Technical note on incorporating natural variability in master recession curves

The paper focus on incorporating natural variability in master recession curves. It is of great significance for recession analysis. The topic has received much attention in recent years. However, there are still many key issues that need to clarify.

Firstly, there has been a great development of methods for streamflow recession analysis, and there are many alternatives to the correlation method, so why not consider other more popular and sophisticated methods, such as recession analysis based on -dQ/dt~Q. Secondly, the correlation method faces challenges on applications, such as the observation noise in streamflow bring large uncertainty for the calculation of K, especially during low flow period, the inability to consider the continuous recession process by mainly only using the information from the adjacent days. Further, the appropriateness of generating MRCs with frequency from the percentiles of the distribution of K has not been adequately demonstrated. Thus, the robustness of the correlation method and the rationality on computed MRCs at different frequency are needed.

Detail comments:

Lines 11-13. How about the other three catchments?

The section of Introduction. It is hard to catch the key points.

Lines 34-54. This paragraph suggests a tabular presentation. More introduction on the research of the natural variability of recession processes is suggested.

Line 64. How to use the correlation method to compute MRC is not clear. More details are needed.

Figure 1. More evidences or refences are needed to justify kmax.

Line 86. What is the mean of ‘ile’. Is it percentile?

Figure 3. How is the starting point of the MRC determined and how is the observed recession superimposed on the calculated MRC?

This technical note presents a concept that the master recession curve (MRC) is time-variable. While the manuscript introduces some interesting ideas, the ideas and their novelty are not fully described and developed to a degree that would warrant publication at this stage. The current manuscript is difficult to follow, and the ideas need to be better organized and streamlined. Thus, I recommend rejection.

Major Comments

1. Unclear Novelty and Lack of Litureature Review

The novelty of the manuscript is unclear. Numerous previous studies have discussed the time-variability of flow recession dynamics. As the authors themselves note, ‘an MRC represents the average rate of decline in streamflow,’ implying that the MRC characterizes the representative behavior of a catchment. Therefore, it is not surprising that individual flow recession events may deviate from the MRC. Uncertainty associated with the MRC has also been widely discussed in the literature. Furthermore, the authors appear to suggest that the MRC itself is time-variable; if this is the case, the definition must first be clarified—particularly since it is unclear whether it should still be referred to as a ‘master’ recession curve.

As previously noted, many studies have addressed the uncertainty related to the MRC, either directly or indirectly, within the broader literature on recession analysis, even if the term ‘master recession curve’ was not always explicitly used (e.g., Kirchner, 2009). As indicated in Lines 209–212, Gao et al. (2023) considered the uncertainty (see also Thomas et al., 2015). Although a difference from Gao et al. (2023) is briefly mentioned, it is not sufficiently developed to convincingly establish the uniqueness of the current study.

The discussion of related work appears too late in the manuscript (e.g., Gao et al., 2023, in Lines 209–212) or is missing entirely (e.g., Thomas et al., 2015). A more thorough and critical literature review should have been presented in the Introduction. The current review in Lines 27–44 is too brief and merely lists previous studies without offering sufficient critical analysis. A deeper review—incorporating Gao et al. and other relevant studies addressing similar aspects—should be integrated earlier in the manuscript to better contextualize the research.

Thomas, B.F., Vogel, R.M., Famiglietti, J.S., 2015. Objective hydrograph baseflow recession analysis. J. Hydrol. 525, 102–112.

Additionally, accounting for losses in flow recession dynamics is not a novel concept; see, for example, Wang and Cai (2009).

Wang, D.; Cai, X. (2009) Detecting Human Interferences to Low Flows through Base Flow Recession Analysis. Water Resources Research

In the discussion, the authors employ a two-bucket model, which is commonly used in the flow recession literature; however, relevant previous studies are not referenced. See Gao et al. (2017) for example.

Gao, M.; Chen, X.; Liu, J.; Zhang, Z.; Cheng, Q. (2017) Using Two Parallel Linear Reservoirs to Express Multiple Relations of Power-Law Recession Curve. Journal of Hydrologic Engineering.

