Algorithms for automatic,real-time tsunami detection in wind–wave measurements Part I: Implementation strategies and basic tests

Several, although not all, wind–wave gages are equipped with sensors capable of detecting sea-level oscillations within the tsunami frequency band. The present paper looks at the algorithms to be implemented in the software of these gages in order to automatically perform the real-time detection of a possible tsunami within recorded signals. In particular, a new algorithm is proposed and tested. The first part of the paper concentrates on the algorithms' characteristics, implementation strategies and basic testing. First of all, the situations in which wind–wave measurements are either essential, or useful for real-time tsunami detection are discussed. In the second place, already existing algorithms are recalled, specifying their characteristics and fields of application. Then, the characteristics of the new proposed algorithm – mainly based on an infinite impulse response, time domain filter – are illustrated and analyzed. Performance and efficiency of the considered algorithms are compared using synthetic time series. The second part of the paper discusses the algorithms' use in the framework of Tsunami Early Warning Systems (TEWS), testing them in actual cases.     

The 26 December 2004 Sumatra tsunami recorded on the coast of West Africa

Analysis of sea-level data obtained from the Atlantic Global Sea Level Observing System (GLOSS) sea-level station at Takoradi, Ghana, West Africa, clearly reveals a tsunami signal associated with the M_w = 9.3 Sumatra earthquake of 26 December 2004 in the Indian Ocean. The tsunami arrived at this location on 27 December 2004 at approximately 01:38 UTC (which is close to the expected tsunami arrival time at that site), after travelling for more than 24 hours. The first wave was negative (trough), in contrast with the South African stations where the first wave was mainly positive (crest). The dominant observed period at Takoradi was about 42 minutes. The maximum trough-to-crest wave height (41cm) was observed on 28 December at 00:15 UTC. There were two distinct tsunami 'bursts', separated in time by about 14 hours, the larger being the second burst. A small residual lowering of the sea level (～15cm) during the tsunami and for several days afterwards, and a delayed (～4.5 days) lowering of seawater temperature (up to ～4.5°C), was observed, possibly indicating the presence of internal waves through the Gulf of Guinea associated with propagating tsunami waves. The prominent tsunami signal found in the Takoradi record suggests that tsunami waves could also be found at other sites off the West African coast.     

Spectra of the Black-Sea tsunamis

We perform the analysis of the time spectra of four tsunamis generated in the Black Sea by the earthquakes of 26.07.1927, 11.09.1927, 26.12.1939, and 12.07.1966. For the analysis of the spectra, we used digitized marigrams obtained for 12 points of the Black-Sea coast. The obtained spectra are, as a rule, multimode and have 1–4 spectral maxima. One maximum corresponds to the periods typical of tsunami waves and the other maxima correspond to the oscillations of the sea level with lower frequencies. It seems likely that the events of tsunami are accompanied by low-frequency oscillations of the level caused by the atmospheric forcing, seiches, or other factors. In numerous cases, the oscillations from the predominant energy range lie outside the characteristic range of periods of the tsunami waves. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 5, pp. 21–30, September–October, 2007.     

The possibility of tsunami in the Sea of Okhotsk caused by deep-focus earthquakes

The earthquake that occurred on May 24, 2013, in the basin of the Sea of Okhotsk with a magnitude of 8.3 was the strongest in this region. We have modeled a possible tsunami caused by such an earthquake. The simulations confirm that the wave heights were sufficiently small because the earthquake epicenter depth was 640 km. We analyze the oscillations of the DART buoys in the vicinity of the earthquake source and show that they were not associated with the tsunami waves. Analysis of the available pressure gauge records at different points of the Sea of Okhotsk show that only in one case (Iturup Island) can the observed oscillations of the sea level with a height of approximately 4 cm be classified as tsunami waves.     

