Numerical modeling of the long surface waves scattering for the 2011 Japan tsunami: Case study

The March 11, 2011, megaquake caused a catastrophic tsunami recorded throughout the Pacific. This paper presents an analysis of the sea-level records obtained from deep-water tsunami meters (DART and NEPTUNE). To evaluate the effect of the sea-level oscillations’ decay, a statistical analysis of observations and numerical modeling of tsunami generation and propagation have been conducted. The main goal is to uncover physical mechanisms of the tsunami wave field formation and evolution at scales up to tens of thousands of kilometers in space and a few days in time. It is shown that the tsunami lifetime is related to the wave-energy diffusion and dissipation processes. The decay time of the variance of the tsunami-generated level oscillations is about 1 day. Multiple reflections and scattering by irregularities of the bottom topography make the field of the secondary tsunami waves stochastic and incoherent: the distribution of the wave energy in the ocean reaches a statistical equilibrium in accordance with the Rayleigh-Jeans law of equipartition of the wave energy per degree of freedom. After the tsunami front has passed, the secondary-wave energy density turns out to be inversely proportional to the water depth.     

Relevance of Bathymetry for Tsunami Run‐up Modeling

Abstract

Marine positioning is relevant for several aspects of tsunami research, observation, and prediction. These include accurate positioning of instruments on the ocean bottom for determining the deep‐water signature of the tsunami, seismic observational setups to measure the earthquake parameters, equipment to determine the tsunami characteristics during the propagation phase, and instruments to map the vertical uplift and subsidence that occurs during a dip‐slip earthquake.

In the accurate calculation of coastal tsunami run‐up through numerical models, accurate bathymetry is needed, not only near the coast (for tsunami run‐up) but also in the deep ocean (for tsunami generation and propagation). If the bathymetry is wrong in the source region, errors will accumulate and will render the numerical calculations inaccurate. Without correct and detailed run‐up values on the various coastlines, tsunami prediction for actual events will lead to false alarms and loss of public confidence.     

Analysis of the Tsunami of December 26, 2004, on the Kerala Coast of India—Part III: Inundation and Initial Withdrawal

During the Indian Ocean tsunami of December 26, 2004, specific observations were made by our survey team about the arrival times of several tsunami waves, their amplitudes, maximum extent of horizontal inundation on land and initial withdrawal of the ocean. Here the observations on the horizontal inundation and initial withdrawal are presented and briefly discussed.     

Analysis of the Tsunami of December 26, 2004, on the Kerala Coast of India—Part III: Inundation and Initial Withdrawal

During the Indian Ocean tsunami of December 26, 2004, specific observations were made by our survey team about the arrival times of several tsunami waves, their amplitudes, maximum extent of horizontal inundation on land and initial withdrawal of the ocean. Here the observations on the horizontal inundation and initial withdrawal are presented and briefly discussed.     

Problems and prospects of creating a global land–ocean seismic network

The paper discussed the advantages and limitations of seismic signal detection on the ocean bottom. The need to create long-term seismic monitoring systems in areas of industrial development on the shelf and continental slope, as well as in areas with high seismic and tsunami hazards, is justified. The results of employing broadband bottom seismographs during expeditions of the Shirshov Institute of Oceanology of the Russian Academy of Sciences (IO RAS) are described. Autonomous broadband bottom seismographs with operational communication via satellite or radio channels are proposed for creating a global marine seismic network.     

HF radar detection of tsunamis

This paper demonstrates that HF radar systems can be used to detect tsunamis well before their arrival at a coastline. We solve the equations of motion and continuity on the ocean surface using models to simulate the signals produced by a tsunami approaching the east U.S. coast. Height and velocity profiles are derived along with expressions for the radar-observed current velocities in terms of bathymetry and tsunami height and period. Simulated tsunami-generated radial current velocities are superimposed on typical maps of radial velocity generated by a Rutgers University HF radar system. A detection parameter is defined and plotted to quantify the progress of the tsunami, which is shown to be detectable well before its arrival at the coast. We describe observations/warnings that would have been provided by HF radar systems at locations in the path of the 2004 Indian Ocean tsunami.     

