Generalized Vertical Coordinates in Ordinate Types Within the Domain

Home , Boundary current

or collective redistirbution or collective of this by of any article portion Th ADVANCES IN COMPUTATIONAL OCEANOGRAPHY published in been has is article Oceanography , Volume 1, a quarterly journal of Th 19, Number photocopy machine, reposting, or other means reposting, is only photocopy machine, permitted e Oceanography Society. Copyright e Oceanography 2006 by Th

VERTICAL all correspondence to: Society. Send e Oceanography [email protected] or Th COORDINATES FOR EDDYRESOLVING GLOBAL AND COASTAL OCEAN FORECASTS ted to in teaching copy this and research. for use article Repu BY ERIC P. CHASSIGNET, HARLEY E. HURLBURT,

OLE MARTIN SMEDSTAD, GEORGE R. HALLIWELL, MD 20849-1931, USA. 1931, Rockville, Box PO Society, e Oceanography ALAN J. WALLCRAFT, E. JOSEPH METZGER, BRIAN O. BLANTON, CARLOS LOZANO, DESIRAJU B. RAO, PATRICK J. HOGAN, AND ASHWANTH SRINIVASAN blication, systemmatic reproduction,

118 Oceanography Vol. 19, No. 1, Mar. 2006 NUMERICAL MODELING STUDIES over the past broad partnership of institutions1 is addressing these objectives several decades have demonstrated progress both in model ar- by building global and basin-scale ocean prediction systems us- chitecture and in the use of rapidly advancing computational ing the versatile HYbrid Coordinate Ocean Model (HYCOM) resources. Perhaps the most notable aspect of this progression (more information available at http://www.hycom.org). has been the evolution from simulations on coarse-resolution The choice of the vertical coordinate system in an ocean horizontal and vertical grids that outline basins of simpli- model remains one of the most important aspects of its design.

fi ed geometry and bathymetry and that are forced by idealized In practice, the representation and parameterization of the pro- surface fl uxes, to fi ne-resolution simulations that incorporate cesses not resolved by the model grid are often directly linked realistic coastline defi nition and bottom topography and that to the vertical coordinate choice (Griffi es et al., 2000). Oceanic are forced by observational data on relatively short time scales general circulation models traditionally represent the vertical

(Hurlburt and Hogan, 2000; Smith et al., 2000; Chassignet and in a series of discrete intervals in either a depth, density, or ter-

Garraffo, 2001; Maltrud and McClean, 2005). rain-following unit. Recent model comparison exercises per-

The Global Ocean Data Assimilation Experiment (GODAE) formed in Europe (Willebrand et al., 2001) and in the United is a coordinated international effort envisioning a global system States (Chassignet et al., 2000) have, however, shown that the of observations, communications, modeling, and assimilation that use of only one vertical coordinate representation cannot be will deliver regular, comprehensive information on the state of the optimal everywhere in the ocean. These and earlier compari- oceans in a way that will promote and engender wide utility and son studies (Chassignet et al., 1996; Marsh et al., 1996, Roberts availability of this resource for maximum benefi t to the commu- et al., 1996) show that all the models considered were able to nity. Specifi c objectives of GODAE are to apply state-of-the-art simulate large-scale characteristics of the oceanic circulation ocean models and data assimilation methods to produce short- reasonably well, but the interior water-mass distribution and range open ocean forecasts, initial and boundary conditions to associated thermohaline circulation are strongly infl uenced extend the predictability of coastal and regional subsystems, and by localized processes that are not represented equally by each to provide initial conditions for climate forecast models (Inter- model’s vertical discretization. national GODAE Steering Team, 2000). In the United States, a

1 University of Miami, Naval Research Laboratory (NRL), National Aeronautics and Space Administration/Goddard Institute for Space Studies (NASA/GISS), National Oceanic and Atmospheric Administration/National Centers for Environmental Prediction (NOAA/NCEP), National Oceanic and Atmospheric Administration/Atlantic Oceanographic Meteorological Laboratory (NOAA/AOML), National Oceanic and Atmospheric Administration/Pacifi c Marine Environmental Laboratory (NOAA/PMEL), Planning Systems, Inc. (PSI), Fleet Numerical Meteorology and Oceanography Center (FNMOC), Naval Oceanographic Offi ce (NAVOCEANO), Service Hydrographique et Océanographique de la Marine (SHOM), Laboratoire des Ecoulements Géophy- siques et Industriels (LEGI), Open Source Project for a Network Data Access Protocol (OPeNDAP), University of North Carolina, Rutgers, University of South Florida, Fugro GEOS, Roff er’s Ocean Fishing and Forecasting Service (ROFFS), Orbimage, Shell, ExxonMobil.

