Uncertainty Quantification of Landslide Generated Waves Using Gaussian Process Emulation and Variance-Based Sensitivity Analysis^†

Round 1

Reviewer 1 Report

General Comments:

This study developed a Gaussian process emulator of a Smoothed Particle Hydrodynamics  model to assess uncertainty in landslide generated waves. Maximum wave amplitude, positive displaced volume of the wave, and the empirical estimate of the run-up are selected as metrics to perform the sensitivity analyses of submergence depth, viscosity, yield stress, shear thinning exponent, etc. This manuscript is well-structured, and the results presented are promising. I recommend this manuscript to be published with minor revisions. My specific comments are as below:

Introduction: To provide a better introduction, I suggest elaborating on the effects of landslide volume, submergence depth, initial acceleration on LGW hazard. Line 93: does the “literature review” refer to [22, 23]? Please specify. Line 136: denotation “beta” is used for both slope and vector of coefficients. 4-7: the parameters do not have units. It is important to have units for all parameters, unless they are dimensionless.

Author Response

Thank you for your feedback. We are very pleased that you have recommended our submission for publication with minor revisions. Please find our responses to your specific feedback below.

Introduction: We have expanded on the specific landslide characteristics and surrounding geometry that are understood to affect the wave.

Line 136: We changed the 'beta' describing the vector of coefficients in equation 1 to a 'B' to distinguish this variable from the inundated slope angle denoted by β.

Line 93: "literature review" here refers to the references we discuss in the subsequent paragraphs. We have now also listed these references at line 93 for clarity.

Units in figures 4-7: we have added units to the input parameters in figures 4 and 5. Space is limited in figures 6-8 so we have included the list of input parameters with their corresponding units in the captions of these figures.

Reviewer 2 Report

In this paper, the uncertainty study of landslide generated waves (LGW) is carried out by using the Gaussian process emulator (GPE) and the LGW metrics are obtained by using the smooth particle hydrodynamics (SPH) simulation. The topic is interesting, but the purpose is vague. The conclusion is weak. This paper is quite difficult to understand. Followings are the reviewer’s comments.

More details should be demonstrated in Figure 1. For example, showing the symbol representing the slope angle of the beach and the symbol which represents the angle at the toe of the sliding mass would help readers to understand what the authors are talking about. Is the “beta” in Eq. (1) the same as the one in Eq. (7)? Is there only one beach sloping angle in all the SPH simulations? How many simulations were carried out? Could there be a list? What does the symbol “d” represent? Is it the same as “D” in Figure 1? Where is the maximum wave height observed? How far is it from the edge of the sliding mass? In the geometry shown in Figure 1, the two ends of the domain are vertical walls. One is in shallow water while the other is in deep water. Then what is the definition of the “run-up”? Where will the run-up show up when the mass slides? In line 136, it is said “…, beta is a vector of coefficients, …” What does that mean? Is beta a number, or it represents a series of numbers? Using bold fonts to represent matrices and vectors would help to make it more comprehensible.

Author Response

Thank you for your insightful and detailed comments on our submission. We have taken your feedback on board and made the revisions described below in response to your feedback. We believe the paper is clearer as a result.

Purpose vague: The purpose is outlined in the second and third paragraphs of the introduction. We have added a reiteration of this purpose in the conclusions to make it clearer throughout.

Conclusion: We have added a paragraph to the conclusions that discusses the implications of our findings for future studies in more detail. Specifically we talk about being able to focus computational cost on those parameters that make a large contribution to variance in the output, and discounting input parameters that consistently contribute little to variance.

Difficult to understand: We have made changes according to the specific feedback given below which we think has improved the continuity of the paper as a whole. Specifically we have extended Figure 1 and expanded our explanations of how the three different output metrics were calculated, particularly the empirical run-up estimates.

Figure 1: We have added a sketch to Figure 1 showing the relationship between the SPH simulation domain and the empirical run-up estimate. We have also added the two input parameters needed for the empirical run-up estimate to the list in Table 1. The first eight parameters in Table 1 pertain to the SPH simulations, the last two are only used for the empirical run-up estimate.

Beta confusion: We changed the 'beta' describing the vector of coefficients in Equation 1 to a 'B' to distinguish this variable from the angle of the inundated slope denoted by β. We have also ensured this vector is represented by a bold font B in the text as well as in Equation 1. The length of the vector B depends on the order of the Gaussian Process trend function (constant, linear, quadratic etc). We added a sentence in section 2.3 to this effect.

List of simulations: There were 120 SPH simulations (see final paragraph of section 2.2). A list could be provided as supplementary material?

D/d confusion: D represents the initial submergence depth of the sliding mass in the SPH simulations. d represents the maximum open ocean water depth used in the empirical run-up estimate. We have expanded Figure 1 and Table 1 so that they now show both parameters.

Max wave height observations: We calculated the maximum wave height reached during each SPH simulation seaward of the slide, i.e. the maximum height of the wave propagating in the direction of the slide motion. We have added an explanation of this at the end of section 2.2.

Clarify run-up: We estimate run-up using equation 7. We take H₀ to be the maximum wave height from our SPH simulations. d and β are treated as two additional uncertain input parameters. We therefore set bounds on these and sample the parameter space between these bounds 120 times. These input parameter samples, along with the calculated values for run-up form a new training dataset, which we can apply GPE and VBD to. We have expanded section 2.5.2 to clarify this part of our methodology.

Round 2

Reviewer 2 Report

Please see the uploaded file.

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Round 3

Reviewer 2 Report

It could be accepted now.