Tidal Effects on Determining a Point at the Bottom of the Sea by Combining GPS and Sonar Observations

This paper discusses tidal effects on an observation scheme to determine a point at the bottom of the sea by combining GPS and Sonar observations. For the purpose, three kinds of Earth tides are introduced (i.e., the crust tide, the equipotential surface point (ocean depth) tide, and the geoid tide). The corresponding mathematical expressions are derived to demonstrate the tidal effects on GPS and Sonar observations. The relations between the Earth tides are also discussed. Theoretical results imply a very interesting conclusion, namely that, for a local area, the static position of a point at the bottom of sea can be obtained by the dynamic observations without any tidal correction. Actually, the tidal effects cancel each other in the mentioned observation scheme. It therefore indicates that the observation scheme is free of tidal effects. Furthermore, we learned that the divergence caused by any error source on ocean surface is canceled and does not affect the final results. Therefore, to determine the position of a point at the bottom of sea, we need not consider any tidal effects.     

Tidal Effects on Determining a Point at the Bottom of the Sea by Combining GPS and Sonar Observations

This paper discusses tidal effects on an observation scheme to determine a point at the bottom of the sea by combining GPS and Sonar observations. For the purpose, three kinds of Earth tides are introduced (i.e., the crust tide, the equipotential surface point (ocean depth) tide, and the geoid tide). The corresponding mathematical expressions are derived to demonstrate the tidal effects on GPS and Sonar observations. The relations between the Earth tides are also discussed. Theoretical results imply a very interesting conclusion, namely that, for a local area, the static position of a point at the bottom of sea can be obtained by the dynamic observations without any tidal correction. Actually, the tidal effects cancel each other in the mentioned observation scheme. It therefore indicates that the observation scheme is free of tidal effects. Furthermore, we learned that the divergence caused by any error source on ocean surface is canceled and does not affect the final results. Therefore, to determine the position of a point at the bottom of sea, we need not consider any tidal effects.     

一个覆盖太平洋区域的地震海啸波幅预报系统及检验

基于线性长波方程和缓变地形近岸波幅格林公式建立了覆盖整个太平洋区域的准实时地震海啸波幅预报系统。系统利用了GPU并行加速技术,可在90 s之内完成太平洋区域32 h的海啸传播计算和中国沿海城市岸段的波幅特征值预报。筛选了自2006年以来的9次发生在太平洋区域,矩震级（Mw）超过8.0且资料丰富的历史地震海啸事件,对预报系统进行了后报检验。结果表明,线性长波模型能够很好的模拟海啸在大洋中的传播过程;格林公式能够较为准确的估算缓变水深和开阔地形条件下的近岸海啸最大波幅,波幅预警准确率可达80%,基本满足海啸预警需求。以2011年日本Mw9.0地震海啸为例,评估了该系统对中国城市岸段的波幅预警能力,结论基本合理。需要注意的是,利用该系统计算对海啸源特别敏感的近场海啸波幅可能产生较大偏差。提出了若要进一步提高定量海啸波幅预警的准确率,可从以下两个方面加强研究和业务实践:一是采用多数据联合反演方法提升海啸源的精度;二是提高格林公式的适用性,或者构建高效的近岸精细化海啸数值预报系统。     

Calculation of the initial elevation at the tsunami source using analytical solutions

We have obtained an analytical solution to the problem of determining the initial elevation at the tsunami source, which was formed by small residual deformations of a flat sloping bottom. This solution, which is newly derived, is compared with the known analytical solution of an equivalent problem over a horizontal bottom. It is shown that applying an analytical solution over a horizontal bottom for calculating the initial perturbations in the sources of realistic tsunami provides sufficient accuracy.     

