Improving surface tidal accuracy through two-way nesting in a global ocean model
Introduction
Global surface tides have been studied in barotropic (two-dimensional) and baroclinic (three-dimensional) forward and data-assimilative simulations (Arbic et al., 2004; Arbic et al., 2009; Buijsman et al., 2015; Egbert and Ray, 2001; Egbert et al., 2004; Green and Nycander, 2013; Ngodock et al., 2016; Shriver et al., 2012; Stammer et al., 2014). Despite recent progress in reducing tidal sea-surface-height root-mean-square errors (RMSE) in the global HYbrid Coordinate Ocean Model (HYCOM), the model used in this paper, the errors in the North Atlantic near Hudson Strait, and near coastal-shelf areas in general, are still relatively large (Buijsman et al., 2015; Ngodock et al., 2016; Shriver et al., 2012). Coastal-shelf bathymetry is imperfectly known and represented in models, and may be a likely cause of tidal model errors (Egbert et al., 2004). Moreover, the large errors in the North Atlantic may be attributed to the inability of the model to correctly simulate the known semidiurnal tidal resonances in the North Atlantic (Wünsch, 1972).
Both analytical models of coastal tides (e.g. the classic quarter-wavelength resonance model, see for instance Defant, 1961) and more realistic numerical models of coastal tides have long treated the open ocean as representing an unchanging boundary condition acting on a coastal region that may or may not achieve resonance depending on its geometry. However, in analytical and numerical studies, Arbic et al. (2009), Arbic et al. (2007), and Arbic and Garrett (2010) have shown that there is a substantial “back-effect” of coastal tides upon the open-ocean tides. They showed that if both the shelf sea and ocean basin are near resonance, small geometry changes to the shelf sea can have a large impact on the open-ocean tides. This suggests that if we better resolve the coastal geometry by increasing the model resolution, we may not only improve the coastal tides, but also the open-ocean tides through the back-effect, in particular if the shelf and ocean basins are near resonance, as is the case in the North Atlantic near Hudson Strait.
In general, higher resolution yields more accurate tides in forward models (Egbert et al., 2004). However, high-resolution model simulations are computationally expensive and require large data storage. To achieve higher resolution in regions of interest without dramatically increasing the cost of a basin- or global-scale model, one can use two-way nesting, as introduced in Spall and Holland (1991). The basic idea of two-way nesting is to apply a high-resolution (fine) grid only to a small area of interest, i.e., the ‘child’ domain, and a low-resolution (coarse) grid to the entire ‘parent’ domain. In two-way nesting, information is allowed to propagate from the coarse grid to the fine grid and vice versa. In this way, the improved solution on the child grid may also improve the solution on the parent grid. In this paper, we implement a two-way nesting framework for barotropic HYCOM simulations to better simulate the local surface tides, e.g. on Hudson shelf, as well as the remote tides in the open ocean.
In the two-way nesting framework, the data exchange between the child and parent domains occurs in two opposing directions. In the first ‘coarse-to-fine’ direction, the information of the parent domain is transferred to the child domain via the lateral boundaries of the child domain. Data exchange in this direction is also referred to as ‘one-way nesting’. In one-way nesting, the parent domain is not updated with the child grid solution. One-way nesting has been extensively used for basin-scale modeling (Chassignet et al., 2007; Hogan and Hurlburt, 2006; Mason et al., 2010; Penven et al., 2006). In the second ‘fine-to-coarse’ direction, the coupling variables in the high-resolution child domain are transferred to the relatively low-resolution parent grid. The two-way nesting approach has been widely applied in atmospheric modeling (Bowden et al., 2012; Lorenz and Jacob, 2005), and in coupling of multiple climate models (Lam et al., 2009; Ličer et al., 2016; Wahle et al., 2017) as well as ocean modeling (Barth et al., 2005; Debreu et al., 2012; Ginis et al., 1998). To make the updated variables continuous across the nesting boundaries of the parent and child domains in the second direction, smoothing filters were sometimes applied to physical variables, and/or the bottom topography of the child domain was relaxed with that of the parent domain (Debreu et al., 2012; Fox and Maskell, 1995; Ginis et al., 1998; Mason et al., 2010). The artifacts at the nesting boundary are amplified when the grid-resolution ratio of the child and parent domains increases (Spall and Holland, 1991). In this study, barotropic pressure, velocity, and bottom topography are linearly relaxed near the boundary of the child domain to allow for a smooth transition of these data between the child and parent domains, which the grid-resolution ratio is three.
