Eric P. Chassignet

Abstract An ocean forecasting system has three essential components (observations, data assimilation, numerical model). Observational data, via data assimilation, form the basis of an accurate model forecast; the quality of the ocean forecast will depend primarily on the ability of the ocean numerical model to faithfully represent the ocean physics and dynamics. Even the use of an infinite amount of data to constrain the initial conditions will not necessarily improve the forecast against persistence of a poorly performing ocean numerical model. In this chapter, some of the challenges associated with global ocean modeling are introduced and the current state of numerical models formulated in isopycnic and hybrid vertical coordinates is reviewed within the context of operational global ocean prediction systems.

The main purpose of this chapter is to review the current state of numerical models formulated in isopycnic and hybrid vertical coordinates and discuss their applications within the context of operational global ocean prediction systems and GODAE (Global Ocean Data Assimilation Experiment). In addition to this author's work, this review chapter relies heavily on articles, notes, and review papers by R. Bleck, S. Griffies, A. Adcroft, and R. Hallberg. Appropriate references will be made, but it is inevitable that some similarities in content and style to these publications will be present throughout this chapter.

As stated in Bleck and Chassignet (1994), numerical modeling of geophysical fluid started half a century ago with numerical weather prediction. Ocean model development lagged behind that of atmospheric models, primarily because of

Center for Ocean-Atmospheric Predictions Studies, Florida State University, Tallahassee, FL 32306, USA e-mail: [email protected]

A. Schiller, G. B. Brassington (eds.), Operational Oceanography in the 21st Century, 263

DOI 10.1007/978-94-007-0332-2_11, © Springer Science+Business Media B.V. 2011

the societal needs for meteorological forecasts, but also because of the inherently greater complexity of circulation systems in closed basins and a nonlinear equation of state for seawater. Furthermore, the computing power required to resolve the relevant physical processes (such as baroclinic instabilities) is far greater for the ocean than the atmosphere since these processes occur on much smaller scale in the ocean. Historically, ocean models have been used primarily to numerically simulate the dominant space-time scales that characterize the ocean system. Simulations of physical integrity require an ability to both accurately represent the various phenomena that are resolved, and to parameterize those scales of variability that are not resolved (Chassignet and Verron 1998). For example, the representation of transport falls into the class of problems addressed by numerical advection schemes, whereas the parameterization of subgrid scale transport is linked to turbulence closure considerations. Although there are often areas of overlap between representation and parameterization, the distinction is useful to make and generally lies at the heart of various model development issues.

Before the Navier-Stokes differential equations can be solved numerically, they must be converted into an algebraic system, a conversion process that entails numerous approximations. Numerical modelers strive to achieve numerical accuracy. Otherwise, the discretization or "truncation" error introduced when approximating differentials by finite differences or Galerkin methods becomes detrimental to the numerical realization. Sources for truncation errors are plentiful, and many of these errors depend strongly on model resolution. Examples include horizontal coordinates (spherical and/or generalized orthogonal), vertical and horizontal grids, time-stepping schemes, representation of the surface and bottom boundary layers, bottom topography representation, equation of state, tracer and momentum transport, sub-grid scale processes, viscosity, and diffusivity. Numerical models have improved over the years not only because of better physical understanding, but also because modern computers permit a more faithful representation of the differential equations by their algebraic analogs.

A key characteristic of rotating and stratified fluids, such as the ocean, is the dominance of lateral over vertical transport. Hence, it is traditional in ocean modeling to orient the two horizontal coordinates orthogonal to the local vertical direction as determined by gravity. The more difficult choice is how to specify the vertical coordinate. Indeed, as noted by various ocean modeling studies such as DYNAMO (Meincke et al. 2001; Willebrand et al. 2001) and DAMEE-NAB (Chassignet and Malanotte-Rizzoli 2000), the choice of a vertical coordinate system is the single most important aspect of an ocean model's design. The practical issues of representation and parameterization are often directly linked to the vertical coordinate choice. Currently, there are three main vertical coordinates in use, none of which provide universal utility. Hence, many developers have been motivated to pursue research into hybrid approaches.

As outlined by Griffies et al. (2000a), there are three regimes of the ocean that need to be considered when choosing an appropriate vertical coordinate. First, there is the surface mixed layer. This region is generally turbulent and dominated by transfers of momentum, heat, freshwater, and tracers. It is typically very well mixed in the vertical through three-dimensional convective/turbulent processes. These processes involve non-hydrostatic physics, which requires very high horizontal and vertical resolution to be explicitly represented (i.e., a vertical to horizontal grid aspect ratio near unity). A parameterization of these processes is therefore necessary in primitive equation ocean models. In contrast, tracer transport processes in the ocean interior predominantly occur along constant density directions (more precisely, along neutral directions). Therefore, water mass properties in the interior tend to be preserved over large space and time scales (e.g., basin and decadal scales). Finally, there are several regions where density driven currents (overflows) and turbulent bottom boundary layer processes act as a strong determinant of water mass characteristics. Many such processes are crucial for the formation of deep water properties in the world ocean.

The simplest choice of vertical coordinate (Fig. 11.1) is z, which represents the vertical distance from a resting ocean surface. Another choice for vertical coordinate is the potential density referenced to a given pressure. In a stably stratified adiabatic ocean, potential density is materially conserved and defines a monotonic layering of the ocean fluid. A third choice is the terrain-following a coordinate. The depth or z coordinate provides the simplest and most established framework for ocean modeling. It is especially well-suited for situations with strong vertical/diapycnal mixing and/or low stratification, but has difficulty in accurately representing the ocean interior and bottom. The density coordinate, on the other hand, is well-suited to modeling the observed tendency for tracer transport to be along density (neutral) directions, but is inappropriate in unstratified regions. The a coordinate provides a suitable framework in situations where capturing the dynamical and/or boundary layer effect associated with topography is important. Terrain-following a coordinates are particularly well suited for modeling flows over the continental shelf, but remain unproven in a global modeling context. They have been used extensively for

Fig. 11.1 Schematic of an ocean basin illustrating the three regimes of the ocean germane to the considerations of an appropriate vertical coordinate. The surface mixed layer is naturally represented using fixed depth z (or pressure p) coordinates, the interior is naturally represented using isopycnic ppot (potential density tracking) coordinates, and the bottom boundary is naturally represented using terrain-following a coordinates. (Adapted from Griffies et al. 2000a)

Fig. 11.1 Schematic of an ocean basin illustrating the three regimes of the ocean germane to the considerations of an appropriate vertical coordinate. The surface mixed layer is naturally represented using fixed depth z (or pressure p) coordinates, the interior is naturally represented using isopycnic ppot (potential density tracking) coordinates, and the bottom boundary is naturally represented using terrain-following a coordinates. (Adapted from Griffies et al. 2000a)

coastal engineering applications and prediction (see Greatbatch and Mellor (1999) for a review), as well as for regional and basin-wide studies.

