Estimation Of Run-up Research Articles

Run-up on vertical piles due to regular waves: Small-scale model tests and prediction formulae

In wave-structure interaction, one of the most important phenomena clearly identified is wave run-up on offshore structures. In this study, wave run-up on a slender pile due to non-breaking regular waves is investigated by means of small-scale experiments performed in the 2m-wide wave flume of Leichtweiss-Institute for Hydraulic Engineering and Water Resources (LWI) in Braunschweig, Germany. The test programme is designed to generate a comprehensive data set covering a broader range of wave conditions including not only deep and intermediate water conditions but also nearly shallow and shallow water conditions, which are missing in the available laboratory studies on wave run-up on piles. The relative wave height (H/h), relative water depth (h/L) and slenderness of pile (D/L) are identified as the key parameters governing the relative wave run-up (Ru/H). Based on these parameters, new formulae covering the range of tested conditions (0.028≤H/h≤0.593, 0.042≤h/L≤0.861, 0.003≤D/L≤0.206) are developed to predict regular non-breaking wave run-up on single piles using a combination of the M5 model tree and nonlinear regression techniques. Using statistical accuracy metrics such as agreement index Ia, squared correlation coefficient R2 and scatter index SI, the performance of the developed formulae is evaluated. It is shown that the new formulae outperform the current formulae in predicting regular wave run-up on single piles. This success is in part due to the explicit account for the water depth in the new experiments and formulae. The proposed model is valid for a wider range of wave conditions and, therefore, more appealing for engineering practice compared to those available for the estimation of regular wave run-up.

The influence of seasonal to interannual nearshore profile variability on extreme water levels: Modeling wave runup on dissipative beaches

Wave runup, an important contributor to storm-induced extreme water levels, is commonly predicted via empirical formulations that parameterize coastal morphology using simple metrics such as the foreshore beach slope. However, spatially and temporally complex nearshore morphology, such as subtidal sandbars, have the potential to alter surf zone wave dissipation patterns and therefore influence setup, swash, and runup levels observed at the shoreline. In this study, a suite of numerical experiments using XBeach demonstrate reasonable skill in reproducing wave runup observations in dissipative settings, explore the relative influence of seasonal to interannual variability in nearshore morphology on runup and its constitutive components, and illustrate differences between empirical and numerically modeled estimates of runup. The numerical model results show that interannual variability in sandbar configuration, associated with net offshore sandbar migration, has a larger influence on wave runup than does seasonal sandbar variability. Although the particular configuration of sandbars was estimated to influence runup by as much as 0.18m during storm conditions, natural variability in subaerial beach topography has a stronger influence on runup than subtidal morphology. XBeach demonstrates that both wave setup and infragravity swash have morphologic controls. In experiments simulating storm conditions in which both nearshore and beach morphology was varied, natural interannual variability in beach topography explained about 80% of the variance in runup and its constituents. While XBeach predictions of setup, swash, and runup compare favorably with empirical predictors for low wave conditions, the numerical model predicts higher runup levels for storm-conditions on dissipative beaches raising potential concerns about coastal hazards assessments that use these empirical models to estimate extreme total water levels.

Estimation of regular wave run-up on slopes of perforated coastal structures constructed on sloping beaches

This study was carried out to investigate the regular wave run-up phenomenon on smooth slopes of perforated coastal structures constructed on sloping beaches and the various parameters that affect wave run-up. Experiments were conducted using various hydraulic and structural parameters. The relative coastal structure distance, relative depth, relative wave height, beach slope, coastal structure inclination, and surf similarity parameter were found to be positively correlated to the relative wave run-up. The wave steepness and coastal structure perforation percentage were found to be negatively correlated to the relative wave run-up. The results also show that the coastal structure perforation percentage plays a dominant role in the attenuation of short waves but a less significant role in the attenuation of long waves. The quantitative analyses were performed using multiple additive regression trees (MART) and multilayer perceptron neural networks (MLP) methods. The results indicate that the MART method׳s prediction accuracy and avoidance of over-fitting were superior to those of the MLP method. The percentage improvement in the root mean square error of the MART model over the MLP model in predicting relative wave run-up was 57.56%. The analysis results suggest that MART-based modeling is effective in predicting wave run-up.

