Exact analytical solutions of nonlinear problems of tsunami wave run-up on slopes with different profiles

A review of papers investigating tsunami wave run-up on a beach is given and the control parameters of the problem are revealed. There are two such parameters in the case of ideal fluid: the bottom sloping angle and the breaking parameter. A stage-by-stage approach for finding run-up characteristics is formulated: the linear calculation of shoreline oscillations and the subsequent non-linear transformation of the solution according to the Riemann method. Solution of the nononedimensional problems of wave run-up on a beach in the linear formulation is obtained.     

Fully nonlinear Boussinesq equations for long wave propagation and run-up in sloping channels with parabolic cross sections

A general framework for derivation of long wave equations in narrow channels, and their transformation to Lagrangian coordinates is briefly established. Then, fully nonlinear Boussinesq equations are derived for channels of parabolic cross sections. The simplified version with normal nonlinearity is compared with corresponding models from the literature, and propagation properties are discussed. A Lagrangian run-up model is adapted to the fully nonlinear set. This model is tested by means of controlled residues and by a well-controlled comparison to exact analytic solutions from the literature. Then, run-up of solitary waves in simple geometries is simulated and compared to a semi-analytic solution that is derived for propagation and run-up in a composite channel. The dispersive model retains the higher run-up height in a parabolic channels, as reported in the recent literature for NLSW solutions, as compared to a rectangular channel.     

基于随机暴雨移置方法的城市设计暴雨分析

城市地区暴雨洪灾发生频繁，合理计算设计暴雨是解决城市洪涝的重要前提。采用随机暴雨移置方法（Stochastic Storm Transposition，SST），设定暴雨移置区并提取出暴雨目录，通过区域性概率重采样与暴雨空间变换相结合的方式进行降雨频率分析，估计本地化的极端暴雨频率。以上海地区为例，研究发现暴雨移置区内暴雨分布具有空间异质性，暴雨随机移置概率不均，计算得到的设计暴雨方案包含了降雨时空分布信息，在不同重现期下设计暴雨的时空结构存在变异性，说明传统方法中采用的简化雨型和均一化空间分布假设会增加设计暴雨的不确定性。     

Revealing effect of bathymetry over tsunami run-up through factor analysis

The east coast of Tamil Nadu, particularly Chennai–Nagapattinam was worstly affected by the 2004 tsunami. Run-up shows remarkable variation of 2–8 m with maximum at Cuddalore port and minimum at Marina beach. Factors like width of dislocation, source distance, orientation of the coastline, and bathymetry guide tsunami surge. While most of the parameters are similar in characteristics for the entire coast, it is presumed that variation in bathymetry have played an imperative role in guiding run-up. Based on gradient bathymetry, up to 50 km off the coast was classified into five classes, viz shallow, moderate, and steep continental slope and continental shelf. Statistical analysis was performed between offshore bathymetry and run-up. The results clearly indicate that moderate slopes have guided tsunami to attain maximum height. While steeper slope have acted as barriers and gentle slopes have shoaled tsunami surge resulting in reduced run-up height. The study offers early but potentially meaningful guidance on the role of bathymetry on run-up.     

基于随机暴雨移置方法的城市设计暴雨分析

城市地区暴雨洪灾发生频繁，合理计算设计暴雨是解决城市洪涝的重要前提。采用随机暴雨移置方法（Stochastic Storm Transposition，SST），设定暴雨移置区并提取出暴雨目录，通过区域性概率重采样与暴雨空间变换相结合的方式进行降雨频率分析，估计本地化的极端暴雨频率。以上海地区为例，研究发现暴雨移置区内暴雨分布具有空间异质性，暴雨随机移置概率不均，计算得到的设计暴雨方案包含了降雨时空分布信息，在不同重现期下设计暴雨的时空结构存在变异性，说明传统方法中采用的简化雨型和均一化空间分布假设会增加设计暴雨的不确定性。     

Significance of nearshore wave parameters in identifying vulnerable zones during storm and normal conditions along Visakhapatnam coast,India

