Rapid tsunami force prediction by mode-decomposition-based  surrogate modeling

Tozato, Kenta; Takase, Shinsuke; Moriguchi, Shuji; Terada, Kenjiro; Otake, Yu; Fukutani, Yo; Nojima, Kazuya; Sakuraba, Masaaki; Yokosu, Hiromu

doi:https://doi.org/10.5194/nhess-22-1267-2022

Articles | Volume 22, issue 4

https://doi.org/10.5194/nhess-22-1267-2022

© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/nhess-22-1267-2022

© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 22, issue 4

Research article

|

11 Apr 2022

Research article |

| 11 Apr 2022

Rapid tsunami force prediction by mode-decomposition-based surrogate modeling

Kenta Tozato, Shinsuke Takase, Shuji Moriguchi, Kenjiro Terada, Yu Otake, Yo Fukutani, Kazuya Nojima, Masaaki Sakuraba, and Hiromu Yokosu

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Final revised paper (published on 11 Apr 2022)
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Preprint (discussion started on 07 May 2021)

Interactive discussion

Status: closed

RC1:
'Comment on nhess-2021-77', Anonymous Referee #1, 17 May 2021

How do you consider the impact of something being destroyed, such as a levee breach? If that impact is not considered, I don't think any good surrogate model can make predictions!

Citation: https://doi.org/10.5194/nhess-2021-77-RC1
- AC1: 'Reply on RC1', Shuji Moriguchi, 19 May 2021
  
  Thank you for your valuable comment.
  
  This study mainly aims to present a framework for instant tsunami prediction using a reliable surrogate model and to demonstrate its potential by numerical examples. As you pointed out, it is important to consider the effect of building destruction in the risk evaluation of tsunami run-up. However, as you may know, the failure of buildings caused by the tsunami force can hardly simulated in itself, since relevant numerical methods have not been fully developed yet or, equivalently, are not available. In addition, even if we had them at hand, the results would be unreliable in most actual situations because the input parameters and analysis conditions involve lots of uncertainties. If the validity of the calculation results cannot be guaranteed, the corresponding surrogate model does not make sense. Therefore, we think that this is hardly the time for considering the effects of the building destruction in the proposed framework. Nevertheless, continued challenges must be tackled both in simulating failure due to the tsunami force and in constructing a surrogate model in consideration of the simulation results. These are left to future work.
  
  Citation: https://doi.org/10.5194/nhess-2021-77-AC1
RC2:
'Comment on nhess-2021-77', Anonymous Referee #2, 27 Jun 2021

Real-time Tsunami Force Prediction by Mode Decomposition-Based Surrogate Modeling

By K. Tozato et al. (https://doi.org/10.5194/nhess-2021-77)

This paper examines how tsunami impact can be predicted rapidly using mode decomposition of the results from 2D (shallow-water) propagation modelling coupled with 3D (Navier-Stokes) inundation modelling. The surrogate model with mode decomposition reproduces quite well the time-series and maps of run-up and impulses. The mini work-flow of how the mode decomposition surrogate model is clearly presented in Figure 1. What is a little more unclear to me is the overall workflow and purpose of the work. The title uses the term "Real-time" which, in my world, is reserved for urgent or situation computations where the process is initiated by a real-world trigger (observational data or human intervention) and that the computations are running against a real-world clock. Is this the case? Otherwise, "Rapid" is probably a better term – that indicates fast computation.

With regards to the total workflow, is it the intention that the full numerical simulations are calculated beforehand and the surrogate model saved for application when a new tsunami event occurs? Or are all the calculations performed in a new event and the surrogate model used to interpolate the outcome to different parts of the parameter space to those calculated in the 2D/3D simulations?

In any case, there will be a significant variability of the tsunami impact as the source parameters vary (c.f. Table 1) – how is the decision made as to which are the appropriate parameters to be looking at when interpolating the predicted impact using the surrogate model? Is it by real-time comparison between observations and predictions?

Answering the above questions in the paper would help enormously in making the context of these calculations clear.

What exactly do the "data vectors" in Equation (8) contain? ("data arranged according to a certain rule") – is it wave heights at the different grid points? Velocities? It would be useful to know which values are stored for each grid point (h,ux,uy?)