2. Regarding the transmission loss

The authors appear to emphasize transmission loss; however, it is unclear whether transmission loss can be adequately assessed using discharge data alone, based on the reasoning provided in the manuscript. In Lines 60–62, the authors argue that transmission loss is reflected in the deviation of the MRC (which can be estimated from the data) from the recession behavior the catchment would exhibit in the absence of transmission loss—though there is no guarantee that such a reference curve can be reliably determined from the data. Throughout the manuscript, it also seems to be implicitly assumed that a catchment without transmission loss would necessarily follow linear reservoir behavior, which requires further clarification and justification.

Furthermore, the assumption that a faster flow recession than exponential decay (as predicted by linear reservoir theory) is necessarily attributable to transmission loss is not well justified. Is this merely an assumption? Are there no other possible explanations for observing a steeper decline in discharge besides transmission loss?

Moreover, the emphasis on transmission loss appears to diminish as the manuscript progresses, with greater focus shifting toward the role of initial conditions at the onset of flow recession. Although the authors seem to attempt to link these two aspects, the connection is not fully developed and is difficult to follow (e.g., Lines 261–263).

3. Method

The method introduces certain criteria and parameters without providing sufficient justification or clear explanation. Some examples are outlined below.

• Criterion 2 (Line 117) — It appears that the authors exclude all recession events that do not exhibit a ‘maximum recession constant’ midway through the recession. It seems that the authors have chosen to focus on a specific subset of events, but this decision is not well explained in the manuscript. In addition, this criterion could potentially exclude a large number of recession events across many catchments. Therefore, it should be introduced and justified much more carefully. Also, this criterion appears to implicitly rely on the linear reservoir theory. It is unclear why such a model should be adopted in this context.
• The various criteria for selecting recession periods are scattered across the manuscript and should be consolidated and explained earlier.
• Several choices—such as excluding periods where dQ/dt = 0 (Lines 127–128) and applying a minimum duration threshold—are not adequately justified. For instance, by excluding periods with dQ/dt = 0, the authors may unintentionally bias the analysis toward steeper portions of the recession, particularly when flows are low and measurement resolution becomes an important consideration.
• The number of selected events are too small; it is unclear whether meaningful statistical analysis is possible (Table 1).

Additionally, the method is not described clearly enough for readers to follow easily. See below for some examples.

• The correlation technique is not sufficiently explained; the reader should not be required to consult external sources.
• Manual allocation (L163–170) is poorly described and hard to follow.
• It is unclear how starting points in Figure 3 were chosen.
• Some figure descriptions conflict with the figure contents (e.g., general wet/dry periods in Figure 4).

Minor Comments

• L46–53: This paragraph appears intended to describe applications, but the content within the parentheses following Nathan and McMahon, and O’Brien, discusses methods or techniques rather than applications.
• L51: It does not seem appropriate to discuss “residence time” based solely on recession analysis.
• L62: Is transmission loss the only possible explanation for the observed deviation? On what basis is this claim made? Is it an assumption?
• L66: The reference to “the above limits” is unclear—what limits are being referred to?
• L67: This step seems to be clearly explained within this manuscript rather than referring readers to another study.
• L75: The term “traditionally” is used multiple times, but it is unclear what specific tradition is being referenced. There are various interpretations of the master recession curve (MRC) in the literature. The authors should clearly define the version of the MRC they are using rather than relying on the vague notion of a traditional definition.
• L84: The meaning of “sub-storages” is unclear.
• L92: The phrase “stochastic process rate” is ambiguous.
• L164: Clarify what is meant by “the value of the observed daily recession.”
• L193: What is meant by “the minimum that can be estimated under field conditions”?
• L210–212: The discussion of previous results is not well handled, and the rationale for the authors’ interpretation is not sufficiently explained.
• L216: The statement here is very unclear and needs clarification.
• L222–228: Either Figure 4 or the corresponding description seems to be inaccurate. It is unclear what is meant by “general wet and dry periods.”
• L227: It is questionable whether the phrase “near identical” is necessary or helpful in this context.
• L231-232 “initial climate condition”: I guess it is not “initial climate condition”.
• Definitions of terms such as “aleatory uncertainty” and “epistemic uncertainty” are unclear or appear to be misused.