The nearshore parameters, viz., wave runup, wave setup, and wave energy have been estimated during storm and normal conditions of SW monsoon (June–September) and NE monsoon (November–February) by empirical parameterization along Visakhapatnam coast. These results were compared with the field observations during three storms of SW monsoon season in the year 2007. The higher nearshore wave energies were observed at R.K. Beach, Jodugullapalem beach, and Sagarnagar beach during both the seasons. During storm events, the higher wave energies associated with higher wave runups cause severe erosion along the wave convergence zones. The storm wave runups (SWRUs) were higher at R.K. Beach, Palm beach, Jodugullapalem beach, and Sagarnagar Beach. The yearly low wave energy was observed at Lawson’s Bay with lowest wave runup, considered as safest zone. R.K. Beach, Palm beach, and Jodugullapalem beach are identified as vulnerable zones of wave attack. It is noteworthy that in addition to wave energies, wave runups and wave setups also play a vital role in endangering the coast.     

Implementation/optimization of moving least squares response surfaces for approximation of hurricane/storm surge and wave responses

One of the important recent advances in the field of hurricane/storm modelling has been the development of high-fidelity numerical simulation models for reliable and accurate prediction of wave and surge responses. The computational cost associated with these models has simultaneously created an incentive for researchers to investigate surrogate modelling (i.e. metamodeling) and interpolation/regression methodologies to efficiently approximate hurricane/storm responses exploiting existing databases of high-fidelity simulations. Moving least squares (MLS) response surfaces were recently proposed as such an approximation methodology, providing the ability to efficiently describe different responses of interest (such as surge and wave heights) in a large coastal region that may involve thousands of points for which the hurricane impact needs to be estimated. This paper discusses further implementation details and focuses on optimization characteristics of this surrogate modelling approach. The approximation of different response characteristics is considered, and special attention is given to predicting the storm surge for inland locations, for which the possibility of the location remaining dry needs to be additionally addressed. The optimal selection of the basis functions for the response surface and of the parameters of the MLS character of the approximation is discussed in detail, and the impact of the number of high-fidelity simulations informing the surrogate model is also investigated. Different normalizations of the response as well as choices for the objective function for the optimization problem are considered, and their impact on the accuracy of the resultant (under these choices) surrogate model is examined. Details for implementation of the methodology for efficient coastal risk assessment are reviewed, and the influence in the analysis of the model prediction error introduced through the surrogate modelling is discussed. A case study is provided, utilizing a recently developed database of high-fidelity simulations for the Hawaiian Islands.     

Upper Cretaceous Gongila Formation in the Hawal Basin, northeast Benue Trough: a storm and wave dominated regressive shoreline complex

The Gongila Formation in the Hawal Basin displays lithological characteristics, textural variations and sedimentary structures that facilitate palaeoenvironmental reconstruction. The 41 m thick Gongila succession is divisible into: (i) a mudstone facies association (at the bottom) composed of fossiliferous limestone, clay shale, and sharp-based, graded and swaly-bedded shell debris; and (ii) a cross-stratified sandstone facies association that constitutes the uppermost 60% of the entire succession. The cross-stratified sandstone facies association is further subdivided, on the basis of sedimentary structures, into: (i) a lower interval represented by a coarsening upward fine- to medium-grained sandstone, siltstone and shale in which units characterised by parallel lamination and hummocky cross-stratification pass upward through a zone of small-scale low angle cross-stratification into units characterised by planar cross-stratification and sparse Teichichnus and Skolithos burrow traces; and (ii) an upper interval dominated by fine- to medium-grained sandstone and bioturbated siltstone characterised by erosive based, high angle tangential foresets, subhorizontal laminations and burrow structures belonging to the Thalassinoides, Ophiomorpha and Skolithos ichnogenera.The overall sequence of the Gongila Formation represents progradation on a wave influenced coast, passing from shelf mudstone at the base to lower and upper shoreface sandstones at the top. Each facies association displays an alternation between relatively high energy conditions when sediment was mainly deposited by decelerating suspension laden currents, and relatively low energy conditions when wave reworked fine-grained sediment as it was deposited from suspension. The influence of storms in these conditions is inferred from the associated lithofacies, textural characteristics and sedimentary structures.     

