10:45 AM - 12:15 PM
[HDS06-P10] Consideration of tsunami nonlinearity in numerical tsunami simulation: Case study of the 2016 Mw 6.9 off-Fukushima earthquake
Keywords:Tsunami, Tsunami propagation, Nonlinearity, Energy dissipation
Background
Recently, it has been reported that the tsunami nonlinearities sometimes strongly affect the first cycle portions of coastal tsunami waveforms. Tsushima et al. (2022, JpGU) conducted numerical tsunami calculations for the 2016 Mw 6.9 off Fukushima earthquake and showed that the nonlinear long wave (NLL) simulation can reproduce the first parts of coastal tsunami waveforms, whereas the reproducibility got worse when using the linear long wave (LLW) equation: for example, the tsunami amplitude at station Onahama is overestimated more than 1.5 times. Yamanaka and Tanioka (2022, SSJ Fall Meeting) performed tsunami simulation for the 2003 Mw 8.3 Tokachi-oki earthquake and showed that the first parts of coastal waveforms are distorted due to the nonlinearities, that the contribution of advection is stronger than that of bottom friction, and that the advection works significantly at breakwater openings in the ports.
This study focuses on the following feature seen in the case of the 2016 off Fukushima earthquake: at tide gauge station Onahama the first tsunami amplitude becomes small in the NLL simulation, compared to in the LLW simulation. If the main factor of the amplitude reduction is bottom friction, it means that bottom friction also has strong effect on the first part of coastal tsunami waveforms as well as advection. In contrast, if advection is dominant, a new question will arise as to why the amplitude is reduced by advection not involving physical dissipation. To clarify it, I conducted numerical tsunami experiments of the 2016 off Fukushima earthquake.
Method
I used numerical tsunami model JAGURS (Baba et al., 2015) to solve the NLL equation with bottom friction and/or advection, and LLW equation. The slip distribution of the 2016 off Fukushima earthquake inverted from the S-net pressure data (Kubota et al., 2021) was used as the initial condition. I adopted the nested grid system (1350, 450, 150 and 50 m) and used the gridded bathymetric dataset provided by the Central Disaster Prevention Council (2003). The 50 m grid was applied around the Onahama port area, and coastal structures were incorporated as topography.
Results
The results of the numerical tsunami simulations showed that advection mainly causes the decrease of the first tsunami amplitude at station Onahama. A comparison of the results of the NLL simulation without bottom friction and the LLW simulation showed that advection had a strong effect when a large-amplitude tsunami passed through narrow waterways. These features are consistent with those of Yamanaka and Tanioka (2022) for the 2003 Tokachi-oki earthquake.
To investigate why the amplitude decease occurred in the NLL simulation without bottom friction, I integrated tsunami energy over the Onahama port area. According the resultant time variation, I found that the energy decreased at the almost same time as the large tsunami passed the narrow waterways and the advection worked strongly.
Discussion
Since that advection is a physical phenomenon not involving dissipation, numerical dissipation is considered to be the cause of the energy decrease in the NLL simulation without bottom friction. In the simulation of this study, the advection term was calculated using the first-order upwind differencing method for which the truncation error produces numerical viscosity. The following may be happening: when the tsunami passes through the narrow waterway, the strong advection effect makes the wavefront leaning forward, and the numerical viscosity due to the advection calculation are strongly activated, resulting in the energy dissipation.
It is noteworthy that the calculated tsunami waveform at station Onahama matches the observation well. If the calculated waveform is significantly affected due to numerical dissipation, it is expected to be inconsistent with the observed one. Since the tsunami source fed into the simulation were estimated accurately owing to the abundant offshore tsunami waveforms, it is unlikely that the inaccuracy of the tsunami source and the numerical dissipation compensated for each other, leading to the accidental waveform agreement. One possibility is that the numerical dissipation would take the place of the physical dissipation associated with physical processes, such as wave breaking, which is not considered in the numerical simulations of this study but may occur in the real coastal area.