Variability of the Baltic Sea level and floods in the Gulf of Finland

The statistical analysis of the long-term data on the variability of the Baltic Sea level has revealed the complicated character of the wave field structure. The wave field formed by the variable winds and the disturbances of the atmospheric pressure in the Baltic Sea is a superposition of standing oscillations with random phases. The cross spectral analysis of the synchronous observation series of the level in the Gulf of Finland has shown that the nodal lines of the standing dilatational waves are clearly traced with frequencies corresponding to the distance from the nodal line to the top of the gulf (a quarter of the wave length). Several areas of the water basin with clearly expressed resonant properties may be distinguished: the Gulfs of Finland, Riga, and Bothnia, Neva Bay, etc. The estimations of the statistical correlation of the sea level oscillations with the variation of the wind and atmospheric pressure indicate the dominant role of the zonal wind component during the formation of the floods in the Gulf of Finland. The probable reason for the extreme floods in St. Petersburg may be the resonance rocking of the eigenmode oscillations corresponding to the basic fundamental seiche mode of the Gulf of Finland with a period of 27 h when the repeated atmospheric disturbances in the Baltic Sea occur with a period of 1–2 days.     

海堤坡角变化对海啸波传播过程影响数值分析

针对近岸海域极端海况的防灾减灾问题,准确模拟追踪海啸波传播过程,再现液面局部射流、崩破波等波面湍动现象。建立SPH数值水槽,边界条件基于固壁粒子法,减少海堤坡角改变对计算域精度的影响,讨论粒子间距设置对模拟精度的影响。模拟7种不同海堤坡角下波浪的爬高与衰减情况,讨论了海堤坡角变化对消波系数的影响。当粒子间距设置为0.002 m时,模型能准确地捕捉海啸波的强非线性现象。随着海堤坡角增大,海啸波峰值爬升率增大,波浪越堤后因崩破波的产生,波能衰减进一步加剧。当坡角较小时,消波系数随坡角的增大提升明显,而后趋于缓慢增长。     

有限断层模型在2015年9月16日智利Mw8.3级地震海啸数值模拟中的应用与评估

2015年9月16日22时54分（当地时间）智利中部近岸发生M_w8.3级地震,震源深度25 km。同时,强震的破裂区长200 km,宽100 km,随之产生了中等强度的越洋海啸。海啸影响了智利沿岸近700 km的区域,局部地区监测到近5 m的海啸波幅和超过13 m的海啸爬坡高度。太平洋区域的40多个海啸浮标及200多个近岸潮位观测站详细记录了此次海啸的越洋传播过程,为详细研究此次海啸近场及远场传播及演化规律提供了珍贵的数据。本文选择有限断层模型和自适应网格海啸数值模型建立了既可以兼顾越洋海啸的计算效率又可以实现近场海啸精细化模拟的高分辨率海啸模型。模拟对比分析了海啸的越洋传播特征,结果表明采用所建立的模型可以较好地再现远场及近场海啸特征,特别是对近场海啸的模拟结果非常理想。表明有限断层可以较好地约束近场、特别是局部区域的破裂特征,可为海啸预警提供更加精确的震源信息,结合高分辨率的海啸数值预报模式实现海啸传播特征的精细化预报。本文结合观测数据与数值模拟结果初步分析了海啸波的频散特征及其对模型结果的影响。同时对观测中典型的海啸波特征进行的简要的总结。谱分析结果表明海啸波的能量主要分布在10~50 min周期域内。这些波特征提取是现行海啸预警信息中未涉及,但又十分重要的预警参数。进一步对这些波动特征的详细研究将为海啸预警信息及预警产品的完善提供技术支撑。     

The role of bottom friction in models of nonbreaking tsunami wave runup on the shore

The role of bottom friction in the runup of nonbreaking long waves on the shore is analyzed. The case of the normal incidence of monochromatic waves is considered. The relief of the model region consists of an even horizontal bottom area conjugated with a flat slope. The energy dissipation is estimated as the work of bottom friction forces over the wave field obtained using the known analytical solution based on the Carrier-Greenspan transforms. Estimates of energy losses for waves whose periods are typical for tsunami waves have been obtained. The energy dissipation is shown to be not concentrated in the shore line area as a rule. The question about the practicability of using partially reflecting boundary conditions on the coast to take into account the bottom friction in large-scale models of tsunami propagation is considered.     