The two-way nesting approaches can be classified into two categories: (i) internal, and (ii) external coupling. In internal coupling, a nesting framework is included in the source code of ocean models (Barth et al., 2005; Debreu and Blayo, 2008; Haley Jr. and Lermusiaux, 2010; Herrnstein et al., 2005; Santilli and Scotti, 2015; Tang et al., 2014). This approach requires more complicated nesting algorithms than a single resolution (no-nesting) case. In external coupling, a separate coupler facilitates the communication between numerical models. The main advantage of using such a coupler is that the modification of the source code of these models is minimal. It is only necessary that the Application Programming Interface (API) of the coupler be built into the existing source codes. In addition, external couplers provide a wide variety of interpolation schemes and efficient search algorithms that can be used to calculate interpolation (remapping) coefficients. The data that are transferred between coupled models need to be interpolated for use in the destination domain because the grid cells in the destination domain may not be located at the same coordinates as the grid cells in the source domain. Several external couplers have been developed and applied (Valcke et al., 2012). The Earth System Modeling Framework (ESMF) can be used to couple multiple domains with different resolutions (Qi et al., 2018). In recent research, the AGRIF and OASIS3-MCT coupling toolkits have been widely applied. The AGRIF (Adaptive Grid Refinement In Fortran) coupler has been used to couple ocean circulation models (Debreu et al., 2012; Penven et al., 2006; Urrego-Blanco et al., 2016). The OASIS3-MCT coupler (Valcke et al., 2015) has been used to couple climate models (Juricke et al., 2014; Ličer et al., 2016; Wahle et al., 2017; Will et al., 2017). OASIS3-MCT is an integrated version of OASIS3 (Ocean Atmosphere Sea Ice and Soil) by CERFACS in France and MCT (Model Coupling Toolkit) by the Argonne National laboratory in USA. We utilize OASIS3-MCT as a coupler for the HYCOM to HYCOM two-way nesting because its partition option, grid and mask, and parallel computing by Message Passing Interface (MPI) are more compatible with HYCOM as compared to AGRIF. Scientists at the Service Hydrographique et Océanographique de la Marine (SHOM; Brest, France) applied AGRIF to facilitate the HYCOM to HYCOM coupling, but found it hard to maintain as the HYCOM code was updated (personal communication with Remy Baraille, 2015).
HYCOM provides reliable results as a multi-layer global ocean circulation model and contributes to the United States Navy's operation (Arbic et al., 2010; Chassignet et al., 2007; Metzger et al., 2010; Ngodock et al., 2016; Shriver et al., 2012). The forward barotropic tide simulations (single layer), used in this paper, employ astronomical tidal forcing, a spatially-varying self-attraction and loading (SAL) term, a linear topographic wave drag (Buijsman et al., 2015), and an atmospheric mean sea level pressure forcing, which modulates the S2 tide and is obtained from the atmospheric NAVGEM (NAVy Global Environmental Model; Hogan et al., 2014). HYCOM is also capable of improving basin-scale modeling with offline one-way nesting (Chassignet et al., 2007; Hogan and Hurlburt, 2006). However, the offline one-way nesting in HYCOM has some drawbacks. First, it requires additional data storage for nesting data, whose size increases proportionally to the resolution of the computational domain. Second, global-scale modeling on the parent grid must be performed in advance of regional/basin-scale modeling on the child grid to provide boundary conditions for the child domain. Third, offline one-way nesting is useful only for improving the solution in the child domain, while the parent domain does not receive any feedback from the child domain. An online two-way nesting framework is able to resolve these issues and improve the accuracy in HYCOM for both regional/basin- and global-scale modeling. The most complicated issue in applying OASIS3-MCT to HYCOM is how to deal with barotropic time stepping in conjunction with the baroclinic time steps that are based on the second-order leapfrog scheme. This study synchronizes nesting variables at the barotropic time steps of the parent domain without any other treatments (Santilli and Scotti, 2015; Urrego-Blanco et al., 2016), and stores them so that they can be used at the next baroclinic time level.