Oceanography Vol. 19, No. 1, Mar. 2006 119 Because none of the three main verti- HYBRID VERTICAL dinate by the hybrid coordinate genera- cal coordinates (depth, density, and ter- COORDINATES tor after all equations are solved (Bleck, rain-following) (see Box 1 for details) Hybrid vertical coordinates can mean 2002; Chassignet et al., 2003; Halliwell, provide universal optimality, it is natural different things to different people: they 2004) and for the fact that there is a non- to envision a hybrid approach that com- can be a linear combination of two or zero horizontal density gradient within bines the best features of each vertical more conventional coordinates (Song all layers. HYCOM is thus classifi ed as coordinate. Isopycnic (density-track- and Haidvogel, 1994; Ezer and Mellor, a Lagrangian Vertical Direction (LVD) ing) layers work best for modeling the 2004; Barron et al., 2006) or they can be model in which the continuity (thickness deep stratifi ed ocean, levels at constant truly generalized (i.e., aiming to mimic tendency) equation is solved forward in fi xed depth or pressure are best to use to different types of coordinates in different time throughout the domain, while an provide high vertical resolution near the regions of a model domain) (Bleck, 2002; Arbitrary Lagrangian-Eulerian (ALE) surface within the mixed layer, and ter- Burchard and Beckers, 2004; Adcroft and technique is used to re-map the vertical rain-following levels are often the best Hallberg, 2006; Song and Hou, 2006). coordinate and maintain different co- choice for modeling shallow coastal re- The generalized vertical coordinates in ordinate types within the domain. This gions. In HYCOM, the optimal vertical HYCOM deviate from isopycnals (con- differs from Eulerian Vertical Direction coordinate distribution of the three ver- stant density surfaces) wherever the latter (EVD) models with fi xed vertical coor- tical coordinate types is chosen at every may fold, outcrop, or generally provide dinates that use the continuity equation time step. The hybrid vertical coordinate inadequate vertical resolution in portions to diagnose vertical velocity (Adcroft and generator makes a dynamically smooth of the model domain. HYCOM is at its Hallberg, 2006). The ability to adjust the transition among the coordinate types core a Lagrangian layer model, except vertical spacing of the coordinate sur- using the continuity equation. for the remapping of the vertical coor- faces in HYCOM simplifi es the numeri-

BOX 1: OCEAN REGIMES AND VERTICAL COORDINATES

Schematic of an ocean basin illustrating the three regimes of the ocean germane z to the considerations of an appropriate vertical coordinate. Th e surface mixed layer is naturally represented using ﬁ xed- depth z (or pressure p) coordinates, the ρ interior is naturally represented using isopycnic ρ (density tracking) coordinates; and the bottom boundary is naturally represented using terrain-following σ coordinates (after Griﬃ es et al., 2000). σ

