How does multiscale modelling and inclusion of realistic palaeobathymetry affect numerical simulation of the Storegga Slide tsunami?

The ∼8.15 ka Storegga submarine slide was a large (∼3000 km³), tsunamigenic slide off the coast of Norway. The resulting tsunami had run-up heights of around 10–20 m on the Norwegian coast, over 12 m in Shetland, 3–6 m on the Scottish mainland coast and reached as far as Greenland. Accurate numerical simulations of Storegga require high spatial resolution near the coasts, particularly near tsunami run-up observations, and also in the slide region. However, as the computational domain must span the whole of the Norwegian-Greenland sea, employing uniformly high spatial resolution is computationally prohibitive. To overcome this problem, we present a multiscale numerical model of the Storegga slide-generated tsunami where spatial resolution varies from 500 m to 50 km across the entire Norwegian-Greenland sea domain to optimally resolve the slide region, important coastlines and bathymetric changes. We compare results from our multiscale model to previous results using constant-resolution models and show that accounting for changes in bathymetry since 8.15 ka, neglected in previous numerical studies of the Storegga slide-tsunami, improves the agreement between the model and inferred run-up heights in specific locations, especially in the Shetlands, where maximum run-up height increased from 8 m (modern bathymetry) to 13 m (palaeobathymetry). By tracking the Storegga tsunami as far south as the southern North sea, we also found that wave heights were high enough to inundate Doggerland, an island in the southern North Sea prior to sea level rise over the last 8 ka.     

Reconstructing tsunami run-up from the characteristics of tsunami deposits on the Thai Andaman Coast

Tsunamis can leave deposits on the land surface they inundate. The characteristics of tsunami deposits can be used to calculate tsunami run-up height and velocity. This paper presents a reconstruction of tsunami run-up from tsunami deposit characteristics in a simple mathematical model. The model is modified and applied to reconstruct tsunami run-ups at Ao Kheuy beach and Khuk Khak beach, Phangnga province, Thailand. The input parameters are grain-size and maximum run-up distance of the sediment. The reconstructed run-up heights are 4.16–4.91 m at Ao Kheuy beach and 5.43–9.46 m at Khuk Khak beach. The estimated run-up velocities (maximum velocity) at the still water level are 12.78–19.21 m/s. In the area located 70–140 m inland to the end of run-up inundation, estimated mean run-up velocities decrease from approximately 1.93 m/s to 0 m/s. Reasonably good agreements are found between reconstructed and observed run-up heights. The tsunami run-up height and velocity can be used for risk assessment and coastal development programs in the tsunami affected area. The results show that the area from 0 to 140 m inland was flooded by high velocity run-ups and those run-up energies were dissipated mainly in this area. The area should be designated as either an area where settlement is not permitted or an area where effective protection is provided, for example with flood barriers or forest.     

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.     

Historical tsunami in the Makran Subduction Zone off the southern coasts of Iran and Pakistan and results of numerical modeling

Tsunami hazard in the Makran Subduction Zone (MSZ), off the southern coasts of Iran and Pakistan, was studied by numerical modeling of historical tsunami in this region. Although the MSZ triggered the second deadliest tsunami in the Indian Ocean, among those known, the tsunami hazard in this region has yet to be analyzed in detail. This paper reports the results of a risk analysis using five scenario events based on the historic records, and identifies a seismic gap area in western Makran off the southern coast of Iran. This is a possible site for a future large earthquake and tsunami. In addition, we performed numerical modeling to explain some ambiguities in the historical reports. Based on the modeling results, we conclude that either the extreme run-up of 12–15 m assigned for the 1945 Makran tsunami in the historical record was produced by a submarine landslide triggered by the parent earthquake, or that these reports are exaggerated. The other possibility could be the generation of the huge run-up heights by large displacements on splay faults. The results of run-up modeling reveal that a large earthquake and tsunami in the MSZ is capable of producing considerable run-up heights in the far field. Therefore, it is possible that the MSZ was the source of the tsunami encountered by a Portuguese fleet in Dabhul in 1524.     

