Discussion of “Wave setup and setdown generated by obliquely incident waves” by T.-W. Hsu et al., Coastal Engineering, 53, 865–877, 2006

In the recent paper by Tai-Wen Hsu, John R.-C. Hsu, Wen-Kai Weng, Swun-Kwang Wang, and Shan-Hwei Ou (Coastal Engineering, 53, 865–877, 2006), the authors derived theoretical formulations for calculating the wave setup and setdown induced by obliquely incident waves on a beach. The derivation of an expression for setdown contains errors which would lead to an imbalance in longshore momentum flux outside the surfzone. We correct their derivation and give results in terms of the radiation stress concept in a general case including an oblique wave incidence. We also point out that the correct form of wave setdown is important to describe the zero-net force in the momentum balance outside the surfzone.     

A numerical scheme for morphological bed level calculations

The typical equation for bed level change in sediment transport in river, estuary and near shore systems is based on conservation of sediment mass. It is generally a nonlinear conservation equation for bed level. The physics here are similar to shallow water wave equations and gas dynamics equation which will develop shock waves in many circumstances. Many state-of-art morphological models use classical lower order Lax–Wendroff or modified Lax–Wendroff schemes for morphology which are not very stable for long time sediment transport processes simulation. Filtering or artificial diffusion are often added to achieve stability. In this paper, several shock capturing schemes are discussed for simulating bed level change with different accuracy and stability behaviors. The conclusion is in favor of a fifth order Euler-WENO scheme which is introduced to sediment transport simulations here over other schemes. The Euler-WENO scheme is shown to have significant advantages over schemes with artificial viscosity and filtering processes, hence is highly recommended especially for phase-resolving sediment transport models.     

Mitigating damage costs from hurricane strikes along the southeastern U.S. Coast: A role for insurance markets

Damage costs from hurricanes have increased dramatically as hurricane strikes, populations, and property values have increased along the U.S. southeastern and Gulf Coast states. Federal expenditures in hurricane affected areas and coastal property insurance costs have increased as well. We discuss current public and private sector actions that impact damage costs and consider ways to mitigate future damage costs and government financial exposure. Encouraging adaptive and avoidance measures through market signals and government policies, and protecting areas such as wetlands which mitigate storm damage will help limit damage from hurricanes.     

Predicting suitable habitat for the cold-water coral Lophelia pertusa (Scleractinia)

Ecological-niche factor analysis (ENFA) was applied to the reef framework-forming cold-water coral Lophelia pertusa. The environmental tolerances of this species were assessed using readily available oceanographic data, including physical, chemical, and biological variables. L. pertusa was found at mean depths of 468 and 480 m on the regional and global scales and occupied a niche that included higher than average current speed and productivity, supporting the theory that their limited food supply is locally enhanced by currents. Most records occurred in areas with a salinity of 35, mean temperatures of 6.2–6.7  °C and dissolved oxygen levels of 6.0–6.2 ml l⁻¹. The majority of records were found in areas that were saturated with aragonite but had low concentration of nutrients (silicate, phosphate, and nitrate). Suitable habitat for L. pertusa was predicted using ENFA on a global and a regional scale that incorporated the north-east Atlantic Ocean. Regional prediction was reliable due to numerous presence points throughout the area, whereas global prediction was less reliable due to the paucity of presence data outside of the north-east Atlantic. However, the species niche was supported at each spatial scale. Predicted maps at the global scale reinforced the general consensus that the North Atlantic Ocean is a key region in the worldwide distribution of L. pertusa. Predictive modelling is an approach that can be applied to cold-water coral species to locate areas of suitable habitat for further study. It may also prove a useful tool to assist spatial planning of offshore marine protected areas. However, issues with eco-geographical datasets, including their coarse resolution and limited geographical coverage, currently restrict the scope of this approach.     

Nutrient flux into an intense deep chlorophyll layer in a mode-water eddy

An intense deep chlorophyll layer in the Sargasso Sea was reported near the center of an anticyclonic mode-water eddy by McGillicuddy et al. [2007. Eddy–wind interactions stimulate extraordinary mid-ocean plankton blooms, Science, accepted]. The high chlorophyll was associated with anomalously high concentrations of diatoms and with a maximum in the vertical profile of ¹⁴C primary productivity. Here we report tracer measurements of the vertical advection and turbulent diffusion of deep-water nutrients into this chlorophyll layer. Tracer released in the chlorophyll layer revealed upward motion relative to isopycnal surfaces of about 0.4 m/d, due to solar heating and mixing. The density surfaces themselves shoaled by about 0.1 m/d. The upward flux of dissolved inorganic nitrogen, averaged over 36 days, was approximately 0.6 mmol/m²/d due to both upwelling and mixing. This flux is about 40% of the basin wide, annually averaged, nitrogen flux required to drive the annual new production in the Sargasso Sea, estimated from the oxygen cycle in the euphotic zone, the oxygen demand below the euphotic zone, and from the ³He excess in the mixed layer. The observed upwelling of the fluid was consistent with theoretical models [Dewar, W.K., Flierl, G.R., 1987. Some effects of wind on rings. Journal of Physical Oceanography 17, 1653–1667; Martin, A.P., Richards, K.J., 2001. Mechanisms for vertical nutrient transport within a North Atlantic mesoscale eddy. Deep-Sea Research II 48, 757–773] in which eddy surface currents cause spatial variations in surface stress. The diapycnal diffusivity at the base of the euphotic zone was 3.5±0.5×10⁻⁵ m²/s. Diapycnal mixing was probably enhanced over more typical values by the series of storms passing over the eddy during the experiment and may have been enhanced further by the trapping of near-inertial waves generated within the eddy.     

