NOAA Technical Report NOS CS 31

THE DESIGN, CALIBRATION AND VALIDATION OF A 

COUPLED NUMERICAL OCEAN MODELING SYSTEM FOR 

THE WEST FLORIDA SHELF 

Silver Spring, Maryland 

May 2011 

noaa National Oceanic and Atmospheric Administration 

U.S. DEPARTMENT OF COMMERCE 

National Ocean Service 

Coast Survey Development Laboratory 
Office of Coast Survey 

National Ocean Service 

National Oceanic and Atmospheric Administration 

U.S. Department of Commerce

The Office of Coast Survey (OCS) is the Nation’s only official chartmaker. As the oldest 

United States scientific organization, dating from 1807, this office has a long history. 

Today it promotes safe navigation by managing the National Oceanic and Atmospheric 

Administration’s (NOAA) nautical chart and oceanographic data collection and 

information programs. 

There are four components of OCS: 

The Coast Survey Development Laboratory develops new and efficient techniques 

to accomplish Coast Survey missions and to produce new and improved products 

and services for the maritime community and other coastal users. 

The Marine Chart Division acquires marine navigational data to construct and 

maintain nautical charts, Coast Pilots, and related marine products for the United 

States. 

The Hydrographic Surveys Division directs programs for ship and shore-based 

hydrographic survey units and conducts general hydrographic survey operations. 

The Navigational Services Division is the focal point for Coast Survey customer 

service activities, concentrating predominately on charting issues, fast-response 

hydrographic surveys, and Coast Pilot updates. 
NOAA Technical Report NOS CS 31 

THE DESIGN, CALIBRATION AND VALIDATION OF A 

COUPLED NUMERICAL OCEAN MODELING SYSTEM FOR 

THE WEST FLORIDA SHELF 

Lyon W. J. Lanerolle and Richard C. Patchen 

Office of Coast Survey, Coast Survey Development Laboratory, 

Silver Spring, MD 

May 2011

noaa National Oceanic and Atmospheric Administration 

U. S. DEPARTMENT National Oceanic and National Ocean Service 

OF COMMERCE Atmospheric Administration David Kennedy 

Gary Locke, Dr. Jane Lubchenco Assistant Secretary 

Under Secretary Administrator 

 

Office of Coast Survey Coast Survey Development Laboratory 

Captain John Lowell, NOAA Mary Erickson 
ii 

NOTICE 

Mention of a commercial company or product does not constitute an 

endorsement by NOAA. Use for publicity or advertising purposes of 

information from this publication concerning proprietary products or the 

tests of such products is not authorized. 

. 
iii 

TABLE OF CONTENTS 

LIST OF FIGURES ....................................................................................................................... iv 

LIST OF TABLES ......................................................................................................................... vi 

EXECUTIVE SUMMARY .......................................................................................................... vii 

1. INTRODUCTION AND MOTIVATION ..................................................................................1 

2. COUPLED DOMAINS, GRIDS AND BATHYMETRY ..........................................................5 

3. COUPLING METHODOLOGY, INITIAL, BOUNDARY AND COMPATIBILITY 

 CONDITIONS ............................................................................................................................9 

3.1. Initial Conditions ........................................................................................................9 

3.2. Surface and Bottom Boundary Conditions .................................................................9 

3.3. Lateral Boundary Conditions ...................................................................................10 

3.4. Other Coupling Compatibility Conditions ...............................................................11 

4. COUPLING VALIDATION .....................................................................................................15 

5. COUPLING APPLICATION TO A SYNOPTIC HINDCAST SIMULATION ......................18 

5.1. Coupling Calibration Experiments ...........................................................................18 

 5.1.1 Calibration of the Surface Forcing .................................................................18 

 5.1.2 Calibration of the Vertical Eddy-Viscosity Parameterization ........................19 

 5.1.3 Calibration of the Tides ..................................................................................19 

5.2. Comparison of Model Predictions with Observations ..............................................21 

 5.2.1 Water Elevation Comparisons ........................................................................21 

 5.2.2 Currents Comparisons ....................................................................................22 

 5.2.3 Temperature and Salinity Comparisons .........................................................24 

6. SUMMARY, CONCLUSIONS AND FUTURE DIRECTIONS ..............................................27 

ACKNOWLEDGMENTS .............................................................................................................25

