The Budyko hypothesis has been widely used to assess catchment water balance and hydrological response under climate change. There are several equations for the Budyko hypothesis, and it has been attracting many attentions to give more physical explanations on the parameter of those equations. This manuscript conducted numerical experiments using a vegetation optimality model and three conceptual hydrological models to understand the convergence and self-organization around Budyko curve. And it shows an interesting phenomenon that increasing precipitation increases vegetation, which leads to more evaporation. As a result of the change in vegetation, there appears a perfect Budyko relationship among P, E0, E with a constant parameter. It indicates two aspects of new understanding, i.e. on the one hand, the change in vegetation can’t be ignored when assessing the impact of climate change on runoff; and the other hand, the parameter of the Budyko curve holds constant for a special catchment although vegetation is changed due to climate change for a long term time, since the change in vegetation leads to the convergence of catchments on the Budyko curve. In addition, it falls within the scope of Hydrology and Earth System Sciences. Therefore, I recommend accepted after addressing the following issues.

1. This manuscript used three conceptual hydrological models to model evaporation under different vegetation conditions. In the current version, it isn’t clear how to deal with the impact of changing vegetation in the hydrological models. More descriptions on the parameterization of vegetation, including root depth, are required.
2. I suggest a flow chart for the experimental design, which can help readers more easily understand the design scheme.
3. It is interesting that n might initially increase in response to suddenly reduced P, and only slowly returns to into original. It is valuable to exhibit the evolution process that the parameter n slowly returns to its original, and how long it can return to its original value. In a previous study, Zhang et al. (2016, GRL, doi:10.1002/2015GL066952) found a linear relationship of n with vegetation during 1982-2011, which possibly indicates that n can’t return to its original for a 30-years period.

I agree with the authors that vegetation is a result of climate. Yang et al. (2014, JoH, http://dx.doi.org/10.1016/j.jhydrol.2014.05.062) found that the parameter n has a logarithmic relationship with catchment slope, but doesn’t have a significant relationship with vegetation coverage. I guess that vegetation is the result of climate and catchment characteristics (such as slope, topography, permeability and etc.), and consequently the relationship of n with vegetation can be contained in the relationship of n with catchment characteristics.

This study intends to bridge the gap between vegetation optimality model and Budyko framework, which is classic problem in ecohydrology. I found this study is innovative, and fits the scope of HESS. But there are still issues need to be clarified, before considering for acceptance.

1. Why did the authors use rooting depth in the vegetation optimality model? Since the conceptual models, e.g. FLEX, used the root zone storage capacity as the term in modeling. What is the relationship between the rooting depth and the root zone storage capacity? Since root zone storage capacity is a more meaningful term to describe the interaction between ecosystems and hydrology in catchment scale, like previous studies (https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2014GL061668; https://hess.copernicus.org/articles/20/1459/2016/hess-20-1459-2016.pdf), rather than their depth. I’d like to hear the authors’ thoughts. And this part needs more clarification.
2. There are lack of equations described the vegetation model. For readers who did not have enough background about this model, it is very necessary to give some equations, illustrating how the model describes the core processes. Adding a table showing the equations might be a good idea.
3. I found the experiment design are hard to follow. And the VOM and three hydrological models are not well linked. A workflow chart might be helpful.
4. The Budyko equations are not the same as we widely used. This brings in much difficulty to review this manuscript. I did not see a clear reason to use Rn rather than potential evaporation (Ep) in the traditional Budyko equation.
5. The authors conducted the study for 37 years (1-1-1980 until 31-12-2017). I am curious to know whether there were any changes during these 37 years. This needs more clarification and discussion.

Minor comments:

1. In Section 2.3.2, what does this mean “a permeable soil block with layers of 0.2 m thickness, and a total thickness of 30 m”?
2. The equations used in TUWmodel and FLEX to estimate evaporation are the same, although with a bit different term definition. That is why all three conceptual models have very similar performance. It seems not necessary to use three conceptual models in this study.