If the numerical dissipation due to the advection term causes significant energy dissipation, the dissipation may affect not only the first cycle portions of the coastal tsunami waveforms, but also the long-time tsunami energy evolution. This point will be discussed in the presentation.
Recently, it has been reported that the tsunami nonlinearities sometimes strongly affect the first cycle portions of coastal tsunami waveforms. Tsushima et al. (2022, JpGU) conducted numerical tsunami calculations for the 2016 Mw 6.9 off Fukushima earthquake and showed that the nonlinear long wave (NLL) simulation can reproduce the first parts of coastal tsunami waveforms, whereas the reproducibility got worse when using the linear long wave (LLW) equation: for example, the tsunami amplitude at station Onahama is overestimated more than 1.5 times. Yamanaka and Tanioka (2022, SSJ Fall Meeting) performed tsunami simulation for the 2003 Mw 8.3 Tokachi-oki earthquake and showed that the first parts of coastal waveforms are distorted due to the nonlinearities, that the contribution of advection is stronger than that of bottom friction, and that the advection works significantly at breakwater openings in the ports.
This study focuses on the following feature seen in the case of the 2016 off Fukushima earthquake: at tide gauge station Onahama the first tsunami amplitude becomes small in the NLL simulation, compared to in the LLW simulation. If the main factor of the amplitude reduction is bottom friction, it means that bottom friction also has strong effect on the first part of coastal tsunami waveforms as well as advection. In contrast, if advection is dominant, a new question will arise as to why the amplitude is reduced by advection not involving physical dissipation. To clarify it, I conducted numerical tsunami experiments of the 2016 off Fukushima earthquake.
Method
I used numerical tsunami model JAGURS (Baba et al., 2015) to solve the NLL equation with bottom friction and/or advection, and LLW equation. The slip distribution of the 2016 off Fukushima earthquake inverted from the S-net pressure data (Kubota et al., 2021) was used as the initial condition. I adopted the nested grid system (1350, 450, 150 and 50 m) and used the gridded bathymetric dataset provided by the Central Disaster Prevention Council (2003). The 50 m grid was applied around the Onahama port area, and coastal structures were incorporated as topography.
Results
The results of the numerical tsunami simulations showed that advection mainly causes the decrease of the first tsunami amplitude at station Onahama. A comparison of the results of the NLL simulation without bottom friction and the LLW simulation showed that advection had a strong effect when a large-amplitude tsunami passed through narrow waterways. These features are consistent with those of Yamanaka and Tanioka (2022) for the 2003 Tokachi-oki earthquake.
To investigate why the amplitude decease occurred in the NLL simulation without bottom friction, I integrated tsunami energy over the Onahama port area. According the resultant time variation, I found that the energy decreased at the almost same time as the large tsunami passed the narrow waterways and the advection worked strongly.
Discussion
Since that advection is a physical phenomenon not involving dissipation, numerical dissipation is considered to be the cause of the energy decrease in the NLL simulation without bottom friction. In the simulation of this study, the advection term was calculated using the first-order upwind differencing method for which the truncation error produces numerical viscosity. The following may be happening: when the tsunami passes through the narrow waterway, the strong advection effect makes the wavefront leaning forward, and the numerical viscosity due to the advection calculation are strongly activated, resulting in the energy dissipation.
It is noteworthy that the calculated tsunami waveform at station Onahama matches the observation well. If the calculated waveform is significantly affected due to numerical dissipation, it is expected to be inconsistent with the observed one. Since the tsunami source fed into the simulation were estimated accurately owing to the abundant offshore tsunami waveforms, it is unlikely that the inaccuracy of the tsunami source and the numerical dissipation compensated for each other, leading to the accidental waveform agreement. One possibility is that the numerical dissipation would take the place of the physical dissipation associated with physical processes, such as wave breaking, which is not considered in the numerical simulations of this study but may occur in the real coastal area.
If the numerical dissipation due to the advection term causes significant energy dissipation, the dissipation may affect not only the first cycle portions of the coastal tsunami waveforms, but also the long-time tsunami energy evolution. This point will be discussed in the presentation.