Ideally, an ocean model should retain its water mass characteristics for centuries of integration (a characteristic of density coordinates), have high vertical resolution in the surface mixed layer for proper representation of thermodynamical and biochemical processes (a characteristic of z coordinates), maintain sufficient vertical resolution in unstratified or weakly stratified regions of the ocean, and have high vertical resolution in coastal regions (a characteristic of terrain-following a coordinates). This has led to the recent development of several hybrid vertical coordinate numerical models that combine the advantages of the different types of vertical coordinates in optimally simulating coastal and open-ocean circulation features.

Within the GODAE context, the global ocean models presently used or tested for ocean forecasting systems can be divided into two categories: fixed coordinates (MOM, NEMO, MITgcm, NCOM, POP, OCCAM, ...) or primarily Lagrangian coordinates (NLOM, MICOM, HYCOM, POSEIDON, GOLD, ...). The reader is referred to the Appendix for a definition of the acronyms and references.

11.2 Ocean Model Requirements for GODAE

The specific objectives of GODAE are to:

a) Apply state-of-the art ocean models and assimilation methods to produce short-range open-ocean forecasts, boundary conditions to extend predictability of coastal and regional subsystems, and initial conditions for climate forecast models.

b) Provide global ocean analyses for developing improved understanding of the oceans and improved assessments of the predictability of ocean variability, and for serving as a basis for improving the design and effectiveness of a global ocean observing system.

The requirements for the ocean model differ among these objectives. High-resolution operational oceanography requires accurate depiction of mesoscale features, such as eddies and meandering fronts and of upper ocean structure. Coastal applications require accurate sea level forced by wind, tidal forces, and surface pressure. Seasonal-to-interannual forecasts require a good representation of the upper ocean mass field and coupling to an atmosphere. This diversity of applications implies that no single model configuration will be sufficiently flexible to satisfy all the objectives.

For high-resolution operational oceanography (see Hurlburt et al. (2008, 2009) for a review), the models have to be global and eddy-resolving, with high vertical resolution and advanced upper-ocean physics, and use high-performance numerical code and algorithms. To have a good representation of the mesoscale variability, the horizontal grid spacing must be fine enough to be able to resolve baroclinic insta bility processes. Most numerical simulations to date suggest that a minimum grid spacing on the order of 1/10° (see AGU monograph by Hecht and Hasumi 2008 for a review) is needed for a good representation of western boundary currents (including their separation from the coast) and of the eddy kinetic energy. The computational requirements for global ocean modeling at this resolution are extreme and demand the latest in high-performance computing. For that reason, there are only a few eddy-resolving global ocean models currently being integrated with or without data assimilation: NLOM 1/32° (Shriver et al. 2007), POP 1/10° (Maltrud and Mc-Clean 2005), HYCOM 1/12° (Chassignet et al. 2009), and MERCATOR/NEMO 1/12° (Bourdalle-Badie and Drillet personal communication).

As the mesh is refined, ocean models faceseveral challenges. This section summarizes the challenges that this author thinks are most relevant to GODAE's goal of high-resolution operational oceanography.

Model-Related Data Assimilation Issues In data assimilation, there is a much larger burden on ocean models than on atmospheric models because (1) synoptic oceanic data is overwhelmingly at the surface, (2) ocean models must use simulation skills in converting atmospheric forcing into an oceanic response, and (3) ocean model forecast skill is needed in the dynamical interpolation of satellite altimeter data (since the average age of the most recent altimeter data on the repeat tracks is 1/2 the repeat cycle plus the delay in receiving the real-time data, typically 1-3 days at present). Specifically, the model must be able to accurately represent ocean features and fields that are inadequately observed or constrained by ocean data. This is an issue for re-analyses, for real-time mesoscale resolving nowcasts and short-range forecasts (up to ~1 month), and for seasonal-to-interannual forecasts, including the geographical distribution of anomalies. Ocean simulation skill is especially important for mean currents and their transports (including flow through straits), the surface mixed layer depth, Ekman surface currents, the coastal ocean circulation, the Arctic circulation, and the deep circulation (including the components driven by eddies, the thermohaline circulation, and the wind).

To order to assimilate the SSH (Sea Surface Height) anomalies determined from satellite altimeter data into the numerical model, it is necessary to know the oceanic mean SSH over the time period of the altimeter observations. Unfortunately, the earth's geoid is not presently known with sufficient accuracy to provide an accurate mean SSH on scales important for the mesoscale. Several satellite missions are underway or planned to help determine a more accurate geoid, but not on a fine enough scale to entirely meet the needs of mesoscale prediction. Thus, it is of the utmost importance to have a model mean that is reasonably accurate since most oceanic fronts and mean ocean current pathways cannot be sharply defined from hydrographic climatologies alone.

A number of additional issues, theoretical or technical, are raised when the numerical ocean model is used in conjunction with data assimilation techniques. In all data assimilation methods, nonlinearities are a major source of sub-optimality. Variational methods often require development of the adjoint model, which is a demanding task. Depending on the vertical coordinates, difficulties arise in dealing with non-Gaussian statistics in isopycnic coordinate models with vanishing layers, or with convective instability processes throughout the vertical columns in z coordinate models. Finally, defining prior guess errors, model errors, and, to a lesser degree, observation errors, is difficult.

Forcing The ocean model will respond to the prescribed atmospheric forcing fields. The present models' inability to reproduce the present-day ocean circulation when run in free mode is a consequence of inaccuracies in both the forcing and in the numerical models themselves, as well as of the intrinsic nonlinearity of the Navier-Stokes equations. Accurate atmospheric forcing, when computed using bulk formulas that combine the model SST and the atmospheric data, have been shown to be essential for a successful forecast of the sea surface temperature, sea surface salinity, and mixed layer depths. It is important to mention here that the prescription of the surface forcing fields, as currently done in many ocean forecasting systems, does not allow for atmospheric feedback. This may have a limited impact on a 15-day forecast, but coupling to an atmospheric model is essential in seasonal-to-interannual forecasting of events such as ENSO (Philander 1990; Clarke 2008).