REFERENCES ..............................................................................................................................31 

APPENDIX A. COUPLING VALIDATION ...............................................................................35 

APPENDIX B. COUPLING APPLICATION TO A SYNOPTIC HINDCAST 

 SIMULATION ....................................................................................................39 
iv 

LIST OF FIGURES 

Figure 1. NGOM model domain with the NWFS-3D sub-domain (left) and NWFS-3D 

 Model grid (right). Red dots on the right figure indicate NGOM grid point 

 locations ........................................................................................................................5 

Figure 2. The NWFS-3D grid in the Tampa Bay (left) and Charlotte Harbor (right) 

 regions ...........................................................................................................................6 

Figure 3. Along-shore (left) and cross-shore (right) grid resolution (m) for the NWFS-3D 

 grid ................................................................................................................................6 

Figure 4. NGOM (left) and NWFS-3D (right) model bathymetries (m) ......................................7 

Figure 5. NGOM (left) and NWFS-3D (right) model bathymetries (m) ......................................8 

Figure 6. Water elevation (m) time evolution : propagation of a pulse in the NWFS-3D 

 domain and the effect of lateral boundary conditions ..................................................12 

Figure 7. USGS river data source and river discharge locations in the NWFS-3D 

 model............................................................................................................................18 

Figure 8. NWFS-3D model temperature and salinity comparison stations on the WFS ............19 

Figure 9. Water elevation comparison at the entrance to Tampa Bay with and without 

 tides ..............................................................................................................................20 

Figure 10. Water elevation (WL1-WL4), current (C1-C5) and T/S (TS1-TS8) model- 

 observation comparison stations in the NWFS-3D model domain ............................22 

Figure A1. Comparison of the barotropic flow variables (water elevations and currents) ...........35 

Figure A2. Comparison of the U- (true east) and V- (true north) currents components at a 

 depth of 5m .................................................................................................................36

Figure A3. Comparison of the temperature and salinity at a depth of 5m ....................................37 

Figure B1. Water elevation model-observation comparisons at Tampa Bay (WL1) entrance 

 and Big Carlos Pass (WL4)........................................................................................39 

Figure B2. Model-observation comparison of the 5m depth currents at COMP-ADCP 

 EC4 (C2) and EC5 (C4) stations .................................................................................40 

Figure B3. T/S vertical profile model-observation comparisons at stations TS1, TS2, TS3 

 and TS4 .......................................................................................................................41 
v 

Figure B4. T/S vertical profile model-observation comparisons at stations TS5, TS6, TS7 

 and TS8 ......................................................................................................................42 

Figure B5. T (top, o

C) and S (bottom, PSU) comparisons between NWFS-3D (blue), 

 NGOM (green) and observations (red) at a 5m depth for 2005 .................................43 

Figure B6. T (top, o

C) and S (bottom, PSU) comparisons between NWFS-3D (blue), 

 NGOM (green) and observations (red) at a 10m depth for 2005 ...............................44 

Figure B7. T (top, o

C) and S (bottom, PSU) comparisons between NWFS-3D (blue), 

 NGOM (green) and observations (red) at a 15m depth for 2005 ................................45 
vi 

LIST OF TABLES 

Table 1. Optimal non-reflection open ocean coupling boundary conditions ................................10 

Table 2. Amplitude and phase errors for the water elevations at stations shown in 

 Figure 10 .........................................................................................................................19 

Table 3. Amplitude and phase errors for currents at comparison stations shown in Figure 10. 