A mathematical model of calculating local tsunami wave source constraints and propagation

This paper presents a local tsunami simulation, including the initial displacement field model of tsunami source and tsunami wave propagation model. We deduced the tsunami wave equation; applied the ma...     

Seasonal variations of wind and waves over Taiwan waters

We here investigate the frequency and intensity of oscillations in oceanographic data within intraseasonal time scales using spectral analysis of surface wind and wave time-series data collected at off-island weather stations or moored buoys around Taiwan. Data from marine weather stations were used to trace atmospheric conditions, while we used buoy data to examine sea states. The spectra and wavelet scalogram of the wind fields revealed oscillations with a period of around 20–33 days, and the energy density of the wind field at the off-island stations was stronger than that at the data buoy stations. However, the wavelet scalogram of the wave height measured at the buoy stations was stronger than its associated wind field. This long-period oscillation is consistent with the wavelet scalogram of the wind field calculated from the off-island weather stations. About 20–33 day oscillations exist within intraseasonal variations, which are closely linked to the atmospheric environment and to wind and ocean wave fields. Oscillations with a period of 5–10 days are a pronounced feature over northeastern Taiwan waters during the winter season and can be interpreted as the wave pattern following synoptic weather systems.     

Thermohydrodynamics of the ocean decay of nonlinear oscillations in a bounded basin of variable depth

We study the time decay of surges of a liquid in a round shallow-water basin of variable depth. The dependence of the logarithmic decrement of oscillations on the bottom topography and wind velocity is analyzed. The role of convective acceleration and bottom friction in the formation of both the level of vertical displacement of the surface of the basin and the velocity field of horizontal wave currents is estimated. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 2, pp. 3–11, March–April, 2006.     

基于震级上限估计的渤海海啸危险性与共振特征研究

根据渤海区域地质断层特征和历史地震活动规律,分析得出渤海内潜在最大震级上限为8.1级,并对该海啸源可能的两组震源机制分别进行了数值模拟。模拟结果显示：渤海局部区域海啸波幅最大可达 1.5 m,最大流速可达2.8~3.0 m/s,具备造成灾害损失的风险。在该海啸源情景下,渤海海盆内易激发长期的水位自由振荡,部分区域水位振荡可持续 20 h以上,振荡波幅的大小与海啸首波波幅相当或更大。基于快速傅里叶变换方法对海啸波进行频谱分析,部分长周期频谱成分满足区域固有共振特征。因此,渤海内一旦发生海啸,不仅要关注海啸首波可能造成的灾害性影响,还要密切关注海啸首波到达后,可能产生的长时间、长周期的海啸波共振以及往复式海啸流造成的影响。     

Analysis of the Tsunami of December 26, 2004, on the Kerala Coast of India—Part I: Amplitudes

The Indian Ocean tsunami of December 26, 2004, not only affected the Bay of Bengal coast of India but also part of the Arabian Sea coast of India. In particular, the tsunami caused loss of life and heavy damage on some parts of the Kerala coast in southwest India. The tsunami traveled west, south of Sri Lanka, and some of the tsunami energy was diffracted around Sri Lanka and the southern tip of India and moved northward into the Arabian Sea. However, tsunami, being a long gravity wave with a wave length of a few hundred kilometers, has to take a wide turn. In that process, it missed the very southern part of the Kerala coast and did not achieve large amplitudes there. However, further north, the tsunami achieved amplitudes of upto 5 m and caused loss of life and significant damage. Here we identify the physical oceanographic processes that were responsible for selective amplification of the tsunami in certain locations.     

Propagating tsunami wave and subsequent resonant response signals detected by HF radar in the Kii Channel,Japan

Signals from the tsunami waves induced by the March 11, 2011 moment magnitude (M_w) 9.0 Tohoku-Oki earthquake and from subsequent resonances were detected as radial velocity variability by a high-frequency ocean surface radar (HF radar) installed on the eastern coast of the Kii Channel, at a range of about 1000 km from the epicenter along the eastern to southern coasts of Honshu Island. A time–distance diagram of band-passed (9–200 min) radial velocity along the beam reveals that the tsunami waves propagated from the continental shelf slope to the inner channel as progressive waves for the first three waves, and then natural oscillations were excited by the waves; and that the direction of the tsunami wave propagation and the axis of the natural oscillations differed from that of the radar beam. In addition, spectral analyses of the radial velocities and sea surface heights obtained in the channel and on the continental shelf slope suggest complex natural oscillation modes excited by the tsunami waves.     