Can you comment on the boundary between the 2D analysis and 3D analysis?

It is typical to specify a given water depth at which the 3D-analysis would take over but the line indicated in Figure (6) cuts across a bay very close to the inundation area with very shallow water on each side. How does the transition from 2D to 3D happen on such a boundary? Would it have been feasible to take the boundary further out to sea?

In Figure 8, it would be helpful to have an indication of scale on each of the panels. Is each panel a zoom-in of the previous panel? Does Figure 12 show us something fundamentally different to Figure 8? If so, it would be very valuable to know what is fundamentally different. It looks like there are triangular elements in Figure 12 but not in Figure 8. Is this significant?

In Figure 7, the colour scheme is a little unfortunate with low-lying areas coloured in blue. Whenever I see this Figure, I assume that I am seeing tsunami inundation with the blue areas representing the region with inundation. Would it be possible to have blue at sea level and below and non-blue for the region above land – or at least a clear line indicating the pre-tsunami coastline?

The confusion continues into Figure 9 where I guess it is the white which represents the inundation.

It would be nice to have the link to the inundation height observations in the caption to Figure 10. This is for the journal to decide I guess.

Is the data matrix X in Equation (19) the same as the data matrix X in Equation (8)? I am guessing not as I see the matrix in Equation 8 being a spatial discretization of simulation parameters (time-dependent or not time-dependent?) Is the matrix X time-series for a single metric at one point evaluated for different slip and rake as a function of time? What about the X in Equation (8)? This is something evaluated for many points. I think all of this needs clearing up.

What is the quantity we are seeing in Figure 13? It goes from 1 to -1 – it is a fully-normalized data vector? So there is no direct physical interpretation of these numbers? This should be made clear in the figure caption.

There are very many figures and I think a lot of care needs to be taken to make it clear in the caption what is different for each figure from similar figures. (e.g. Figure 17 has a map with the locations of evaluation points and we do not see until Figure 26 where these are applied. There are 29 figures in total and I would ask as to whether all are necessary. The reader struggles to understand the significance of each of them. (e.g. Figure 28 and 29 are almost identical – we get the point.)

Citation: https://doi.org/10.5194/nhess-2021-77-RC2
- AC2: 'Reply on RC2', Shuji Moriguchi, 13 Jul 2021
  
  Thank you for your valuable comments. Our responses are summarized in attached PDF file. We would like to prepare revised manuscript in consideration of the review comments.
  
  Citation: https://doi.org/10.5194/nhess-2021-77-AC2
CC1:
'Comment on nhess-2021-77', Randall LeVeque, 05 Aug 2021

This paper contains a very interesting analysis and you have obtained some impressive results. Here are a few comments / suggestions that I hope might be useful.
There were a few things I was confused about regarding the mathematical description of the algorithm that perhaps you could clarify:
In forming the covariance matrix (9), I guess you are assuming that the columns of X have already had their means subtracted?
In line 121, j=1,...,n should be j=1,...,N I think? and also in the summation in the denominator of the equation on line 126 it should be N not n.
In line 138 where you say C and C' have common eigenvalues, I think in general they have a different number of eigenvalues, but any excess ones are all zero. You never make it clear how many rows the matrix X has in this section, i.e. the number of observations, but I guess this is greater than N

in general so that C is a larger matrix than C'?
In line 156 do you mean only the coefficients $\alpha_{ij}$ for j=1,..,r not for j=1,...,p ? I guess so from (16), but worth clarifying. So f(\beta) in general is a vector of length r.
In this paragraph why do you use subscript j rather than k as used in (15) and (16)?
In (17), I think the \exp(...) after the second = sign should be