Evaluation of the Parameters of Tsunami Waves along the South Coast of the Crimean Peninsula

Within the framework of a nonlinear model of long waves, we present the estimates of the parameters of tsunami waves along the south coast of the Crimean Peninsula (from Cape Khersones to Cape Meganom) with a space resolution of 2.5 km. The numerical analysis is carried out for four typical positions of the elliptic zones of generation and the range of magnitudes 6.5–7.5. We study the space structure of waves and determine the amplitudes and periods of oscillations of the level at 11 points of the analyzed part of the coastline of the Black Sea. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 3, pp. 3 – 10, May–June, 2005.     

Extreme storms in 2006–2007 on Shikotan Island and their impact on the coastal relief and deposits

This paper describes the results of investigations of the consequences of the storms on the Pacific coast of Shikotan Island that occurred on October 7–10, 2006 and January 6–8, 2007. These storms and their impact on the coastal zone can be considered as extreme events for the last 40–50 years. The heights and flooding area of the storm surges within bay coasts of different types were measured. The coastal relief’s changes are described. During the storms, a cover of deposits was formed having a size of up to 30 m outside the beach zone and up to 52 m in the near-mouth zones. The grain-size composition of the storm deposits is analyzed and their difference from other coastal facies, including tsunami sands, are established.     

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.     

Tsunami Inundation Modelling for the Coast of Kerala,India

The disastrous tsunami of December 26, 2004, exposed the urgent need for implementing a tsunami warning system. One of the essential requirements of a tsunami warning system is the set up of tsunami inundation models which can predict inundation and run-up along a coastline for a given set of seismic parameters. The Tsunami Warning Centre and the State/District level Disaster Management Centres should have tsunami inundations maps for different scenarios of tsunami generation. In the event of a tsunamigenic earthquake, appropriate decisions on issue of warnings and/or evacuation of coastal population are made by referring to such maps. The nature of tsunami inundation and run-up along the Kerala coast for the 2004 Sumatra and 1945 Makran, and a hypothetical worst-case scenario are simulated using the TUNAMI N2 model and the results are presented in this paper. Further, scenarios of tsunami inundation arising out of possible rise in sea level as projected by the Intergovernmental Panel on Climate Change (IPCC 2001) are also simulated and analysed in the paper. For the study, three representative sectors of the Kerala coast including the Neendakara-Kayamkulam coast, which was the worst hit by the 2004 tsunami, are chosen. The results show that the southern locations and certain locations of central Kerala coast are more vulnerable for Sumatra when compared to Makran 1945 tsunami. From the results of numerical modelling for future scenarios it can be concluded that sea level rise can definitely make pronounced increase in inundation in some of the stretches where the backshore elevation is comparatively low.     

On the run-up and back-wash processes of single and double solitary waves — An experimental study

The run-up and back-wash processes of single and double solitary waves on a slope were studied experimentally. Experiments were conducted in three different wave flumes with four different slopes. For single solitary wave, new experimental data were acquired and, based on the theoretical breaking criterion, a new surf parameter specifically for breaking solitary waves was proposed. An equation to estimate maximum fractional run-up height on a given slope was also proposed. For double solitary waves, new experiments were performed by using two successive solitary waves with equal wave heights; these waves were separated by various durations. The run-up heights of the second wave were found to vary with respect to the separation time. Particle image velocimetry measurements revealed that the intensity of the back-wash flow generated by the first wave strongly affected the run-up height of the second wave. Showing trends similar to that of the second wave run-up heights, both the back-wash breaking process of the first wave and the reflected waves were strongly affected by the wave–wave interaction. Empirical run-up formula for the second solitary wave was also introduced.     

Run-up of tsunamis and long waves in terms of surf-similarity

In this paper we review and re-examine the classical analytical solutions for run-up of periodic long waves on an infinitely long slope as well as on a finite slope attached to a flat bottom. Both cases provide simple expressions for the maximum run-up and the associated flow velocity in terms of the surf-similarity parameter and the amplitude to depth ratio determined at some offshore location. We use the analytical expressions to analyze the impact of tsunamis on beaches and relate the discussion to the recent Indian Ocean tsunami from December 26, 2004. An important conclusion is that extreme run-up combined with extreme flow velocities occurs for surf-similarity parameters of the order 3–6, and for typical tsunami wave periods this requires relatively mild beach slopes. Next, we compare the theoretical solutions to measured run-up of breaking and non-breaking irregular waves on steep impermeable slopes. For the non-breaking waves, the theoretical curves turn out to be superior to state-of-the-art empirical estimates. Finally, we compare the theoretical solutions with numerical results obtained with a high-order Boussinesq-type method, and generally obtain an excellent agreement.     

