In the paper “The Role of Radial Vorticity Gradient in the Intensification of Tropical Cyclones,” the authors use a three-variable model to treat tropical cyclones (TCs) as a dynamical system, with which they explore the role of SST and vorticity gradient in the stable states of the model and examine how changes in these variables can cause rate-induced tipping. This paper provides a fresh perspective on the study of TC intensification and is worth publication after fixing the following issues.

I have the following questions and comments regarding the simple model:

1. The construction of this model is quite interesting. However, the enthalpy transport from the ocean to the boundary layer between r_{b1} and r_{b2} is not considered in the model. The enthalpy transfer in this region could contribute significantly to the total enthalpy transfer (ref 1). I hope the authors can explain why this part was excluded or how neglecting it might affect the results.

2. The four equilibrium states (unstable no wind, stable low wind, unstable mid wind, and stable high wind) are a distinguishing result of this model. My question is whether the stable low-wind state is detectable in TC simulations. Here I direct the authors to consider (ref 2), in which Figure 2 shows TC intensity jumping between two states, implying the existence of two stable states rather than the traditionally thought one stable state. Successfully linking the model with existing TC simulations could strengthen this paper.

Regarding rate-induced tipping:

1. The authors claim in the introduction that they use the model to explore eyewall replacement cycles (ERC). This should be approached with caution, as the model only includes wind speeds at two locations and is therefore unable to reveal multiple wind maxima in ERC. The wording should reflect this limitation to avoid overstatement.

2. Although the title is “The Role of Radial Vorticity Gradient…,” the focus of the paper seems to be on rate-induced tipping by various parameters (including vorticity gradient, SST, and possibly others) rather than the role of vorticity gradient itself. I suggest rephrasing the title and abstract to better reflect the real focus of the paper.

3. To make this paper more attractive to general readers, I suggest the authors add a conceptual figure explaining rate-induced tipping in TC rapid intensification, similar to Figure 1 of ref 3 but using the states of their model. This will make the paper more understandable to readers who are not familiar with rate-induced tipping.

Reference

1. Rotunno, R., and K. A. Emanuel, 1987: An Air–Sea Interaction Theory for Tropical Cyclones. Part II: Evolutionary Study Using a Nonhydrostatic Axisymmetric Numerical Model. J. Atmos. Sci., 44, 542–561
2. Ramsay, Hamish A., Martin S. Singh, and Daniel R. Chavas. "Response of tropical cyclone formation and intensification rates to climate warming in idealized simulations." Journal of Advances in Modeling Earth Systems 12.10 (2020): e2020MS002086
3. Ritchie, Paul DL, et al. "Rate-induced tipping in natural and human systems." Earth System Dynamics 14.3 (2023): 669-683.

Summary:

The authors focused on the role of the radial vorticity gradient in tropical cyclone (TC) dynamics with a low–order conceptual model. In this study, for two parameters of the vortex shape in the storm outer radii and sea surface temperature, transitions from a stable state to another stable state (linked to intensification or dissipation in TC) were examined. They found rate-dependent behavior in the simple model framework by changing the two parameters. 

General comments:

I think that the manuscript is well-organized in each part and essential behaviour of the intensity changes in TC is well captured by the simple model framework with external forcing. As mentioned by the authors, there are few researches on dynamical systems such as the present manuscript in TC literatures. Thus, the authors' work can potentially contribute to update and improvement of the understanding of dynamics and intensity changes in TCs. I recommend it is enough for publishing after minor revision. 

Minor comments:

Equation (8): The vorticity gradient is defined as the r_{b2} derivative of the \zeta_{b2}. However, r_{b2} is one point value (not continuous valiable). I consider the definition may be simply \partial \zeta / \partial r. Please clarify it. 

L315-317: The phrase "(boundary layer inflow matches troposphere outflow)" may be confused in readers. Exactly, the vertical integral of the lateral mass flux in the boundary layer is identical to that in the troposphere outflow layer. However, the speed of the boundary layer inflow is not identical to the speed of the troposphere outflow. I recommend that the phrase may need to be deleted. 

Equation (A15): The symbol of q* is better that q because the saturation is indicated by the asterisk. 

L364: Is the unit of T (temperature) "degrees Celsius"? Please clarify it.