Determination of mangrove forest performance in reducing tsunami run-up using physical models

Coastal ecosystems such as mangroves fringing tropical coastlines have been recognized as natural protectors of the coastal areas against destructive attack of a tsunami. In this paper, the authors aim to investigate the interaction of a tsunami wave on a typical mangrove forest and to determine its performance in reducing the run-up. A laboratory experiment using a hydraulic flume with a mangrove forest model was carried out in which tests were conducted by varying the vegetation widths of 0, 1, 2 and 3?m and average densities of 8, 6 and 4 trees per 100?cm² using a scale ratio of 1:100. Two conditions of water levels were considered in the experiments at several tsunami wave heights between 2.4 and 14?cm. The dam break method used in the experiments produced two types of waves. At low water condition, a bore was developed and subsequently, a solitary wave was produced during high water. The results of the experiments showed that in general, vegetation widths and densities demonstrate a dampening effect on tsunami run-up. A larger vegetation width was found to be more effective in dissipating the wave energy. The first 1?m width of mangrove forest could reduce 23?C32?% during high water and 31?C36?% during low water. Increasing the mangrove forest width to 2 and 3?m could further increase the average percentage of run-up reduction by 39?C50?% during high water and 34?C41?% during low water condition. It was also observed that densities of the mangrove forest do not influence the run-up reduction as significantly as the forest widths. For mangrove forest densities to be significantly enough to reduce more tsunami run-up, an additional density of 4 trees/100?m² needs to be provided. The experiments also showed that mangrove roots are more effective in reducing the run-up compared to the trunks and canopies. The experiments managed to compare and present the usefulness of mangrove forests in dissipating wave energy and results produced are beneficial for initiating design guidelines in determining setback limits or buffer zones for development projects in mangrove areas.     

Simplified formulae for designing coastal forest against tsunami run-up: one-dimensional approach

In the present study, laboratory experiments were conducted to validate the applicability of a numerical model based on one-dimensional nonlinear long-wave equations. The model includes drag and inertia resistance of trees to tsunami flow and porosity between trees and a simplified forest in a wave channel. It was confirmed that the water surface elevation and flow velocity by the numerical simulations agree well with the experimental results for various forest conditions of width and tree density. Further, the numerical model was applied to prototype conditions of a coastal forest of Pandanus odoratissimus to investigate the effects of forest conditions (width and tree density) and incident tsunami conditions (period and height) on run-up height and potential tsunami force. The modeling results were represented in curve-fit equations with the aim of providing simplified formulae for designing coastal forest against tsunamis. The run-up height and potential tsunami forces calculated by the curve-fit formulae and the numerical model agreed within ± 10% error.     

Hurricane Katrina storm surge delineation: implications for future storm surge forecasts and warnings

The storm surge in coastal Mississippi caused by Hurricane Katrina was unprecedented in the region. The height and geographic extent of the storm surge came as a surprise to many and exceeded pre-impact surge scenarios based on SLOSH models that were the basis for emergency preparedness and local land use decision-making. This paper explores the spatial accuracy of three interpolated storm surge surfaces derived from post-event reconnaissance data by comparing the interpolation results to a specific SLOSH run. The findings are used to suggest improvements in the calibration of existing pre-event storm surge models such as SLOSH. Finally, the paper provides some suggestions on an optimal surge forecast map that could enhance the communication of storm surge risks to the public.     