Topography With high-resolution modeling comes the need for high-resolution topography. The most commonly used global bathymetric database is the Smith and Sandwell (1997, 2004) database, which is derived from a combination of satellite altimeter data and shipboard soundings. The latest version (http://topex.ucsd. edu/WWW_html/srtm30_plus.html) is at 1/2 min resolution and covers the entire globe, with patches from the IBCAO topography (Jakobsson et al. 2000) in the Arctic and from various high-resolution sounding data where such data are available. Most, but not all, of the other available global bathymetric data sets, for instance, the latest GEBCO bathymetry, ETOPO2, DBDB2, and so on, utilize the Smith and Sandwell database in the deep ocean. Differences can often be found among various bathymetry products in shallow water, where satellite altimetry is much less useful, and where local high-quality datasets are often used. While modern acoustic sounding data can achieve lateral resolutions of about 100 m, such data cover only a small fraction of the open ocean. In areas not covered by such data, the true feature resolution of the Smith and Sandwell datasets is approximately given by n times the water column depth, i.e., about 10-20 km. Goff and Arbic (2010) have recently created a synthetic data set in which the topographic anomalies depend on local geophysical conditions such as seafloor spreading rate. The synthetic topography can be overlaid on the Smith and Sandwell datasets to create global bathymetries that have the right statistical texture (roughness), even if the "bumps" are not deter-ministically correct.

Meridional Overturning Circulation A good representation of the overturning circulation is essential for a proper representation of the oceanic surface fields. This is especially true in the North Atlantic where the contribution of the thermohaline meridional overturning circulation accounts for a significant portion of the Gulf Stream transport. Many factors, such as mixed layer physics, ice formation, overflow representation, and interior diapycnal mixing, affect the strength and pathways of the meridional overturning circulation.

Ice Models A global ocean model needs to be coupled to an ice model to have the proper forcing at high latitudes and hence the correct dense water mass formation and circulation. A good representation of the ice cycle is challenging, especially when the atmospheric fields are prescribed. Another related issue is the mixed layer parameterization below the ice.

Overflows Sill overflows typically involve passages through the ridge and are under the control of hydraulic effects, each of which is highly dependent on topographic details. The downslope flow of dense water, typically in thin turbulent layers near the bottom, may strongly entrain ambient waters and is modulated by mesoscale eddies generated near the sill. The simulation of downslope flows of dense water differs strongly among ocean models based on different vertical coordinate schemes. In z coordinate models, difficulties arise from the stepwise discretization of topography, which tends to produce gravitationally unstable water parcels that rapidly mix with the ambient fluid as they flow down the slope. The result is a strong numerically induced mixing of the outflow water downstream of the sill. This numerically induced mixing will in principle decrease as the horizontal and vertical grid spacing is refined. It is, however, still an issue at the above mentioned resolution of 1/10° (see review article by Legg et al. 2009).

Diapycnal Mixing This observational field is the least well known and the most difficult to model correctly, especially in fixed coordinate models (Griffies et al. 2000b; Lee et al. 2002) due to the typically small levels of mixing in the ocean interior away from boundaries (Ledwell et al. 1993). Excessive numerically induced diapycnal mixing will lead to incorrect water mass pathways and a poor representation of the thermohaline circulation.

Internal Gravity Waves/Tides Improperly resolved internal gravity waves generate numerically induced diapycnal mixing in fixed-coordinate models. Several numerical techniques can be used to slow the gravity waves, but ultimately it would be desirable to have a diapycnal mixing parameterization based on the model representation of internal gravity waves. The inclusion of astronomical tidal forcing in ocean models generates barotropic tides, which in turn generate internal tides in areas of rough topography. Until recently, global modeling of the oceanic general circulation and of tides have been separate endeavors. A first attempt to model the global general circulation and tides simultaneously and at high horizontal resolution is described in Arbic et al. (2010). In contrast to earlier models of the global internal tides, which included only tidal forcing and which utilized a horizontally varying stratification, the stratification can vary horizontally in a model that also includes wind- and buoyancy-forcing. Arbic et al. (2010) show that the horizontally varying stratification affects tides to first order, especially in polar regions. Inclusion of tides in general circulation models is also more likely to properly account for the effects of the quadratic bottom boundary layer drag term. Many ocean general circulation models insert an assumed tidal background flow, typically taken to be about 5 cm/s, into the quadratic drag formulation (e.g., Willebrand et al. 2001). However, in the actual ocean tidal velocities vary from about 1-2 cm/s in the abyss to about 0.5-1 m/s in areas of large coastal tides. Thus an assumed tidal background flow of 5 cm/s is too strong in the abyss and too weak in coastal areas. By actually resolving the (spatially inhomogeneous) tidal flows in a general circulation model, this problem can be corrected.

Barotropic Motions The use of high-frequency (e.g., 3-hourly) forcing generates strong non-steric barotropic motions that are not temporally resolved by satellite altimeters (Stammer et al. 2000). In addition, Shriver and Hurlburt (2000) report that between 5 and 10 cm rms SSH non-steric variability are generated in major current systems throughout the world ocean.

Viscosity Closure Despite the smaller mesh size, the viscosity parameterization remains of importance for the modeled large-scale ocean circulation (Chassignet and Garraffo 2001; Chassignet and Marshall 2008; Hecht et al. 2008). When the grid spacing reaches a certain threshold, the energy cascade from small to large scales should be properly represented by the model physics. Dissipation should then be prescribed for numerical reasons only to remove the inevitable accumulation of enstrophy on the grid scale. This is the reason higher-order operators such as the biharmonic form of friction have traditionally been favored in eddy-resolving or eddy-permitting numerical simulations. Higher-order operators remove numerical noise on the grid scale and leave the larger scales mostly untouched by allowing dynamics at the resolved scales of motion to dominate the subgrid-scale parameterization (Griffies and Hallberg 2000). In addition to numerical closure, the viscosity operator can also be a parameterization of smaller scales. One of the most difficult tasks in defining the parameterization is the specification of the Reynolds stresses in terms of only the resolved scales' velocities. The common practice has been to assume that the turbulent motion acts on the large-scale flow in a manner similar to molecular viscosity. However, the resulting Laplacian form of dissipation removes both kinetic energy and enstrophy over a broad range of spatial scales, and its use in numerical models in general implies less energetic flow fields than in cases with more highly scale-selective dissipation operators. Some Laplacian dissipation is still needed to define viscous boundary layers and to remove eddies on space scales too large to be removed by biharmonic dissipation and too small to be numerically accurate at the model grid resolution.