Evolution and preservation potential of fluvial and transgressive deposits on the Louisiana inner shelf: understanding depositional processes to support coastal management

The barrier-island systems of the Mississippi River Delta plain are currently undergoing some of the highest rates of shoreline retreat in North America (~20 m/year). Effective management of this coastal area requires an understanding of the processes involved in shoreline erosion and measures that can be enacted to reduce loss. The dominant stratigraphy of the delta plain is fluvial mud (silts and clays), delivered in suspension via a series of shallow-water delta lobes that prograded across the shelf throughout the Holocene. Abandonment of a delta lobe through avulsion leads to rapid land subsidence through compaction within the muddy framework. As the deltaic headland subsides below sea level, the marine environment transgresses the bays and wetlands, reworking the available sands into transgressive barrier shorelines. This natural process is further complicated by numerous factors: (1) global sea-level rise; (2) reduced sediment load within the Mississippi River; (3) diversion of the sediment load away from the barrier shorelines to the deep shelf; (4) storm-induced erosion; and (5) human alteration of the littoral process through the construction of hardened shorelines, canals, and other activities. This suite of factors has led to the deterioration of the barrier-island systems that protect interior wetlands and human infrastructure from normal wave activity and periodic storm impact. Interior wetland loss results in an increased tidal prism and inlet cross-sectional areas, and expanding ebb-tidal deltas, which removes sand from the littoral processes through diversion and sequestration. Shoreface erosion of the deltaic headlands does not provide sufficient sand to balance the loss, resulting in thinning and dislocation of the islands. Abatement measures include replenishing lost sediment with similar material, excavated from discrete sandy deposits within the muddy delta plain. These sand bodies were deposited by the same cyclical processes that formed the barrier islands, and understanding these processes is necessary to characterize their location, extent, and resource potential. In this paper we demonstrate the dominant fluvial and marine-transgressive depositional processes that occur on the inner shelf, and identify the preservation and resource potential of fluvio-deltaic deposits for coastal management in Louisiana.     

Impact of dynamic feedbacks between sedimentation,sea-level rise,and biomass production on near-surface marsh stratigraphy and carbon accumulation

Salt marshes accrete both organic and inorganic sediments. Here we present analytical and numerical models of salt marsh sedimentation that, in addition to capturing inorganic processes, explicitly account for above- and belowground organic processes including root growth and decay of organic carbon. The analytical model is used to examine the bias introduced by organic processes into proxy records of sedimentation, namely ¹³⁷Cs and ²¹⁰Pb. We find that accretion rates estimated using ²¹⁰Pb will be less than accretion rates estimated using the ¹³⁷Cs peak in steadily accreting marshes if (1) carbon decay is significant and (2) data for ²¹⁰Pb extend below the ¹³⁷Cs peak. The numerical model expands upon the analytical model by including belowground processes such as compaction and root growth, and by explicitly tracking the evolution of aboveground biomass and its effect on sedimentation rates. Using the numerical model we explore how marsh stratigraphy responds to sediment supply and the rate of sea-level rise. It is calibrated and tested using an extensive data set of both marsh stratigraphy and measurements of vegetation dynamics in a Spartina alterniflora marsh in South Carolina, USA. We find that carbon accumulation in marshes is nonlinearly related to both the supply of inorganic sediment and the rate of sea-level rise; carbon accumulation increases with sea-level rise until sea-level rise reaches a critical rate that drowns the marsh vegetation and halts carbon accumulation. The model predicts that changes in carbon storage resulting from changing sediment supply or sea-level rise are strongly dependent on the background sediment supply: if inorganic sediment supply is reduced in an already sediment poor marsh the storage of organic carbon will increase to a far greater extent than in a sediment-rich marsh, provided that the rate of sea-level rise does not exceed a threshold. These results imply that altering sediment supply to estuaries (e.g., by damming upstream rivers or altering littoral sediment transport) could lead to significant changes in the carbon budgets of coastal salt marshes.     

Rational approximations in the parabolic equation method for water waves

Approximations based on minimax principles are developed in order to allow for large-angle propagation in the parabolic equation method. Numerical studies show that the minimax approximations do not cause any significant degradation of accuracy at small angles of incidence when compared with an existing model based on a (1,1) Padé approximant, and that they allow for much more successful treatment of large angles of incidence than is possible using the previously available methods.