The role of wave reworking on the architecture of storm sandstone facies, Bell Island Group (Lower Ordovician), eastern Newfoundland

Stacked shallow marine cycles in the Lower Ordovician, Bell Island Group, of Bell Island, Newfoundland, show upward thickening and upward coarsening sequences which were deposited on a storm-affected shelf. In the Beach Formation each cycle has a facies sequence comprised, from base to top, of dark grey mudstones, light grey mudstones, tabular sandstones and mudstones, lenticular sandstones and mudstones, and thick bedded lenticular sandstones, reflecting a progressive increase of wave orbital velocities at the sediment surface. The mudstones and tabular sandstones reflect an environment in which the sea floor lay in the lower part of the wave orbital velocity field and in which tempestites were deposited as widespread sheets from weak combined flow currents. The lenticular sandstones in the succeeding facies are wave reworked sands, commonly lying in erosional hollows and having erosional tops and internal hummocky cross-stratification. Planar lamination is relatively uncommon and sole marks are mainly absent. In this facies oscillatory currents were dominant and accumulated sand in patches generally 10–30 m in diameter. The facies formed on the inner shelf where the oscillatory currents generated by storm waves had powerful erosional effects and also determined the depositional bedforms. Mud partings and second-order set boundaries within sandstone beds are believed to separate the products of individual storms so that many lenticular sandstone beds represent the amalgamation of several event beds. This interpretation has important implications for attempts to estimate event frequency by counting sandstone beds within a sequence and for estimates of sand budgets during storm events. The thick bedded lenticular facies appears to have been formed by erosion of the mud beds between the lenticular sands, leading to nearly complete amalgamation of several lenticular sand bodies except for residual mud partings. In the overlying Redmans Formation the process of amalgamation progressed even further so that nearly all the mud partings were removed, resulting in the formation of thick bedded tabular sandstones. Sequence stratigraphic analysis of the cyclical sequence suggests that the cycles were eustatically controlled. The rising limb of the sea level curve produced only the dark grey mudstone part of the cycle while the remainder of the cycle was deposited on the falling limb. There is a gradational but rapid facies transition from the tabular to the lenticular sandstone facies which is interpreted as occurring at the inflexion point on the falling limb. The thick bedded facies of the Beach Formation and the thick bedded tabular facies of the Redmans Formation represent periods of maximum sea level fall. The stacked cycles in the Beach Formation are interpreted as an aggradational, high frequency sequence or parasequence set bounded at the top by a sequence boundary and succeeded by the three aggradational parasequences of the Redmans Formation. The recognition of storm facies with sandstone beds of very different bed length has important implications for the reservoir modelling of such facies.     

Tsunamis versus storm deposits from Thailand

Along the Andaman (west) coast of Thailand, the 2004 tsunami depositional features associated with the 2004 tsunami were used to describe the characteristics of tsunamis in a place far away from the effect of both recent and ancient storms. The current challenge is that a lack of precise sedimentological characteristics have been described that will differentiate tsunami deposits from storm deposits. Here, in sedimentological senses, we reviewed the imprints of the sedimentological characteristics of the 2004 tsunami and older deposits and then compared them with storm deposits, as analyzed from the deposits found along the eastern (Gulf of Thailand; GOT) coast of Thailand. We discuss the hydraulic conditions of the 2004 tsunami and its predecessors, on the Andaman coast, and compare them to storm flows found on the coast of the GOT. Similar to an extensive tsunami inflow deposit, a storm flow overwash has very similar sedimentary structures. Well-preserved sedimentary structures recognized in sand sheets from both tsunami and storms include single and multiple normal gradings, reverse grading, parallel, incline and foreset lamina, rip-up clasts, and mud drapes. All these sedimentary structures verify the similarity of tsunami and storm inflow behavior as both types of high-energy flow start to scour the beach zone. Antidunes are likely to be the only unique internal sedimentary structures observed in the 2004 tsunami deposit. Rip-up clasts are rare within storm deposits compared to tsunami deposits. We found that the deposition during the outflow from both tsunami and storms was rarely preserved, suggesting that it does not persist for very long in the geological record.     

