Considerations in the Calculation of Vertical Velocity in Three-Dimensional Circulation Models

The vertical velocity, w, in three-dimensional circulation models is typically computed from the three-dimensional continuity equation assuming that the depth-varying horizontal velocity field was calculated earlier in the solution sequence. Computing w in this way appears to require the solution of an over-determined system since the continuity equation is first order, yet w must satisfy two boundary conditions (one at the free surface and one at the bottom). At least three methods have been previously proposed to compute w: (i) the “traditional” method that solves the continuity equation with the bottom boundary condition and ignores the free surface boundary condition, (ii) a “vertical derivative” method that solves the vertical derivative of the continuity equation using both boundary conditions and (iii) an “adjoint” approach that minimizes a cost functional comprised of residuals in the continuity equation and in both boundary conditions. The latter solution is equivalent to the "traditional" solution plus a correction that increases linearly over the depth and is proportional to the misfit between the "traditional" solution at the surface and the surface boundary condition. In this paper we show that the "vertical derivative" method yields inaccurate and physically inconsistent results if it is discretized as has been previously proposed. However, if properly discretized the "vertical derivative" method is equivalent to the “adjoint” method if the cost function is weighted to exactly satisfy the boundary conditions. Furthermore, if the horizontal flow field satisfies the depth-integrated continuity equation locally, one of the boundary conditions is redundant and w obtained from the "traditional" method should match the free surface boundary condition. In this case, the “traditional,” “adjoint” and properly discretized “vertical derivative” approaches yield the same results for w. If the horizontal flow field is not locally mass conserving, the mass conservation error is transferred into the solution for w. This is particularly important for models that do not guarantee local mass conservation, such as some finite element models

Transient Tidal Circulation and Momentum Balances at a Shallow Inlet

An analysis of transient momentum balances is carried out to elucidate circulation, dynamics, and exchange mechanisms at shallow barotropic tidal inlets. Circulation is computed using a depth-integrated, fully nonlinear, time-stepping, finite-element model with variably spaced grids having horizontal resolution down to 50 m. Velocity and elevation fields from the model are used to directly evaluate the contribution of each term in the momentum equations to the overall momentum balance. A transformation of the x-y momentum terms into an s-n coordinate system is used to simplify the interpretation of the dynamics and provide vivid illustrations of the forces and resulting accelerations in the flow. The analysis is conducted for an idealized inlet and contrasted with a highly detailed model of Beaufort Inlet, North Carolina. Results show that momentum balances in the immediate vicinity of these inlets vary significantly in time and space and oscillate between two dynamical states. Near maximum ebb or flood, the alongstream momentum balances are dominated by advective acceleration, pressure gradient, and bottom friction. Cross-stream balances are dominated by centrifugal acceleration and pressure gradients. Near slack, balances more closely follow linear wave dynamics, with local accelerations balancing pressure gradients, and (to a lesser degree) Coriolis. Comparisons between the idealized inlet and Beaufort Inlet show broad similarities in these momentum balances. However, natural inlet geometry and bottom topography, as well as the tidal transmission characteristics of the sounds behind Beaufort Inlet produce strong asymmetries. Moreover, momentum balances are highly localized, often with subkilometer length scales. The dynamics are used to explain the physical mechanisms for inlet exchange. In particular, the results indicate that the cross-stream dynamics generate a ''wall'' along the length of an inlet during the stronger phases of the tide. The wall is established by opposing cross-inlet pressure gradients and centrifugal forces, and it poses a significant barrier to cross-inlet exchange during the stronger phases of the tide but is absent near slack

A comparison between measured wave properties and simple wave hindcasting models in shallow water

Significant wave heights and wave periods obtained from field measurements in Lake Balaton, Hungary, were compared with two versions of the shallow water wave hindcasting model published by the U.S. Army Corps of Engineers. The version presented in CERC [3, 4] was found to give very good hindcasts of wave height but fall —20% low on wave period. The model presented in CERC [5] was 15-20% above the earlier version at long fetches and approximately equivalent at shorter fetches