Revisiting the February 6th 1783 Scilla (Calabria, Italy) landslide and tsunami by numerical simulation

On February 6th, 1783, a landslide of about 5 × 10⁶ m³ triggered by a 5.8 M earthquake occurred near the village of Scilla (Southern Calabria, Italy). The rock mass fell into the sea as a rock avalanche, producing a tsunami with a run-up as high as 16 m. The tsunami killed about 1,500 people, making it one of the most catastrophic tsunamis in Italian history. A combined landslide-tsunami simulation is proposed in this paper. It is based on an already performed reconstruction of the landslide, derived from subaerial and submarine investigation by means of geomorphological, geological and geomechanical surveys. The DAN3D model is used to simulate the landslide propagation both in the subaerial and in the submerged parts of the slope, while a simple linear shallow water model is applied for both tsunami generation and propagation. A satisfying back-analysis of the landslide propagation has been achieved in terms of run-out, areal distribution and thickness of the final deposit. Moreover, landslide velocities comparable to similar events reported in the literature are achieved. Output data from numerical simulation of the landslide are used as input parameters for tsunami modelling. It is worth noting that locations affected by recordable waves according to the simulation correspond to those ones recorded by historical documents. With regard to run-up heights a good agreement is achieved at some locations (Messina, Catona, Punta del Faro) between computed and real values, while in other places modelled heights are overestimated. The discrepancies, which were most significant at locations characterized by a very low slope gradient in the vicinity of the landslide, were probably caused by effects such as wave breaking, for which the adopted tsunami model does not account, as well as by uncertainties in the historical data.     

Analysis of the intensification of tsunami waves near the South Coast of Crimea

We perform the numerical analysis of the intensification of tsunami waves in the course of their propagation from the open part of the Black Sea to the shelf zone. For this purpose, we use a one-dimensional model of nonlinear long waves taking into account the effect of bottom friction. We study four profiles of the bottom corresponding to the south coast of the Crimean Peninsula and establish the predominant role of the bottom pattern and insignificant contribution of nonlinearity to the transformation of waves in the process of their propagation in the direction of the coast. Down to depths of 50 m, all changes in the height of waves are described by the Green law. For the evaluation of vertical run-up of waves, it is important to take into account nonlinear effects. The highest vertical run-ups of waves are observed in the parts of the shelf zone located near Yalta and Alushta. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Numerical investigation of tsunami-like wave hydrodynamic characteristics and its comparison with solitary wave

Solitary waves have been commonly used as an initial condition in the experimental and numerical modelling of tsunamis for decades. However, the main component of a tsunami waves acts at completely different spatial and temporal scales than solitary waves. Thus, use of solitary waves as approximation of a tsunami wave may not yield realistic model results, especially in the coastal region where the shoaling effect restrains the development of the tsunami wave. Alternatively, N-shaped waves may be used to give a more realistic approximation of the tsunami wave profile. Based on the superposition of the sech²(*) waves, the observed tsunami wave profile could be approximated with the N-shaped wave method, and this paper presents numerical simulation results based on the tsunami-like wave generated based on the observed tsunami wave profile measured in the Tohoku tsunami. This tsunami-like wave was numerically generated with an internal wave source method based on the two-phase incompressible flow model with a Volume of Fluid (VOF) method to capture the free surface, and a finite volume scheme was used to solve all the governing equations. The model is first validated for the case of a solitary wave propagating within a straight channel, by comparing its analytical solutions to model results. Further, model comparisons between the solitary and tsunami-like wave are then made for (a) the simulation of wave run-up on shore and (b) wave transport over breakwater. Comparisons show that use of these largely different waveform shapes as inputs produces significant differences in overall wave evolution, hydrodynamic load characteristics as well as velocity and vortex fields. Further, it was found that the solitary wave uses underestimated the total energy and hence underestimated the run-up distance.     

