Reconstruction of Sea Level Around the Korean Peninsula Using Cyclostationary Empirical Orthogonal Functions

Since the advent of the modern satellite altimeter era, the understanding of the sea level has increased dramatically. The satellite altimeter record, however, dates back only to the 1990s. The tide gauge record, on the other hand, extends through the 20th century but with poor spatial coverage when compared to the satellites. Many studies have been conducted to create a dataset with the spatial coverage of the satellite datasets and the temporal length of the tide gauge records by finding novel ways to combine the satellite data and tide gauge data in what is known as sea level reconstruction. However, most of the reconstructions of sea level were conducted on a global scale, leading to reduced accuracy on regional levels, especially when there are relatively few tide gauges. The seas around the Korean Peninsula are one such area with few tide gauges before 1960. In this study, new methods are proposed to reconstruct past sea level around the Korean Peninsula. Using spatial patterns obtained from a cyclostationary empirical orthogonal function decomposition of satellite data, we reconstruct sea level over the period from 1900 to 2014. Sea surface temperature data and altimeter data are used simultaneously in the reconstruction process, leading to an elimination of reliance on tide gauge data. Although we did not use the tide gauge data in the reconstruction process, the reconstructed sea level has a better agreement with the tide gauge observations in the region than previous studies that incorporated the tide gauge data. This study demonstrates a reconstruction technique that can potentially be used at regional levels, with particular emphasis on areas with poor tide gauge coverage

Wave interactions with multiple-row curtainwall-pile breakwaters

In this study, a mathematical model has been developed that can compute various hydrodynamic characteristics of a multiple-row curtainwall-pile breakwater. To examine the validity of the developed model, laboratory experiments have been conducted for double- and triple-row breakwaters with various combinations of drafts of curtain walls, porosities between piles, and distances between rows. Comparisons between measurement and prediction show that the mathematical model adequately reproduces most of the important features of the experimental results. As a whole, the transmission coefficient decreases with an increase in relative water depth, whereas the reflection coefficient, normalized run-up and force exhibit an opposite trend in their variations. With fixed values of the draft of the curtain wall and the porosity of lower perforated part of the first row of a double-row breakwater, as these values of the second row increase and decrease, respectively, the transmission coefficient decreases, as expected. On the other hand, their effects on wave reflection, run-up, and wave force change with the relative depth. As for the distance between the rows, the transmission coefficient becomes a maximum when it is about one half of the wave length, suggesting that this condition should be avoided to achieve the advantage of the breakwater in reducing wave transmission. It is shown that for prototype breakwaters, on an average, the transmission coefficient would be smaller than 0.3 for wave periods less than 6.0 s, and it would be about 0.45 even for the wave period of 9.0 s, although there would be a variation depending on the geometry of the breakwater. It is also shown that wave transmission is significantly reduced by multiple-row breakwaters compared with a single-row breakwater, while the difference between double-row and triple-row breakwaters is marginal. Finally, engineering monograms are provided for double-row breakwaters to be used in practical engineering applications of the breakwaters.http://dx.doi.org/10.1016/j.coastaleng.2009.12.00

An analytic solution to the mild slope equation for waves propagating over an axi-symmetric pit

An analytic solution to the mild slope equation is derived for waves propagating over an axi-symmetric pit located in an otherwise constant depth region. The water depth inside the pit decreases in proportion to an integer power of radial distance from the pit center. The mild slope equation in cylindrical coordinates is transformed into ordinary differential equations by using the method of separation of variables, and the coefficients of the equation in radial direction are transformed into explicit forms by using the direct solution for the wave dispersion equation by Hunt (Hunt, J.N., 1979. Direct solution of wave dispersion equation. J. Waterw., Port, Coast., Ocean Div., Proc. ASCE, 105, 457-459). Finally, the Frobenius series is used to obtain the analytic solution. Due to the feature of the Hunts solution, the present analytic solution is accurate in shallow and deep waters, while it is less accurate in intermediate depth waters. The validity of the analytic solution is demonstrated by comparison with numerical solutions of the hyperbolic mild slope equations. The analytic solution is also used to examine the effects of the pit geometry and relative depth on wave transformation. Finally, wave attenuation in the region over the pit is discussed.author's final versio

Application of reliability design methods to Donghae harbor breakwater

Reliability design methods have been developed for breakwater designs since the mid-1980s. The reliability design method is classified into three categories depending on the level of probabilistic concepts being employed, i.e., Level 1, 2, and 3 methods. Each method gives results in different forms, but all of them can be expressed in terms of probability of failure so that the difference can be compared among the different methods. In this study, we apply the reliability design methods to the stability of armor blocks and sliding of caissons of the breakwater of Donghae Harbor located in the east coast of Korea, which was constructed by traditional deterministic design methods to be damaged in 1987 and reinforced in 1991. Analyses are made for the breakwaters before the damage and after the reinforcement. The allowable probability of failure of a Tetrapod armor layer of 50 years lifetime is proposed as 40% for existing stability formulas, whilst that for caisson sliding as 20% with the failure criterion for the cumulative sliding distance over the lifetime of 0.1 m. The probability of failure before the damage is much higher than the allowable value for both stability of armor blocks and sliding of caissons, indicating that the breakwater was under-designed. The probability of failure for the reinforced breakwater is lower than the allowable value, indicating that the breakwater became stable after the reinforcement. On the other hand, the results of different reliability design methods were in fairly good agreement, confirming that there is not much difference among the different methods.author's final versio