= \sum_{i=1}^N w_i \exp(...)
At first glance (18) seems to be a square N by N linear system so it seems no regression is needed, so maybe it's worth pointing out that it is really Nr by N since f(\beta) has length r.
Lines 188-190 weren't clear to me. Maybe say the slip was varied from 0.7 to 1.4 times the original slip in the model of Figure 2. When I first read this I also thought you were varying the rake between -20 and +25 degrees, which would be wrong for a subduction event, so maybe also make it even clearer that these are the range of perturbations in the rake angle from the ones given by Fujii-Satake?
In Figure 5 the cyan lines for the Obs. are very hard to see, maybe make these lines black or red?
Line 209, by "concrete connection method" I think you mean the method for coupling the 2D and 3D methods together, but this was confusing to me at first. Maybe say something like "To couple the 2D and 3D models together, the method used in the study of Takase et al (2016) was employed." (By "concrete" I think you mean the specific method employed here, and it might be better to use "specific" here and some other places. Since in English concrete is also a building material, and you are talking about forces on buildings, there could be some confusion.)
Line 231, discussing the 2D mesh used for evaluating the tsunami force: do you average (or sum?) the force over all vertical building faces that happen to lie in the 10m cell? It seems like this would vary a lot from cell to cell just based on the particular geometry of the buildings. In particular some cells might include no walls and hence have 0 force (?) while neighboring cells might have one wall or perhaps at the corner of a building a cell has two walls. So I'm surprised the plots of forces look as smooth as they do and perhaps you can say more about this?
It is great that you can get a surrogate model that reproduces the time evolution as well as it does, in addition to the spatial patterns. But I wonder if this is mainly because you are only considering perturbations to the Fujii-Satake model in which the basic spatial structure of the fault slip is always the same and so the time evolution shows similar sets of waves and arrival times, just somewhat varying magnitudes? The results are still impressive, but I wonder if you can comment on how this might be extended to developing a surrogate model that could be useful in real time for some earthquake that is not a small perturbation of 2011 (which the next big one almost certainly won't be).
To develop a surrogate model that would handle a greater variety of quakes, perhaps it would be necessary to give up on trying to model the full time-dependent solution and instead build a surrogate model that only attempts to predict the maximum inundation depth and force, which might be much easier to do and still very useful.
I don't understand some of the discussion in the paragraph just below Table 2 (lines 312-320). You say "the ratio of mean values was 434%...". I think a ratio should just be a number, not a percent. Do you mean the ratio was 4.34? And what mean values is this the ratio of? Is it the ratio of the error to the true result, i.e. the relative error? This isn't clear.
Maybe this would be clearer if you included also tables of the raw numbers you are comparing, it's not clear where these numbers come from or how they relate to Table 2.
In line 316-317 you give ratios like 0.78%. Again I'm not sure what you mean by a ratio as a percent, do you mean the ratio of error to true value is 0.0078?
In spite of my questions and possible confusion, in general I like the paper and believe it should be published after some clarifications.

Citation: https://doi.org/10.5194/nhess-2021-77-CC1
- CC2: 'Reply on CC1', Shuji Moriguchi, 14 Aug 2021
  
  Thank you for your valuable comments and kind suggestions. Our responses are summarized in attached PDF file.
  
  Citation: https://doi.org/10.5194/nhess-2021-77-CC2
RC3:
'Comment on nhess-2021-77', Anonymous Referee #3, 22 Sep 2021

Comments on “Real-time Tsunami Force Prediction by Mode Decomposition-Based Surrogate Modeling” by Kenta Tozato et al. submit to the journal of NHESS. The authors tried to estimate the hydrodynamic force of tsunami acting on building through 2D and 3D FEM. The paper is interesting, and from my personal point of view, the topic of this manuscript fits well with the scope of the journal of NHESS. There are too many figures (snapshots), however few explanations and not ready. Animations or supplementary files may be attached to improve readability. Some other major issues are listed below:

1. One faulting model of Tohoku Earthquake 2011 is used in this study, however but it may not (and should not) be reactivate at the same location and did not have the same magnitude. So it cannot be applied to other events, nor can it "predict" damages. Therefore, “real-time” tsunami force predictions may not be useful because the events of 2011 have already occurred. The term "real time" may change with the reassessment of the power of the tsunami...

2. The method proposed by the authors is a time-consuming task and not taking into account the faulting parameter of individual event. Likewise, the term "real-time" may not be a suitable term.

3. There are too many figures, but similar…, need to be simplified. The wording of the manuscript should be further elaborated so that the reader can understand what the author wants to express, regarding to the figures.