Coastal Transition Zones A strong demand for ocean forecasts will come from the offshore industry, which has extended its activities from the shallow shelf seas to exploration and production on the continental slope, where oceanographic condi tions play a much more critical role in safe and environmentally acceptable operations. Exploration and production are now taking place in water depths in excess of 2000 m in a number of oil and gas basins around the world. The proper modeling of the transition area between the deep ocean and the shallow continental shelves imposes strong requirements on the ocean model. It should be capable of modeling the typical shallow waters on the shelf, with their characteristic well-mixed water masses and strong tidal and wind-driven currents. Furthermore, it also must properly represent and distinguish between water masses of vastly different characteristics in the deep ocean and near the surface during very long time integrations. The interaction with the continental shelf/slope is also an intriguing problem due to the impact on internal tides and the wave modes developing and propagating along the continental shelf/slope. This includes remotely generated wave modes, such as equatorially generated Kelvin waves, which play a large role in El Niño events and which can strongly impact distant coastal regions.

11.4 On the Use of Potential Density as a Vertical Coordinate

As stated in the introduction, the choice of a vertical coordinate system is the single most important aspect of an ocean model's design and, because of the practical issues of representation and parameterization, many of the challenges listed in the previous sections are directly linked to the vertical coordinate choice. There is no "best" choice of vertical coordinate since all solutions of the discretized equations with any vertical coordinate should converge toward the solutions of the corresponding differential equations as mesh size goes to zero. Each coordinate system is afflicted with its own set of truncation errors, the implications of which must be understood and prioritized.

Isopycnic (potential density) coordinate modeling seeks to eliminate truncation errors by reversing the traditional role of depth as an independent variable and potential density as a dependent variable. More specifically, mixing in turbulent stratified fluids where buoyancy effects play a role takes place predominantly along isopycnic or constant potential density surfaces (Iselin 1939; Montgomery 1940; McDougall and Church 1986). If the conservation equations for salt and temperature are discretized in (x,y,z) space, that is, if the three-dimensional vectorial transport of these quantities is numerically evaluated as the sum of scalar transports in (x,y,z) direction, experience shows that it is virtually impossible to avoid diffusion of the transported variables in those three directions (Veronis 1975; Redi 1982; Cox 1987; Gent and McWilliams 1990, 1995; Griffies et al. 2000b). Thus, regardless of how the actual mixing term in the conservation equations is formulated, numerically induced mixing is likely to have a cross-isopycnal ("diapycnal") component that may well overshadow the common diapycnal processes that occur in nature (Griffies et al 2000b). This type of truncation error can be mostly eliminated in isopycnic coordinate modeling by transforming the dynamic equations from (x,y,z)

to (x,y,p) coordinates (Bleck 1978, 1998; Bleck et al. 1992; Bleck and Chassignet 1994).

First, the prognostic primitive equations are rewritten in (x,y,s) coordinates where s is an unspecified generalized vertical coordinate (Bleck 2002).

ds J dp

where v=(u,v) is the horizontal vector, p is pressure, 6 represents any one of the model's thermodynamic variables, a = p— is the potential specific volume, g = dv/dxs - du/dys is the relative vorticity, M = gz + pa is the Montgomery potential, f is the Coriolis parameter, k is the vertical unit vector, v and f are the eddy viscosity and diffusivity, t is the wind- and/or bottom-drag induced shear stress vector, and H is the sum of diabatic source terms acting on 6 including diapycnal mixing. Subscripts indicate which variable is held constant during partial differentiation. Distances in the x,y direction, as well as their time derivatives u,v, are measured in the projection onto an horizontal plane. This conversion renders the coordinate system nonorthogonal in 3-D space, but eliminates metric terms related to the slope of the 5 surface (Bleck 1978). Other metric terms, created when vector products involving (V) or (Vx) are evaluated on a non Cartesian grid (e.g. spherical coordinates), are absorbed into the primary terms by evaluating vorticity and horizontal flux divergences in (11.1)-(11.3) as line integrals around individual grid boxes (see Griffies et al. 2000a for more details). Note that applying V to a scalar, such as v2/2 in (11.1), does not give rise to metric terms.

Second, by performing a vertical integration over a coordinate layer bounded by two surfaces stop and sbot, the continuity Eq. (11.2) becomes a prognostic equation for the layer weight per unit area, Ap = pbot - Ptop.

The expression (sdp/ds) represents the vertical mass flux across an 5 surface, taken to be positive in the +p downward direction. Multiplication of (11.1) by dp/ds and integration over the interval (s sbot), followed by division by Ap/As, changes the shear stress term to g/Ap(xtop - Tbot) while the lateral momentum mixing term

integrates to (Ap)-1 Vs-(vApVsv). All the other terms in (11.1) retain their formal appearance. The layer integrated form of (11.3) is

The above prognostic equations are complemented by several diagnostic equations, including the hydrostatic equation, dM/da = p, an equation of state linking potential temperature T, salinity S, and pressure p to ppot, and an equation prescribing the vertical mass flux (sdp/ds) through an 5 surface.

Isopycnic models solve the above equations by using the potential density, p as the vertical coordinate 5. Where the fluid is adiabatic, potential density is conserved and transport in the x,y direction then takes place in the model on isopycnic surfaces. This makes isopycnic models very adiabatic and allows them to avoid introducing the numerical diffusion in the vertical that can be troublesome in z or a coordinate models. Transport in the z direction translates into transport along the ppot axis and can be entirely suppressed if so desired; that is, it has no unwanted diapycnal component. As a result, spurious heat exchange between warm surface waters and cold abyssal waters and horizontal heat exchange across sloping isopyc-nals such as those marking frontal zones are minimized. Potential density surfaces are not, however, neutral surfaces (McDougall and Church 1986) and dianeutral fluxes may therefore be present when potential density is used as the vertical coordinate. As coordinate surfaces deviate from neutral, advection and diffusion acting along these surfaces will induce some dianeutral mixing. The impact of dianeutral fluxes from diffusion can be reduced/eliminated by rotating the diffusion operator to act along neutral directions in a manner analogous to that employed in fixed coordinates models (Griffies et al. 2000a). Furthermore, the nonlinear equation of state in the ocean introduces new physical sources of mixing, i.e., the independent transport of two active tracers (temperature and salinity) requires remapping algorithms to retain fields within pre-specified density classes. The level of dianeutral mixing introduced by remapping algorithms is usually negligible, but it has yet to be systematically documented (Griffies and Adcroft 2008). A reference pressure of 2000 db is now the norm for isopycnic coordinates models since it leads to few regions with coordinate inversions and the slopes of the a2 (potential density referred to 2000 db) surfaces are closest to neutral surfaces. Inclusion of thermobaricity (i.e., compressibility of sea water in the equation of state) in isopycnic coordinate ocean models is described in Sun et al. (1999) and Hallberg (2005). The necessity to properly reconcile estimates of the free surface height when using mode-splitting time stepping scheme is discussed in Hallberg and Adcroft (2009).