120 Oceanography Vol. 19, No. 1, Mar. 2006 cal implementation of several physical two others with six layers added at the low the Arctic to be included in a global processes (e.g., mixed-layer detrainment, top—one with pressure-level coordinates ocean model. The HYCOM global con- convective adjustment, sea-ice modeling) and the other with terrain-following fi guration uses an Arctic dipole patch without harming the model of the basic coordinates over the shelf—because in matched to a standard Mercator grid and numerically effi cient resolution of many coastal applications it is desirable at 47°N (Figure 2). Because our tar- the vertical that is characteristic of iso- to provide higher resolution from sur- get horizontal resolution is 1/12° at the pycnic models throughout most of the face to bottom to adequately resolve the equator (i.e., 9 km), the location of the ocean’s volume (Bleck and Chassignet, vertical structure of water properties and dipoles at 47°N gives us a good resolu- 1994; Chassignet et al., 1996). of the bottom boundary layer in shallow tion at mid latitude (i.e., 7 km) as well The default confi guration of HYCOM water. Halliwell et al. (in preparation) as in the Arctic Ocean (i.e., 3.5 km at the is isopycnic in the open stratifi ed ocean, document the advantages and disadvan- North Pole) where the Rossby radius of but makes a dynamically smooth tran- tages of the choices shown in Figure 1. deformation is smaller. An advantage sition to terrain-following coordinates of this pole-shifting projection, as op- in shallow coastal regions and to fi xed COMPUTATIONAL ASPECTS posed to most others, is that all the grid pressure-level coordinates in the surface Before one can numerically solve (i.e., points below 47°N remain on regular mixed layer and/or unstratifi ed seas (Fig- discretize) the model’s equations, one grid spacing (i.e., x-y grid ratio of 1). ure 1). In doing so, the model takes ad- must decide on a global projection and The corresponding numerical array size vantage of the different coordinate types on how to treat the singularity associ- is 4500 by 3298 with 32 hybrid layers in in optimally simulating coastal and open- ated with the North Pole (the South the vertical. The complete system will ocean circulation features. A user-chosen Pole, being over land, is not an issue). include the Los Alamos Sea Ice Model option allows specifi cation of the vertical There are several projections that al- (CICE) (Hunke and Lipscomb, 2004) on coordinate separation that controls the transition among the three coordinate Eric P. Chassignet ([email protected]) is Professor, Rosenstiel School of systems. The assignment of additional Marine and Atmospheric Science, Division of Meteorology and Oceanography, University coordinate surfaces to the oceanic mixed of Miami, Miami, FL, USA. Harley E. Hurlburt is Senior Scientist for Ocean Modeling and layer also allows the straightforward im- Prediction, Naval Research Laboratory, Oceanography Division, Stennis Space Center, MS, plementation of multiple vertical mixing USA. Ole Martin Smedstad is Principal Scientist, Planning Systems Inc., Stennis Space turbulence closure schemes (Halliwell, Center, MS, USA. George R. Halliwell is Research Associate Professor, Rosenstiel School of 2004). The choice of the vertical mixing Marine and Atmospheric Science, Division of Meteorology and Oceanography, University of parameterization is also of importance Miami, Miami, FL, USA. Alan J. Wallcraft is Computer Scientist, Naval Research Labora- in areas of strong entrainment, such as tory, Ocean Dynamics and Prediction Branch, Stennis Space Center, MS, USA. E. Joseph overfl ows (Xu et al., submitted). Metzger is Meteorologist, Naval Research Laboratory, Ocean Dynamics and Prediction Figure 1 illustrates the transition Branch, Stennis Space Center, MS, USA. Brian O. Blanton is Research Assistant Professor, among pressure, terrain-following, and University of North Carolina, Ocean Processes Numerical Modeling Laboratory, Chapel Hill, isopycnic coordinates in 1/25° West NC, USA. Carlos Lozano is Physical Scientist, Environmental Modeling Center, National Florida Shelf simulations nested within Centers for Environmental Prediction, National Oceanic and Atmospheric Administration, a 1/12° North Atlantic confi guration, Camp Springs, MD, USA. Desiraju B. Rao is Branch Chief, Environmental Modeling Center, and it demonstrates the fl exibility with National Centers for Environmental Prediction, Marine Modeling and Analysis Branch, which vertical coordinates can be chosen National Oceanic and Atmospheric Administration, Camp Springs, MD, USA. Patrick J. and the capability of adding additional Hogan is Oceanographer, Naval Research Laboratory, Ocean Dynamics and Prediction vertical resolution. The original vertical Branch, Stennis Space Center, MS, USA. Ashwanth Srinivasan is Assistant Scientist, Rosen- discretization used in the 1/12° North stiel School of Marine and Atmospheric Science, Division of Meteorology and Oceanogra- Atlantic confi guration is compared to phy, University of Miami, Miami, FL, USA.

