selected)? Why do the two rainfall tracer time series presented in Figure S1 are similar? When should we expect a spatially interpolated value to be similar to at-a-point measurement and when we shouldn’t?
I personally like the arguments provided in L392-395 as they read like the additional information (the information used in the kriging) is valuable in the SAS function model (though unclear if the authors would get to the same conclusion if they chose another location for the ‘raw’ case). However, it is not clearly stated in the Conclusion section (e.g., in L516-519). That part of the Conclusion may be to be modified.
3. Other comments
Figures S1 and S2: The figures illustrate one of the most important results, i.e., the interpolation results. It would greatly enhance the manuscript's comprehensibility if these figures were included in the main manuscript not in the supplement, as they are essential to understand the study.
L224: The meaning of '2.5% and 97.5% CIs' is unclear.
L227: The definition provided for 'backward' median transit time seems to align more with the definition of 'forward' median transit time.
L356-357: I would recommend removing such trivial and somewhat unrelated results and interpretations from the manuscript.
L505-507: The same argument repeated in the Conclusions section. It is unclear if this trivial statement is relevant to the uncertainty explored in this study.
L356-357, L505-507: I noticed that I have already provided the same comment for the previous manuscript. I still do not see the relevance of this argument in this study. If the authors think that the argument is necessary, please explain how you arrived at the argument based on the findings presented in this study.
Figure 3: Please correct the legend.
L402: The term 'uniform' may not be appropriate here. It seems that the authors are referring to potential event-to-event variations in the flow pathway during low-flow conditions. (Maybe I am wrong here.)
'raw' vs. 'kriged': Just a suggestion, it may be better with something like 'at-a-point' vs. 'kriged'.
L162-164: The use of 'time steps' in these sentences is confusing. It might be better to replace the first instance with something like 'finer temporal resolution'.
L412: The meaning of "true" model parameterization is unclear.
L455-456: Not clear in what sense the median transit time has relevant implications for water ‘quantity’.
L489: What does 'data fitting' refer to here? |