The dynamical interaction between currents, bathymetry, waves, and estuarine
outflow has significant impacts on the surf zone. We investigate the impacts
of two strategies to include the effect of surface gravity waves on an ocean
circulation model of the south shore of O'ahu, Hawaii. This area provides an
ideal laboratory for the development of nearshore circulation modeling
systems for reef-protected coastlines. We use two numerical models for
circulation and waves: Regional Ocean Modeling System (ROMS) and Simulating
Waves Nearshore (SWAN) model, respectively. The circulation model is nested
within larger-scale models that capture the tidal, regional, and wind-forced
circulation of the Hawaiian archipelago. Two strategies are explored for
circulation modeling: forcing by the output of the wave model and online,
two-way coupling of the circulation and wave models. In addition, the
circulation model alone provides the reference for the circulation without
the effect of the waves. These strategies are applied to two experiments:
(1) typical trade-wind conditions that are frequent during summer months, and
(2) the arrival of a large winter swell that wraps around the island. The
results show the importance of considering the effect of the waves on the
circulation and, particularly, the circulation–wave coupled processes. Both
approaches show a similar nearshore circulation pattern, with the presence of
an offshore current in the middle beaches of Waikiki. Although the pattern of
the offshore circulation remains the same, the coupled waves and circulation
produce larger significant wave heights (
Our objective is to describe how ocean waves and
currents interact in the south shore of the island of O'ahu, Hawaii, with a
goal towards the development of an operational ocean forecast system. Much of
the focus on ocean predictability has been at the larger scales within the
ocean basins or on the continental slopes; however, human–ocean interaction
is primarily within the nearshore surf zone. Dynamical interplay between
currents and bathymetry, currents and waves, ocean waters and estuaries,
breaking waves, etc. may all significantly influence the predictability in
the nearshore regions. In this paper, we investigate the impacts of surface
gravity waves on the nearshore circulation in a high-resolution regional
ocean model for the coast of Honolulu, Hawaii (Fig.
Bathymetry map of the
In Mamala Bay, all scales of ocean dynamics are present from strong planetary mean flows, aperiodic mesoscale eddies impinging on the coastal region, internal tides, barotropic tides, and strong and variable trade winds. The south shore of O'ahu within Mamala Bay is an ideal site for a case study to understand the primary drivers of the nearshore circulation, quantify the particular contribution of the surface gravity waves to the circulation under different conditions, and determine what the best options are to represent such processes in operational forecast systems for exposed coral reef areas.
Among these processes influencing the nearshore circulation,
The intermittent discharge of freshwaters from the Ala Wai Canal
(Fig.
In addition to the complicated bathymetry and the freshwater input from the
Ala Wai Canal, there are a number of processes that impact the nearshore
currents near Waikiki. There are highly variable winds as the island
mountains serve to create a wake region of lower but variable winds
While focusing on the fate of harmful bacteria from the Ala Wai plume,
Therefore, a different approach to the wave–current interaction off the south shore of O'ahu is necessary. This paper aims to clarify (i) the effective contribution from the surface waves under different conditions, (ii) the importance of coupled ocean currents and surface wave processes for the local dynamics, and (iii) the influence of different approaches for forecasting the nearshore current field.
This research uses a suite of numerical models to examine these main
questions, as there is little observational data available. Although the Kilo
Nalu cabled reef observatory once provided real-time observations of several
physical and biogeochemical parameters
The ROMS is a 3-D primitive equation ocean model using hydrostatic and
Boussinesq approximations. A full description of the model can be found in
We utilize a horizontally variable grid with
The open boundaries of the nearshore domain are forced with barotropic tides
and circulation, temperature, and salinity from the coarser 250 m
parent grid. The horizontal resolution minimizes the errors in the resolved
circulation, as shown in comparisons with observations by
The models use surface forcing fields from a locally produced WRF model run
performed under the PacIOOS project. Eleven tidal constituents obtained from
the Oregon State University TOPEX/Poseidon Global Inverse Solution (TPXO)
As described by
As described by
SWAN is a third-generation spectral wave model developed at the Delft
University of Technology. It solves the spectral action density balance to
describe the evolution of wave energy over direction and frequency, time, and
space. It is able to resolve the wave generation by winds, energy transfer by
the wave–wave interactions, shoaling and refraction due to the bathymetry
and currents, and wave dissipation by white capping, bottom friction, and
breaking in the nearshore area. It has been a proven tool for modeling
complex wave fields in coastal regions with the varying bathymetry and in the
presence of complex currents. The model was developed by
With the same computational grid as the nearshore ROMS simulations shown in
Fig.