Rethinking Flood Analytics: Proceedings from the 2017 Flood Analytics Colloquium

This report documents outcomes from the Flood Analytics Colloquium held at the Renaissance Computing Institute (RENCI) in Chapel Hill, NC, on November 7-9, 2017. The Colloquium was sponsored jointly by the Coastal Resilience Center of Excellence (CRC), RENCI, and two organizations within the U.S. Department of Homeland Security’s Science and Technology Directorate: the First Responders Group (FRG) and the Office of University Programs. The overall purpose of the Colloquium was to support the Flood Apex Program, which is managed by the FRG with the goals of reducing fatalities and property losses from future flood events, increasing community resilience to disruptions caused by flooding, and developing better investment strategies to prepare for, respond to, recover from and mitigate against flood hazards. The Colloquium convened a group of approximately 50 selected persons from a variety of sectors and disciplines to explore the future of flood analytics and how it can better address the increasingly complex needs of society in dealing with flood events

A Retrospective Evaluation of the Storm Surge Produced by Hurricane Gustav (2008): Forecast and Hindcast Results

The evolution and convergence of modeled storm surge were examined using a high-resolution implementation of the Advanced Circulation Coastal Ocean and Storm Surge (ADCIRC) model for Hurricane Gustav (2008). The storm surge forecasts were forced using an asymmetric gradient wind model (AWM), directly coupled to ADCIRC at every time step and at every grid node. A total of 20 forecast advisories and best-track data from the National Hurricane Center (NHC) were used as input parameters into the wind model. Differences in maximum surge elevations were evaluated for ensembles comprised of the final 20, 15, 10, and 5 forecast advisories plus the best track. For this particular storm, the final 10-12 forecast advisories, encompassing the last 2.5-3 days of the storm's lifetime, give a reasonable estimate of the final storm surge and inundation. The results provide a detailed perspective of the variability in the storm surge due to variability in the meteorological forecast and how this changes as the storm approaches landfall. This finding is closely tied to the consistency and accuracy of the NHC storm track forecasts and the predicted landfall location and, therefore, cannot be generalized to all storms in all locations. Nevertheless, this first attempt to translate variability in forecast meteorology into storm surge variability provides useful insights for guiding the potential use of storm surge models for forecast purposes. Model skill was also evaluated for Hurricane Gustav by comparing observed water levels with hindcast modeled water levels forced by river flow, tides, and several sources of wind data. The AWM (which ingested best-track information from NHC) generated winds that were slightly higher than those from NOAA's Hurricane Research Division (HRD) HWind analyses and substantially greater than the North American Mesoscale (NAM) model. Surge obtained using the AWM more closely matched the observed water levels than that computed using HWind; however, this may be due to the neglect of the contribution of wave setup to the surge, especially in exposed areas. Several geographically distinct storm surge response regimes, some characterized by multisurge pulses, were identified and described

A Once and Future Gulf of Mexico Ecosystem: Restoration Recommendations of an Expert Working Group

