Essential components and technical details of regional ocean forecasting systems configured from the Regional Ocean Modeling System are discussed with the goal of bridging the gap between user and ocean modeling communities. Recent development of these systems and applications are also surveyed. Design considerations of such a system for the South China Sea are discussed, based on regional dynamic characteristics and potential applications.

Introduction

During the past ten years or so, regional ocean forecasting systems were developed for various regions around the world. These systems tend to be high-resolution (order 1 km horizontal grid spacing), assimilate data, include tidal forcing, and provide a web interface for user applications (Chao et al., 2009; Farrara et al., 2013; Schmidt and Gangopadhyay, 2013; Warner et al., 2010). Various applications, supporting scientific field experiments, search and rescue operation, gas and oil industry, and scientific research were also developed for these systems.

This article summarizes the development of various ocean data assimilation systems along the U.S. coast, mainly based on the work of the Regional Ocean Modeling System Group at the Jet Propulsion Laboratory, California Institute of Technology and the University of California at Los Angeles. With the intention to bridge the gap between societal needs and products from regional ocean forecasting systems, the purpose of this review is fourfold. First, we provide a basic description of a regional ocean forecasting system for the benefit of general users whose field is not physical oceanography or atmospheric sciences. Second, we describe applications that use products from this type of system. Third, we discuss design considerations of such a system for the South China Sea. Fourth, we comment on some recent developments in the field and future directions that will raise the bar for the next generation of regional ocean forecasting systems.

Regional ocean forecasting systems

Several regional ocean forecasting systems were set up for various regions along the U.S. coast. These regions include the Monterey Bay (Chao et al., 2009; Wang et al., 2009), the Southern California Bight (Li et al., 2015), the Prince William Sound, Alaska (Farrara et al., 2013), and the Gulf of Mexico (Farrara et al., 2012). Despite the different physical environment that these ocean forecasting systems were developed for, all of these systems share some common characteristics. Figure 1 is a schematic diagram showing the components of a regional ocean forecasting system and their functions. In general, a regional ocean forecasting system includes six components: (1) Acquisition of atmospheric forcing fields, (2) acquisition of lateral boundary conditions, (3) acquisition of ocean observations, (4) data assimilation, (5) forecasting and (6) result monitoring and visualization. The data assimilation and forecasting components were put in one box because of the close connection between these two components. The development of an ocean forecasting system requires detailed planning about different aspects of the components, data exchange, coordination of computing time, contingency plans if there are failures in one or more components, etc. The operational stage of such a system requires monitoring of each and every component and diagnosis of issues if one component does not perform as expected.

Figure 1.

Schematic diagram indicating six essential components of a regional ocean forecasting system, from acquiring atmospheric forcing fields to results monitoring and visualization. A web interface can be built for the entire system and users can access data from the user interface.

Figure 1.

Schematic diagram indicating six essential components of a regional ocean forecasting system, from acquiring atmospheric forcing fields to results monitoring and visualization. A web interface can be built for the entire system and users can access data from the user interface.

Regional Ocean Modeling System

The central part of a regional ocean forecasting system is a general circulation model. The Regional Ocean Modeling System (ROMS) is a community modeling tool, which is widely used in regional applications. ROMS solves the Navier-Stokes equations under hydrostatic and Boussinesq assumptions in order to describe the evolution of velocity, temperature, and salinity fields. The computation kernel of ROMS is free-surface, split-explicit, and terrain-following (Shchepetkin and McWilliams, 2005, 2009). ROMS explicitly describes the time evolution of the free surface, as opposed to the approach of Bryan (1969) who used a rigid-lid assumption and solved a two-dimensional Poisson equation for surface pressure and hence surface height. The evolution of the free surface is governed by the depth-integrated momentum equation (often called the barotropic mode), which is governed by fast processes, such as surface gravity waves, and can only be integrated using small time steps satisfying the Courant–Friedrichs–Lewy (CFL) condition. The residual part (often called the baroclinic modes) is governed by processes of longer time scales, for example, Rossby waves and subgridscale mixing, and can be integrated using longer time steps. The separation of barotropic and baroclinic modes in ROMS allows separation of boundary conditions so that tides can easily be implemented through lateral boundary conditions when the domain involved is relatively small.