 Depending on the current analysis orientation, the U-current is either in the true east 

 or cross-shore direction and the V-current is either in the true north or along-shore 

 direction ..........................................................................................................................20 
vii 

EXECUTIVE SUMMARY 

Global and basin-scale numerical ocean models run on model grids which are too coarse to 

resolve most bays and estuaries. Conversely, using bay and estuary resolving grids with such 

models would produce grids with prohibitively large numbers of grid points and the time step 

restrictions for running on such grids would be unacceptably strict. Therefore, model coupling 

(or nesting) is a reasonable way to downscale global/basin-scale models to perform high 

resolution computations in localized regions. Model coupling can be carried out either as a twoway nesting within the same model or by coupling two separate models sharing common 

interfaces through which model boundary information is passed. Due to the greater degree of 

flexibility associated with the latter, it is often preferred and this approach is also adopted in the 

present research. In this report, a ROMS-based high resolution model (NWFS-3D) for the west 

Florida shelf (WFS) is coupled to a POM-based, basin-scale Gulf of Mexico model (NGOM). 

The coupling is effected through the initialization fields and the lateral and surface boundary 

condition fields all of which are interpolated on to the NWFS-3D model grid from the NGOM 

grid. A specific boundary condition treatment for the barotropic velocities was necessary to 

alleviate the entrapment of barotropic waves within the NWFS-3D model domain and allowed 

them to be freely transmitted in and out of it. The model coupling was calibrated and validated 

through a 15-day NWFS-3D simulation after its bathymetry and coastline had been replaced with 

those of the lower resolution NGOM model. A comparison of the water elevations, currents, 

temperature and salinity showed that NWFS-3D was able to faithfully reproduce the 

corresponding fields from NGOM. The coupled system was then employed to perform a 6-

month synoptic hindcast simulation from June 15, 2005 to December 15, 2005 for which NGOM 

model output fields and observed data were available. This period also included the presence of 

five hurricanes (Dennis, Emily, Katrina, Rita, Wilma) which enabled the numerical stability, 

robustness and reliability of the coupled system to be severely tested. Comparisons of the 

NWFS-3D water elevation, currents, temperature and salinity fields with observations showed 

that they were in good general agreement with each other and within the NOAA/NOS skill 

assessment standards – that is, within 15 cm for water elevation amplitudes, 26 cm/s for currents 

speeds, 2o

C for temperature and 3.5 PSU for salinity. The NWFS-3D predictions were 

consistent with those of NGOM as well. Extension of this research effort could involve : (i) rerunning the synoptic hindcast simulation with a range of surface forcing meteorological 

products (for example, those from the Global Forecast System (GFS), the North American 

Regional Renalysis (NARR) model, the National Digital Forecast Database (NDFD), etc.) to 

possibly further improve the NWFS-3D model predictions and obtain ensemble predictions and 

(ii) the operational implementation of the NWFS-3D set-up to run in real-time and generate daily 

model forecasts for the WFS region. The coupling methodology designed and proven in this 

report are sufficiently general and flexible that they are not restricted to modeling applications in 

WFS region only but are generally applicable to any region around the world. 
viii 
1 

1. INTRODUCTION AND MOTIVATION 

Global and basin-scale numerical ocean models run on model grids with spatial grid resolutions 

of 5 km or greater. At such resolutions, it is impossible to resolve bays, estuaries and 

embayments sufficiently. If however, these models are operated at spatial resolutions capable of 

resolving bays, estuaries and embayments, the model grids will have a prohibitively large 

number of grid points, to be run even on a supercomputer, with a suitable parallelization mode 

such as Message Passing Interface (MPI) or Open Multi-Processing (OpenMP), in a reasonable 

amount of time. Furthermore, the time-step restrictions for numerical stability of such models 

will be dictated by the smallest of the spatial scales and thus the time-stepping procedure will be 

too time consuming. Moreover, using excessively fine grid spacings and time-steps in regions 

for which there is no such necessity would constitute a waste of computational effort. 