城市暴雨积水过程的模拟

在对城市排水系统产汇流特性分析的基础上,采用水文学与水力学相结合途径,建立了城市地面积水数学模型。模型能够可靠地模拟暴雨造成的城市地面积水的量级、面积、深度和历时,并借助GIS的功能动态地演示地面积水的涨消过程,为制定城市防汛减灾对策和措施提供水情及涝情信息。     

Laboratory experiments of tsunami run-up and withdrawal in patchy coastal forest on a steep beach

Laboratory experiments were carried out to study tsunami flow dynamics in the presence of patchy macro-roughness, representing coastal forest, on a 1:10 steep beach. The experimental setup included four cross-shore rows of roughness patches affixed to the dry beach in a staggered array, such that 12 % of the staggered array region had higher roughness. The flow field during run-up and withdrawal was quantified using point measurements of velocity and flow depth at 20 locations, while high-resolution video was used to track bore position during run-up. Data analysis revealed that while inundated area was marginally impacted when patchy roughness was present, flow depths and flow force were, respectively, increased by more than 40 and 30 % in some areas within the patch array; a decrease in flow force was also observed in some areas. Alongshore variation in flow depth, induced by the roughness patches, was most pronounced during withdrawal. These findings suggest that patchy macro-roughness, like that created by coastal forest, will simultaneously lead to increased protection in some areas and decreased protection in others.     

Hurricane storm surge simulations for Tampa Bay

Using a high resolution, three-dimensional, primitive equation, finite volume coastal ocean model with flooding and drying capabilities, supported by a merged bathymetric-topographic data set and driven by prototypical hurricane winds and atmospheric pressure fields, we investigated the storm surge responses for the Tampa Bay, Florida, vicinity and their sensitivities to point of landfall, direction and speed of approach, and intensity. All of these factors were found to be important. Flooding potential by wind stress and atmospheric pressure induced surge is significant for a category 2 hurricane and catastrophic for a category 4 hurricane. Tide, river, and wave effects are additive, making the potential for flood-induced damage even greater. Since storm surge sets up as a slope to the sea surface, the highest surge tends to occur over the upper reaches of the bay, Old Tampa Bay and Hillsborough Bay in particular. For point of landfall sensitivity, the worst case is when the hurricane center is positioned north of the bay mouth such that the maximum winds associated with the eye wall are at the bay mouth. Northerly (southerly) approaching storms yield larger (smaller) surges since the winds initially set up (set down) water level. As a hybrid between the landfall and direction sensitivity experiments, a storm transiting up the bay axis from southwest to northeast yields the smallest surge, debunking a misconception that this is the worst Tampa Bay flooding case. Hurricanes with slow (fast) translation speeds yield larger (smaller) surges within Tampa Bay due to the time required to redistribute mass.     

Advances in surrogate modeling for storm surge prediction: storm selection and addressing characteristics related to climate change

This paper establishes various advancements for the application of surrogate modeling techniques for storm surge prediction utilizing an existing database of high-fidelity, synthetic storms (tropical cyclones). Kriging, also known as Gaussian process regression, is specifically chosen as the surrogate model in this study. Emphasis is first placed on the storm selection for developing the database of synthetic storms. An adaptive, sequential selection is examined here that iteratively identifies the storm (or multiple storms) that is expected to provide the greatest enhancement of the prediction accuracy when that storm is added into the already available database. Appropriate error statistics are discussed for assessing convergence of this iterative selection, and its performance is compared to the joint probability method with optimal sampling, utilizing the required number of synthetic storms to achieve the same level of accuracy as comparison metric. The impact on risk estimation is also examined. The discussion then moves to adjustments of the surrogate modeling framework to support two implementation issues that might become more relevant due to climate change considerations: future storm intensification and sea level rise (SLR). For storm intensification, the use of the surrogate model for prediction extrapolation is examined. Tuning of the surrogate model characteristics using cross-validation techniques and modification of the tuning to prioritize storms with specific characteristics are proposed, whereas an augmentation of the database with new/additional storms is also considered. With respect to SLR, the recently developed database for the US Army Corps of Engineers’ North Atlantic Comprehensive Coastal Study is exploited to demonstrate how surrogate modeling can support predictions that include SLR considerations.