In vertical direction, ROMS uses a stretched sigma coordinate (s-coordinate) discretization that follows bathymetry. The vertical discretization transforms the Cartesian height to a new coordinate. For instance, ocean free surface corresponds to in the new coordinate system and ocean bottom corresponds to . Compared with a traditional sigma-coordinate discretization, the coordinate system used in ROMS provides more flexibility in choosing vertical levels in specific vertical domains, such as the surface boundary layer and the bottom boundary layer (Song and Haidvogel, 1994). Horizontally, a curvilinear grid is used to specify the domain of interest. Submodels, for example, biological models of different complexity or a sea ice model, can be coupled with the ocean circulation model, as needed by each application. A suite of subgridscale parameterizations are provided in ROMS in order to represent processes that have spatial scales smaller than the model grid size, e.g. the K-Profile Parameterization (KPP) of Large et al. (1994) parameterizations that represent turbulent mixing of momentum and mass (Haidvogel et al., 2008).

Nested domains and boundary conditions

To allow high spatial resolution in regions of interest, ROMS allows online nested domains. Online nesting allows the enclosing and enclosed domains to run simultaneously and exchange boundary conditions at every time step. By way of contrast, offline nesting integrates each domain one after the other. To illustrate domain nesting, Figure 2 shows the nested model domains used for the Prince William Sound, Alaska studies of Wang et al. (2013a) and Colas et al. (2013). In this case the outermost model domain (L0, the region that has bathymetry in color) has the coarsest resolution and covers the U.S. and Canadian western coastal region from 42.61N to 61.31N. The intermediate model domain covers the northern part of Gulf of Alaska (L1, the black line). The finest-resolution model domain (L2, the small triangle [red line]) zooms in on the Prince William Sound. The nesting of the model domains is realized through the Adaptive Grid Refinement in FORTRAN (AGRIF) package, which is based on the use of pointers (Blayo and Debreu, 1999). During the development stage of the Prince William Sound system, the nesting between model domains (between L0 and L1, and between L1 and L2) was one-way. The coarse-resolution domain provides boundary conditions for the fine-resolution domain and the solution of the fine-resolution domain does not feed back to the coarse-resolution domain. The updated version of ROMS allows two-way nesting (Debreu et al., 2012).

Figure 2.

Three nested domains for the ocean forecasting system for the Prince William Sound, Alaska. The large, middle, and small domains have horizontal grid spacing of, respectively, 10 km, 3 km, and 1 km.

Figure 2.

Three nested domains for the ocean forecasting system for the Prince William Sound, Alaska. The large, middle, and small domains have horizontal grid spacing of, respectively, 10 km, 3 km, and 1 km.

Because of the split-explicit scheme for the barotropic and baroclinic modes, different boundary conditions can be used for these two modes. The Flather (1976) boundary condition is used along the western, southern, and eastern open boundaries for the normal barotropic velocity to allow the propagation of dynamic signals into the model domain. The Chapman (1985) boundary condition is used for sea surface height along the open boundaries. For the Chapman boundary condition, it is assumed that the dominant wave packet approaching the boundary is non-dispersive gravity waves and the phase speed is estimated based on depth. For baroclinic velocity, temperature, and salinity, we used adaptive open boundary conditions (Marchesiello et al., 2001). The adaptive open boundary conditions treat inward and outward wave packets differently. When the phase speed estimated from the interior solution is outward, these wave packets can propagate out of the model domain (Orlanski, 1976; Raymond and Kuo, 1984). When the phase speed is inward, the interior solution at the boundary is relaxed to the exterior solution with a specified time scale of three days.

When predicting regional ocean circulation, the lateral boundary conditions of the region are a necessary input and exert influence on the circulation within the domain of interest. The boundary condition algorithm was extensively tested (Marchesiello et al., 2001). Later on, boundary conditions of barotropic normal velocity that can include tides were also introduced (Wang et al., 2009). The baroclinic lateral boundary conditions for the largest domain of the Prince William Sound and Monterey Bay systems were taken from a monthly-mean climatology (Da Silva et al., 1994). Since, in general, the time span of ocean forecasting of these systems was 3 days or less and data was heavily used in the finest model domain, the use of climatological boundary conditions for the largest domain (L0) does not have significant impact on the innermost domain (L2). For longer or more accurate forecasts, the output from global operational ocean forecasting systems (Metzger et al. 2014) can be used to provide lateral boundary conditions for regional forecasting systems. For example, Liu et al. (2009) used the Navy Coastal Ocean Model output (Shulman et al., 2004) as lateral boundary conditions for a high-resolution model along the Oregon coast. For the Gulf of Mexico ocean forecasting system (Farrara et al., 2012), ocean prediction fields from the Navy Oceanographic Office were used (Metzger et al., 2014). Before such lateral boundary conditions are used, however, systematic evaluation of hindcast needs to be conducted to analyze their compatibility with and influence on the nested regional simulation.