Oceanography Vol. 19, No. 1, Mar. 2006 121 the same grid. The ocean and ice models will run simultaneously, but on sepa- rate sets of processors (a much smaller number for CICE), communicating via an Earth System Modeling Framework (ESMF)-based coupler (Hill et al., 2004). HYCOM’s basic parallelization strategy is two-dimensional domain decom- position (i.e., the entire model domain is divided up into smaller sub-domains, or tiles, and each processor “owns” one tile). A halo region is added around each tile to allow communication operations (e.g., updating the halo) to be completely separated from computational kernels, greatly increasing the maintain- ability and expandability of the code base. Rather than the conventional one- or two-grid points-wide halo, HYCOM has a six-grid-point-wide halo, which is “consumed” over several operations to reduce halo communication overhead. For global and basin-scale applications, it is important to avoid calculations over land. HYCOM fully “shrink wraps” calculations on each tile and discards tiles that are completely over land (Bleck et al., 1995). HYCOM goes farther than most structured grid ocean models in land avoidance by allowing more than one neighboring tile to the north and south. Figure 2 shows the current tiling for the 1/12° global domain with equal

Figure 1. Cross sections of layer density and model interfaces across the West Florida Shelf sized tiles that (a) allows rows to be offset in a 1/25° West Florida Shelf subdomain covering the Gulf of Mexico east of 87°W and from each other if this gives fewer tiles north of 23°N and embedded in a 1/12° Atlantic basin HYCOM simulation (Halliwell et al., over the ocean and (b) allows two tiles to in preparation). Th is fi gure illustrates the transition among pressure, terrain-following, and isopycnic coordinates in 1/25° West Florida Shelf simulations nested within a 1/12° North be merged into one larger tile if less than Atlantic confi guration, and it demonstrates the fl exibility with which vertical coordinates 50% of their combined area is ocean. The can be chosen and the capability of adding additional vertical resolution. Mediterranean region of Figure 2 illustrates both these optimizations. In the example presented in Figure 3, the global model is initialized from an oceanic climatology of temperature

122 Oceanography Vol. 19, No. 1, Mar. 2006 and salinity. The model is forced by tendency for the ocean/sea-ice system OCEAN PREDICTION prescribed climatological atmospheric to form ice appropriately. Figure 3 Although HYCOM is a relatively sophis- wind, thermal, and precipitation fi elds compares the sea surface height (SSH) ticated model that includes a large suite while evaporation is computed using variability from the climatologically of physical processes and incorporates the modeled sea surface temperature forced 1/12° global HYCOM to the Oct. numerical techniques that are optimal (SST). There is also a weak relaxation 1992–Nov. 1998 SSH variability based on for dynamically different regions of the to climatological surface salinity. These Topex-Poseidon, ERS-1, and ERS-2 altim- ocean, data assimilation is still essential simulations use a simple thermodynamic eter data (derived by Collecte Localisa- for ocean prediction because (a) many sea-ice model (CICE is running stand- tion Satellite (CLS), France). Overall, the ocean phenomena are due to nonlinear alone on the global Arctic patch grid, but modeled regions of high variability are processes (i.e., fl ow instabilities) and thus we are awaiting ESMF-based coupling in reasonably good agreement with the are not a deterministic response to at- between HYCOM and CICE before run- observations, especially in the Antarctic mospheric forcing, (b) errors exist in the ning a coupled case). Even without ice Circumpolar Current region. The equa- atmospheric forcing, and (c) ocean mod- dynamics, the seasonal cycle of ice cover- torial Pacifi c is an exception because the els are imperfect, including limitations in age is good overall (not illustrated). One altimeter data include interannual vari- numerical algorithms and in resolution. reason for the good agreement is that the ability not present in the model (e.g., Substantial information about the atmospheric forcing is based on an ac- the large variability associated with the ocean surface’s space-time variability curate ice extent, which provides a strong 1997–1998 El Niño). is obtained remotely from instruments

Figure 2. Current tiling for the 1/12° global domain with equal-sized tiles that (a) allows rows to be oﬀ set from each other if this gives fewer tiles over the ocean and (b) allows two tiles to be merged into one larger tile if less than 50 percent of their combined area is ocean. Th e Mediterranean region especially illustrates both these optimizations; out of the original 1152 (36 by 32) approximately equal- sized tiles, 371 tiles are entirely land and are dis- carded, leaving 781. Th e Arctic “wraps” between the left and right halves of the top edge.