In this study, the improvement through two-way nesting is evaluated and validated by comparing the nesting results to tide gauge data and the TPXO9-atlas and FES2014 global tidal solutions. TPXO9-atlas (volkov.oce.orst.edu/tides/tpxo9_atlas.html) is an altimetry-constrained tidal solution (Egbert and Erofeeva, 2002). FES2014 (https://www.aviso.altimetry.fr/) is the latest global solution of the FES (Finite Element Solutions) model, which is constrained with altimetry and tide gauge data (Carrère et al., 2015). Stammer et al. (2014) compared the numerical results of forward and data-assimilative tide models to the tide gauge data separately in the deep ocean, shelf sea, and coastal regions. According to Stammer et al. (2014), TPXO8-atlas (the previous version of TPXO9-atlas) is more accurate in the deep ocean than FES2012 (the previous version of FES2014), whereas TPXO8-atlas has larger root-mean-square errors with the tide gauge data in the shelf seas than FES2012. The FES2014 tidal solution has improved its tidal accuracy compared to its previous versions (Cancet et al., 2018), and so has TPXO9-atlas. Hence, we compare the two-way nesting results to both the TPXO9-atlas and FES2014 solutions, as well as to the tide gauge data of Stammer et al. (2014).
This paper is organized as follows. The online two-way nesting framework in HYCOM is described in Section 2. The developed nesting framework is validated with semi-idealized basin-scale simulations in Section 3. The framework is then applied to a realistic global-scale simulation and validated against tide gauge data, FES2014, and TPXO9-atlas in Section 4. Finally, we end with a discussion and conclusions in Section 5.
Section snippets
Data exchange in HYCOM
In solving the layer-integrated nonlinear momentum equations, HYCOM uses a split-explicit time-stepping scheme that separates the fast barotropic mode (single layer) from the slow baroclinic modes (multiple layers) for numerical efficiency (Bleck and Smith, 1990). In barotropic HYCOM simulations, as in this paper, this split-explicit time-stepping scheme is still used. In this case, HYCOM performs the calculations over two layers: a surface layer with a varying thickness and a bottom layer with
Validation of the nesting framework
The developed nesting framework is validated with six semi-idealized model simulations. Experiments 1–2 concern one-way nesting and Experiments 3–6 concern two-way nesting. The parent and child grid resolutions are the same in Experiments 1–4, while they differ in Experiments 5–6. Experiment pairs 1–2, 3–4, and 5–6 concern the sensitivity to equal and different time steps on the parent and child grids. The grid resolutions and time steps of the parent and child domains in Experiment 6 are the
Global barotropic tides
To improve the tidal accuracy in the global HYCOM simulations, we apply the two-way nesting framework to a high-resolution child domain (1/75°) and a relatively low-resolution global parent domain (1/25°). The child domain, referred to as HBF, and its surroundings are shown in Fig. 11. Since the southeast entrance of Fury and Hecla Strait is blocked as land in the relatively low-resolution (1/25°) domain, and Hudson Bay plays an important role in the resonance of the M2 barotropic tide in
Discussion and conclusions
We have implemented an online two-way nesting framework in a global ocean circulation model (HYCOM) to improve global surface tides. The barotropic pressure and velocity are exchanged between a parent and a child domain with an external coupler, OASIS3-MCT. We modified the masks in both the first coarse-to-fine and the second fine-to-coarse directions, and set the limits of the search area in the first direction to reduce the computing time of the remapping coefficients in OASIS3-MCT.