Therefore, it would be reasonable to couple/nest spatio-temporally high resolution local or 

regional models to the larger global or basin-scale models where the former would be used to 

cover individual bays and estuaries to resolve their physics sufficiently. The model surface and 

lateral boundary forcing for the local/regional models can be derived from the global/basin-scale 

models which could also provide any necessary initial conditions and river forcing fields. 

Model coupling can be achieved in two ways : (i) via a two-way nesting procedure within the 

same model (Debreau and Balyo, [2009], Sheng, et.al, [2005], Blayo and Debreu, [2006]) or (ii) 

by coupling two different numerical ocean models sharing common interfaces (Weisberg, et. al, 

[2009], Alvera and Barth, [2009], Zavatarelli and Pinardi, [2003], Kourafalou and Tsiaras, 

[2007]). In addition to the fact that two-way nesting algorithms still have not reached full 

maturity in the field of numerical ocean modeling, (ii) has the specific advantages that : (a) a 

reliable technology to carry out this coupling is currently available, (b) it allows the use of 

different numerical ocean models (if necessary) for the global/basin-scale and nested/coupled 

domains whereby an improved model can be used for the latter and the user is not limited by the 

former, (c) the forcings associated with the nested/coupled domain can be refined or modified 

according to need and (d) the physical processes to be modeled within the nested/coupled 

domain are not limited by those of the global/basin-scale domain and different or additional 

physical processes can be included in the former – for example, non-hydrostatic effects, 

sediment transport, the use of a different vertical eddy-viscosity formulation, data assimilation, 

etc. Therefore, option (ii) gives the user a greater degree of flexibility and this is also the 

approach adopted in the present research. Hereafter, the term nested will be omitted and the term 

coupled will be used consistently throughout the remainder of this report. 

In the present research, a shelf-scale Rutgers University’s Regional Ocean Modeling System 

(ROMS) model is coupled to a basin-scale Princeton Ocean Model (POM) model. ROMS is a 

split-explicit, finite difference based orthogonal, curvilinear grid numerical ocean model 

(Shchepetkin and McWilliams, 2004). The vertical grid is of a stretched, terrain-following, 

sigma coordinate (Song and Haidvogel, 1994) type. The momentum and tracer advection terms 

are discretized using high resolution, third order upstream-biased advection schemes which 

alleviate the need to add explicit horizontal viscosity/diffusivity in the numerical computations 

(Shchepetkin and McWilliams, 1998). The hydrostatic pressure gradient terms are also 

discretized using an extremely robust and accurate piecewise cubic spline construction 
2 

(Shchepetkin and McWilliams, 2003). The vertical turbulence/eddy mixing is carried out using a 

standard Mellor-Yamada 2.5 scheme (Mellor and Yamada, 1982), a non-local K-Profile 

Parameterization (KPP) scheme or a family of General Length Scale (GLS) schemes consisting 

of k-ε, k-τ and k-ω schemes (Warner et. al., 2005). Along the ocean bottom bathymetry, friction 

can be prescribed with a logarithmic, linear, quadratic law or a Bottom Boundary Layer (BBL) 

formulation (Styles and Glenn, 2000). At the ocean surface, the surface meteorological forcing 

can be imposed in two ways in ROMS – (a) if the wind stresses and net heat fluxes are available 

then, they can be prescribed directly but otherwise, (b) the wind speeds, air pressure, air 

temperature, relative humidity, net shortwave radiation flux and downward longwave radiation 

flux observations when available are specified and then the wind stresses and the net heat flux 

are estimated internally using a Bulk Flux formulation (Liu et. al, 1979; Fairall et. al, 1996a,b). 

If downward longwave radiation data is unavailable, the net longwave radiation can be computed 

internally using the Berliand formulation (Berliand and Berliand, 1952). The perfect restart 

mechanism contained in the ROMS allows lengthy computations to be carried out in reasonably 

sized run segments. 