The key advantages of isopycnic coordinate models can be summarized as follows: (a) they are well suited for representing tracer transport without any large numerically induced vertical mixing as long as the isopycnals are reasonably parallel to neutral surfaces; (b) they conserve density classes under adiabatic motions; (c) the bottom topography is represented in a piecewise linear fashion, hence avoiding top the need to distinguish bottom from side as traditionally done in z coordinate models; and (d) the overflows are well represented. The main drawback of an isopycnic coordinate model is its inability to properly represent the surface mixed layer or the bottom boundary layer since these layers are mostly unstratified. Examples of iso-pycnal models are NLOM (Wallcraft et al 2003), MICOM (Bleck et al. 1992; Bleck and Chassignet 1994; Bleck 1998), HIM (Hallberg 1995, 1997), OPYC (Oberhuber 1993) and POSUM.

As already stated, none of three main vertical coordinates currently in use (z, isopycnal, or a) provides universal utility, and hybrid approaches have been developed in an attempt to combine the advantages of different types of vertical coordinates in optimally simulating the ocean. The term "hybrid vertical coordinates" can mean different things to different people: it can be a linear combination of two or more conventional coordinates (Song and Haidvogel 1994; Ezer and Mellor 2004; Barron et al. 2006) or it can be truly generalized, i.e., aiming to mimic different types of coordinates in different regions of a model domain (Bleck 2002; Burchard and Beckers 2004; Adcroft and Hallberg 2006; Song and Hou 2006). Adcroft and Hallberg (2006) classify generalized coordinates ocean models as either a Lagrang-ian Vertical Direction (LVD) or an Eulerian Vertical Direction (EVD) models. In LVD models, the continuity (thickness tendency) equation is solved forward in time throughout the domain, while an Arbitrary Lagrangian-Eulerian (ALE) technique is used to re-map the vertical coordinate and maintain different coordinate types within the domain. This differs from the EVD models with fixed depth and terrain-following vertical coordinates that use the continuity equation to diagnose vertical velocity.

The hybrid or generalized coordinate ocean models that have much in common with isopycnal models and are classified as LVD models are POSEIDON (Schopf and Loughe 1995) and HYCOM (Bleck 2002; Chassignet et al. 2003; Halliwell 2004). Other generalized vertical coordinate models currently under development are HYPOP and GOLD. HYPOP is the hybrid version of POP and differs from HYCOM and POSEIDON in the sense that the momentum equations continue to be solved on z coordinates while the tracer equations are solved using an ALE scheme for the vertical coordinate. Such an approach allows the model to utilize depth as the vertical coordinate in the mixed layer while using a more Lagrangian (e.g. isopycnal) coordinate in the deep ocean. GOLD, the "Generalized Ocean Layer Dynamics" model, is intended to be the vehicle for the consolidation of all of the climate ocean model development efforts at GFDL, including MOM and HIM.

11.5 Application: The HYbrid Coordinate Ocean Model (HYCOM)

The generalized vertical coordinates in HYCOM deviate from isopycnals (constant potential density surfaces) wherever the latter may fold, outcrop, or generally provide inadequate vertical resolution in portions of the model domain.

HYCOM is at its core a Lagrangian layer model, except for the remapping of the vertical coordinate by the hybrid coordinate generator after all equations are solved (Bleck 2002; Chassignet et al. 2003; Halliwell 2004) and for the fact that there is a nonzero horizontal density gradient within all layers. HYCOM is thus classified as an LVD model. The ability to adjust the vertical spacing of the coordinate surfaces in HYCOM simplifies the numerical implementation of several physical processes (e.g., mixed layer detainment, convective adjustment, sea ice modeling) without harming the model of the basic and numerically efficient resolution of the vertical that is characteristic of isopycnic models throughout most of the ocean's volume (Bleck and Chassignet 1994; Chassignet et al. 1996).

HYCOM is the result of a collaboration initiated in the late nineties by ocean modelers at the Naval Research Laboratory, Stennis, MS, who approached colleagues at the University of Miami's Rosenstiel School of Marine and Atmospheric Science regarding an extension of the range of applicability of the U.S. Navy operational ocean prediction system to coastal regions (e.g., the U.S. Navy systems at the time were seriously limited in shallow water and in handling the transition from deep to shallow water). HYCOM (Bleck 2002) was therefore designed to extend the range of existing operational Ocean General Circulation Models (OGCMs). The freedom to adjust the vertical spacing of the generalized (or hybrid) coordinate layers in HYCOM simplifies the numerical implementation of several processes and allows for a smooth transition from the deep ocean to coastal regimes. HYCOM retains many of the characteristics of its predecessor, MICOM, while allowing coordinates to locally deviate from isopycnals wherever the latter may fold, outcrop, or generally provide inadequate vertical resolution. The collaboration led to the development of a consortium for hybrid-coordinate data assimilative ocean modeling supported by NOPP to make HYCOM a state-of-the-art community ocean model with data assimilation capability that could (1) be used in a wide range of ocean-related research; (2) become the next generation eddy-resolving global ocean prediction system; and (3) be coupled to a variety of other models, including littoral, atmospheric, ice and bio-chemical. The HYCOM consortium became one of the U.S. components of GODAE, a coordinated international system of observations, communications, modeling, and assimilation that delivers regular, comprehensive information on the state of the oceans (see Chassignet and Verron (2006) for a review). Navy and NOAA applications such as maritime safety, fisheries, the offshore industry, and management of shelf/coastal areas are among the expected beneficiaries of the HYCOM ocean prediction systems (http://www.hycom.org). More specifically, the precise knowledge and prediction of ocean mesoscale features helps the Navy, NOAA, the Coast Guard, the oil industry, and fisheries with endeavours such as ship and submarine routing, search and rescue, oil spill drift prediction, open ocean ecosystem monitoring, fisheries management, and short-range coupled atmosphere-ocean, coastal and near-shore environment forecasting. In addition to operational eddy-resolving global and basin-scale ocean prediction systems for the U.S. Navy and NOAA, respectively, this project offered an outstanding opportunity for

NOAA-Navy collaboration and cooperation ranging from research to the operational level (see Chassignet et al. 2009).