The Deepwater Horizon (DWH) well blowout released more petroleum hydrocarbons into the marine environment than any previous U.S. oil spill (4.9 million barrels), fouling marine life, damaging deep sea and shoreline habitats and causing closures of economically valuable fisheries in the Gulf of Mexico. A suite of pollutants — liquid and gaseous petroleum compounds plus chemical dispersants — poured into ecosystems that had already been stressed by overfishing, development and global climate change. Beyond the direct effects that were captured in dramatic photographs of oiled birds in the media, it is likely that there are subtle, delayed, indirect and potentially synergistic impacts of these widely dispersed, highly bioavailable and toxic hydrocarbons and chemical dispersants on marine life from pelicans to salt marsh grasses and to deep-sea animals. As tragic as the DWH blowout was, it has stimulated public interest in protecting this economically, socially and environmentally critical region. The 2010 Mabus Report, commissioned by President Barack Obama and written by the secretary of the Navy, provides a blueprint for restoring the Gulf that is bold, visionary and strategic. It is clear that we need not only to repair the damage left behind by the oil but also to go well beyond that to restore the anthropogenically stressed and declining Gulf ecosystems to prosperity-sustaining levels of historic productivity. For this report, we assembled a team of leading scientists with expertise in coastal and marine ecosystems and with experience in their restoration to identify strategies and specific actions that will revitalize and sustain the Gulf coastal economy. Because the DWH spill intervened in ecosystems that are intimately interconnected and already under stress, and will remain stressed from global climate change, we argue that restoration of the Gulf must go beyond the traditional “in-place, in-kind” restoration approach that targets specific damaged habitats or species. A sustainable restoration of the Gulf of Mexico after DWH must: 1. Recognize that ecosystem resilience has been compromised by multiple human interventions predating the DWH spill; 2. Acknowledge that significant future environmental change is inevitable and must be factored into restoration plans and actions for them to be durable; 3. Treat the Gulf as a complex and interconnected network of ecosystems from shoreline to deep sea; and 4. Recognize that human and ecosystem productivity in the Gulf are interdependent, and that human needs from and effects on the Gulf must be integral to restoration planning. With these principles in mind, we provide the scientific basis for a sustainable restoration program along three themes: 1. Assess and repair damage from DWH and other stresses on the Gulf; 2. Protect existing habitats and populations; and 3. Integrate sustainable human use with ecological processes in the Gulf of Mexico. Under these themes, 15 historically informed, adaptive, ecosystem-based restoration actions are presented to recover Gulf resources and rebuild the resilience of its ecosystem. The vision that guides our recommendations fundamentally imbeds the restoration actions within the context of the changing environment so as to achieve resilience of resources, human communities and the economy into the indefinite future

Once and Future Gulf of Mexico Ecosystem: Restoration Recommendations of an Expert Working Group

The Deepwater Horizon (DWH) well blowout released more petroleum hydrocarbons into the marine environment than any previous U.S. oil spill (4.9 million barrels), fouling marine life, damaging deep sea and shoreline habitats and causing closures of economically valuable fisheries in the Gulf of Mexico. A suite of pollutants—liquid and gaseous petroleum compounds plus chemical dispersants—poured into ecosystems that had already been stressed by overfishing, development and global climate change. Beyond the direct effects that were captured in dramatic photographs of oiled birds in the media, it is likely that there are subtle, delayed, indirect and potentially synergistic impacts of these widely dispersed, highly bioavailable and toxic hydrocarbons and chemical dispersants on marine life from pelicans to salt marsh grasses and to deep-sea animals. As tragic as the DWH blowout was, it has stimulated public interest in protecting this economically, socially and environmentally critical region. The 2010 Mabus Report, commissioned by President Barack Obama and written by the secretary of the Navy, provides a blueprint for restoring the Gulf that is bold, visionary and strategic. It is clear that we need not only to repair the damage left behind by the oil but also to go well beyond that to restore the anthropogenically stressed and declining Gulf ecosystems to prosperity-sustaining levels of historic productivity. For this report, we assembled a team of leading scientists with expertise in coastal and marine ecosystems and with experience in their restoration to identify strategies and specific actions that will revitalize and sustain the Gulf coastal economy. Because the DWH spill intervened in ecosystems that are intimately interconnected and already under stress, and will remain stressed from global climate change, we argue that restoration of the Gulf must go beyond the traditional "in-place, in-kind" restoration approach that targets specific damaged habitats or species. A sustainable restoration of the Gulf of Mexico after DWH must: 1. Recognize that ecosystem resilience has been compromised by multiple human interventions predating the DWH spill; 2. Acknowledge that significant future environmental change is inevitable and must be factored into restoration plans and actions for them to be durable; 3. Treat the Gulf as a complex and interconnected network of ecosystems from shoreline to deep sea; and 4. Recognize that human and ecosystem productivity in the Gulf are interdependent, and that human needs from and effects on the Gulf must be integral to restoration planning. With these principles in mind, the authors provide the scientific basis for a sustainable restoration program along three themes: 1. Assess and repair damage from DWH and other stresses on the Gulf; 2. Protect existing habitats and populations; and 3. Integrate sustainable human use with ecological processes in the Gulf of Mexico. Under these themes, 15 historically informed, adaptive, ecosystem-based restoration actions are presented to recover Gulf resources and rebuild the resilience of its ecosystem. The vision that guides our recommendations fundamentally imbeds the restoration actions within the context of the changing environment so as to achieve resilience of resources, human communities and the economy into the indefinite future