Oceanography Vol. 19, No. 1, Mar. 2006 123 Figure 3. Comparison between the (observed) Oct. 1992–May 2005 sea surface height (SSH) variability based on Topex-Poseidon, ERS-1, and ERS-2 altimeter data (top) (derived by Col- lecte Localisation Satellite [CLS], France) and three years of (modeled) sea surface height (SSH) variability from the climatologically forced 1/12° global HYCOM (bottom). Overall, the modeled regions of high variability are in good agreement with the observations, especially in the Antarctic Circumpolar Current region. Th e equatorial Paciﬁ c is an exception because the altimeter data include interannual variability not present in the model, for example, the large variability associated with the 1997–1998 El Niño.

aboard satellites, but these observations tics determined from past observations referred to Chassignet et al. (in press). are insuffi cient for specifying the sub- as well as our present understanding of The present Navy near-real-time surface variability. Vertical profi les from ocean dynamics. By combining all of 1/12° North Atlantic HYCOM ocean expendable bathythermographs (XBT), these observations through data assimi- forecasting system is the fi rst step toward conductivity-temperature-depth (CTD) lation into an ocean model, it is possible the fully global 1/12° HYCOM predic- profi lers, and profi ling fl oats (e.g., Argo, to produce a dynamically consistent de- tion system. The North Atlantic system which measures temperature and salinity piction of the ocean. It is, however, ex- assimilates daily, real-time satellite al- in the upper 2000 m of the ocean) pro- tremely important that the freely evolv- timeter data (Geosat-Follow-On [GFO], vide another substantial source of data. ing ocean model (i.e., non-data-assimila- Environmental Satellite [ENVISAT] 1, Even together, these data sets are insuffi - tive model) has skill in hindcasting and and Jason-1). These data are provided cient to determine the state of the ocean in predicting ocean features of interest. via the Altimeter Data Fusion Center completely, so it is necessary to exploit For a detailed overview of the HYCOM (ADFC) at the Navel Oceanographic prior knowledge in the form of statis- data assimilative system, the reader is Offi ce (NAVOCEANO) to generate the