天文潮与海啸耦合数学模型研究——以东中国海温州湾为例

在COMCOT海啸数学模型中加入潮汐边界条件,建立了东中国海天文潮与海啸耦合数学模型。在琉球海沟内侧设计震级为7.6级的海底地震,根据地震板块的错动方向不同,设计正波先行与负波先行两种海啸波,通过调整海啸波发生时间,使海啸波波峰遭遇温州湾天文高潮位。将天文潮与海啸耦合模型计算结果与线性叠加计算结果进行比较,结果表明:无论正波先行还是负波先行,天文潮与海啸耦合计算相比线性叠加的结果,海啸波的到达时间均有所提前;而从海啸波波高来看,线性叠加的计算结果则比耦合计算结果偏高。     

The reduction effects of mangrove forest on a tsunami based on field surveys at Pakarang Cape,Thailand and numerical analysis

Using an integrated approach including satellite imagery analysis, field measurements, and numerical modeling, we investigated the damage to mangroves caused by the 2004 Indian Ocean tsunami at Pakarang Cape in Pang Nga Province, Thailand. Comparing pre- and post-tsunami satellite imagery of the study area, we found that approximately 70% of the mangrove forest was destroyed by the tsunami. Based on field observations, we found that the survival rate of mangroves increased with increasing stem diameter. Specifically, we found that 72% of Rhizophora trees with a 25–30 cm stem diameter survived the tsunami impact, whereas only 19% with a 15–20 cm stem diameter survived. We simulated the 2004 Indian Ocean tsunami using the nonlinear shallow-water wave theory to reproduce the tsunami inundation flow and investigated the bending moment acting on the mangrove trees. Results of the numerical model showed that the tsunami inundated areas along the mangrove creeks, and its current velocity reached 5.0 m s⁻¹. Based on the field measurements and numerical results, we proposed a fragility function for mangroves, which is the relationship between the probability of damage and the bending stress caused by the maximum bending moment. We refined the numerical model to include the damage probability of mangrove forests using the obtained fragility function to investigate the tsunami reduction effect of mangrove forest. Under simple numerical conditions related to the mangrove forest, ground level, and incident wave, the model showed that a mangrove forest of Rhizophora sp. with a density of 0.2 trees m⁻² and a stem diameter of 15 cm in a 400 m wide area can reduce the tsunami inundation depth by 30% when the incident wave is assumed to have a 3.0 m inundation depth and a wave period of 30 min at the shoreline. However, 50% of the mangrove forest is destroyed by a 4.5 m tsunami inundation depth, and most of the mangrove forest is destroyed by a tsunami inundation depth greater than 6 m. The reduction effect of tsunami inundation depth decreased when the tsunami inundation depth exceeded 3 m, and was mostly lost when the tsunami inundation depth exceeded 6 m.     

渤海海域地震海啸灾害概率性风险评估

渤海作为我国地震活动性最为活跃的近海,其地震海啸风险不可忽视。本文应用概率性海啸风险评估方法对渤海周边区域的海啸风险进行评估。根据历史地震目录建立了渤海区域的震级-频率关系,基于蒙特卡洛算法随机生成了一套10万年的地震目录,最终通过对地震事件的海啸数值模拟及最大波幅的统计分析给出了环渤海区域典型重现期的最大波幅分布以及重点城市的海啸波幅曲线。评估结果表明,渤海地区海啸风险主要集中在渤海湾和莱州湾周边,波幅可达到1~3 m,辽东湾地区海啸风险较低。     

An integrated numerical method for simulation of drifted objects trajectory under real-world tsunami waves