In HYCOM, the optimal vertical coordinate distribution of the three vertical coordinate types (pressure, isopycnal, sigma) is chosen at every time step and in every grid column individually. The default configuration of HYCOM is isopycnic in the open stratified ocean, but it makes a dynamically and geometrically smooth transition to terrain-following coordinates in shallow coastal regions and to fixed pressure-level (mass conserving) coordinates in the surface mixed layer and/or un-stratified open seas. In doing so, the model takes advantage of the different coordinate types in optimally simulating coastal and open-ocean circulation features (Chassignet et al. 2003, 2006, 2007, 2009). A user-chosen option allows specification of the vertical coordinate separation that controls the transition among the three coordinate systems (Chassignet et al. 2007). The assignment of additional coordinate surfaces to the oceanic mixed layer also allows the straightforward implementation of multiple vertical mixing turbulence closure schemes (Halliwell 2004). The choice of the vertical mixing parameterization is also of importance in areas of strong entrainment, such as overflows (Papadakis et al. 2003; Xu et al. 2006, 2007; Legg et al. 2009).

The implementation of the generalized vertical coordinate in HYCOM follows the theoretical foundation set forth in Bleck and Boudra (1981) and Bleck and Benjamin (1993): i.e., each coordinate surface is assigned a reference isopycnal. The model continually checks whether grid points lie on their reference isopycnals, and, if not, attempts to move them vertically toward the reference position. However, the grid points are not allowed to migrate when this would lead to excessive crowding of coordinate surfaces. Thus, vertical grid points can be geometrically constrained to remain at a fixed pressure depth while being allowed to join and follow their reference isopycnals in adjacent areas (Bleck 2002). After the model equations are solved, the hybrid coordinate generator then relocates vertical interfaces to restore isopycnic conditions in the ocean interior to the greatest extent possible, while enforcing the minimum thickness requirements between vertical coordinates (see Chassignet et al. (2007) for details). If a layer is less dense than its isopycnic reference density, the generator attempts to move the bottom interface downward so that the flux of denser water across this interface increases density. If the layer is denser than its isopycnic reference density, the generator attempts to move the upper interface upward to decrease density. In both cases, the generator first calculates the vertical distance over which the interface must be relocated so that volume-weighted density of the original plus new water in the layer equals the reference density. The minimum permitted thickness of each layer at each model grid point is then calculated using the criteria provided by the user and the final minimum thickness is then calculated using a "cushion" function (Bleck 2002) that produces a smooth transi tion from the isopycnic to the p and a domains. The minimum thickness constraint is not enforced at the bottom in the open ocean, permitting the model layers to collapse to zero thickness there, as in MICOM. Repeated execution of this algorithm at every time step maintains layer density very close to its reference value as long as a minimum thickness does not have to be maintained and diabatic processes are weak. To ensure that a permanent p coordinate domain exists near the surface year round at all model grid points, the reference densities of the uppermost layers are assigned values smaller than any density values found in the model domain.

Figure 11.2 illustrates the transition that occurs betweenp/a and isopycnic (p ) coordinates in the fall and spring in the upper 400 m and over the shelf in the East

Fig. 11.2 Upper 400 m north-south velocity cross-section along 124.5°E in a 1/25° East China and Yellow Seas HYCOM embedded in a 1/6° North Pacific configuration forced with climatological monthly winds. a In the fall, the water column is stratified over the shelf and can be represented with isopycnals (ppot). b In the spring, the water column is homogenized over the shelf and the vertical coordinate becomes a mixture of pressure (p) levels and terrain-following (a) levels. The isopycnic layers are numbered over the shelf; the higher the number, the denser the layer. (From Chassignet et al. 2007)

Fig. 11.2 Upper 400 m north-south velocity cross-section along 124.5°E in a 1/25° East China and Yellow Seas HYCOM embedded in a 1/6° North Pacific configuration forced with climatological monthly winds. a In the fall, the water column is stratified over the shelf and can be represented with isopycnals (ppot). b In the spring, the water column is homogenized over the shelf and the vertical coordinate becomes a mixture of pressure (p) levels and terrain-following (a) levels. The isopycnic layers are numbered over the shelf; the higher the number, the denser the layer. (From Chassignet et al. 2007)

China and Yellow Seas. In the fall, the water column is stratified and can be largely represented with isopycnals; in the spring, the water column is homogenized over the shelf and is represented by a mixture of p and a coordinates. A particular advantage of isopycnic coordinates is illustrated by the density front formed by the Ku-roshio above the peak of the sharp (lip) topography at the shelfbreak in Fig. 11.2a. Since the lip topography is only a few grid points wide, this topography and the associated front is best represented in isopycnic coordinates. In other applications in the coastal ocean, it may be more desirable to provide high resolution from surface to bottom to adequately resolve the vertical structure of water properties and of the bottom boundary layer. Since vertical coordinate choices for open-ocean HY-COM runs typically maximize the fraction of the water column that is isopycnic, it is often necessary to add more layers in the vertical-to-coastal HYCOM simulations nested within larger-scale HYCOM runs. An example using nested West Florida Shelf simulations (Halliwell et al. 2009) is illustrated in the cross sections in Fig. 11.3. The original vertical discretization is compared to two others with six layers added at the top: one with p coordinates and the other with a coordinates over the shelf. This illustrates the flexibility with which vertical coordinates can be chosen by the user.