124 Oceanography Vol. 19, No. 1, Mar. 2006 two-dimensional Modular Ocean Data every Wednesday and produces a 10-day with up to 15 terrain-following σ coordi- Assimilation System (MODAS) SSH hindcast and a 14-day forecast. The Navy nates over the shelf), but provides an ex- analysis (Fox et al., 2002). The MODAS Operational Global Atmospheric Predic- cellent starting point for even higher-res- analysis is an optimal interpolation tion System (NOGAPS) (Rosmond et al., olution coastal ocean prediction systems. technique that uses complex covariance 2002) provides the atmospheric forcing, The model resolution should increase functions, including spatially varying but in the 14-day forecasts, the forcing to 1/25° (3–4 km at mid-latitudes) by length and time scales as well as propa- linearly reverts toward climatology af- the end of the decade. An important at- gation terms derived from many years of ter fi ve days. During the forecast period, tribute of the data assimilative HYCOM altimetry (Jacobs et al., 2001). The mod- the SST is relaxed toward climatologi- simulations is, therefore, its capability to el SST is relaxed to the daily MODAS cally corrected persistence of the nowcast provide boundary conditions to regional SST analysis that uses daily Multi-Chan- SST with a relaxation time scale of one- and coastal models. nel Sea Surface Temperature (MCSST) fourth the forecast length (i.e., one day To increase the predictability of data derived from the 5-channel Ad- for a four-day forecast). The impact of coastal regimes, several partners within vanced Very High Resolution Radiome- these choices is discussed by Smedstad et the HYCOM consortium are develop- ters (AVHRR)—globally at 8.8 km reso- al. (2003) and Shriver et al. (in press). For ing and evaluating boundary conditions lution and at 2 km in selected regions. an evaluation of the North Atlantic sys- for coastal prediction models based on To properly assimilate the SSH tem, the reader is referred to Chassignet the HYCOM data assimilative system anomalies determined from satellite et al. (2005, in press). outputs. The inner nested models may altimeter data, the oceanic mean SSH The near real-time North Atlantic ba- or may not be HYCOM, so the coupling over the altimeter observation period sin model outputs are made available to of the global and coastal models must be must be determined. In this mean, it is the ocean science community within 24 able to handle dissimilar vertical grids. essential that the mean current systems hours via the HYCOM Consortium data Coupling HYCOM to HYCOM is now and associated SSH fronts be accurately server (more information available at routine via one-way nesting (Zamu- represented (position, amplitude, and http://www.hycom.org/dataserver) using dio et al., in preparation). Outer model sharpness). Unfortunately, Earth’s a familiar set of tools such as OPeNDAP, fi elds are periodically interpolated to geoid is not presently known with Live Access Server (LAS), and fi le trans- the horizontal mesh of the nested model suffi cient accuracy for this purpose, fer protocol (FTP). These tools have (specifi ed by the user, but typically daily) and coarse hydrographic climatologies been modifi ed to perform with hybrid and stored in an archive fi le. The num- (~1° horizontal resolution) cannot vertical coordinates to provide HYCOM ber of coordinates can be increased to provide the spatial resolution necessary. subsets to coastal or regional nowcast/ augment the vertical resolution of the HYCOM, therefore, uses a mean SSH forecast partners as initial and boundary nested model and to ensure that there is from a previous fully eddy-resolving conditions. The LAS has been imple- suffi cient vertical resolution to resolve ocean model simulation that was found mented with an intuitive user interface the bottom boundary layer. The nested to have fronts in the correct position to enhance the usability of ocean pre- model is initialized from the fi rst archive and is consistent with hydrographic diction system outputs and to perform fi le; the entire set of archives provides climatologies (Chassignet and Garraffo, diagnostics. boundary conditions during the nested 2001). Several satellite missions are run, ensuring consistency between initial either underway or planned to determine BOUNDARY CONDITIONS FOR and boundary conditions. Coupling HY- a more accurate geoid, but until the REGIONAL MODELS COM to other fi nite difference models, accuracy reaches a few centimeters on The chosen horizontal and vertical reso- such as the Navy Coastal Ocean Model horizontal scales of about 30 km, the lution for the above HYCOM predic- (NCOM) or the Regional Ocean Model present approach will be necessary. tion system only marginally resolves the System (ROMS), has already been dem- The North Atlantic system runs weekly coastal ocean (7 km at mid latitudes, onstrated, and coupling of HYCOM to

Oceanography Vol. 19, No. 1, Mar. 2006 125 unstructured grid/fi nite element models versity of North Carolina (UNC)-SAB the density fi eld held fi xed. The atmo- is in progress. (National Ocean Partnership Program spheric (buoyancy and momentum) and We now describe the use of near-real- [NOPP]-funded South Atlantic Bight river fl uxes are turned on. The timing is time HYCOM nowcasts and forecasts as Limited Area Model [SABLAM], South- synchronized such that the fl uxes are ac- boundary and initial-condition provid- East U.S. Atlantic Coastal Ocean Observ- tive for one day at the time the HYCOM ers to a nested coastal simulation in the ing System [SEACOOS]) (Blanton, 2003) fi elds are valid. South Atlantic Bight (SAB) region of uses the fi nite element coastal ocean An example of this nested system is the eastern U.S. coast. The 1/12° North model QUODDY (Lynch et al., 1996). shown in Figure 4. The HYCOM now- Atlantic HYCOM does not necessarily Terrestrial buoyancy inputs to the conti- cast for November 28, 2005 is used to include all forcing and physics relevant nental shelf, strong tides, and a vigorous initialize the regional model domain, at the coastal region scale (e.g., lack of western boundary current contribute to onto which the tides and high-resolu- tidal forcing in the present simulation). the complexity of this region. To simu- tion atmospheric fl uxes are applied. The The nesting of higher-resolution models late the density-dependent dynamics, resulting solution is used to initialize and within the basin-scale HYCOM there- the UNC-SAB modeling system is nested drive the limited-area, estuary-resolving fore allows limited-area regional forc- within the HYCOM GODAE near-real- fi nite element implementation. The ef- ings (terrestrial buoyancy inputs, tides), time system. Boundary and initialization fects of both the Gulf Stream, as provid- physics (wetting and drying), and coastal data for the SAB regional-scale model ed by the HYCOM initial and boundary geometry (tidal inlets, estuaries) to add are obtained from the HYCOM GODAE conditions, and the local tides are seen in value to the larger-scale HYCOM ocean- Live Access Server and are mapped to the the limited-area model (Figure 4, right). state estimates. fi nite element regional model domain. Strong along-shelf and poleward fl ow The quasi-operational regional-scale For each forecast, the system spins up the is seen at the shelfbreak. The poleward, modeling system developed at the Uni- regional tides for fi ve model days, with offshelf-directed fl ow on the shelf is due