ROMS is compatible with both OpenMP and MPI parallel computing paradigms. For real-time regional forecasting systems with dedicated computers and a forecasting range of 2–3 days, a one-hour wall clock time for integration of one day is commonly used, which allows adequate time for preprocessing of model input, data assimilation, and post processing of model output.

Atmospheric forcing fields

The generation of accurate regional atmospheric forcing fields for regional ocean forecasting systems requires the assimilation of atmospheric data in high-resolution regional models that can resolve complex boundary layer dynamics and local features of the coastline (He et al., 2004). Because of their complexity and interdisciplinary nature, oceanic forecasting systems are usually developed through group effort. That is, the various atmospheric and oceanic data assimilation tasks are typically distributed between multiple groups at different institutions. In such situations, it is important to carefully coordinate data formats, variable units, etc. Ocean model forcing is often derived using bulk formulae based on the following surface atmospheric fields: 10-m vector wind, relative humidity, air temperature, short and long wave radiation, and precipitation. Surface fluxes of momentum, heat, and freshwater are subsequently computed using the formulae of Large and Pond (1981) and Kondo (1975). The bulk formulae allow one-way ocean-atmosphere coupling through the feedback of sea surface temperature on stability, longwave radiation, and surface fluxes. Downwelling shortwave radiation that is not reflected at the ocean surface is allowed to penetrate the ocean model below the surface level with an exponential decay coefficient.

Data assimilation

Different data assimilation methods have been used in the meteorology and oceanography communities with different levels of sophistication ranging from the relatively simple uni- and multi-variate statistical (optimal) interpolations, Kalman Filter, smoothers, and variational data assimilation methods implemented for both three-dimensional (3DVAR) and four-dimensional (4DVAR) problems (for a review, see Daley, 1991; Li and Navon, 2001). More sophisticated algorithms usually generate better analyses and forecasts, although with a higher computational cost. For the real-time nowcast and forecast systems described here, the end-to-end computing time has to be less than a day. This time requirement restricts utilization of full 4DVAR, Kalman Filter, and smoother methodologies, and instead requires the development of less expensive approaches, i.e. optimal interpolation and approximate filters (e.g. the ensemble Kalman Filter; Evensen, 2003). The systems that we describe herein are based on a 3DVAR algorithm. 3DVAR was introduced at the major meteorological centers in the late 1980s and early 1990s and is still widely used in many operational applications. The algorithm has been described in detail in two companion papers (Li et al., 2008a,b). Here we provide a brief overview of the approach, as implemented in our regional ocean forecasting systems.

The objective of the 3DVAR method is to generate the best estimate of the ocean state by using the model forecast and all the available observations . Here and are column vectors with size , where is the total number of three dimensional model prognostic variables. is a column vector of available observations. The 3DVAR method finds a solution for by minimizing the cost function
formula
(1)
in which is an observation operator that maps model state variables to observations so that , in which is the observation error. is the model forecast error covariance matrix defined as
formula
(2)
in which represents the true ocean state. Superscript is the matrix transpose operator and reprsents mathematical expectation. is the observation error covariance matrix defined as
formula
(3)
where is the true value of the observed quantity and represents observations plus noise. In our implementation of 3DVAR, we convert the total fields to incremental fields:
formula
(4)
formula
(5)
The motivation to work with incremental rather than total fields is to retain the original forecast fields and apply all the operations to the incremental fields. With these two transformations, the cost function can be written
formula
(6)
Let correspond to the solution that minimizes , then
formula
(7)

The solution depends on the specifications of and . A systematic method to estimate is discussed in Li et al. (2008b). needs to be specified based on measurement and model representation errors: an example of the former is instrument noise and an example of the latter is temporal and spatial scales in the observations that do not match the variability that can be resolved by the model. The minimization algorithm used to find is limited-memory quasi-Newton method (Liu and Nocedal, 1989), because of its extensive use in solving nonlinear problems and its computational efficiency and reliability.

Recent developments

The field of regional ocean forecasting became much more mature after several intensive field experiments in the Monterey Bay, California, the Prince William Sound, Alaska, the Mid-Atlantic Bight, and many other regions. Some recent developments of regional ocean forecasting systems include ensemble ocean forecasting and forecasting from coupled systems.