Maximum-recorded overland run-ups of major nearfield paleotsunamis during the past 3000 years along the Cascadia margin, USA, and Canada

Maximum-recorded run-up estimates of six major nearfield paleotsunamis, dating from 0.3 to 2.8 ka, are compiled from reported studies at 12 reliable localities distributed over a north–south distance of 1000 km in the Cascadia subduction zone. The run-up estimates are based on surveyed elevations and positions of terminal sand sheet layers that were deposited by the dated paleotsunamis. Maximum terminal deposit elevations from open-coastal sites range from 3 to 12 m NAVD88. Paired proximal and distal run-up sites at four localities demonstrate landward vertical attenuation gradients (−2.5 to −4.2 m km−1) of decreasing terminal sand deposit elevation with increasing distance inland. An averaged attenuation gradient is reversed (3.0 m km−1) to project paleotsunami run-up elevations to adjacent ocean shorelines. The run-up projections are further adjusted by paleotsunami age and relative sea level curves to estimate shoreline inundation elevations under modern sea level conditions. The tsunami shoreline inundation elevations range from 3 ± 2 to 15 ± 2 m NAVD88, with the largest values occurring along the central Cascadia margin and the smallest values occurring in the eastern Juan de Fuca Strait. Contradictory to some numerical tsunami modeling assumptions, there is no apparent correlation between duration of interseismic strain accumulation or estimated upper-plate elastic flexure and corresponding paleotsunami run-up heights on the central Cascadia margin. The short duration since the last Cascadia megathrust rupture (0.3 ka) cannot be used to imply smaller run-up values for a near-future Cascadia tsunami. Coastal communities should plan for the maximum paleotsunami run-ups as recorded at the nearest reliable run-up localities.

Estimation of wave runup on shorelines based on long-term variation of wave conditions

This article provides a simple analytical method which can be used to give estimates of the wave runup on shorelines based on long-term variation of wave conditions. This is achieved by providing bivariate distribution of significant wave height with the wave runup. This wave runup is defined in terms of significant wave height and spectral peak period in deep water. This article presents the mean value and the standard deviation, that is, more precisely the conditional expected value and the conditional variance of the wave runup for given significant wave height. Examples of results corresponding to typical field conditions are also given. Based on, for example, global wave statistics, the present analytical results can be used to make estimates of the wave runup.

Wave Runup in a Sand Bed Physical Model

AbstractThe extreme phenomena induced by climate change have generated new interest in analyses of wave runup on beaches. Extreme runup quantification is essential for coastal management and protection against coastal flooding. Several formulations deduced from empirical studies are available for runup estimation, although scattering is high when applied to practical cases. This paper presents the results of a physical model experiment carried out in the Laboratory for Maritime Experimentation at CEDEX on three sand bed beaches with uniform slopes of 1/20, 1/30, and 1/50. The performance of each formulation is discussed with the aim of choosing the best formulations available for coastal engineering. A new formulation is proposed that accounts for beach slope. Choosing the most extreme beach profile prior to a storm reaching the shore in this formulation provides the required model for risk analysis.

Runup estimations on a macrotidal sandy beach

This paper presents a methodological approach to calculate runup from the analysis of morphodynamic conditions on a macrotidal sandy beach. The method is based on measurements of the elevation of high-tide deposits and on the analysis of morphological and hydrodynamic changes. A series of measurements has been carried out on the beach of Vougot (Brittany, France) under different wave conditions. This allowed to assess runup formula effectiveness on a macrotidal sandy beach and to determine the best slope parameters to estimate runup. The results suggest that on that macrotidal sandy beach the slope of the active section of the upper beach should be used instead of the entire slope of the foreshore, the latter resulting in an underestimation of runup elevations when used in predictive equations from the literature. Results obtained with widely used equations are relatively well correlated with observed values (r2=0.63). An analysis of the relationship between observed runup elevations and various variables has enabled the establishment of a runup estimation formula with a relatively good fit to the study site (r2=0.86).

PHYSICAL MODEL AND REVISION OF THEORETICAL RUNUP

Several formulations deduced from empirical studies are available for runup estimation. Scattering is high when applied to practical cases. Through a state of the art best formulations are chosen. This equations are also studied in a physical model carried out in the Laboratory for Maritime Experimentation of CEDEX with three beaches with slopes 1/20, 1/30 and 1/50 and with sand bed. The performance of each formulation is discussed. A new formulation is proposed in order to give more weight to the beach slope thus reducing scatter.