In the
Acknowledgment
C.-H.J., M.C.B., B.K.A., and J.G.R. gratefully acknowledge funding from the project “Improving global surface and internal tides through two-way coupling with high resolution coastal models” as part of the Office of Naval Research (ONR) grant N00014-15-1-2288. A.J.W. and J.F.S. acknowledge support from the Naval Research Laboratory (NRL) contract N00014-15-WX-01744. Finally, P.J.H. acknowledges financial support from the project “Arctic shelf and large rivers seamless nesting in global HYCOM”
References (46)
- et al.
A coupled oscillator model of shelf and ocean tides
Cont. Shelf Res.
(2010) - et al.
The accuracy of surface elevations in forward global barotropic and baroclinic tide models
Deep-Sea Res. II
(2004) - et al.
Concurrent simulation of the eddying general circulation and tides in a global ocean model
Ocean Model
(2010) - et al.
Two-way nested model of mesoscale circulation features in the Ligurian Sea
Prog. Oceanogr.
(2005) - et al.
Optimizing internal wave drag in a forward barotropic model with semidiurnal tides
Ocean Model
(2015) - et al.
Arctide2017, a high-resolution regional tidal model in the Arctic Ocean
Adv. Space Res.
(2018) - et al.
The HYCOM (HYbrid Coordinate Ocean Model) data assimilative system
J. Mar. Syst.
(2007) - et al.
Two-way nesting in split-explicit ocean models: algorithms, implementation and validation
Ocean Model
(2012) - et al.
Structured adaptive mesh refinement using leapfrog time integration on a staggered grid for ocean models
Ocean Model
(2005) - et al.
At-sea real-time coupled four-dimensional oceanographic and acoustic forecasts during Battlespace Preparation 2007
J. Mar. Syst.
(2009)
Procedures for offline grid nesting in regional ocean models
Ocean Model
Simulated and observed circulation in the Indonesian seas: 1/12° global HYCOM and the INSTANT observation
Dyn. Atmos. Oceans
On improving the accuracy of the M2 barotropic tides embedded in a high-resolution global ocean circulation model
Ocean Model
Evaluation and application of the ROMS 1-way embedding procedure to the central California upwelling system
Ocean Model
FVCOM one-way and two-way nesting using ESMF: development and validation
Ocean Model
The stratified ocean model with adaptive refinement
J. Comput. Phys.
An overset grid method for integration of fully 3D fluid dynamics and geophysics fluid dynamics models to simulate multiphysics coastal ocean flows
J. Comput. Phys.
On the resonance and influence of the tides in Ungava Bay and Hudson Strait
Geophys. Res. Lett.
On tidal resonance in the global ocean and the back-effect of coastal tides upon open-ocean tides
Atmosphere-Ocean
A wind-driven isopycnic coordinate model of the North and Equatorial Atlantic Ocean: 1. Model development and supporting experiments
J. Geophys. Res.
Examining interior grid nudging techniques using two-way nesting in the WRF model for regional climate modeling
J. Clim.
Initialization of the shallow water equations with open boundaries by the bounded derivative method
Tellus
FES2014, a New Tidal Moel on the Global Ocean with Enhanced Accuracy in Shallow Seas and in the Arctic Region, EGU General Assembly 2015, Vienna, Austria, 12–17 April, 5481
Cited by (10)
Remote internal wave forcing of regional ocean simulations near the U.S. West Coast
2023, Ocean ModellingIncorporating tides and internal gravity waves within global ocean general circulation models: A review
2022, Progress in OceanographyCitation Excerpt :Because coastal regions impact open-ocean tides, more accurate modeling of coastal tides may improve the modeling of open-ocean tides as well. Simulations with two-way nesting, and higher horizontal resolution, in regions of large coastal tides, do indeed see an improved accuracy in the modeled open-ocean tides (Jeon et al., 2019). However, the improvements come with a substantial added computational cost.
The transition of tidal Kelvin waves to hybrid Kelvin edge and internal waves in the global ocean
2022, Continental Shelf ResearchA likely role for stratification in secular changes of the global ocean tides
2023, Research SquareTwo-Way Nesting in a Split-Implicit Ocean Model: NCOM
2023, Journal of Atmospheric and Oceanic Technology