Maintaining hybrid vertical coordinates can be thought of as upwind finite volume advection. The original grid generator (Bleck 2002) used the simplest possible scheme of this type, the 1st order donor-cell upwind scheme. A major advantage of this scheme is that moving a layer interface does not affect the layer profile in the down-wind (detraining) layer, which greatly simplifies re-mapping to isopycnal layers. However, the scheme is diffusive when layers are re-mapped (there is no diffusion when layer interfaces remain at their original location). Isopycnal layers require minimal re-mapping in response to weak interior diapycnal diffusivity, but fixed coordinate layers often require significant re-mapping, especially in regions with significant upwelling or downwelling. Therefore, to minimize diffusion associated with the remapping, the grid generator was first replaced by a piecewise linear method (PLM) with a monotonized central-difference (MC) limiter (van Leer 1977) for layers that are in fixed coordinates while still using donor-cell upwind for layers that are non-fixed (and hence tending to isopycnal coordinates). PLM replaces the "constant within each layer" profile of donor-cell with a linear profile that equals the layer average at the center of the layer. The slope must be limited to maintain monotonicity. There are many possible limiters, but the MC limiter is one of the more widely used (Leveque 2002). The most recent version of the grid generator uses a weighted essentially non-oscillatory (WENO)-like piecewise parabolic method (PPM) scheme for increased accuracy. The generator also has been modified for situations when there is a too-light layer on top of a too-dense layer, i.e., when each layers attempts to gain mass at the expense of the other. Previously the generator chose each layer half of the time, but in practice the thicker of the two layers tended to gain mass and over time, the thinner layer tended to become very thin and stay that way. Now the thinner of the two layers always gains mass from the thicker layer, greatly reducing this tendency for layers to collapse.

11.5.2 The HYCOM Ocean Prediction Systems (http://www.hycom.org)

Data assimilation is essential for ocean prediction because (a) many ocean phenomena are due to nonlinear processes (i.e., flow instabilities) and thus are not a deterministic response to atmospheric forcing; (b) errors exist in the atmospheric forcing; and (c) ocean models are imperfect, including limitations in numerical algorithms and in resolution. Most of the information about the ocean surface's space-time variability is obtained remotely from instruments aboard satellites (i.e. sea surface height and sea surface temperature), but these observations are insufficient for specifying the subsurface variability. Vertical profiles from expendable bathythermographs (XBT), conductivity-temperature-depth (CTD) profilers, and profiling floats (e.g., Argo, which measures temperature and salinity in the upper 2000 m of the ocean) provide another substantial source of data. Even together, these data sets are insufficient to determine the state of the ocean completely, so it is necessary to use prior statistical knowledge based on past observations as well as our present understanding of ocean dynamics. By combining all of these observations through data assimilation into an ocean model, it is possible, in principle, to produce a dynamically consistent depiction of the ocean. However, to have any predictive capabilities, it is extremely important that the freely evolving ocean model (i.e., non-data-assimilative model) has skill in representing ocean features of interest.

To properly assimilate the SSH anomalies determined from satellite altimeter data, the oceanic mean SSH over the altimeter observation period must be provided. In this mean, it is essential that the mean current systems and associated SSH fronts be accurately represented in terms of position, amplitude, and sharpness. Unfortunately, the earth's geoid is not presently known with sufficient accuracy for this purpose, and coarse hydrographic climatologies (~0.5°-1° horizontal resolution) cannot provide the spatial resolution necessary when assimilating SSH in an eddy-resolving model (horizontal grid spacing of 1/10° or finer). At these scales of interest, it is essential to have the observed means of boundary currents and associated fronts sharply defined (Hurlburt et al. 2008). Figure 11.4 shows the climatological mean derived on a 0.5° grid using surface drifters by Maximenko and Niiler (2005) as well as a mean derived for the 1/12° Navy global HYCOM prediction system (see following section for details). The HYCOM mean was constructed as follows: a 5-year mean SSH field from a non-data assimilative 1/12° global HYCOM run was compared to available climatologies and a rubber-sheeting technique (Carnes et al. 1996) was used to modify the model mean in two regions (the Gulf Stream and the Kuroshio) where the western boundary current extensions were not well represented and where an accurate frontal location is crucial for ocean prediction. Rubber-sheeting involves a suite of computer programs that operate on SSH fields, overlaying contours from a reference field and moving masses of water in an elastic way (hence rubber-sheeting).

Fig. 11.4 Mean SSH (in cm) derived from surface drifters (Maximenko and Niiler 2005) (top panel) and from a non-data assimilative HYCOM run corrected in the Gulf Stream and Kuroshio regions using a rubber-sheeting technique (bottom panel). The RMS difference between the two fields is 9.2 cm. (From Chassignet et al. 2009)

18 -1.6 -1 4 -1.2 -1 -0 8 0 6 -0.4 -0 2 0 0.2 0 4 0 6 0.8

Fig. 11.4 Mean SSH (in cm) derived from surface drifters (Maximenko and Niiler 2005) (top panel) and from a non-data assimilative HYCOM run corrected in the Gulf Stream and Kuroshio regions using a rubber-sheeting technique (bottom panel). The RMS difference between the two fields is 9.2 cm. (From Chassignet et al. 2009)

Two systems are currently run in real-time by the U.S. Navy at NAVOCEANO, Stennis Space Center, MS, and by NOAA at NCEP, Washington, D.C. The first system is the NOAA Real Time Ocean Forecast System for the Atlantic (RTOFS-Atlantic), which has been running in real-time since 2005. The Atlantic domain spans 25°S-76°N with a horizontal resolution varying from 4 km near the U.S. coastline to 20 km near the African coast. The system is run daily with one-day nowcasts and five-day forecasts. Prior to June 2007, only the sea surface temperature was assimilated. In June 2007, NOAA implemented the 3D-Var data assimilation of (1) sea surface temperature and sea surface height (JASON, GFO, and soon ENVISAT), (2) temperature and salinity profile assimilation (ARGO, CTD, moorings, etc.), and (3) GOES data. Plans are to expand this system globally using the U.S Navy configuration described in the following paragraph. The NCEP

RTOFS-Atlantic model data is distributed in real time through NCEP's operational ftp server (ftp://ftpprd.ncep.noaa.gov) and the NOAA Operational Model Archive and Distribution System (NOMADS, http://nomads6.ncdc.noaa.gov/ncep_data/in-dex.html) server. The latter server is also using OPeNDAP middleware as a data access method. NCEP's RTOFS-Atlantic model data is also archived at the National Oceanographic Data Center (NODC, http://data.nodc.noaa.gov/ncep/rtofs).