Figure 4. (Left) 1/12° North Atlantic HYCOM-GODAE sea surface temperature (SST) nowcast for November 28, 2005. Th e three-dimensional solution for this date is used to initialize the University of North Carolina-South Atlantic Bight (UNC-SAB) fi nite element modeling system (middle, every 5th model vector). Th e surface temperature and velocity are shown, after addition of the regional tides and atmospheric fl uxes. Th e limited-area fi nite element implementation (right, every 3rd model vector) includes the estuary and tidal inlets along the Georgia/South Carolina coast and extends to the shelf-break. Th is snapshot also shows surface temperature and velocity and is for three days after initialization. Th e color scales between the HYCOM and nested plots are not the same.

126 Oceanography Vol. 19, No. 1, Mar. 2006 to the tides. SAB. The SABSOON observational net- OUTLOOK Evaluation of the near real-time HY- work, situated on the Georgia continental The long-term goal of the HYCOM COM outputs relative to available ob- shelf, has been making routine and real- consortium is an eddy-resolving, fully servations in the SAB consists of com- time observations of water properties for global ocean prediction system with parisons to National Ocean Service water three years. Figure 5b shows observed data assimilation to be transitioned to levels along the coast and mid-shelf tem- SABSOON R2 near-surface temperature the U.S. Naval Oceanographic Offi ce at perature from an established continental and HYCOM mixed-layer temperature. 1/12° equatorial (~7 km mid-latitude) shelf observational network (SABSOON) The HYCOM mixed layer covers most resolution in 2007 and 1/25° resolution (Seim, 2000). Variability in observed of the water column vertical grid in this by 2011. Development of the global sys- coastal water levels is due to tides, wind- region. The root mean square (RMS) er- tem is underway and includes the ocean stress-driven and other lower-frequency ror between the signals (where both are model, ice model, tides, and data assimi- fl uctuations (deep-ocean contributions available) is 1.4° C. Strong, prolonged lation. Data assimilation is traditionally to shelf-wide sea level). In the SAB, tides cooling of the SAB continental shelf dur- formulated as a least-squares estimation account for at least 90% of the total water ing summer 2003 is seen in the HYCOM problem. In spite of a fairly simple theo- level variability. Figure 5a shows subtidal temperature (Figure 5b), and is attrib- retical framework, application to non- coastal water levels for two stations in utable to a variety of coincident envi- linear numerical models of the ocean the SAB. Lower-frequency, seasonal-scale ronmental conditions (for a review see circulation is far from trivial (Brasseur, variations are well captured by HYCOM. Aretxabaleta et al. [submitted]). The HY- 2006). The diffi culty is in fi nding algo- Weather-band fl uctuations are also rea- COM best-prior-estimates from summer rithms that provide an acceptable solu- sonably well represented. Observations of 2003 are being used, with the regional tion in terms of computer resources. The in situ water fi elds (salinity, temperature) modeling system, to examine the physical size of the problem makes it indeed very are comparatively less available in the nature of this extreme cooling event. diffi cult to use sophisticated assimilation

ab 28 Ft. Pulaski 0.4 Observed Observed HYCOM 26 HYCOM

0.2 24

0 22

20 -0.2

Water level (m) 18

0.2 Temperature (°C) 16 0 14 Virginia Key -0.2 12 Jun03 Sep03 Dec03 Mar04 Jun04 Sep04 Dec04 Mar05 Jun05 Jun03 Sep03 Dec03 Mar04 Jun04 Sep04 Dec04 Mar05 Jun05 Figure 5. (a) Water level comparison for two stations in the SAB. Daily HYCOM best-estimate water levels (blue) and observed NOS water levels (red) are shown for Fort Pulaski, Georgia and Virginia Key, Florida. Th e two stations are arbitrarily oﬀ set for clarity. (b) Observed, near-surface temperature (blue) and HYCOM mixed-layer temperature (red) for the SABSOON mid-shelf station R2. Th e root mean square (RMS) error at this location is 1.4°C.