With the increased number of regional ocean forecasting systems, occasionally there can be several systems that provide forecasting for the same region. During the period of October and November 2009, a field experiment was conducted in the Mid-Atlantic Bight to test the concept of a coastal ocean observatory. A multi-model ensemble forecasting system was developed that could combine forecasts from four individual models using a Bayesian model averaging method (Raftery et al., 2005; Wang et al., 2013b). Figure 3 compares the forecasting skill from these four individual models and ensemble forecasting from two ensemble methods. It is clear that even a straightforward average of four model forecasts can improve the forecasting skill (Figure 3e). When forecasts from four models were combined optimally (Figure 3f), the ensemble forecast provided the most accurate prediction compared with the four individual models (Figures 3a–d).

Figure 3.

The root-mean-square error for daily averaged SST of four individual models and two ensemble forecasts for the period of 1–15 November 2009. Top left for COAWST model (a), top right for ESPRESSO model (b), middle left for NYHOPS model (c), middle right for SMAST-HOPS model (d), bottom left for Equal-Weight (EQ) ensemble (e) and bottom right for ensemble by optimally combining four individual model forecasts (OBJ).

Figure 3.

The root-mean-square error for daily averaged SST of four individual models and two ensemble forecasts for the period of 1–15 November 2009. Top left for COAWST model (a), top right for ESPRESSO model (b), middle left for NYHOPS model (c), middle right for SMAST-HOPS model (d), bottom left for Equal-Weight (EQ) ensemble (e) and bottom right for ensemble by optimally combining four individual model forecasts (OBJ).

When computation power permits, ensemble forecasting from a single model by perturbing the initial condition or the boundary condition can also improve the forecasting skill and quantify the uncertainties involved in the forecasting. Using a forecasting system for the Gulf of Mexico, the results from Farrara et al. (2012) indicate that single-model ensemble forecasting is generally better than individual forecasting. The forecasting system of the Gulf of Mexico has sufficient skill to predict loop current eddy shedding events several weeks in advance.

Ocean forecasting from coupled models have also started to appear. A Coupled Ocean Atmosphere Wave Sediment model was used to provide ocean forecasts for a broad region from the Cape Hatteras to the north of the Cape Cod (Warner et al., 2010). This reflects the recent trend to provide environmental information for potential users from a single system instead of from separate atmospheric, wave, ocean, and other models. A coupled system can better represent complex interactions among the different physical components. Data assimilation methods for such coupled systems, however, are at an early stage. For example, no data was directly assimilated in the above coupled system except for temperature and salinity, which were restored to the output of a real-time ocean forecasting system from the Naval Research Lab with a relaxation time scale of 4 days.

Applications

Support field experiment

Different applications motivated the development of the regional ocean forecasting systems discussed herein. Most of these systems were developed to support field experiments. Retrospectively, both observationalists and modelers benefited from these field experiments. The practice also reflects one issue with regional ocean forecasting. For most of the world's coastal oceans, for periods without intensive observational field experiments, the data is too sparse to make skillful prediction on kilometer spatial scales. The Monterey Bay forecasting systems was developed for the Adaptive Ocean Sampling Network of 2003 (Chao et al., 2009). During the experiment, three models were used to predict the oceanic condition around the Monterey Bay. These predictions were used to guide the sampling strategy of the gliders. This concept was pushed one step further during the Ocean Observatories Initiative experiment in November of 2009. During the experiment, the forecasts from four individual models and two ensemble methods were provided to the glider planning system, which was used to produce an optimal path for a glider to reach its targeted destination points. The resulting path was then communicated to a glider during its periodic surfacing times (Wang et al., 2013b).

Search and rescue

An important application of regional ocean forecasting systems is surface drifter trajectory computations based on ocean current predictions, which can help search and rescue missions. The web user interface of all these systems provides a surface drifter trajectory tool based on ocean current prediction. Farrara et al. (2013) describe an example of surface drifter trajectory prediction based on surface current. For the Prince William Sound ocean prediction system, the model has demonstrable skill in reproducing the trajectory of real surface drifters. The prediction of drifter trajectories, however, is sensitive to small perturbations of initial location. A slight perturbation of the initial location can cause large changes in its final location. By providing ensemble drifter trajectory forecasts, the uncertainty of the drifter trajectory forecast can be assessed. The uncertainty information can be very useful in prioritizing the search area of search and rescue missions.

