Greetings. The manuscript entitled “The general formulation for runoff components estimation and attribution at mean annual time scale” with the issue of estimating the various flow components for water resources management purposes. The structure and goals are clear, and the results are consistent with data. This paper can certainly be published after some major adjustments, listed below. I limited the previous revision to the Introduction and Methodology part, I think these need to be fixed before further going down the publication way. These itemized improvements would make the work more scientifically sound and robust. These considerations come from my expertise as a hydrogeologist, so they will pertain to this sphere of competency. Furthermore, I recommend incorporating ‘recommended references’ and at least having a quick glimpse at ‘further reading’ for a more precise framing of the work. Best regards.

• From line 36 on: the description and the classification of these different baseflow components are pretty gross. I understand that the purpose of the work is to categorize all of them as baseflow hydrograph volume portions, but putting in the ‘same box’ phenomena that are much different from each other doesn’t sound good to me. Please discern (from below): deep leakage (if any, if conceptualized); groundwater flow; subsurface (hyporheic) flow; snowmelt. Moreover, these can be caused by highly varying flow sources. We need a strong specification of phenomena and how to consider them here. At least, we should say that there may be geological and climatic (not in the sense of climate change, but yearly-decadal climate cycle) causes. Groundwater flows and similar ones are related to the local aquifers’ geology as the main uncertainty source (see e.g., Schiavo, 2023), while the heterogeneous recharge has a negligible impact (see e.g., D’Oria et al., 2018). Snowmelt is due to yearly-decadal climatic cycles.
• As a ‘groundwater guy’, I usually think that the common ways of defining baseflow from the viewpoint of surface hydrographs partition lack precision (Cheng et al., 2022) or even conceptual correctness (Cartwright et al., 2014).
• An important point in baseflow estimation is that the structure of the aquifer is not deterministically achievable; rather than it can be assessed in a Monte Carlo framework. Hence, groundwater baseflow (or, simply, groundwater discharges) should be assessed by achieving multiple realizations upon varying geological conditions (Schiavo, 2023). Where does the role of homogeneous/heterogeneous aquifers may be appraised? At least, one should take the spatial average of the Monte Carlo runs as the most feasible discharge estimation. I think this introductory/discussion point should be incorporated into the work.
• From line 78 on: one may argue that the aridity index and the estimation of potential evaporation are ‘subjective’, hence no robust estimations are provided: how to answer this point?
• Table 1. I usually prefer to retrieve parameters from numerical calibration or so. What about the exponent b and the catchment storage capacity? How have they been inferred in the various models? If they are empirically based, do they find any confirmation in numerical applications?
• I would strongly recommend somehow connecting the baseflow estimations to previous numerical estimations; otherwise, the initial groundwater abstraction ‘lambda’ indices are pretty vaguely defined. Maybe also the work done by Zuecco et al. (2019) can be helpful.
• Another major issue is that it has been clear to the scientific community for at least 5 years that groundwater flow is highly spatially heterogeneous, as it is conveyed in preferential pathways where discharges are much higher than elsewhere. Any idea of how to incorporate this viewpoint?

Recommended references:

Cheng et al., 2022. Evaluation of baseflow separation methods with real and synthetic streamflow data from a watershed. Journal of Hydrology, 613, Part A, 128279. https://doi.org/10.1016/j.jhydrol.2022.128279

Schiavo, M., 2023. The role of different sources of uncertainty on the stochastic quantification of subsurface discharges in heterogeneous aquifers. J. Hydrol. 617 (4), 128930. https://doi.org/10.1016/j.jhydrol.2022.128930

Further reading:

Cartwright, I., Gilfedder, B., and Hofmann, H.: Contrasts between estimates of baseflow help discern multiple sources of water contributing to rivers, Hydrol. Earth Syst. Sci., 18, 15–30, https://doi.org/10.5194/hess-18-15-2014, 2014.

D’Oria et al., 2018. Quantifying the impacts of climate change on water resources in northern Tuscany, Italy, using high-resolution regional projections. https://doi.org/10.1002/hyp.13378

Zuecco et al., 2019. Quantification of subsurface hydrologic connectivity in four headwater catchments using graph theory. https://doi.org/10.1016/j.scitotenv.2018.07.269

The manuscript ‘The general formulation for runoff components estimation and attribution at mean-annual time scale’ proposes a concise MPS framework for partitioning total runoff into surface and baseflow components. The topic is timely and the presentation generally clear. With several focused revisions—mainly on scope, definitions, robustness checks, and uncertainty, the paper will be suitable for publication.

Concerns:

1. Please explicitly delimit applicability to small/medium catchments and justify the exclusion (or stratified analysis) of large basins, where digital filters can misclassify delayed stormflow as baseflow. Provide a short area-threshold sensitivity (e.g., ≤500/1,000/2,500/5,000 km²) showing effects on BFI and on MPS fits; discuss implications for scaling to large rivers (cf. recent global assessments).
2. Clarify the boundary between baseflow/slow flow and surface/fast flow. At minimum, acknowledge that baseflow aggregates multiple processes (groundwater discharge, hyporheic/subsurface flow, delayed snowmelt, and—if relevant—deep leakage).
3. Strengthen the interpretation of Wp, Vp, and Up: (1) outline hypothesized controls (soil/rock properties, storage capacity, seasonality); (2) report basic identifiability/collinearity checks (against Budyko-type indices); (3) add a cross-region transfer test (China→CONUS and vice versa) to show portability; (4) explain how to calculate the changes in parameters when attributing the variations in runoff components, such as ∆Up.
4. Discuss how known aquifer heterogeneity and preferential flow may map onto parameter dispersion (notably Vp).

Minor comments

• Unify color scales/units; add 95% confidence bands to CDF/scatter plots.
• Provide a concise symbol table (first occurrence) and standardize terminology (‘runoff components’ vs ‘flow components’; ‘baseflow/slow flow’).
• Briefly document missing-data criteria, period lengths by region, and QC steps.
• In Table 1, state whether exponents/capacities are calibrated or empirical and, where possible, cite numerical/observational backing.
• Add a short analysis or paragraph on precipitation seasonality effects on BFI and on partitioning assumptions at the annual scale.
• For the phrase ‘As for ∆𝑄 attribution’ on line 394, perhaps ‘attribution’ should be removed.