As described by
The models were coupled via the MCT, which allows the exchange of information
between the ocean and wave models. This exchange of information is
independent of each model's grid and time step, and we a use coupling time
step of 120
As described by
Three groups of simulations were designed to study the impact of the surface gravity waves on the currents: (1) stand-alone ROMS model without considering the waves (NOWAVE), (2) ROMS model including hourly forcing from SWAN (WAVEFORCE), and (3) two-way coupled ROMS–SWAN simulations (WAVECOUPLE) using the MCT.
Each of these simulations were run for two 5-day experimental periods with
different wave conditions:
Experiment 1 took place on 8–13 September 2013 with moderate south waves (1 Experiment 2 took place 21–26 January 2014 with a large north swell that
wrapping
around the island with the presence of a southeast swell, generating waves
above 2
The wave conditions were chosen based on 2 years of data from the Kilo Nalu
observatory
Despite the difference in the time step at which the wave parameters are
provided to the circulation model in the WAVEFORCE (1
Wave conditions for the south shore of O'ahu as measured by the Kilo
Nalu observatory.
NOAA National Database Buoy Center (NDBC) buoys shown in Fig.
Root-mean-squared deviations for the wave significant height
(
In contrast, both the wave hindcast and measurements in the nearshore buoys
51201, 51202, 51203, and 51204 show large northwest swells with peak period above
15
Comparison of the significant wave height, peak period, and direction
between the NDBC buoys displayed in Fig.
Comparison of the significant wave height, peak period, and direction
between the NDBC buoys displayed in Fig.
Maps of differences in wave direction (
In general, the root-mean-square deviations (RMSDs) show a good agreement
between the model results and the buoy data (Table
Similar to the waves, there is no data available on the nearshore currents
in the south shore of O'ahu during the experiment period. Nevertheless, the
model system that provides the boundary conditions of the coastal domain has
been validated against satellite sea level anomaly, sea surface temperature,
and high-frequency radar surface currents
The HFR data give widespread surface current data for the south shore of
O'ahu – the region of interest of the present study. Although they do not
provide observations of the nearshore circulation, they do provide an
important constraint to the outer grid surface velocities used as boundary
conditions to the nearshore domain. In their Figs. 2 and 3,
The WAVECOUPLE simulation has longer periods (
The ocean currents modify the group velocities
Following
The spatial variability of the differences in
WAVECOUPLE exhibits
In the return flow area in the middle of bay formed by the Waikiki beach (see
Fig.
To analyze the effect of the circulation on the waves, the differences in
wave direction and
Time-averaged alongshore currents (
Time-averaged cross-shore currents (
Although the effect of the Ala Wai Canal discharge in the nearshore
circulation can be significant during large rain events
The resulting mean circulations obtained from the three modeling strategies
(Figs.
The alongshore component of the velocity (Fig.
The modification of the circulation by the waves is expressed by the
right-hand-side terms in Eq. (1). It includes the influences of the vortex
force, Bernoulli head, and non-conservative wave forces. These wave effects
enter the ROMS primitive equations as momentum and tracer fluxes. The vortex
force (VF) terms represent the interaction between the Stokes drift and the
vorticity of the mean flow. Since this term is not explicitly written in the
model output, it is difficult to quantify its contribution to the momentum
balance. Nevertheless, it is directly related to the Stokes drift velocities
obtained from the resolved wave field, as expressed by
The maps in Fig.
Maps of the time-averaged Stokes drift velocities (red arrows –
Time-averaged SSH difference (m) between the simulations that
include the effect of surface gravity waves (WAVEFORCE and WAVECOUPLE) and
the NOWAVE case for experiment 1
Sections of pressure gradient per density unit and surface
cross-shore velocities for experiment 1
Maps of the time mean wave energy dissipation by depth-induced wave
breaking (
Cross-shore sections 1
This difference in the Stokes drift velocities, however, is not enough to
explain the observed differences in the total currents. Taking only the wave
effects into consideration, the differences in the total velocity intensities
are mainly a consequence of the wave setup/setdown. The presence of
cross-shore current cells is the main feature in the velocity maps of
Fig.
Therefore, it is necessary to quantify the modification of the sea level by
the waves and the balance with the dissipation of wave energy. To achieve
this, the SSH differences between the simulations that
include the effects of the waves (WAVEFORCE and WAVECOUPLE) and the NOWAVE
were calculated and are presented in Fig.