Oil and gas industry

The oil and gas industry can greatly benefit from regional ocean forecasting products both for its normal operation and in case of emergency. In the Gulf of Mexico loop-current eddy-shedding region, the movement of eddies westward poses risks for the operation of oil platforms because of strong current and strong vertical shear of the current associated with the eddy. If the location and the movement of these eddies can be predicted with skill, the information would be very useful for daily operations. Farrara et al. (2012) discuss an example Gulf of Mexico prediction system during the period of November to December 2010, during which an eddy shedding event occurred. The study indicates that their Gulf of Mexico forecasting system has skill to predict eddy shedding events several weeks in advance. In case of emergency, for example, the Deepwater Horizon oil spill event of 2010, trajectory forecasting can be made based on output from regional ocean forecasting systems for the treatment of spilled oil (Liu et al., 2011).

Design considerations for an ocean forecasting system of the South China Sea

The South China Sea (SCS) is the largest semi-enclosed sea in the western tropical Pacific Ocean. The circulation of SCS is influenced by many factors, the complex geometry, the seasonal cycle of monsoon, exchange with adjacent seas, the intrusion of western boundary current from the Pacific subtropical gyre, and freshwater discharge from rivers (Hu et al., 2000; Su, 2004). As an example, Figure 4 compares flow patterns from January and July of 2004 based on a data assimilation product from the Estimating the Circulation and Climate of the Ocean, Phase 2 project (ECCO2; Menemenlis et al., 2008). It is clear that during wintertime the southern part of SCS is controlled by a cyclonic gyre and during summertime by an anticyclonic gyre. These features are generally consistent with previous work in the region (Hu et al., 2000; Su, 2004; Liu et al., 2008). Another prominent feature is that during wintertime the intrusion of western boundary current to SCS region is more evident. The eddy activity is also very strong at the northern part of SCS regardless of season.

Figure 4.

Three-day averaged surface current field of South China Sea for 1–3 January 2004 (left) and 12–14 July 2004 (right) based on an ECCO2 global ocean state estimate. Distinctive seasonal features, especially at the southern part of South China Sea, and intrusion of western boundary current from the subtropical gyre are clearly visible.

Figure 4.

Three-day averaged surface current field of South China Sea for 1–3 January 2004 (left) and 12–14 July 2004 (right) based on an ECCO2 global ocean state estimate. Distinctive seasonal features, especially at the southern part of South China Sea, and intrusion of western boundary current from the subtropical gyre are clearly visible.

An ocean forecasting system for a large marginal sea such as SCS with kilometer-resolution is still a challenging task computationally. Nevertheless, a few such systems with different levels of maturity are starting to appear. Peng et al. (2015) configured a system that can provide atmospheric, wave, and ocean forecasting for the region. Currently the evaluation is for the prediction of tropical cyclone trajectories. Wang et al. (2015) developed a forecasting system for SCS with capability to assimilate sea surface temperature and sea surface height anomaly observations.

Development of an ocean forecasting system for SCS, based on current computational capabilities and experience from previous similar systems, needs to include following design considerations. The nesting technique still needs to be used with fine resolution (kilometer level) for regions of interest and coarse resolution (several kilometers) for a large domain that includes part of the Western Pacific and Eastern Indian Ocean. Since the potential application may include gas and oil industry (Zhang et al., 2010), the generation and propagation of internal tides should be included. The freshwater discharge from major rivers should also be included in the forecasting system. Since the biological activity may be part of its application, a biological module of the ROMS should be included and modified to fit the needs of applications. In situ observations are sparse and are not available on a regular basis, with no prospects of improvement of this situation in the near future. Satellite observation, such as altimeter sea surface height and sea surface temperature, will still be the main source of data to be used in a potential forecasting system for SCS. A fine-resolution atmosphere model with data assimilation capability that can provide high-quality atmospheric forcing fields will also be needed before a coupled system is used to provide forecasting for the region. The initial and boundary conditions for the atmospheric model of SCS can be from operational global meteorological forecasting products from institutions such as NCEP or other agencies based on evaluation. The lateral boundary condition for the ocean model can come from operational global ocean forecasting products (Metzger et al., 2014). For hindcast evaluation and SCS ocean reanalysis data products, ocean retrospective analyses, such as those provided by the ECCO project, can be used.

