Thank you for this interesting analysis and for the draft report which is clear and well-structured. I agree with previous posts for the possible improvements in the investigation of the physical predictors, especially for the possibility of including climate indices, and eventually seasonal precipitation statistics. I would like to stress a few points and propose possible complementary elements:
1 – I agree with Guillaume Thirel that it could be interesting to see also the scatterplots of the seasonal correlations against the physical predictors. The investigation by scatterplots could allow visualizing possible “threshold” effects that could be hidden in the box-plots (see for instance Figures 6, 7 and 8). In particular, I think that it would be interesting to further investigate the effect of the basin size on the river memory. The box-plots in Figure 6 correspond to groups of basins with a very wide range of catchment areas, especially for the group of largest catchments (from 1557 to 70091 km2). An additional graphical analysis of the effect of basin size for the largest catchments could validate the expectation of finding an enhanced seasonal river memory for larger scale systems, possibly emerging above a threshold size.
It is good to use quantiles for separating the catchment set in groups having the same sample size; however, this approach leads to a very wide range of characteristics within each group, especially for the classes including extreme values. Maybe the use of a larger number of classes for separating the catchment set could be useful? I agree also on the interest of using a statistical non-parametric test for the assessment of significance of differences between classes.
2 – For a potential additional analysis for improving the physical interpretation: an estimation of the characteristic response time of the catchment could be considered, as the time to peak. The estimation could be based on different approaches, either by using streamflow data only or by cross-correlation between streamflow and precipitation (if P series are available, as for the French basins). This additional analysis would aim at investigating whether the seasonal river memory for the high flow season is enhanced for slow-response catchments, as it could be intuitively expected, and quantify this possible trend.
3 – I think that the analysis by country is less significant than the use of physical descriptors, and could be reduced. For example, I was wondering whether it is meaningful to show the box-plots by country (e.g. Figure 3b and 5b) or if it would be sufficient to report the geographical distribution by a map as in Figure 2. By the way, by looking at the map in fig. 2a, we can see a geographical trend within France, since the highest correlation coefficients are located in the northern part of France, which is subject to oceanic climate and slower catchment response.
Also, I agree with the comment in the text of the draft on section 4.8.3 (Country-level verification) saying that this part seems less meaningful, and redundant with other parts.
These are only complementary suggestions. The general protocol of the report is already very good. I look forward to see and discuss the developments of the work. Thank you!