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The manuscript titled addresses the challenge of accurately estimating the segment length parameter (N) for the Smooth Minima Method (SMM) in baseflow separation. By employing Symbolic Regression (SR) on a dataset of 855 catchments across the Contiguous United States, the authors aim to overcome the limitations of fixed default values or simple power-law functions traditionally used in the literature. The study successfully identifies three interpretable mathematical expressions that link parameter N to catchment area, saturated hydraulic conductivity, and snow day fraction. The validation results demonstrate that the SR-derived formulas significantly improve predictive performance (improving R2 from 0.23 to 0.54) and achieve higher Kling-Gupta Efficiency in baseflow separation compared to existing methods. Additionally, the use of Specific Electrical Conductance (SEC) mass balance serves as a robust independent validation of the proposed regionalization approach. Overall, this work provides valuable insights into the physical controls of baseflow processes and demonstrates the utility of interpretable machine learning in hydrology.

However, I have several concerns regarding the physical consistency of the derived formulas, the justification for choosing SR over other methods, and the robustness of the performance evaluation thresholds. These issues, along with comments on terminology and methodology, are detailed below.

1. The abstract states that “N increases exponentially with catchment area...”. However, the derived formulas are power-law functions, not exponential functions.

2. The introduction of SR in the current manuscript is relatively brief (lines 61-71). While the authors highlight the interpretability of SR compared to Random Forest (RF), there is a lack of review regarding the application of SR in the broader field of hydrology. It would strengthen the rationale of the study if the authors could briefly mention successful applications of SR in other hydrological contexts (Chadalawada et al., 2020) before narrowing down to baseflow separation. This would demonstrate that SR is a proven tool in the domain.

3. The Introduction highlights the role of environmental tracer data in parameter optimization (Line 48) but lacks specificity. I suggest briefly listing common tracers, specifically including SEC, in this paragraph. Since the reference dataset used in this study is SEC-optimized (as detailed in Section 2), explicitly mentioning SEC early on would provide the reader with necessary context regarding the physical basis of the ground truth parameters.

4. The statement in Line 84 that optimal N shows “no clear spatial patterns” is ambiguous, particularly since the subsequent analysis links N to spatially structured attributes. I suggest clarifying this phrasing to avoid apparent contradiction.

5. Section 3.1 describes the parameters N and M well but briefly lacks a description of the algorithmic procedure. Adding one or two sentences explaining how the method iterates (e.g., dividing the hydrograph into blocks of N days, identifying minima, and comparing adjacent minima using M) would make the method section more self-contained.

6. In Section 3.2, the manuscript does not specify whether the input variables (catchment characteristics) were normalized or standardized prior to SR training. Based on the discussion in Section 4.1 (where specific thresholds like A < 100 km2 are mentioned), it implies that raw data with physical units were used.

If raw data were used, the term \left(A+K_{sat}\right) in Formulas F_2 and F_3 is dimensionally inhomogeneous, adding Area (L^2) to Hydraulic Conductivity (L/T). This makes the formula valid only for the specific combination of units chosen in this study (km2 and mm/h) and undermines the claim of physical meaningfulness.

Even if the variables were normalized (rendering them dimensionless), the authors should interpret the physical meaning of the additive structure \left(A+K_{sat}\right). This structure implies a direct substitutability between catchment size and soil permeability in generating baseflow delay. What is the hydrological justification for this specific interaction form, rather than, for example, a multiplicative interaction \left(A+K_{sat}\right) which is more common in hydraulic process laws?

7. Section 3.2 outlines the SR setup but omits key hyperparameters required for reproducibility, such as population size, number of generations, and mutation/crossover rates used in the PySR configuration. I suggest including these details, perhaps in the Appendix.

8. The legend in Figure 7b includes categories like F_1&F_2, implying a tie in performance. However, the manuscript lacks an explicit definition of the threshold used to categorize these ties (e.g.,\Delta R^2<0.02?). Crucially, the choice of this threshold is intrinsic to the discussion on the complexity-accuracy trade-off (Section 5.3). A strict threshold (e.g., \Delta R^2=0) favors complex models F3 even for negligible gains, while a practical threshold (e.g., \Delta R^2<0.01) might reveal that the simpler F1 is good enough for a much larger portion of the CONUS.Therefore, beyond simply clarifying the current threshold, I suggest the authors perform a brief sensitivity analysis on this threshold. For instance, how does the spatial pattern of the best formula change if the tolerance for a tie is set to 0.01 vs. 0.03? This would provide a more robust and transparent visualization of where the added complexity of F3 yields substantial benefits versus marginal statistical gains.

9. In Section 5.1, the manuscript motivates the use of SR by contrasting it with the black box nature of RF. I suggest the authors provide a more precise definition of what constitutes interpretability in this context.

In hydrological literatures (Chen et al., 2022; Guillon et al., 2020), tree-based models are often considered interpretable via tools like SHAP values, which can quantify driver-response relationships much like the derivatives in SR. Given the significant drop in predictive skill (RF R2=0.80 vs. SR R2=0.54), it would be helpful to clarify why the explicit mathematical form of SR is preferred over the higher accuracy of RF. Is the interpretability here strictly defined as having a closed-form equation? A brief discussion about the definition of interpretability would provide a more balanced perspective.

References

Chadalawada, J., Herath, H.M.V.V., Babovic, V., 2020. Hydrologically Informed Machine Learning for Rainfall-Runoff Modeling: A Genetic Programming-Based Toolkit for Automatic Model Induction. Water Resour. Res. 56, e2019WR026933. https://doi.org/10.1029/2019WR026933

Chen, Y., Li, D., Zhao, Q., Cai, X., 2022. Developing a generic data-driven reservoir operation model. Adv. Water Resour. 167, 104274. https://doi.org/10.1016/j.advwatres.2022.104274

Guillon, H., Byrne, C.F., Lane, B.A., Sandoval Solis, S., Pasternack, G.B., 2020. Machine Learning Predicts Reach-Scale Channel Types From Coarse-Scale Geospatial Data in a Large River Basin. Water Resour. Res. 56, e2019WR026691. https://doi.org/10.1029/2019WR026691