Estimating the Spatial Extent of Bottom-Water Hypoxia and Habitat Degradation in a Shallow Estuary

Bottom-water hypoxia (≤ 2 mg 1-1 dissolved oxygen [DO]) greatly modifies the benthic habitat of estuaries, depending upon spatial extent, duration, and frequency. Bottom-water hypoxia often develops under conditions of density stratification, which inhibits vertical mixing, and warm temperatures, which enhance biological oxygen demand. Long-term, mid-channel data from the Neuse River Estuary in North Carolina permitted evaluation of how stratification and temperature combined to affect DO concentrations at the bottom. Salinity stratification (DS) and water temperature (T) explained respectively 30 and 23% of the variance in bottom-water DO concentrations. The amount of salinity stratification required to induce bottom-water hypoxia declined with increasing water temperature. About 80% of observed hydrographic profiles exhibited bottom hypoxia when DS exceeded 5 psu and T exceeded 20°C. Using cross-channel hydrographic surveys as verification, we derived a general set of methods to estimate the lateral extent of low-DO bottom water from midchannel hydrographic profiles. The method involves cross-estuary and along-estuary extrapolation based on assumption of a flat oxycline. Occasional violation of this assumption resulted in modest overestimation in cross-channel extent of low DO. Application of this method produced estimates ranging from 0 to 116 km2 of bottom area (0 to 42% of the estuarine study area) exposed to hypoxia over all sample dates in summer 1997. The maximal bottom area exposed to hypoxia corresponded closely with an independent estimate of the area (100 km2) that experienced almost complete mortality of Macoma spp. clams, the key benthic resource for demersal fishes and crabs. Consequently, mid-channel hydrographic profiles taken along the mid-channel of the estuary can be employed to assess the spatial scale of bottom habitat degradation due to hypoxia

Extratropical storm inundation testbed : intermodel comparisons in Scituate, Massachusetts

Author Posting. © American Geophysical Union, 2013. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Oceans 118 (2013): 5054–5073, doi:10.1002/jgrc.20397.The Integrated Ocean Observing System Super-regional Coastal Modeling Testbed had one objective to evaluate the capabilities of three unstructured-grid fully current-wave coupled ocean models (ADCIRC/SWAN, FVCOM/SWAVE, SELFE/WWM) to simulate extratropical storm-induced inundation in the US northeast coastal region. Scituate Harbor (MA) was chosen as the extratropical storm testbed site, and model simulations were made for the 24–27 May 2005 and 17–20 April 2007 (“Patriot's Day Storm”) nor'easters. For the same unstructured mesh, meteorological forcing, and initial/boundary conditions, intermodel comparisons were made for tidal elevation, surface waves, sea surface elevation, coastal inundation, currents, and volume transport. All three models showed similar accuracy in tidal simulation and consistency in dynamic responses to storm winds in experiments conducted without and with wave-current interaction. The three models also showed that wave-current interaction could (1) change the current direction from the along-shelf direction to the onshore direction over the northern shelf, enlarging the onshore water transport and (2) intensify an anticyclonic eddy in the harbor entrance and a cyclonic eddy in the harbor interior, which could increase the water transport toward the northern peninsula and the southern end and thus enhance flooding in those areas. The testbed intermodel comparisons suggest that major differences in the performance of the three models were caused primarily by (1) the inclusion of wave-current interaction, due to the different discrete algorithms used to solve the three wave models and compute water-current interaction, (2) the criterions used for the wet-dry point treatment of the flooding/drying process simulation, and (3) bottom friction parameterizations.This project was supported by NOAA via the U.S.IOOS Office (award: NA10NOS0120063 and NA11NOS0120141) and was managed by the Southeastern Universities Research Association. The Scituate FVCOM setup was supported by the NOAA-funded IOOS NERACOOS program for NECOFS and the MIT Sea Grant College Program through grant 2012-R/RC-127.2014-04-0