Tsunami runup in narrow bays: the case of Samoa 2009 tsunami

Abnormal tsunami amplification and runup in narrow bays is studied with respect to the Samoa tsunami of 29 September 2009. The data of the tide gauge in Pago Pago harbour are used to calculate wave runup in the city of Pago Pago (Tutuila, American Samoa) for two approximations of the bottom topography: a plane beach and a narrow bay. Theoretical estimates of tsunami runup are compared with field survey data for the 2009 Samoa tsunami. It is shown that both formulations result in equally good estimates of runup, having approximately the same difference with the field measurements. However, the narrow bay model presents more wave amplification and, consequently, runup, which is the main observation of the field survey. The differences in estimated shoreline velocity, travel time and wave breaking regime, calculated in the framework of these two approximations, are also discussed. It is concluded that wave runup in narrow bays should be calculated by the corresponding formulas, which should be taken into account by tsunami early warning systems.

Stochastic analysis of tsunami runup due to heterogeneous coseismic slip and dispersion

Most tsunami models apply dislocation models that assume uniform slip over the entire fault plane, followed by standard analytical models based on Volterra's theory of elastic dislocations for the seabed deformation. In contrast, we quantify tsunami runup variability for an earthquake with fixed magnitude but with heterogeneous rupture distribution assuming plane wave propagation (i.e., an infinitely long rupture). A simple stochastic analysis of 500 slip realizations illustrates the expected variability in coseismic slip along a fault plane and the subsequent runup that occurs along a coastline in the near field. Because of the need for systematically analyzing different fault geometries, grid resolutions, and hydrodynamic models, several hundred thousand model runs are required. Thus, simple but efficient linear models for the tsunami generation, propagation, and runup estimation are used. The mean value and variability of the maximum runup is identified for a given coastal slope configuration and is analyzed for different dip angles. On the basis of the ensemble runs, nonhydrostatic effects are discussed with respect to their impact on generation, nearshore propagation, and runup. We conclude that for the geometry and magnitude investigated, nonhydrostatic effects reduce the variability of the runup; that is, hydrostatic models will produce an artificially high variability.

A macroseismic model of a tsunami source and estimation of its efficiency by numerical modeling

A typical model of the source of a tsunami (“macroseismic source”) is suggested for use in approximate estimation of maximum tsunami height using straightforward numerical modeling. In this paper the model is tested using three actual events: the 1952 North Kuril Is., 1971 Moneron, and 1994 Shikotan earthquakes, which excited considerable tsunamis at Russia’s Far East coasts. Comparison of the maximum tsunami runup values as obtained in numerical experiments with observations of actual tsunamis showed that the numerical model proposed here is suitable for crude estimation of tsunami runup and tsunami waiting times for coastal population centers in the near zone of a tsunami source.

Role of Vegetation on Beach Run-up due to Regular and Cnoidal Waves

Abstract The effectiveness of measures in protecting the coast against natural hazards depends on the extent of run-up by ocean waves, which is an essential parameter in their planning and design. Although, several formulae have been derived in the past for estimation of run-up in laboratory studies for a variety of wave front structures, certain uncertainties still remain pertaining to flat slopes and long waves. To understand the performance characteristics of vegetation in attenuating run-up, a comprehensive experimental investigation was taken up. The studies were carried out with regular and cnoidal waves propagating over a plane slope of 1 ∶ 30 in the presence and absence of vegetation of different characteristics. The results on the variation of dimensionless run-up as a function of wave and vegetal parameters are presented and discussed in this paper.

Predicting Extreme Wave Run-Up on Natural Beaches for Coastal Planning and Management

A simple empirical model is proposed for predicting extreme wave run-up on natural beaches during severe wave events (deep water wave heights H 0 ≳ 8 m or return periods of about 50 years). The new model departs from traditional approaches that use the slope of the beach face ßf and the Iribarren number ξ0 s parameters for predicting run-up and instead uses the distance offshore xh , to water depth h to estimate a near-shore profile slope as S = h/xh , where the depth of closure is the proposed choice for h. Extreme run-up Rx is then expressed in terms of S as Rx/H0 = CS 2/3. Observations from recent severe storm events in South Africa are used to estimate the dimensionless coefficient C ≃ 7.5. The data are also compared with those of Holman [1986] and the results verify his regression equations and confirm they are valid for significant wave heights extending to 8.5 m for beach-face slopes around 0.1. The run-up predictions of Holman [1986], Nielsen and Hanslow [1991] and Stockdon et al. [2006] are compared to those of the proposed new model. The results suggest that the new model reduces the uncertainties in predicting wave run-up on natural beaches compared with previous models, and thus enables improved estimates of extreme wave run-up and the upper limit of beach change for coastal planning and management.