Temporal variability of tsunami arrival detection distance revealed by virtual tsunami observation experiments using numerical simulation and 1-month HF radar observation

The combination of a high-frequency ocean surface radar and a tsunami detection method should be assessed as the onshore-offshore distribution of tsunami detection probability, because the probability will vary in accordance with the signal-to-noise ratio (SNR) and the tsunami magnitude in addition to the radar system specifications. Here, we statistically examine the tsunami detection distance based on virtual tsunami observation experiments by using signals received by a high-frequency radar in February 2014 installed on the southern coast of Japan and numerically simulated velocities induced by a Nankai Trough earthquake. In the experiments, the Doppler frequencies associated with the simulated velocities were superimposed on the receiving signals of the radar, and the radial velocities were calculated from the synthesized signals by the fast Fourier transform. Tsunami arrival was then detected based on the temporal change in the cross-correlation of the velocities, before and after tsunami arrival, between two points 3 km apart along a radar beam. We found that the possibility of tsunami detection primarily depends on the kinetic energy ratio between tsunami current and background current velocities. The monthly average detection probability is over 90% when the energy ratio exceeds 5 (offshore distance: 9 km ≤ L ≤ 36 km) and reduces to 50% when the energy ratio is approximately 1 (L = 42 km) over the shelf slope. The ratio varied with the background current physics and SNR, which was mainly affected by ocean surface wave heights and ionospheric electron density.     

夏季黄海表面冷水对大气边界层及海雾的影响

海表面温度(SST)是海气界面上的1个物理量,受到海洋潮汐、海底地形等因素影响,并对海洋大气边界层有着重要的影响.夏季的黄海,由于黄海冷水团的存在和陆架锋的影响,或是潮汐混合的作用导致海水的垂直混合,使海表面温度的分布产生复杂的结构.通过对卫星观测的海表面温度数据分析,发现在夏季黄海有几个SST冷中心的存在:辽东半岛以及山东半岛的顶端、朝鲜半岛的西侧、山东半岛南侧、江苏外海和黄海南部等.本文利用一系列船舶观测资料、卫星遥感数据、再分析数据分析等,并运用数值模拟研究黄海的冷中心对其上大气的影响.在冷区之上,大气稳定度增加,抑制了近海面大气的垂直混合,使海表面风速减弱.通过对船测数据的分析,在冷区位置有海雾多发区的存在,黄海南部冷区上的海雾发生频率达到15％以上.Weather Research and Forecasting(WRF)模式的数值模拟表明,冷中心降低上空的温度,使海表面风速减弱,形成厚度达500m的逆温层,为海雾的形成创造了有利的条件.与船测数据结果所不同的是黄海南部冷中心之上的海雾发生频率可以达到30％,去掉冷区影响的试验表明冷区较冷的海表面温度最多可以使海雾的发生频率增加15％以上.     

Tsunami simulation with Green–Naghdi theory

Green–Naghdi (GN) theory is a fully nonlinear wave theory which has been used with success to simulate nonlinear water waves. In previous applications of GN theory to water wave problems the ocean bottom was assumed to be time invariant. In this work no such restriction is made and GN theory is used to simulate tsunami caused by bottom fluctuation. As first test cases we simulate two-dimensional nonlinear surface waves generated by positive bottom movements. The results in the generation region for three different seabed movements compare well against earlier experimental data. The results in the downstream region for impulsive seabed movements show some discrepancies in wave phase and amplitude compared with earlier experimental values. It is suspected that the viscous effects may have played a role. The GN theory is then used to study three-dimensional near-field tsunami amplitudes caused by submarine landslides and slumps spreading in two orthogonal directions. The GN results agree with previous linear solution very well when the ratio of the velocities is v₁/v₂=1.0. But GN theory give more believable results for the case of v_T/v=0.1 and v₁/v₂=0.1.     