Calculation of partial safety factors of breakwater armor stones considering correlation between wave height and wave steepness

author's final versionIn the calculation of partial safety factors of breakwater armor stones, it has been assumed that all the design variables are independent one another. However, some of them are not independent but are correlated each other. In the present study, the partial safety factors are calculated by considering the correlation between wave height and wave steepness. Smaller partial safety factors and smaller armor weight are obtained if the correlation is taken into account. The reduction becomes prominent as the probability of failure decreases (or the design armor weight increases). The correlation between wave height and steepness in real sea is also estimated by using the wave hindcasting data along the Korean coast

An analytical solution to the extended mild-slope equation for long waves propagating over an axi-symmetric pit

author's final versionAn analytic solution to the extended mild-slope equation is derived for long waves propagating over an axi-symmetric pit, where the water depth decreases in proportion to a power of radial distance from the pit center. The solution is obtained using the method of separation of variables and the method of Frobenius. By comparing the extended and conventional mild-slope equations for waves propagating over conical pits with different bottom slopes, it is shown that for long waves the conventional mild-slope equation is reasonably accurate for bottom slopes less than 1:3 in horizontal two-dimensional domains. The effects of the pit shape on wave scattering are discussed based on the analytic solutions for different powers. Comparison is also made with an analytic solution for a cylindrical pit with a vertical sidewall. Finally, wave attenuation in the region over the pit is discussed

Extended Boussinesq Equations for Rapidly Varying Topography

author's final versionWe developed a new Boussinesq-type model which extends the equations of Madsen and Sørensen (1992) by including both bottom curvature and squared bottom slope terms. Numerical experiments were conducted for wave reflection from the Booijs (1983) planar slope with different wave frequencies using several types of Boussinesq equations and extended mild-slope equation. Madsen and Sørensens model results are accurate in the whole slopes in shallow waters but inaccurate in intermediate water depths. Nwogus (1993) model results are accurate up to 1:1 (V:H) slope but significantly inaccurate for steep slopes. The present model results are accurate up to the slope of 1:1 but somewhat inaccurate for very steep slopes. Further, numerical experiments were conducted for wave reflections from a ripple patch and also a Gaussian shaped trench. For the two cases, the results of Nwogus model and the present model are accurate because these models include the bottom curvature term which is important for the cases. However, Madsen and Sørensens model results are inaccurate because this model neglects the bottom curvature term

Extended mild-slope equation for random waves

author's final versionA time-dependent extended mild-slope equation is derived from the elliptic equation of Chamberlain and Porter (1995) using the Taylor series technique. Numerical tests are made on a horizontally one-dimensional case for regular waves over sloping beds and for both regular and irregular waves over a ripple patch. Numerical results prove that the proposed model gives accurate results for both regular and irregular waves over rapidly varying topography

Wave reflection from nearshore depressions

author's final versionThis study employs an existing finite-difference model based on the hyperbolic form of the Modified Mild Slope Equation (MMSE) to investigate wave reflection near bathymetric depressions such as dredged borrow pits and nearshore canyons. First, the model is tested for numerical limitations on the higher order bottom slope and curvature terms using idealized cases of a simple depth transition and a symmetric trapezoidal trench, with comparisons of the MMSE to both the traditional Mild Slope Equation (MSE) solution and a shallow water analytic solution. It is demonstrated that the model gives accurate solutions on slopes as steep as 1:1, and that the solutions from all three models agree in the shallow water region. However, for waves in intermediate depths, predicted wave reflection from nearshore depressions is shown to differ significantly between the MMSE and MSE models. Next, geometrical data from a wide range of existing and proposed borrow pits and a submarine canyon are gathered and analyzed for whether wave reflection is an important process near realistic nearshore depressions. The geometric data show that realistic nearshore depressions lie within the tested range of the MMSE model and that borrow pits are generally not in shallow water, which means it is important to use an MMSE-type model to calculate reflection from these features. In addition, storm conditions on average lead to a 50% increase in reflection coefficient in comparison to the mean wave conditions, due to the increase in wave period. Finally, the results also indicate borrow pit design criteria that can be used to ensure minimal reflection

Generation of random waves in time-dependent extended mild-slope equations using a source function method

We develop techniques of numerical wave generation in the time-dependent extended mild-slope equations of Suh et al. (1997) and Lee et al. (2003) for random waves using a source function method. Numerical results for both regular and irregular waves in one and two horizontal dimensions show that the wave heights and the frequency spectra are properly reproduced. The waves that pass through the wave generation region do not cause any numerical disturbances, showing usefulness of the source function method in avoiding re-reflection problems at the offshore boundary.author's final versio