Recent Capabilities of CMS-Wave: A Coastal Wave Model for Inlets and Navigation Projects

Abstract The Coastal Inlets Research Program (CIRP) of the U.S. Army Engineer Research and Development Center (ERDC), Coastal and Hydraulics Laboratory (CHL) has developed a nearshore spectral wave transformation numerical model to address needs of the U.S. Army Corps of Engineers (USACE) navigation projects. The model is called CMS-Wave and is part of Coastal Modeling System (CMS) for wave estimates in the vicinity of coastal and estuarine navigation channels. It can simulate important wave processes at coastal inlets including wave diffraction, refraction, reflection, wave breaking and dissipation mechanisms, wave-current interaction, and wave generation and growth. This paper describes recent improvements in CMS-Wave that include semi-empirical estimates of wave run-up and overtopping, nonlinear wave-wave interactions, and wave dissipation over muddy bottoms. CMS-Wave may be used with nested grids and variable rectangular cells in a rapid mode to assimilate full-plane wave generation for circulation an...

Experimental insights into the scaling and variability of local tsunamis triggered by giant subduction megathrust earthquakes

Giant subduction megathrust earthquakes of magnitude 9 and larger pose a significant tsunami hazard in coastal regions. In order to test and improve empirical tsunami forecast models and to explore the susceptibility of different subduction settings we here analyze the scaling of subduction earthquake‐triggered tsunamis in the near field and their variability related to source heterogeneities. We base our analysis on a sequence of 50 experimentally simulated great to giant (Mw = 8.3–9.4) subduction megathrust earthquakes generated using an elastoplastic analog model. Experimentally observed surface deformation is translated to local tsunami runup using linear wave theory. We find that the intrinsic scaling of local tsunami runup is characterized by a linear relationship to peak earthquake slip, an exponential relationship to moment magnitude, and an inverse power law relationship to fore‐arc slope. Tsunami variability is controlled by coseismic slip heterogeneity and strain localization within the fore‐arc wedge and is characterized by a coefficient of variation Cv ∼ 0.5. Wave breaking modifies the scaling behavior of tsunamis triggered by the largest (Mw > 8.5) events in subduction settings with shallow dipping (<1–2°) fore‐arc slopes, limits tsunami runup to <30 m, and reduces its variability to Cv ∼ 0.2. The resulting effective scaling relationships are validated against historical events and numerical simulations and reproduce empirical scaling relationships. The latter appear as robust and liberal estimates of runup up to magnitude Mw = 9.5. A global assessment of tsunami susceptibility suggests that accretionary plate margins are more prone to tsunami hazard than erosive margins.

Direct Joint Probability Method for Estimating Extreme Sea Levels

A key design element in coastal structures is the crest elevation which protects against damages due to overflowing and overtopping. In order to avoid overflowing, the design crest elevation should be above the extreme flood level, which is usually composed of tides and storm surges but could also include tsunami, El Nino, and other climatologic and geologic effects. The extreme flood level may be determined with the annual maxima, simple addition, or joint probability methods (JPM). These methods have various limitations in terms of the amount of required data, the representation of factors contributing to sea level fluctuations, the ability to assess the joint probability of these factors, and the degree of data independence required. To minimize overtopping, the design crest elevation should be above the extreme sea level which is evaluated considering wave runup and the extreme flood level. Wave runup estimates are based on selected extreme flood levels and the extreme wave climate, data for which are often dependent. A modification of the JPM, the direct JPM (DJPM), is developed for estimating extreme flood and sea levels. This method may be applied to consider any number of dependent contributing factors. Data for the City of Richmond, B.C., Canada, are used to demonstrate the DJPM. The DJPM provides an estimate of the extreme flood level for Richmond that is within the same range as those obtained using traditional estimation methods. The results indicate a large difference between extreme flood and sea level estimates. The sea levels at Richmond are also increasing due to climate and tectonic effects. A hybrid direct joint probability-simple addition method is applied to consider these effects.

