07 May 2021
07 May 2021
Realtime Tsunami Force Prediction by Mode DecompositionBased Surrogate Modeling
 ^{1}Department of Civil and Environmental Engineering, Tohoku University, AzaAoba 4681, Aramaki, Aobaku, Sendai 9808572, Japan
 ^{2}Department of Civil Engineering and Architecture, Hachinohe Institute of Technology, 881 Ohbiraki, Myo, Hachinohe, Aomori 0318501, Japan
 ^{3}International Research Institute of Disaster Science, Tohoku University, AzaAoba 4681, Aramaki, Aobaku, Sendai 9808572, Japan
 ^{4}Department of Civil and Environmental Engineering, Tohoku University, AzaAoba 6601, Aramaki, Aobaku, Sendai 9808579, Japan
 ^{5}College of Science and Engineering, Kanto Gakuin University, Mutsuura Higashi 1501, Kanazawaku, Yokohamashi, Kanagawa 2368501, Japan
 ^{6}Research and Development Center, Nippon Koei Co., Ltd. Inarihara, 2304, Tsukubashi, Ibaraki 3001259, Japan
 ^{7}Nuclear Safety Research Development Center, Chubu Electric Power Co., Inc., Sakura 5561, Omaezaki, Shizuoka 4371695, Japan
 ^{1}Department of Civil and Environmental Engineering, Tohoku University, AzaAoba 4681, Aramaki, Aobaku, Sendai 9808572, Japan
 ^{2}Department of Civil Engineering and Architecture, Hachinohe Institute of Technology, 881 Ohbiraki, Myo, Hachinohe, Aomori 0318501, Japan
 ^{3}International Research Institute of Disaster Science, Tohoku University, AzaAoba 4681, Aramaki, Aobaku, Sendai 9808572, Japan
 ^{4}Department of Civil and Environmental Engineering, Tohoku University, AzaAoba 6601, Aramaki, Aobaku, Sendai 9808579, Japan
 ^{5}College of Science and Engineering, Kanto Gakuin University, Mutsuura Higashi 1501, Kanazawaku, Yokohamashi, Kanagawa 2368501, Japan
 ^{6}Research and Development Center, Nippon Koei Co., Ltd. Inarihara, 2304, Tsukubashi, Ibaraki 3001259, Japan
 ^{7}Nuclear Safety Research Development Center, Chubu Electric Power Co., Inc., Sakura 5561, Omaezaki, Shizuoka 4371695, Japan
Abstract. This study presents a framework for realtime tsunami force predictions by the application of mode decomposition based surrogate modelling with 2D3D coupled numerical simulations. A limited number of largescale numerical analyses are performed for a selection scenarios with variations in fault parameters to capture the distribution tendencies of the target risk indicators. Then, the proper orthogonal decomposition (POD) is applied to the analysis results to extract the principal modes that represent the temporal and spatial characteristics of tsunami forces. A surrogate model is then constructed by a linear combination of these modes, whose coefficients are defined as functions of the selected input parameters. A numerical example is presented to demonstrate the applicability of the proposed framework to one of the tsunamiaffected areas during the Great East Japan Earthquake of 2011. Combining 2D and 3D versions of the stabilized finite element method, we carry out a series of high precision numerical analyses with different input parameters to obtain a set of time history data of the tsunami forces acting on buildings and the inundation depths. POD is applied to the data set to construct the surrogate model that is capable of providing the predictions equivalent to the simulation results almost instantaneously. Based on the acceptable accuracy of the obtained results, it was confirmed that the proposed framework is a useful tool for evaluating time series data of hydrodynamic force acting on buildings.
Kenta Tozato et al.
Status: final response (author comments only)

RC1: 'Comment on nhess202177', 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!

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 runup. 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.

AC1: 'Reply on RC1', Shuji Moriguchi, 19 May 2021

RC2: 'Comment on nhess202177', Anonymous Referee #2, 27 Jun 2021
Realtime Tsunami Force Prediction by Mode DecompositionBased Surrogate Modeling
By K. Tozato et al. (https://doi.org/10.5194/nhess202177)
This paper examines how tsunami impact can be predicted rapidly using mode decomposition of the results from 2D (shallowwater) propagation modelling coupled with 3D (NavierStokes) inundation modelling. The surrogate model with mode decomposition reproduces quite well the timeseries and maps of runup and impulses. The mini workflow 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 "Realtime" which, in my world, is reserved for urgent or situation computations where the process is initiated by a realworld trigger (observational data or human intervention) and that the computations are running against a realworld 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 realtime 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 3Danalysis 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 zoomin 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 lowlying 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 nonblue for the region above land – or at least a clear line indicating the pretsunami 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 (timedependent or not timedependent?) Is the matrix X timeseries 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 fullynormalized 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.)
 AC2: 'Reply on RC2', Shuji Moriguchi, 13 Jul 2021

CC1: 'Comment on nhess202177', 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 188190 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 FujiiSatake?
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 FujiiSatake 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 timedependent 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 312320). 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 316317 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.
 CC2: 'Reply on CC1', Shuji Moriguchi, 14 Aug 2021

RC3: 'Comment on nhess202177', Anonymous Referee #3, 22 Sep 2021
Comments on “Realtime Tsunami Force Prediction by Mode DecompositionBased 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, “realtime” 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 timeconsuming task and not taking into account the faulting parameter of individual event. Likewise, the term "realtime" 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. AC3: 'Reply on RC3', Shuji Moriguchi, 25 Sep 2021
Kenta Tozato et al.
Kenta Tozato et al.
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