Discussions and conclusions

Over the past ten years, the field of regional ocean forecasting has experienced great success, and developed from a supportive activity to a routine practice. Though the individual components (e.g. ocean modeling, data assimilation, and visualization) have already been developed for other applications, the integration of these different pieces into an operational system to meet the needs of stakeholders remains a challenging task. When a new system is developed for a region, new issues always come out and demand new strategies. For instance, the first version of the Monterey Bay forecasting system had no tides. Because of the interaction of barotropic tides and complex bathymetry there, internal tide generation and propagation plays an important role in regional dynamics. To meet this challenge, tidal boundary conditions were added resulting in a system where the error of barotropic tides is less than 5% in the open ocean and less than 10% in the coastal region (Wang et al., 2009). For the Prince William Sound, Alaska, large amount of freshwater from snow melting and precipitation reaches the ocean in the form of ungauged rivers and streams. To account for the dynamic effect of freshwater input, a hydrodynamic model is used to estimate freshwater discharge at the river mouth, which in turn is used as lateral forcing for the ocean forecasting system (Wang et al., 2013a). These unique regional challenges will continue to need our attention when developing forecasting systems for a new region. Another trend is that user needs and applications are hard to meet with a single component model, be it atmospheric, oceanic, or wave. An interdisciplinary approach is needed and coupled forecasting systems are needed to assess the environment conditions and make forecasts. The development of an oceanic forecasting system for the South China Sea can benefit from previous experience and lessons learned in developing similar systems for other regions. Still, new and unexpected challenges are expected, which will require new developments and solutions.

Acknowledgements

Xiaochun Wang would like to thank Dr. Dongxiao Wang for his invitation to attend the 7th International Workshop on Tropical Marine Environmental Changes in November of 2013. Comments from two reviewers greatly helped the authors in the revision process, by pointing out new references and related work, which had not been included in the first version. This work is contribution 060 of ESMC of Nanjing University of Information Science and Technology.

Funding

Research was supported by the Chinese National Science Foundation (41328006), Nanjing University of Information Science and Technology Faculty Start-up Fund (S8113046001), the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) and Program for Innovation Research and Entrepreneurship Team in Jiangsu Province.