Analysis of the Nonlinear Shallow Water Equations Over Nonplanar Topography

The role played by the beach bottom profile on coastal inundation phenomena is analyzed here by means of approximate analytical solutions of the nonlinear shallow water equations (NSWEs) over uneven bottoms. These are obtained by only using the assumptions of small waves at the seaward boundary and small topographic forcing. Our work, built on the Carrier and Greenspan [1] hodographic transformation and on the solution of the boundary value problem (BVP) for the NSWEs proposed by Antuono and Brocchini [2], focuses on the propagation of nonlinear non-breaking waves over quasi-planar beaches. Since the terms associated with the perturbed bottom only appear in the second-order perturbed solutions, the breaking conditions for the planar-beach bathymetry also predict well the breaking occurring on the nonplanar beaches analyzed here. The most important results, concerning the shoreline position and the near-shoreline velocity, are given for both pulse-like and periodic input waves propagating over two types of nonplanar bathymetries. The solution proposed here is a fundamental benchmark for any numerical and theoretical analyzes concerned with estimates of wave run-up on beaches of complex shape.

Earthquakes and tsunami in November 1755 in Morocco: a different reading of contemporaneous documentary sources

Abstract. Tsunami seldom strike the European Atlantic shores. The great Lisbon Earthquake of 1 November 1755 is the main destructive tsunamigenic event recorded. Since the mid-1990's, many simulations of propagation of tsunami waves from variants of the possible seismic source have been conducted. Estimates of run-up in Morocco are seldom included in publications, maybe for want of reliable historical data to control the simulations. This paper revisits some early accounts, transmitted as translations to European Chanceries, Scientific Societies and Newspapers. A critical analysis of the documents leads us to conclude that the Lisbon earthquake was overestimated because of amalgamation with a later Rifian earthquake. Then, the overestimation of the tsunami through worst interpretation of the scant data available appeared only reasonable, while the moderate measurements or interpretations were not given their due attention. In Morocco the amplitude of the tsunami (i.e. height at shoreline minus expected tide level) may not have exceed the measurement given by Godin (1755) for Cadiz, 2.5 m above the calculated astronomical tide, a crest-to-trough amplitude of 5 m at most. This age-old overestimation of both the earthquake and tsunami is detrimental to the evaluation of the risk for coastal people and activities.

Discrimination of Tsunami Sources (Earthquake versus Landslide) on the Basis of Historical Data in Eastern Sicily and Southern Calabria

Abstract The source mechanisms responsible for large historical tsunamis that have struck eastern Sicily and southern Calabria are a topic of robust debate. We have compiled a database of historical coeval descriptions of three large tsunamis: 11 January 1693, 6 February 1783, and 28 December 1908. By using accounts of run-up and inundation and employing an approach proposed by Okal and Synolakis in 2004, we can provide discriminants to define the nature of the near-field tsunami sources (fault dislocation or landslide). Historical reports for the 1908 event describe affected localities, maximum run-ups, and inundation areas. However, for the 1693 and 1783 tsunamis, reports are limited to inundation and occasional run-up estimates. We calculate run-up values for these events using available relations between inundation and run-up. We employed the model of Okal and Synolakis to the obtained profiles of tsunami run-up along the inundated shorelines. The 1908 run-up data distribution confirms that the tsunami is compatible with a seismic dislocation source, whereas the 1783 data supports contemporary observations and recent offshore investigations suggesting that the tsunami was produced by an earthquake-triggered submarine landslide. Analysis of the 1693 event data suggests that the tsunami was generated during a tectonic event and thus a seismogenic source should be found offshore.

Application of neuro-fuzzy approach in prediction of runup in swash zone

A prominent parameter in dealing with swash and morphological evolution is the runup length or height, defined as the limit of landward sea. Therefore, it is necessary to predict the runup height in this area. In this paper, the abilities of a new Adaptive-Network-Based Fuzzy Inference System (ANFIS) using subtractive fuzzy clustering method, Fuzzy Inference System (FIS), and existing empirical formulas are implemented for predicting and modeling wave runup in the swash zone. The ANFIS and FIS models are established using the slope angle; Iribarren number and antecedent wave runup data. The empirical formulas are also applied to the same data. Statistical measures were used to evaluate the performance of the models. The existing wave runup, bottom slope, and deep water Iribarren number data for regular and irregular waves on smooth, impermeable plane slopes were used as case studies. The comparison of results reveals that, the ANFIS model provides high accuracy and reliability for wave runup estimation, providing better predictions compared to other techniques. The paper demonstrates that the neuro-fuzzy approach developed is a good trade-off between the advantages of the Neural Network (supervised learning capabilities) and of the Fuzzy Logic (knowledge which can be explained and understood) without the generic drawbacks (overfitting, optimization problems, etc.) typical in other approaches.