The elevation of the sea surface near the coast due to the waves is observed for each experiment, followed by a lowering of the sea level towards the open ocean. The WAVECOUPLE cases show overall larger magnitude of elevation, both positive and negative, than the WAVEFORCE. These differences in the sea level impose a cross-shore pressure gradient that affects the local currents.
Taking the cross-shore section (1) shown in Fig.
To analyze how the different phenomena interact to generate the observed
nearshore circulation pattern, the pressure gradient (cross- and
alongshore), the non-conservative wave forces (sum of depth-induced
breaking, white capping, and bottom friction), and the integrated cross-shore
transport by the quasi-Eulerian currents and the Stokes drift are plotted for
the two sections shown in Fig.
At the section (1) (Fig.
Spatial mean correlation factors between the difference in wave
direction and significant height (
There is a large channel in the reef near the region of section (2). As a
consequence of the larger depths close to the coastline, the energy loss by
wave breaking is approximately 6 times smaller than in section (1) and
concentrated near the coast (shorebreak). The balance explained above for
section (1) does not take place, as is evident by the lack of associated
maxima in the cross-shore pressure gradient and Stokes drift velocity
transport. This section, however, is in the convergence zone of alongshore
wave-induced currents observed in Fig.
With the mechanism of cross-shore circulation cells in mind, it becomes clear how the small observed differences in the pressure gradient associated with the wave setup/setdown resolved by the coupled simulations have important impacts on the nearshore circulation. This demonstrates how significant coupled processes are for the resolved currents and for the skill of nearshore forecast systems.
To quantify these differences, Table 3 presents a comparison of the total
velocity, Stokes drift, and setup-associated velocity between the WAVECOUPLE
and WAVEFORCE simulations. The setup-associated velocities were calculated by
subtracting the NOWAVE velocities from the model quasi-Eulerian velocities.
The NOWAVE is taken to represent all of the other contributions not
associated with the waves action. The larger intensity of the Stokes drift in
the WAVECOUPLE simulations is related to the larger
Therefore, the interaction between the surface waves and nearshore circulation has important impacts on the resolved currents, especially in the nearshore region between the reef crest and the coast. This is an important phenomenon that should be taken into consideration when developing forecast systems that aim to provide a useful description of the nearshore currents.
Difference of the total and wave contributions to the surface velocities (%) between the WAVECOUPLE and WAVEFORCE simulations. The results show that while the contribution of the Stokes drift to the total velocities is higher by the same rate for both approaches, the same is not true for the wave setup contribution. A more complex interaction between waves and currents derived from the coupling gives rise to stronger nearshore currents in the WAVECOUPLE simulations (positive values).
Due to the interaction with
the currents that modify the wave number, coupling the circulation and wave
models gives rise to larger
The differences in the resolved wave fields presented feedbacks on the
circulation in the coupled simulations (both WAVEFORCE and WAVECOUPLE), since
the resolved
In this paper, we set out to understand (i) the effective contribution from the surface waves under different conditions, (ii) the importance of coupled ocean currents and surface wave processes for the local dynamics, and (iii) the influence of different approaches for forecasting the nearshore current field.
We found that the surface wave field has significant importance to the
circulation, even in periods of small (under 1
The results show the importance of considering coupled processes when aiming to resolve both the nearshore circulation and the wave characteristics in the reef zone. However, the computational cost involved in coupled simulations presents an important obstacle in the use of this approach for operational forecast systems. Once in possession of the wave model results, the WAVEFORCE approach requires one-sixth of the computational time of WAVECOUPLE. The SWAN run alone (uncoupled) takes about one-quarter the computational time of the WAVEFORCE ROMS run. Although this permits a greater malleability in the use of available machine power and time, it does not consider the coupling between the two models and should be viewed as a compromise solution rather than optimal. The ability of resolving the general pattern of nearshore circulation, however, makes the WAVEFORCE an interesting approach for operational purposes.
The COAWST model source code and documentation are available through the
website
All data used in the present work as well as the operational model results
are publicly available through the PacIOOS website
The authors declare that they have no conflict of interest.
Joao Marcos Azevedo Correia de Souza was supported by NOAA grant no. NA07NOS4730207. Brian Powell was supported by ONR grant no. N00014-09-1-0939. We would like to thank Ning Li for providing the SWAN configuration and boundary conditions and helping in the SWAN model description and evaluation. This is SOEST publication no. 9880. Edited by: A. Sterl Reviewed by: two anonymous referees