The present study focused on tracing tsunami-drifted objects under a real tsunami based on an integrated numerical method. Instead of a solitary wave that is much shorter and steeper than real-world tsunami waves, an extra-long tsunami wave is represented here in a nearshore region using a new approach. To this end, propagation of a seismic tsunami from the source to the nearshore region was simulated using two-dimensional depth-averaged equations. When the waves reached the target coastal area, the time series of the free surface of the tsunami was approximated by a theoretical relation based on a combination of several solitons, which were then used to solve the linearized trajectory equation of the wave-maker to generate the intended time series of the tsunami wave. Finally, in a nearshore model, the movement of drifted bodies under the generated tsunami wave was simulated based on the smoothed-particle hydrodynamics (SPH) method. In order to verify the accuracy of the proposed method in tracing the drifted bodies under a real tsunami, the giant fish-oil tank, which was transported about 300 m during the 2011 Tohoku tsunami of Japan, was selected as the benchmark. The results demonstrate that the time series of the long tsunami wave was successfully generated by the piston wave-maker in the GPU-based SPH model, and the proposed approach can be regarded as a suitable alternative for reproduction of a real tsunami. The results also showed that the simulated fish-oil tank properly followed the estimated trajectory in Ishinomaki but it was transported more than the reported distance, which was expected due to absence of a holding connection between the tank and the ground in the SPH model. It should be emphasized that this study is one of the first studies on three-dimensional tracing of a tsunami-drifted body during a real event, and the tracing can be more accurate in further simulations by applying higher-resolution topography data and faster computation systems that help include more details in the nearshore model.     

海啸波传播的线性和非线性特征及近海陆架效应影响的数值研究

浅水方程被广泛应用于海啸预警报业务及研究,而针对线性浅水方程与非线性浅水方程在不同海区水深地形条件下的适用范围、计算效率问题是海啸研究人员急需了解的。本文应用基于浅水方程的海啸数值预报模型就海啸波在南海、东海传播的线性、非线性特征以及陆架对其传播之影响进行了数值分析研究。海啸波在深水的传播表征为强线性特征,此时线性系统对海啸波幅的模拟计算具有较高的精度和效率,而弱的非线性特征及弱的色散特征对海啸波幅的预报影响甚微,可以忽略不计。海啸波传播至浅水大陆架后受海底坡度变化、海底粗糙度等因素影响,波动的非线性效应迅速传播、积累,与线性浅水方程计算的海啸波相比表现出较大差异,主要表现为:在南海区,水深小于100m时,海啸波首波以后的系列波动非线性特征比较明显,两者波幅差别较大,但首波波幅的区别不大,因此对于该区域在不考虑海啸爬高的情况下,应用线性系统计算得到的海啸波幅也可满足海啸预警报的要求;在东海区由于陆架影响,海啸波非线性特征明显增强,水深小于100m区域,首波及其后系列波波幅均差异较大,故在该区域必须考虑海啸波非线性作用。本文就底摩擦项对海啸波首波波幅的影响进行了数值对比分析,结果表明:底摩擦作用对海啸波首波波幅影响仅作用于小于100m水深。最后,该文通过敏感性试验,初步分析了陆架宽度及陆架边缘深度对海啸波波幅的影响,得出海啸波经陆架传播共振、变形后,海啸波幅的放大或减小与陆架的宽度及陆架边缘水深有关。     

深圳海域潮汐海啸波耦合数值研究

以COMCOT海啸模式和TPXO7.1全球潮汐模式为基础,采用三层嵌套网格,建立了南海海啸与潮汐耦合计算模型,分析深圳海域海啸和潮汐相互作用。潮汐计算结果与实测数据吻合较好,高、低潮位平均误差小于15 cm,20 cm;在潮汐验证的基础上,以马尼拉海沟潜在地震海啸源为案例,进行8.0,9.0级地震海啸与潮汐耦合情景模拟计算,计算结果表明,9级地震海啸在深圳海域外海波高为140~150 cm,如先行波为正波发生在高潮时将产生异常高潮位,负波发生在低潮时将产生异常低潮位,线性叠加计算结果偏大,在25.0 cm之内,到达时间差异小于6 min。