The POM application covers the whole of the Gulf of Mexico and as far as 78o

 W in to the 

Atlantic ocean and the region between the 18o

 N and 31o N latitudes. The nominally 5 km 

resolution POM model application is called the National Oceanographic and Atmospheric 

Administration (NOAA)/National Ocean Service (NOS) Gulf of Mexico (NGOM) model. The 

coupled ROMS domain covers the west Florida shelf from just north of Tampa Bay to just south 

of Cape Romano, FL and out to the 100m isobaths on the shelf. This coupled ROMS 

application is called NOAA/NOS West Florida Shelf three dimensional (NWFS-3D) model and 

is of much higher spatial resolution than NGOM. The NGOM domain does not include Tampa 

Bay and Charlotte Harbor but they are included in the NWFS-3D domain. 

The NWFS-3D model was initialized and forced (surface, lateral and river forcings) using fields 

interpolated from the larger, NGOM model. For initialization, water elevation, temperature and 

salinity fields were employed and the model was spun-up from rest. The surface forcing used 

interpolated wind stresses and (monthly climatological) net heat fluxes. The lateral boundary 

forcing employed water elevation, velocity, temperature and salinity fields. The river forcing 

was done with river volume discharges, river temperatures and salinities. The NWFS-3D – 

NGOM coupled system was calibrated and validated with a 15-day simulation using the lowresolution NGOM bathymetry and coastline and then, ensuring that it was able to reproduce the 

NGOM flow-fields (water elevations, currents, temperature and salinity) sufficiently accurately. 

Thereafter, using the highest resolution bathymetry and coastline available. a 6-month synoptic 

hindcast simulation spanning June 15, 2005 – December 15, 2005 was performed and the model 

predictions (water elevations, currents, temperature and salinity) from NWFS-3D were evaluated 

against those of NGOM and also against observed data. This simulation period was selected due 

to the availability of NGOM fields, observational data and the presence of five hurricanes 

(Dennis, Emily, Katrina, Rita, Wilma) which served to test the numerical stability, robustness 

and reliability of the coupled system. 

The contents of this report are arranged as follows. Section 2 describes the two coupling 

domains, their respective model grids and their bathymetries. In Section 3, the coupling 

methodology in terms of the initial, boundary and other compatibility conditions are explained. 
3 

The validation of the model coupling is documented in Section 4 and the results of the validation 

experiments are provided in Appendix A. The synoptic hindcast simulation is described in 

Section 5 and the model-observations comparisons are given in Appendix B and C. Finally, in 

Section 6 a summary, some conclusions and further directions regarding the present research are 

stated. 
4 
5 

2. COUPLED DOMAINS, GRIDS AND BATHYMETRY 

The basin-scale NGOM model domain and shelf-scale NWFS-3D sub-domain employed in the 

coupling are shown in Figure 1. 

Figure 1. NGOM model domain with the NWFS-3D sub-domain (left) and NWFS-3D 

model grid (right). Red dots on the right figure indicate NGOM grid point locations. 

The NGOM grid spacing is relatively uniform over the WFS area with a model resolution of ~5 

km and it does not include Tampa Bay or Charlotte Harbor. The NWFS-3D grid was generated 

using the Matlab-based SeaGrid grid generating tool (SeaGrid, 2009) and it has 298 x 254 grid 

points in the horizontal and 30 model σ-levels in the vertical. It was made to conform to the 

medium resolution coastline product from NOAA/National Geophysical Data Center (NGDC). 

Tampa Bay and Charlotte Harbor were included as they bring in river discharges and hence also 

nutrients to the WFS region. The upper cross-shore (western) lateral boundary of the NWFS-3D 

grid is close to Palm Harbor, FL which is north of Tampa Bay and the lower cross-shore 

(eastern) lateral boundary is close to Marco, FL which is south of Charlotte Harbor. The alongshore (southern) lateral boundary follows the 100m isobath on the WFS. As shown in Figure 1, 

there are three regions of refinement in the NWFS-3D grid which are (i) Tampa Bay, (ii) 

Charlotte Harbor and (iii) the near-coastal zone (adjacent to the coast). This added refinement 

was incorporated in order to capture the physical processes which occur within these regions. 

