Simulation of nonlinear wave run-up with a high-order Boussinesq model

This paper considers the numerical simulation of nonlinear wave run-up within a highly accurate Boussinesq-type model. Moving wet–dry boundary algorithms based on so-called extrapolating boundary techniques are utilized, and a new variant of this approach is proposed in two horizontal dimensions. As validation, computed results involving the nonlinear run-up of periodic as well as transient waves on a sloping beach are considered in a single horizontal dimension, demonstrating excellent agreement with analytical solutions for both the free surface and horizontal velocity. In two horizontal dimensions cases involving long wave resonance in a parabolic basin, solitary wave evolution in a triangular channel, and solitary wave run-up on a circular conical island are considered. In each case the computed results compare well against available analytical solutions or experimental measurements. The ability to accurately simulate a moving wet–dry boundary is of considerable practical importance within coastal engineering, and the extension described in this work significantly improves the nearshore versatility of the present high-order Boussinesq approach.     

Velocity potential formulations of highly accurate Boussinesq-type models

The highly accurate Boussinesq-type equations of Madsen et al. (Madsen, P.A., Bingham, H.B., Schäffer, H.A., 2003. Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: Derivation and analysis. Proc. R. Soc. Lond. A 459, 1075–1104; Madsen, P.A., Fuhrman, D.R., Wang, B., 2006. A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry. Coast. Eng. 53, 487–504); Jamois et al. (Jamois, E., Fuhrman, D.R., Bingham, H.B., Molin, B., 2006. Wave-structure interactions and nonlinear wave processes on the weather side of reflective structures. Coast. Eng. 53, 929–945) are re-derived in a more general framework which establishes the correct relationship between the model in a velocity formulation and a velocity potential formulation. Although most work with this model has used the velocity formulation, the potential formulation is of interest because it reduces the computational effort by approximately a factor of two and facilitates a coupling to other potential flow solvers. A new shoaling enhancement operator is introduced to derive new models (in both formulations) with a velocity profile which is always consistent with the kinematic bottom boundary condition. The true behaviour of the velocity potential formulation with respect to linear shoaling is given for the first time, correcting errors made by Jamois et al. (Jamois, E., Fuhrman, D.R., Bingham, H.B., Molin, B., 2006. Wave-structure interactions and nonlinear wave processes on the weather side of reflective structures. Coast. Eng. 53, 929–945). An exact infinite series solution for the potential is obtained via a Taylor expansion about an arbitrary vertical position z = zˆ. For practical implementation however, the solution is expanded based on a slow variation of zˆ and terms are retained to first-order. With shoaling enhancement, the new models obtain a comparable accuracy in linear shoaling to the original velocity formulation. General consistency relations are also derived which are convenient for verifying that the differential operators satisfy a potential flow and/or conserve mass up to the order of truncation of the model. The performance of the new formulation is validated using computations of linear and nonlinear shoaling problems. The behaviour on a rapidly varying bathymetry is also checked using linear wave reflection from a shelf and Bragg scattering from an undulating bottom. Although the new models perform equally well for Bragg scattering they fail earlier than the existing model for reflection/transmission problems in very deep water.     

Tsunami generation,propagation, and run-up with a high-order Boussinesq model

In this work we extend a high-order Boussinesq-type (finite difference) model, capable of simulating waves out to wavenumber times depth kh < 25, to include a moving sea-bed, for the simulation of earthquake- and landslide-induced tsunamis. The extension is straight forward, requiring only an additional term within the kinematic bottom condition. As first test cases we simulate linear and nonlinear surface waves generated from both positive and negative impulsive bottom movements. The computed results compare well against earlier theoretical, numerical, and experimental values. Additionally, we show that the long-time (fully nonlinear) evolution of waves resulting from an upthrusted bottom can eventually result in true solitary waves, consistent with theoretical predictions. It is stressed, however, that the nonlinearity used far exceeds that typical of geophysical tsunamis in the open ocean. The Boussinesq-type model is then used to simulate numerous tsunami-type events generated from submerged landslides, in both one and two horizontal dimensions. The results again compare well against previous experiments and/or numerical simulations. The new extension compliments recently developed run-up capabilities within this approach, and as demonstrated, the model can therefore treat tsunami events from their initial generation, through their later propagation, and final run-up phases. The developed model is shown to maintain reasonable computational efficiency, and is therefore attractive for the simulation of such events, especially in cases where dispersion is important.     