The second system is the global U.S. Navy nowcast/forecast system using the 1/12° global HYCOM (6.5 km grid spacing on average, 3.5 km grid spacing at North Pole, and 32 hybrid layers in the vertical), which has been running in near real-time since December 2006 and in real-time since February 2007. The current ice model is thermodynamic, but it will soon include more physics as it is upgraded to the Polar Ice Prediction System (PIPS, based on the Los Alamos CICE ice model). The model is currently running daily at NAVOCEANO using a part of the operational allocation on the machine. The daily run consists of a 5-day hindcast and a 5-day forecast. The system assimilates (1) SSH (Envisat, GFO, and Jason-1), (2) SST (all available satellite and in-situ sources), (3) all available in-situ temperature and salinity profiles (ARGO, CTD, moorings, etc.), and (4) SSMI sea ice concentration. The three-dimensional multivariate optimum interpolation Navy Coupled Ocean Data Assimilation (NCODA) (Cummings 2005) system is the assimilation technique. The NCODA horizontal correlations are multivariate in geopotential and velocity, thereby permitting adjustments (increments) to the mass field to be correlated with adjustments to the flow field. The velocity adjustments are in geostrophic balance with the geopotential increments, and the geopotential increments are in hydrostatic agreement with the temperature and salinity increments. Either the Cooper and Haines (1996) technique or synthetic temperature and salinity profiles (Fox et al. 2002) can be used for downward projection of SSH and SST. An example of forecast performance is shown in Fig. 11.5

Validation of the results is underway using independent data with a focus on the large-scale circulation features, SSH variability, eddy kinetic energy, mixed layer depth, vertical profiles of temperature and salinity, SST and coastal sea levels (Metzger et al. 2008). Figures 11.6 and 11.7 show examples for the Gulf Stream region while Fig. 11.8 documents the performance of HYCOM in representing the mixed layer depth. HYCOM is also an active participant in the international GO-DAE comparison of global ocean forecasting systems.

11.5.3 Distribution of Global HYCOM Hindcasts and Forecasts

The model outputs from the global U.S. Navy hindcast experiment from November 2003 to present are available through the HYCOM consortium web page, http:// www.hycom.org. The HYCOM data distribution team developed and implemented a comprehensive data management and distribution strategy that allowed easy and

Fig. 11.5 Verification of 30-day ocean forecasts: median SSH anomaly correlation vs. forecast length in comparison with the verifying analysis for the global U.S Navy HYCOM over the world ocean and five subregions. The ivd curves verify forecasts using operational atmospheric forcing, which reverts toward climatology after five days. The green curves verify "forecasts" with analysis quality forcing for the duration and the blue curves verify forecasts of persistence (i.e., no change from the initial state). The plots show median statistics over twenty 30-day HYCOM forecasts initialized during January 2004—December 2005, a period when data from three nadir-beam altimeters, Envisat, GFO and Jason-1, were assimilated. The reader is referred to Hurlburt et al. (2008, 2009) for a more detailed discussion of these results. (From Chassignet et al. 2009)

Fig. 11.5 Verification of 30-day ocean forecasts: median SSH anomaly correlation vs. forecast length in comparison with the verifying analysis for the global U.S Navy HYCOM over the world ocean and five subregions. The ivd curves verify forecasts using operational atmospheric forcing, which reverts toward climatology after five days. The green curves verify "forecasts" with analysis quality forcing for the duration and the blue curves verify forecasts of persistence (i.e., no change from the initial state). The plots show median statistics over twenty 30-day HYCOM forecasts initialized during January 2004—December 2005, a period when data from three nadir-beam altimeters, Envisat, GFO and Jason-1, were assimilated. The reader is referred to Hurlburt et al. (2008, 2009) for a more detailed discussion of these results. (From Chassignet et al. 2009)

Fig. 11.6 Surface (top panels) and 700 m (lower panels) eddy kinetic energy from observations (leftpanels) and HYCOM over the period 2004-2006 (rightpanels). The observed surface eddy kinetic energy (upper left panel) is from Fratantoni (2001) and the 700 m eddy kinetic energy (lower left panel) is from Schmitz (1996). The units are in cm2/s2. Overlaid on the top panels is the Gulf Stream north wall position ±1 standard deviation. (From Chassignet et al. 2009)

Fig. 11.6 Surface (top panels) and 700 m (lower panels) eddy kinetic energy from observations (leftpanels) and HYCOM over the period 2004-2006 (rightpanels). The observed surface eddy kinetic energy (upper left panel) is from Fratantoni (2001) and the 700 m eddy kinetic energy (lower left panel) is from Schmitz (1996). The units are in cm2/s2. Overlaid on the top panels is the Gulf Stream north wall position ±1 standard deviation. (From Chassignet et al. 2009)

efficient access to the global HYCOM-based ocean prediction system output to (a) coastal and regional modeling groups; (b) the wider oceanographic and scientific community, including climate and ecosystem researchers; and (c) the general public. The outreach system consists of a web server that acts as a gateway to backend data management, distribution, and visualization applications (http://www.hycom. org/dataserver). These applications enable end users to obtain a broad range of services such as browsing of datasets, GIF images, NetCDF files, FTP requests of data, etc. The 130 Terabytes HYCOM Data Sharing System is built upon two existing software components: the Open Project for a Network Data Access Protocol (OPeNDAP) (Cornillon et al. 2009) and the Live Access Server (LAS) (http://ferret. pmel.noaa.gov/LAS/). These tools and their data distribution methods are described below. In the current setup, the OPeNDAP component provides the middleware necessary to access distributed data, while the LAS functions as a user interface and a product server. The abstraction offered by the OPeNDAP server also makes it possible to define a virtual data set that LAS will act upon, rather than physical files. An sea surf, height 20080908 [90.3]

BSW 30 W 75 W 70W 6SW BOW SSW SOW 45W 4DW

Fig. 11.7 Modeled analysis of the sea surface height field on September 8, 2008. The white line represents the independent frontal analysis of sea surface temperature observations performed by the Naval Oceanographic Office. (From Chassignet et al. 2009)

BSW 30 W 75 W 70W 6SW BOW SSW SOW 45W 4DW

Fig. 11.7 Modeled analysis of the sea surface height field on September 8, 2008. The white line represents the independent frontal analysis of sea surface temperature observations performed by the Naval Oceanographic Office. (From Chassignet et al. 2009)

OPeNDAP "aggregation server" utilizes this approach to append model time steps from many separate files into virtual datasets. The HYCOM Data Service has been in operation for the last four years and has seen a steady increase in the user base. In the last year, the service received approximately 20,000 hits per month. In addition to the numerous requests from educational institutions and researchers, this service has been providing near real-time data products to several private companies in France, the Netherlands, Portugal, and the U.S.

11.5.4 Boundary Conditions for Regional and Coastal Models Nested in HYCOM

An important attribute of the data assimilative HYCOM system is its capability to provide boundary conditions to even higher resolution regional and coastal models. The current horizontal and vertical resolution of the global forecasting

Fig. 11.8 Median bias error (in meters) of mixed laye

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