2017年9月8日墨西哥沿岸Mw8.2级地震海啸观测数据分析与模拟

2017年9月8日4时49分（UTC）,墨西哥瓦哈卡州沿岸海域（15.21°N,93.64°W）发生M_w8.2级地震,震源深度30 km。强震在该海域引发海啸,海啸对震源附近数百千米范围内造成了严重影响。位于太平洋上的多个海啸监测网络捕捉到了海啸信号并详细记录了此次海啸的传播过程。本文选用了近场2个DART浮标和6个验潮站的水位数据,通过潮汐调和分析和滤波分离出海啸信号,对近场海啸特征值进行了统计分析,并采用小波变换分析方法进一步分析了海啸的波频特征。基于Okada弹性位错理论断层模型计算得到了强震引发的海底形变分布,并采用MOST海啸模式对本次海啸事件近场传播特征进行了模拟,模拟结果与观测吻合较好。最后,基于实测和模拟结果,详细分析了此次地震海啸的近场分布特征,发现除受海啸源的强度和几何分布特征影响外,近岸海啸波还主要受地形特征控制,在与特定地形相互作用后波幅产生放大效应,会进一步加剧海啸造成的灾害。     

Numerical modeling of the propagation and strengthening of tsunami waves near the Crimean Peninsula and the Northeast Coast of the Black Sea

The linear model of long waves is used for the evaluation of the parameters of tsunami waves along the South Coast of Crimea, in the near-Kerch zone, and near the northeast coast of the Black Sea. Our numerical investigations are carried out for 24 probable locations of the elliptic zones of tsunami generation over the continental slope of the basin. The amplitude characteristics of tsunamis are computed for 27 sites of the Black-Sea coast. It is shown that significant strengthening of tsunami waves is possible in the course of their propagation toward the coast. The highest waves are formed at the sites of the coast closest to the seismic source. The dependence of the intensity of tsunami waves along the Black-Sea coast on the location of the seismic source and its magnitude is analyzed.     

Statistical Simulation of Boxing Day Tsunami of The Indian Ocean and a Predictive Equation for Beach Run up Heights Based on Work-Energy Theorem

The tsunami similar to the one that has occurred in December 26, 2004 (Boxing Day Tsunami) in the Indian Ocean is simulated using the expression derived from Modified Weibull Distribution (for maximum wave height simulation) for extreme wave height predictions. The tuning coefficient plays a significant role in estimating the tsunami heights at various stages. It follows well defined mathematical laws at different stages. It is time dependent in the first three stages and depth dependent in the last two stages. The beach run-up heights estimated by the expression derived from the work-energy relation are comparable with observed values with reasonable accuracy.     

植被斜坡岸滩海啸波消减数值模拟研究

An explicit one-dimensional model based on the shallow water equations(SWEs) was established in this work to simulate tsunami wave propagation on a vegetated beach. This model adopted the finite-volume method(FVM)for maintaining the mass balance of these equations. The resistance force caused by vegetation was taken into account as a source term in the momentum equation. The Harten–Lax–van Leer(HLL) approximate Riemann solver was applied to evaluate the interface fluxes for tracing the wet/dry transition boundary. This proposed model was used to simulate solitary wave run-up and long-periodic wave propagation on a sloping beach. The calibration process suitably compared the calculated results with the measured data. The tsunami waves were also simulated to discuss the water depth, tsunami force, as well as the current speed in absence of and in presence of forest domain. The results indicated that forest growth at the beach reduced wave energy loss caused by tsunamis. A series of sensitivity analyses were conducted with respect to variable parameters(such as vegetation densities, wave heights, wave periods, bed resistance, and beach slopes) to identify important influences on mitigating tsunami damage on coastal forest beach.     

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。     

Forecasting of tsunami wave heights at the Russian coast of the Black Sea

Forecasting of tsunami wave heights at the Russian coast of the Black Sea is discussed. Prognostic numerical calculations of tsunamis were carried out for the tsunami sources uniformly distributed in the Black Sea basin (a total of 55 events). Their results are compared with the results of numerical modeling of the historical events (in 1939 and 1966) and the data of not numerous measurements. A preliminary forecast is made on this basis for the tsunami wave heights along the Russian coast of the Black Sea.