4. Many figures is not ready, and some parts can be unified. E.g. Fig 6, 7, 8, 11, 17 etc.

Citation: https://doi.org/10.5194/nhess-2021-77-RC3
- AC3: 'Reply on RC3', Shuji Moriguchi, 25 Sep 2021
  
  Thank you for your valuable comments. Our responses are summarized in attached PDF file.
  
  Citation: https://doi.org/10.5194/nhess-2021-77-AC3

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

ED: Reconsider after major revisions (further review by editor and referees) (14 Oct 2021) by Paolo Tarolli

AR by Shuji Moriguchi on behalf of the Authors (26 Oct 2021) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (10 Nov 2021) by Paolo Tarolli

RR by Anonymous Referee #3 (17 Nov 2021)

RR by Anonymous Referee #4 (30 Jan 2022)

Suggestions for revision or reasons for rejection

This paper provides a reduction of the computational cost of a 3-D simulation of tsunami impacts using a surrogate model. The modelling in 3-D is interesting, and the need to use surrogate modelling is justified to explore many scenarios in probabilistic warnings. The POD method is used to create the surrogate, with some benefits and shortcomings. Overall, after the improvements suggested below are taken into account, I am supportive of publication since there is a need for such work.

The main points:
1. The literature review is inadequate.
There are too few references on the relevant past work on surrogate modelling (also known as emulation or meta-modelling or response surface). Please cite several papers (say 5-6?) with various settings (e.g. parameters ranges of earthquakes/landslides sources or other uncertain parameters such as roughness, applications to faster than real time early warning or hazard assessments) for tsunami emulation. There are papers on this topic in NHESS and other journals in the last five years or so, I let the authors decide which ones to cite and comment on to contrast with their approach. Please discuss them a bit to help the reader situate your work. In particular, the mainstream method of Gaussian Process (GP) emulation to create surrogates is powerful as it provides uncertainties and allows for high nonlinearities, so must be mentioned and discussed, as these generalise in some way equation (17) in this paper.
Remove the sentence and references "LeVeque et al. (2016) and Melgar et al. (2016) utilize the Karhunen–Loève expansion to consider the distribution of slips on a fault under various scenarios" as these are irrelevant here and the sentence is out of place.
The other references are relevant and fine to keep.

2. Section 2.3 needs a bit of clarification. line 167 should be "input parameters beta:". The error in equation (18) is not mentioned, but it is present as it is a regression equation and should be in the equation. Line 1801-182 more details are needed on what cross-validation is used, why a Bayesian optimisation if used and how.

3. Table 1 and 4. Conclusion: The design used is a grid, which is much less efficient than Latin Hybercubes or sequential designs for GP emulation, or sparse designs for Polynomial Chaos surrogates: nobody uses a grid anymore to construct emulators. A reference to more efficient methods, ideally in tsunami emulation/surrogate context is needed. The study would have greatly benefited from a better design using the same computational budget.

4. Performance is explored on the 10 cases of +_10 deg rake. This are quite central so may not represent the whole range of inadequacies of the surrogate. Usually a leave-one-out diagnostic is performed and would not cost much here as there is no need for any more simulation. It would show a better picture than this narrow set of scenarios that might be rather easy to predict.

5. Please discuss more the sometimes 50% differences between model and surrogate utputs in fig 18-19: these could be very local aspects of topography that cannot be captured by a global POD approach that assesses the overall variability. This is one major deficiency in this application, so needs to be acknowledged. Please check the relative errors of 400% as they do not seem to match the figures: these should be around 50% max.

Minor points:
1. how do you extract spatial modes in Fig 11 across times and temporal modes in line 274? A bit more clarity about the role of time is needed in the text.

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ED: Publish subject to minor revisions (review by editor) (21 Feb 2022) by Paolo Tarolli

AR by Shuji Moriguchi on behalf of the Authors (03 Mar 2022) Author's response Author's tracked changes Manuscript

ED: Publish as is (04 Mar 2022) by Paolo Tarolli

AR by Shuji Moriguchi on behalf of the Authors (07 Mar 2022)

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Short summary

This study presents a novel framework for rapid tsunami force predictions through the application of mode-decomposition-based surrogate modeling with 2D–3D coupled numerical simulations. A numerical example is presented to demonstrate the applicability of the proposed framework to one of the tsunami-affected areas during the Great East Japan Earthquake of 2011.