References

Blayo, E., Debreu, L.,
1999
.
Adaptive mesh refinement for finite-difference ocean models: first experiments
.
J. Phys. Oceanogr.
29
,
1239
1250
.
Bryan, K.,
1969
.
A numerical method for the study of the circulation of world ocean
.
J. Computational Physics
4
,
347
376
.
Chao, Y., Li, Z., Farrara J., McWilliams, J. C., Bellingham, J. Capet, X., Chavez, F., Choi, J.-K., Davis, R., Doyle J., Fratantoni, D. M., Li, P., Marchesiello, P., Moline, M. A., Paduan, J., Ramp, S.,
2009
.
Development, implementation and evaluation of a data-assimilative ocean forecasting system off the central California coast
.
Deep-Sea Research II
56
,
100
126
.
Chapman, D. C.,
1985
.
Numerical treatment of cross-shelf open boundaries in a barotropic coastal model
.
J. Phys. Oceanogr
15
,
1060
1075
.
Colas, F., Wang, X. Capet, X., Chao, Y., McWilliams, J.C.,
2013
.
Untangling the roles of wind, run-off and tides in Prince William Sound
.
Continental Shelf Research
63
,
79
89
, doi:.
Da Silva, A.M., Young, C., Levitus, S.,
1994
.
Atlas of surface marine data 1994, Vol 1, Algorithms and procedures
.
NOAA Atlas NESDIS
,
6
.
Daley, R.,
1991
.
Atmospheric data analysis
.
Cambridge University Press
, Cambridge.
Debreu, L., Marchesiello P., Penven P., and Cambon G.,
2012
: Two-way nest- ing in split-explicit ocean models: algorithms, implementation and validation
.
Ocean Modelling
49–50
,
1
21
.
Evensen, G.
2003
.
The ensemble Kalman filter: Theoretical formulation and practical implementation
.
Ocean Dyn
.
53
,
343
367
.
Farrara, J., Chao, Y., Li, Z., Wang, X., Zhang, H., Li, Z., He, R., Qian, H.,
2012
.
A ROMS-based data assimilating ocean forecast system for the Gulf Of Mexico
.
AGU Ocean Science Meeting, Abstract
.
Farrara, J., Chao, Y., Li, Z., Wang, X., Jin, X., Zhang, H., Li, P, Vu, Q., Ols- son, P. O., Schoch, G. C., Halverson, M., Moline, M. A., McWilliams, J. C., Colas, F.,
2013
.
A data-assimilative ocean forecasting system for the Prince William Sound and an evaluation of its performance during Sound Predictions 2009
.
Continental Shelf Research
63
,
193
208
.
Flather, R.A.,
1976
.
A tidal model of the north-west European continental shelf
.
Mem. Soc. Roy. Sci. Liege
6
,
141
164
.
Haidvogel, D. B., Arango, H., Budgell, W. P., Cornuelle, B.D., Curchitser, E., Lorenzo E. Di, Fennel, K., Geyer, W. R., Hermann, A. J., Lanerolle, L, Levin, J., McWilliams, J. C., Miller, A. J., Moore, A. M., Powell, T. M., Shchepetkin, A. F., Sherwood, C. R., Signell, R. P., Warner, J. C., Wilkin, J.,
2008
.
Ocean forecasting in terrain-following coordinates: Formulation and skill assessment of the regional ocean modeling system
.
J. Comp. Phys.
227
,
3595
3624
.
He, R., Liu Y., Weisberg R. H.,
2004
.
Coastal ocean wind fields gauged against the performance of an ocean circulation model
.
Geophys. Res. Lett
.
31
,
L143030
, doi:.
Hu, J., Kawamura, H., Hong, H., Qi, Y.,
2000
.
A review on the currents in the South China Sea: Seasonal circulation, South China Sea warm current, and Kuroshio intrusion
.
J. of Oceanography
56
,
607
624
.
Kondo, J.,
1975
.
Air-sea bulk transfer coefficients in diabatic conditions
.
Boundary-Layer Met.
9
,
91
112
.
Large, W.G., and Pond, S.,
1981
.
Open ocean momentum flux measurements in moderate to strong winds, J
.
of Physical Oceanography
11
,
324
336
.
Large, W.G., McWilliams, J.C., Doney, S.C.,
1994
.
Oceanic vertical mixing: a review and a model with nonlocal boundary layer parameterization
.
Rev. Geophys.
32
,
363
403
.
Li, Z., Navon, I. M.,
2001
.
Optimality of variational data assimilation and its relationship with the Kalman filter and smoother
.
Quarterly Journal of the Royal Meteorological Society
127
,
661
683
.
Li, Z., Chao, Y., McWilliams, J. C., Ide, K.,
2008a
.
A three-dimensional variational data assimilation scheme for the Regional Ocean Modeling System
.
J. of Atmospheric and Oceanic Technology
25
,
2074
2090
.
Li, Z., Chao, Y., McWilliams, J. C., Ide, K.,
2008b
.
A three-dimensional variational data assimilation scheme for the Regional Ocean Modeling System: Implementation and basic experiments
.
J. Geophys. Research
113
,
C05002
, doi:.
Li, Z., McWilliams J.C., Ide K., and Fararra J.D.,
2015
.
Coastal ocean data assimilation using a multi-scale three-dimensional variational scheme
.
Ocean Dynamics
, doi:.
Liu, D. C., Nocedal, J.,
1989
.
On the limited memory BFGS method for large scale optimization
.
Math. Program
45
,
503
528
.
Liu, Y., Weisberg, R. H., and Yuan Y.,
2008
.
Patterns of upper layer circulation variability in the South China Sea from satellite altimetry using self-organizing map
.
Acta Oceanologica Sinica
, Vol.
27
,
Supp.
, p
129
144
.