Numerical Simulation of Tsunamis on the Tamil Nadu Coast of India

The State of Tamil Nadu was the most affected region in India during the tsunami of December 26, 2004, in the Indian Ocean, in terms of loss of life and damage. Numerical simulation was made for three tsunamis, the December 26, 2004, event, the Sumatra tsunami of 1833, and a hypothetical tsunami originating in the Andaman-Nicobar region. Since inundation is not included in these simulations, the tsunami amplitudes were deduced at the 10m depth contour in the ocean, off several locations on the coast of Tamil Nadu. The computed amplitudes appear reasonable as compared to known tsunami amplitudes from past events.     

Macro benthic community assemblage before and after the 2007 tsunami and earthquake at Paracas Bay,Peru

Macrobenthic soft bottom community assemblages were studied from December 2006 to December 2007 at Paracas Bay (Atenas Beach, 13°45' S, 76°17' W, Peru), including the period of the tsunami of 15 August 2007, providing a unique opportunity to assess the effects of this type of natural disturbance in soft bottom marine ecosystems. The results show that the tsunami affected the soft bottom community assemblage by changing the sediment granulometry, the biomass and abundance of epifaunal species, and by increasing the silt proportion. The event affected all functional groups, resulting in an increased numbers and biomass of filter feeder and grazers that were followed soon after by predators during the post-tsunami period. A similar pattern was observed for biomass and the abundance of infaunal species without changing the functional groups. The slow recovery observed after four months was likely related to the loss of sediment stability. In summary, there were differences in the structure and composition of soft bottom macrofaunal assemblages before and after the earthquake and posterior tsunami disturbance, forcing benthic communities to initiate re-colonisation processes.     

On the near-bottom pressure variations in the region of the 2003 Tokachi-Oki tsunami source

The Tokachi-Oki earthquake was the strongest seismic event in 2003. The tsunami caused by the earthquake reached a height of four meters at the northeastern coast of Hokkaido. The JAMSTEC successfully recorded the variations of the near-bottom pressure in the region of the tsunami source. An analysis of the data reveals low-frequency (～ 0.15 Hz) elastic vibrations of the water layer. Estimates of the amplitude, velocity, and duration of the bottom deformation at the tsunami source were obtained.     

Ocean depth effects on tsunami amplitudes used in source models in linearized shallow-water wave theory

The aim of this study is to determine the effects of ocean depth on tsunami amplitudes used in source models for use in linear shallow-water wave theory. To determine the effects, 19 ocean depths ranging from 200–2000 m are studied. The results show that it is possible to establish a series-type exploration function to define the depth-amplitude effects. This function with the unknown coefficients related to ruptures of the ocean floor involves the normalized maximum tsunami amplitude. Results obtained from this series-function give good approximations for four or more terms in the series. Two basic source models are considered. Numerical examples are presented.     

Nonlinear dynamics of phase transitions during seawater freezing with false bottom formation

This paper concerns mathematical modeling of the processes of false bottom evolution taking into account water freezing in the opposite direction from the cooled boundary with the atmosphere. The model of the crystallization process is based on the two-phase zone theory complicated by the moving boundaries of phase transitions and turbulent flows of fluid in the ocean near the false bottom boundary. Analytical solutions of the nonlinear problem are found (the distributions of the temperature and the salinity, the proportion of the solid fraction, the laws of the motion of the boundaries between the phase transitions, and the heat fluxes) and a comparative analysis of the results with the field data observations is performed. It is shown that the heat flux caused by the growing false bottom makes a significant contribution to the heat exchange processes between the ocean and the atmosphere.     

Tsunami Travel Time Atlas for the Atlantic Ocean

Compared to the Pacific Ocean, tsunamis are rare both in the Atlantic and Indian Oceans. However, the December 26, 2004, tsunami demonstrated that, no matter how rare they may be, when a major tsunami occurs, it could be very disastrous. The most basic information in tsunami warning center requires are charts showing tsunami travel times to various locations around the rim of the ocean. With this in mind, a tsunami travel time atlas for the Atlantic Ocean is in preparation. The Caribbean Sea is also included in this Atlas, as it is more or less a part of the Atlantic Basin.