Thank you for your response to review comments posted in the interactive discussion, which help to address issues raised by the reviewers.

However, the responses do not yet address all comments raised by Reviewer #2 and the editors, which should be considered before the final draft can be accepted. Please therefore could the authors review the following points and respond with appropriate revisions:

Editorial comment:

In addition to reviewer comments, please consider a further discussion in Section 2.3 of the choice of uniform distributions for the sampled parameters, and justification of the sampling scheme connecting sampled values of cohesion force and internal friction angle through the variable r_i.

Reviewer #2:

Please respond to the reviewer's comment "Because the cohesion and friction angle always are not uniform distributed within two limits, the proposed method is not based physically as called by the authors."

Please also expand on your response to Reviewer #2's third comment (where you say "However, cohesion and internal friction angle were determined based on the lithology map and the rock mechanical handbook, this is the reason why their distributions are different.") by including specific detail of the determination methods and data sources.

Dear Authors

Thank you for your revisions to the manuscript. There are several points where the revised manuscript does not appear to address the referees' or editorial comments in full. I would be grateful if you could please consider the following points carefully and prepare a further revision, addressing each point specifically.

Thank you.


(1) Stability condition

At line 49-50, the conditions given for stability and instability are not consistent with the definition of Fs elsewhere in the paper. Please ensure that a consistent and correct definition is used throughout the paper.

49: The safety factor of each pixel within a forecasting region, Fs (Fs=R/S: where R is shear resistance and S is the driving force) is calculated considering rainfall infiltration, pixels are then identified as unstable (Fs > 1) or stable (Fs < 1).

105: From a deterministic point of view, this physical framework can be briefly drawn as follows: for each pixel in the forecast area, if Fs ?? 1 it’s considered unstable, while pixels with Fs>1 are considered to be stable

At eqn (6), could the authors please clarify if Sum_Fs<1 is a count of the number of occurrences satisfying the instability condition, or a summation?

Line 49-50, Eqn (6), Line 249 and abstract:
Please clarify whether the failure condition is Fs < 1 or Fs <= 1, and correct the text and equation 6 accordingly.

(2) Vertical discretisation of the soil pixel

Reviewer #1 asked for a more detailed explanation of the discretization process and the authors are thanked for adding further text at Line 223-225 in Section 3.2.

The referee’s comment related to line 307 in the original manuscript “Each pixel was divided into 10 layers (along the soil depth in the vertical direction) during the discretization process.”

However, the new text at Line 223-225 refers to the discretisation scheme employed to solve for 1D water flow, which is not the issue under consideration at line 307, and essentially gives a generic description of the discretisation without adding further detail to help a reader understand how it affects the calculation of P and hence the "warning degree".

To address the referee’s comments relating to the discretisation, please revise the text again, focussing on a more detailed description of the pixel-level forecasting algorithm proposed in Section 3.3. This should:

a) Introduce and justify the choice of 10 vertical levels, commenting on the implications of this scheme with respect to regional variations in soil depth.

b) Describe how Eqn (2) was applied within step (2) of the algorithm, making explicit the mathematical connection between H_s in Eqn (2) and the soil depth within any soil layer j.


(3) Parameter uncertainty

The authors have expanded on the discussion of the probabilistic basis of the model, as requested by the referees and editor. However, the revised text does not fully address the issues raised in the discussion. Two issues that require further attention are:

(a)
Referee #2 commented that “the cohesion and friction angle always are not uniform distributed within two limits”, which the authors acknowledge may be the case in their response. However, the implications of the uniformity assumption are not explored in the paper nor in the interactive discussion. The new text at lines 129-131 appears to offer a justification of this choice (of uniform distribution) on the grounds that it was easy to implement. However, other distributional assumptions could also be implemented without great difficulty (e.g. a normal or triangular sampling distribution).

The authors are therefore requested to add further discussion of the distributional assumptions made in the paper, so that the robustness of this choice can be assessed.

(b)
The new text at lines 139-140 does not address the editor’s previous question about the role of the simulated variable r_i. Equations 3 and 4 imply that values drawn for c and phi in each sample are both dependent on a value, r_i, sampled from U(0,1). Please improve the notation to clarify whether r_i in Equation 3 and r_i in Equation 4 represent two independent samples from the U(0,1) distribution. Please also make explicit where subscript i refers to the pixel index, and clarify if c_min, c_max, phi_min and phi_max also vary from pixel to pixel.

Dear Authors,

Thank you for your revisions. Since the online discussion closed, I have received comments from an additional reviewer with expertise in statistics, who wrote regarding the simulation procedure for c and φ, as follows:

“That's an interesting approach, but I doubt very much that they want these two parameters to be perfectly correlated -- this is what they have imposed. The context suggests they want them to be independent. There is a slight chance that they have used separate uniform random variables for the two parameters, and just expressed themselves awkwardly. In this case they merely need to rephrase. Otherwise, they need to redo the analysis.”

In your latest revision, you have clarified that the simulation procedure does indeed impose correlated values of c and φ (“In the whole extracting process, each ri may have different value … but in one extracting step, the calculated ci and φi in Eq. 3 and Eq.4 use a same value of ri.”).

Unfortunately, this raises fundamental concerns about the results reported in the paper. A major revision is therefore required to address the issue raised above.

Yours sincerely,
Rob Lamb