Oceanography Vol. 19, No. 1, Mar. 2006 127 techniques because some of these meth- based wind and thermal forcing, and (c) mate simulations, and theoretical stud- ods can increase the cost of running the the choice of data assimilation technique. ies of the ocean’s dynamics. U.S. ocean model by a factor of 100. The strategy we The NOAA/NCEP group is using a con- modelers have, therefore, engaged in a adopted is to start with a low-cost and fi guration that, for the same number broader dialogue as to whether the vari- simple data assimilation approach (e.g., of grid points as in the regular Merca- ous community modeling efforts could Cooper and Haines, 1996), and then tor projection used in the Navy system, be channeled into an ocean modeling gradually increase the complexity. Sev- has fi ner resolution in the western and environment (see white paper on HOME eral sophisticated data assimilation tech- northern portions of the basin and on [Hybrid Ocean Modeling Environment] niques are already in place to work with shelves (3–7 km), in order to provide available at http://www.hycom.org/ HYCOM and are being evaluated. These higher resolution along the U.S. coast publications.html). A modeling environ- techniques are, in increasing level of so- rather than toward the east and southeast ment is defi ned here as a uniform code phistication, the Naval Research Labo- (7–13 km). The model domain confi gu- comprising a diverse collection of inter- ratory (NRL)’s Coupled Ocean Data ration is from 20°S to 76°N, including changeable algorithms and supporting Assimilation (NCODA), the Singular marginal seas, except for the Mediterra- software from which particular models Evolutive Extended Kalman (SEEK) fi l- nean and Baltic Seas. Atmospheric mo- design can be selected (e.g., HYCOM). ter, the Reduced Order Information Fil- mentum, heat, and water fl uxes are de- It would not only provide diversity of ter (ROIF), the Reduced Order Adaptive rived from the three hourly NCEP-based modeling approaches, but also would Filter (ROAF) (including adjoint), the fi elds. Tidal forcing and river outfl ows standardize coupling with other models Ensemble Kalman Filter (EnKF), and the are prescribed. The observations used in (e.g., atmospheres or ocean sub-models) 4D-VAR Representer method. Although the assimilation at present are remotely and various ways for user specifi cation of these techniques work with HYCOM, it sensed and in situ SST, and work is un- parameters, grids, domains, initial condi- does not mean that they will be used op- derway to add remotely sensed SSH tions, forcings, and diagnostics. erationally: the NCODA and SEEK tech- anomalies and subsurface data. The goals niques are presently being considered as of the NOAA system are to provide (a) ACKNOWLEDGMENTS the next generation data assimilation to accurate estimates and forecasts of the This work was sponsored by the Nation- be used in the near-real-time system. The coastal ocean, (b) initial and boundary al Ocean Partnership Program (NOPP), remaining techniques, because of their conditions to NOAA’s regional and coast- the Offi ce of Naval Research (ONR), and cost, are being evaluated mostly within al models, (c) coupled circulation-wave- the Operational Effects Programs (OEP) specifi c limited areas of high interest or storm-surge models, and (d) coupled Program Offi ce, PMW 150. It was also coastal HYCOM confi gurations. atmosphere-ocean hurricane forecasts. supported in part by a grant of computer Another HYCOM North Atlantic con- The generalized coordinate approach time from the Defense Department High fi guration forms the backbone of the used in HYCOM minimizes the liabilities Performance Computing Modernization National Oceanic and Atmospheric Ad- associated with a single coordinate sys- Program at the Naval Oceanographic Of- ministration (NOAA)/National Centers tem and provides the user with the fl ex- fi ce Major Shared Resource Center. for Environmental Prediction (NCEP)/ ibility to tailor the model to the specifi c North Atlantic Ocean Forecast System application. Generalized hybrid vertical REFERENCES (NAOFS) (more information available at coordinate ocean models are currently Adcroft, A., and R. Hallberg. 2006. 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