The authors used global data sets to analyze an impressive number of catchments in order to calculate their position on the Budyko curve. They use the results to establish correlation between the single parameter of a parametric expression of the Budyko curve and various catchment characteristics. In the discussion, the results are analyzed to provide physical explanations for some of these correlations.

Overall, the paper is sound and the analysis provides new insights, making this an interesting paper that I enjoyed reading. I would like the Introduction to clarify better the role of the parameter. The results indicate there is a temporal trend in the quality of the runoff reconstruction. I would like to see some examples of this for individual catchments, and if possible some more discussion of this.

The readability of the figures is poor because too much information is jammed in many panels comprising a single figure. Trying to read Fig. 7, I had to enlarge it so such a degree that the resolution became too coarse.  At times, the English is a bit hard to comprehend.

Carefully check the notation and explanation of all variables and make them consistent throughout. Two examples: PET and ET₀ both denote the potential evapotranspiration, and Pw and m denote the watershed characteristic parameter.

Figs. 5 and 6 present quantitative data in poorly readable color scales. But placing these in tables is not manageable because of the large number of catchments. Still, information for individual catchments would be useful. Perhaps add such a table as a supplement? Perhaps you can expand the table for annual data, so we can see the trend that you report in the aggregate in the main text for individual catchments.

Additional minor comments are given in the annotated manuscript.

This manuscript proposes a framework to estimate the parameter of a parametric Budyko-type equation. The originality compared to other studies on the same issue is the preliminary classification of the catchments.

In general, I enjoyed reading the paper and some results are very interesting, e.g. the ambiguous role of soil moisture on the evaporative ratio. There are two major comments that I think the authors should respond.

Major comments

1. Some methodological choices are not presented / enough discussed. See the exhaustive list in the minor comments below. Some key information is missing, e.g. the time step used for establishing the equations between m and vegetation fractions, and the settings of the classifier are not presented, as the output of the classification performance.
2. The added value of the classification step is not demonstrated. I suggest the authors compare the performance of the model with relationships for each group with the performance of the model when a single relationship is used for the whole catchment set. At this stage, the classification provides insights in terms of the physical processes but we cannot measure the added value of this refined description in terms of predicted runoff.

Minor comments.

l.48: Note that the climate seasonality is not taken into account in basic Budyko-type equations so the sentence needs modification, maybe change “climatic conditions” by “mean annual climatic conditions”.

Table 1: please add a column with the parameter to be calibrated, the analytical role of the parameter in the equation (increase/decrease of evaporative ratio with increasing parameter value) and it would be highly beneficial to the reader if some information on previous estimation/calibration of these parameters could be given in this table.

l.58-63: At this stage of the manuscript, it is unclear what Pw stands for. Is it an a priori estimation of the parameters that are apparent in the equations of Table 1? To make things clearer the column of table 1 indicating the free parameter could be headed Pw.

l.67-68: Does it depend on the equation? Since the statement is general and not specific to a given equation, this needs more details.

l.72: The term “contradictory” is not appropriate. There is no clear consensus but some results are relatively consensual (e.g. positive relationship between Pw and vegetation cover).

l.78: the term essential is debatable. Splitting into groups leads to non-universal laws. I agree this could lead to better performance and it is, therefore, to be tested but the motivations in terms of the physical process are not clear at this stage of the manuscript. So the term essential is in my opinion too strong and I suggest changing it to "useful".

Data section: it is unclear why data are not taken homogeneously among published datasets and GRDC. The main caveat lies in the differences in the climatic forcing data (P and PET). Why not merge the data and use a single product to derive precipitation? Also, this would allow the authors to homogenize the calibration and validation datasets that appear largely different in terms of geographic locations (and climate settings). Also, is there a criterion on the number of years of data for including a catchment in the dataset? Last, it is not clear if climatic data are aggregated over catchment areas. Do the authors delineate catchment boundaries?

l.95-96: Please indicate the formulation used for potential evaporation.

l.98-100: why not do the same for precipitation data?

l.132-133: why these three watershed characteristics? why only three? why not topographic attributes? These watershed characteristics are not stationary, do the authors change the value of these characteristics each year, or do they use aggregated statistics?

l.133-139: it is not clear how the regression tree is parametrized and optimized. Is it a supervised or unsupervised classification? As stated in lines 130-131, it seems that the authors want a supervised classification, but this would require a preliminary calibration of m. Is the number of groups imposed by the authors or it is the result of a cross-calibration experiment?

l.153-155: Not clear at this stage whether the time step is annual. Numerous studies pointed out the problems of using the Budyko-type equations on an annual time step. This should be taken into account by the authors.

l.159-168: Are the metrics computed on each catchment or all catchment runoff values? What is the minimum number of years for considering a catchment? If the record periods are too short, the resulting performance metrics might be meaningless.

l.170: In the data section, the authors present a calibration and a validation dataset, now, they say they perform bootstrapping... Is it a bootstrapping on the calibration dataset?

l.180-201: I think this should be placed in the Data section.

l.198-201: I think we can assume that the reader knows how to convert volumetric discharge to runoff depth.

Figure 2: not clear at all what is represented. FVC changes each year. Do the authors plot the aggregated FVC over the temporal range of measured streamflow? Do the calibrated m for each year or globally over the entire record period? Figure caption should detail each panel explicitly.