Liu, Y., MacCready P., Hickey B. M., Dever E. P., Korso P. M., and Banas N. S.,
2009
.
Evaluation of a coastal ocean circulation model for the Columbia River plume in summer 2004
,
J. Geophys. Res.
,
114
,
C000B04
, doi:
Liu, Y., Weisberg, R. H., Hu, C., Zheng, L.
2011
,
Trajectory forecast as a rapid response to the Deepwater Horizon oil spill, Monitoring and Modeling the Deepwater Horizon Oil Spill: A record-breaking enterprise
,
Geophysical Monograph Series 195, American Geophysical Union
.
Marchesiello, P., McWilliams, J.C., Shchepetkin, A.,
2001
.
Open boundary condition for long-term integration of regional oceanic models
.
Ocean Modelling
3
,
1
21
.
Menemenlis, D., Campin, J., Heimbach, P., Hill, C., Lee, T., Nguyen A., Schodlok, M., Zhang, H.,
2008
.
ECCO2: High resolution global ocean and sea ice data synthesis
.
Mercator Ocean Quarterly Newsletter
31
,
13
21
.
Metzger, E. J., SSmedstad O. M., Thoppil P. G., Hurlburt H. E., Wallcraft J. A. Cummings, A. J., Zamudio L., Franklin D. F., Posey P. G., Phelps M. W., Hogan P. J., Bub F. L., and Dehaan C. J.,
2014
,
US. Navy operational global ocean and Arctic ice prediction systems
,
Oceanography
27
,
31
43
Orlanski, I.,
1976
.
A simple boundary condition for unbounded hyperbolic flows
.
J. of Computational Physics
21
,
251
269
.
Peng, S., Li Y., Gu X., Chen S., Wang D., Wang H., Zhang S., Lv W., Wang C., Liu B., Liu D., Lai Z., Lai W., Wang S., Feng Y., Zhang J.,
2015
.,
A Real-Time Regional Forecasting System Established for the South China Sea and Its Performance in the Track Forecasts of Tropical Cyclones during 2011–13, Wea
.
Forecasting
30
,
471
485
, doi:.
Raftery, A. E., Gneiting, T., Balabdaoui, F., Polakowski, M.,
2005
.
Using Bayesian model averaging to calibrate forecast ensembles
.
Mon. Wea. Rea.
133
,
1155
1174
.
Raymond, W. H., Kuo, H. L.,
1984
.
A radiation boundary condition for multidimensional flows
.
Quarterly Journal of the Royal Meteorological Society
110
,
535
551
.
Schmidt, A.C.K., Gangopahyay, A.,
2013
.
An operational ocean circulation prediction system for the Northwest Atlantic: hindcast during July-September of 2006
.
Continental Shelf Research
63
,
177
192
.
Shchepetkin, A., McWilliams, J.C.,
2005
.
The Regional Oceanic Modeling System (ROMS): A split-explicit, free-surface, topography-following-coordinate ocean model
.
Ocean Modelling
9
,
347
404
.
Shchepetkin, A., McWilliams, J.C.,
2009
.
Correction and commentary for “Ocean forecasting in terrain-following coordinates: Formulation and skill assessment of the regional ocean modelng system” by Haidvogel et al
.
J. Comp. Phys.
227
, pp.
3595
3624
.
J. Comp. Phys.
228
,
8985
9000
.
Song, Y.T., Haidvogel, D.,
1994
.
A semi-implicit ocean circulation model using a generalized topography-following coordinate system
.
J. Comput. Phys.
115
,
228
244
.
Shulman, I., Kindle, J., Derada, S., Anderson, S., Penta, B., and Martin, P., 2004. Development of hierarchy of nested models to study the California Current System, in Estuarine and Coastal Modeling. pp. 74–88. In: M. L. Spaulding (Ed.), Proceedings of 8th International Conference on Estuarine and Coastal Modeling. Am. Soc. of Civ. Eng., Reston
.
Su, J.,
2004
.
Overview of the South China Sea circulation and its influence on the coastal physical oceanography outside the Pearl River Estuary
.
Conti- nental Shelf Research
24
,
1745
1760
.
Wang, X., Chao, Y., Dong, C., Farrara, J., Li, Z., McWilliams, J.C., Paduan, J.D., Rosenfeld, L.K.,
2009
.
Modeling tides in Monterey Bay, California
.
Deep Sea Research II
56
,
219
231
, doi:.
Wang, X., Chao, Y., Zhang, H., Farrara, J, Li, Z., Jin, X., Park, K., Colas, F., McWilliams, J. C., Paternostro, C., Shum, C. K., Yi, Y., Schoch, C., Olsson, P.,
2013a
.
Modeling tides and their influence on circulation in Prince William Sound, Alaska
.
Continental Shelf Research
63
,
126
137
.
Wang, X., Chao Y., Thompson D. R., Chien S. A., Farrara J., Li P., Vu Q,., and Zhang H., Levin J. C., Gangopadhyay A.,
2013b
.
Multi-model ensemble forecasting and glider path planning in the Mid-Atlantic Bight
.
63
,
223
234
.
Continental Shelf Research
, http://dx.doi.org/
Wang, Y. Wei Z., Lian Z., Yang Y.,
2015
.
Development of an ocean current forecast system for the South China Sea
,
Aquatic Procedia
3
,
157
164
.
Warner, J.C., Armstrong, B., He, R., Zambon, J. B.,
2010
.
Development of a coupled ocean-atmosphere-wave-sediment transport (COAWST) modeling system
.
Ocean Modelling
35
,
230
244
.
Zhang, K., Moridis, G. J., Wu, N., Li, X., Reagan, M. T.,
2010
.
Evaluation of alternative horizontal well designs for gas production from hydrate deposits in the Shenhu Area
,
South China Sea. SPE-131151-PP
,
1
18
.