Rapid prediction of alongshore run-up distribution from near-field tsunamis

Abstract

Rapid prediction of the spatial distribution of the run-up from near-field tsunamis is critically important for tsunami hazard characterization. Even though significant advances have been made over the last decade, physics-based numerical models are still computationally intensive. Here, we present a response surface methodology (RSM)-based model called the tsunami run-up response function (TRRF). Derived from a discrete set of tsunami simulations, TRRF can produce a rapid prediction of a near-field tsunami run-up distribution that takes into account the influence of variable local topographic and bathymetric characteristics in a given region. This new method reduces the number of simulations required to build an RSM model by separately modeling the leading order contribution and the residual part of the tsunami run-up distribution. Using the northern region of Puerto Rico as a case study, we investigated the performance (accuracy, computational time) of the TRRF. The results reveal that the TRRF achieves reliable prediction while reducing the prediction time by six orders of magnitude (computational time: $< 1$ s per earthquake).

Appendices

Appendix 1: Design of experiments

The tsunamigenic–earthquake scenarios were designed in a three-level full factorial. The level of the design of experiments (DoE) was determined based on preliminary simulations where 60 cases were considered as follows. We set a reference case where the fault parameters are as follows: $LON = 66.4^{{\circ }}$ W, $LAT =19.3^{{\circ }}$ N, $STR=90^{{\circ }}$, $DIP=20^{{\circ }}$, $RAK=90^{{\circ }}$, $LEN=90\,{\mathrm{km}}$, $WID=40\,{\mathrm{km}}$, $SLP=3\,{\mathrm{m}}$, $DEP=20\,{\mathrm{km}}$, which are the same as the central level values used in Table 1. Based on the reference case, we performed 60 simulations, varying each of the six fault parameters (LAT, LEN, WID, DIP, SLP, DEP) one at a time through a uniformly distributed array of 10 values within the parameter’s range shown in Table 1. The 60 simulations show that the second-order polynomial model, which requires at least three-level data, is enough to fit the fault parameters to the OS formula’s coefficients a and b (Fig. 16).

Fig. 16

The OS formula coefficients (a and b) variation in terms of RSM parameters: a, b epicenter latitude, c, d dip angle, e, f fault length, g, h fault width, i, j slip, k, l top-edge fault depth. The red dots represent the simulated coefficients and the black line represents the best-fitting curve based on the second-order polynomial model

Appendix 2: Sensitivity test

While developing the TRRF for northern Puerto Rico, we encountered numerical model stability issues with four simulations (0.5% of simulations) among the 729 scenarios. The stability issue occurred when the LAT is $19.6^{{\circ }}$, earthquake magnitude (LEN, WID, SLP) is relatively large, DIP is shallow and DEP is deep (Table 2). Even though it is difficult to fully interpret the reason of this stability problem, we think that one of the reasons may be that some part of the fault lies in the Puerto Rico Trench where the water depth abruptly changes, and the grid resolution used in this study may not be sufficiently resolved for the case when the fault lies in steep slopes (Fig. 2). In order to test whether building the TRRF with 725 instead of 729 simulations affected the accuracy of the TRRF, we conducted a sensitivity test as follows. We randomly chose four simulations among the 725 successful simulations. We built the TRRF with 721 simulations, where the four randomly chosen scenarios were intentionally removed. We tested this TRRF based on the 100 simulation cases used in Test 4, which were never used in developing the TRRF and whose fault parameters were selected randomly. We repeated this procedure 10 different times. The result of the sensitivity test shows that the impact on accuracy of building the TRRF without four additional simulations is negligible (the largest difference of $NRMSE =1.27\%)$.

Table 2 Fault parameter condition of four cases that shows model stability issue