Mangrove expansion and rainfall patterns in Moreton Bay, Southeast Queensland, Australia

Changes in rainfall pattern have been suggested as a mechanism for the landward incursion of mangrove into salt marsh. The aim of the research was to assess the relationship between rainfall patterns and the spatial distribution of mangrove forests at study sites in Moreton Bay, Southeast Queensland, Australia, over a 32-year period from 1972 to 2004. To identify periods of relatively consistent rainfall patterns points at which rainfall patterns changed (change-points) were identified using the non-parametric Pettitt–Mann–Whitney-Statistic and the cumulative sum technique. The change-points were then used to define the temporal periods over which changes to mangrove area were assessed. Both mangrove and salt marsh area were measured by digitizing aerial photographs acquired in 1972, 1990 (the year with the most significant change-point), and 2004. The rates of change in mangrove area pre-1990 (a wetter period) and post-1990 (a drier period) were estimated. A significant positive relationship was demonstrated between rainfall variables and landward mangrove expansion, but not for seaward expansion. We concluded that rainfall variability is one of the principal factors influencing the rate of upslope encroachment of mangrove. However, the rate of expansion may vary from site to site due to site-specific geomorphological and hydrological characteristics and the level of disturbance in the catchment.     

Local and landscape effects on spatial patterns of mangrove forest during wetter and drier periods: Moreton Bay,Southeast Queensland,Australia

Land use/cover and mangrove spatial changes were assessed for ten sites and their sub-catchments in Southeast Queensland, Australia. Two time periods were involved: 1972–1990, a period of relatively high rainfall, and 1990–2004, which was significantly drier. Aerial photographs and Landsat satellite imagery were used to map the inter-tidal wetlands and classify the land use/cover in the sub-catchments. A Maximum Likelihood Classification was used to map three types of land cover: agriculture, built-up and plantation forest. Mangroves (mainly Avicennia marina) were the focus as they have been recorded over recent decades encroaching into salt marsh. The Mangrove-Salt marsh Interface (MSI) Index was developed to quantify the relative opportunity for mangroves to expand into salt marshes, based on the shared boundary between them. The index showed a consistent relationship with mangrove expansion and change. To address problems of high dimensionality and multi-collinearity of predictor variables, a Partial Least Squares Regression (PLSR) model was used. A key finding of this research was that the contribution of environmental variables to spatial changes in the mangroves was altered following a reduction in rainfall. For example, agriculture had more influence on mangrove expansion and change during the wet period than during the dry period.     

The Eltanin asteroid impact: possible South Pacific palaeomegatsunami footprint and potential implications for the Pliocene–Pleistocene transition

Large asteroid impacts are rare, and those into the deep ocean are rarer still. The Eltanin asteroid impact around 2.51 ± 0.07 Ma occurred at a time of great climatic and geological change associated with the Pliocene–Pleistocene boundary. Numerical models of the event indicate that a megatsunami was generated, although there is debate concerning its magnitude and the region‐wide extent of its influence. We summarise the existing evidence for possible Eltanin megatsunami deposits in Antarctica, Chile and New Zealand, while also examining other potential sites from several locations, mainly around the South Pacific region. In reviewing these data we note that these events were unfolding at the same time as those associated with the Pliocene–Pleistocene boundary and, as such, most of the geological evidence from that time has a climatic interpretation. The potential climatic and geological ramifications of the Eltanin asteroid impact, however, have failed to be considered by most researchers studying this time period. Although we are not advocating that all geological activity at that time is connected with the Eltanin asteroid impact, it raises interesting questions about the role potentially played by such catastrophic events in contributing to or even triggering epochal transitions. Copyright © 2012 John Wiley & Sons, Ltd.     

Process length variation of the cyst of the dinoflagellate Protoceratium reticulatum in the North Pacific and Baltic‐Skagerrak region: calibration as an annual density proxy and first evidence of pseudo‐cryptic speciation

Process length variation of cysts of the dinoflagellate Protoceratium reticulatum (Claparède et Lachmann) Bütschli in surface sediments from the North Pacific was investigated. The average process length showed a significant inverse relation to annual seawater density: σ_{t annual} = ?0.8674 × average process length + 1029.3 (R² = 0.84), with a standard error of 0.78 kg m^?3. A sediment trap study from Effingham Inlet in British Columbia revealed the same relationship between average process length and local seawater density variations. In the Baltic–Skagerrak region, the average process length variation was related significantly to annual seawater density: σ_{t annual} = 3.5457 × average process length ? 993.28 (R² = 0.86), with a standard error of 3.09 kg m^?3. These calibrations cannot be reconciled, which accentuates the regional character of the calibrations. This can be related to variations in molecular data (small subunit, long subunit and internal transcribed spacer sequences), which show the presence of several genotypes and the occurrence of pseudo‐cryptic speciation within this species. Copyright © 2012 John Wiley & Sons, Ltd.