Overall, the paper is well written, but I would recommend providing more details to facilitate understanding of the mathematical steps that, although formally correct, are not so obvious, at least to a reader of NHESS. Steps need to be clearly explained even at the cost of some verbosity.

In addition, given the diverse expertise of potential readers, a more extensive explanation of the physical meanings of the variables used in individual equations would be appreciated.

Regarding the theoretical framework, an event size-dependent depletion in analogy with the case of wildfires (Drossel-Schwabl forest-fire model) is innovative and interesting, but would require a stronger phenomenological/physical hypothesis. It is worth explaining why should larger landslides behave like burned areas, the extent of which depends on the interaction of individual adjacent spatial units. 

Minor revisions are in the attached file.

The authors develop a theoretical framework to explain event size dependent exhaustion. They propose a mathematical formulation for the decline of big events capturing statistical behavior of self-organized criticality with a simple cellular automaton forest fore model (DS FFM) as an example. Next, the authors apply this framework to rockslides.

This is an interesting concept and I believe the paper can be of added value to the rockslide/landslide community but only after considering the following points:

1. The mathematical derivations at the heart of this manuscript are, at several points, difficult to follow. I provide some line comments below, but in a more general sense, the text would highly benefit from clear and structured explanations for every assumption made, equations proposed, and parameter values chosen.
2. The model is tested/validated using a very limited dataset with observations. This is almost certainly an incomplete dataset restricted to a relatively small area (on a global scale). The implications of the limited dataset used here should be discussed thoroughly and implications for model accuracy and robustness in general should be made. Also, a reflection should be made on the validity of this framework and SOC models in general. Are rockfalls following self-organized criticality and why is that? Is the mechanism that explains rockfall size similar to the mechanisms that explain forest growth and decay. Some reflection on spatial correlation of rock properties is needed here. Is there potential to scale this exercise up to larger (global) scales?
3. The mathematical framework is proposed as a useful test for larger scale models such as a model published by the same author. Explicit comparison of modelled rockfall (Hergarten, 2012) with this framework in a dedicated section would illustrate this concept more clearly.

Line 27: can be excluded for these two rockfalls

Line 54: Do you mean that a system which exhibits SOC develops an equilibrium between slowly but continuously evolving versus rapid discrete event-based processes? Please clarify

Line 77: nearest-neighbor connections: does this imply only cardinal cells on a square lattice?

Line 96: The overall behavior of the DS FFM simulations is compelling, but I am wondering (i) why the excess occurs at 1e5 and (ii) why the rapid decline and deviation from the power law scaling relationship occurs after. I do not agree it is not relevant here. The fact that this figure will be published warrants explanation for this deviation, regardless of whether it is relevant for the subsequent rockfall analysis. Has this to do with the dimensions of the grid or boundary conditions?

Line 110 describe lambda (add symbol in sentence above)

Line 113: here and at several points: it’s always better to guide the reader a little through the math. Makes the manuscript way more accessible. Here e.g. mention integration and boundary conditions to solve eq. 3

Line 118: Not clear how this is a cumulative formulation. In the given formulation, psi declines for increasing values for s. For a cumulative pareto function, I would expect something of the form 1 – (s_max/s)^alpha. Explain this better. Also, for these and following variables mention realistic parameter value ranges (in the context of rockfall)

Line 120 : definition n is not clear

Line 151: “μ (Eq. 1) is the decay constant” This is not clear.

Line 154: What should that be expected?

Line 155-156: This should be derived and explained much clearer. It is not clear at all to me why this results in respectively 2/3 and 1/3.

Line 162: This is almost certainly an incomplete dataset. How is this influencing the calibration of the model?

Line 178. The derivation of the maximum likelihood is essential to understand figure 4. I recommend including the appendix in the main manuscript. Also on Figure 4: alpha_v is a function gamma (eq. 15). It is unclear how alpha _v and gamma are plotted as (independent?) variables. How is gamma varied for the same value of alpha _v? By changing alpha?

Line 319: why is the likelihood given by the Poisson distribution?

Line 192: not clear how the t0 lines are obtained. More detail is highly needed here.

Line 214: again, does gamma depend on alpha_v (eq 15?)

Line 216: yet another distribution. Explain why this distribution is used. Also explain the symbols…

Line 216 – Line 222. I do not understand what the author does here. Please break this down into clear and understandable pieces, referring to the symbols used in the distribution equation.

Line 234-235: that is, if this model that is calibrated with relatively few datapoints is true.

Line 249 Despite

Line 250: See earlier comments on line 155

Line 254: This is interesting. I recommend giving an explicit example where the author’s earlier modelling work is evaluated using this theoretical framework e.g. for one specific site.

Line 266: True: which is why a clear explanation on how the t0 lines were derived is needed.

Line 275: is this because the topographic configuration does not allow for large rockfalls to materialize?

Line 298: I highly recommend illustrating this with a specific example, see also comment above.