Figure 2 shows the grids associated with (i) and (ii). 

The grid resolution of the NWFS-3D grid is shown in Figure 3. In Tampa Bay and Charlotte 

Harbor it is ~400 m and a nominal value for the shelf is ~800m and is of much higher resolution 

on the WFS than its NGOM counterpart. Hence, the former is expected to be able to capture the 

fine-scale dynamics (e.g. eddies, etc.) which NGOM was not designed to account for. 
6 

Figure 2. The NWFS-3D grid in the Tampa Bay (left) and Charlotte Harbor (right) regions. 

Figure 3. Along-shore (left) and cross-shore (right) grid resolution (m) for the NWFS-3D grid. 

For both the NGOM and NWFS-3D grids, the bathymetry was derived from the NOAA/National 

Ocean Service (NOS) soundings. The soundings were interpolated on to the NWFS-3D grid 

nodes (at wet-points) using an inverse-square distance weighted numerical algorithm. All of the 

depths shallower than 2m were truncated to 2m which was also the depth associated with the 

land/dry points in the computational domain; neither the NGOM nor the NWFS-3D models had 
7 

their wetting-drying capabilities invoked as it was deemed not necessary. The bathymetry of 

the two domains is plotted in Figure 4 and they show the relatively higher resolution of the 

NWFS-3D grid especially in the near-coastal and shelf-break regions. Along the open ocean 

boundary of the NWFS-3D grid, its bathymetry matches the corresponding values on the NGOM 

grid and it was carried out in a smooth fashion over a distance of five grid points using a linear 

interpolation technique. The two bathymetries need to be reconciled at the NWFS-3D open 

boundaries in order to ensure that the volume transport exiting the NGOM domain is indeed that 

entering the NWFS-3D domain or else, mass, heat and salt conservation between the two 

domains would be violated. 

In the vertical, an innovative terrain-following σ-grid formulation is used. In the shallow 

regions, a greater concentration of grid points is clustered near the bottom in order to resolve the 

bottom boundary layer. In the deeper regions, clustering occurs both near the bottom and also in 

the vicinity of the surface in order to resolve the bottom and surface boundary layers 

respectively. 

This grid point distribution is brought about by the following depth-σ transformation where the 

true model depth, h which is a function of the vertical σ level and time, t is prescribed as: 

݄ሺߪ, ݐሻ ൌ ݖ ଴ሺߪሻ ൅ ߟሺݐሻ · ሾ1 ൅ ݖ଴⁄ ሿ ܪ

and, ݖ଴ሺߪሻ ൌ ሺߪ െ ܥఙሻ · ݄஼ ൅ ܪ · ܥఙ and, ܥఙ ൌ െ ቚ൛1 െ ሺ1൅ߪሻଶఏೞൟ

ఏ್

ቚ with ߠ ௕ൌ ߙ· ௠

ݐ݄ܽ݊ሾߚ · ௠ሺܪെߚ௖ሻሿ ൅ ߙ௖. Here, H is the undisturbed bottom depth, ߟሺݐሻ is the water elevation 

as a function of time. For the present application, the constant set employed is, hC = 2, θs = 2, 

αm = 4.5, αc = 5.5, βm = 0.1 and βc = 20.0. The parameter, βc therefore is a switching depth to 

discriminate between the shallower and the deeper regions mentioned above. The nature of this 

σ-grid formulation is exemplified for three different depth regimes (shallow, moderate and deep 

say for a Bay or Estuary) in Figure 5. 

Figure 4. NGOM (left) and NWFS-3D (right) model bathymetries (m). 
8 

Figure 5. Vertical σ-grid point distribution for three bottom depth regimes. 
9 

3. COUPLING METHODOLOGY, INITIAL, BOUNDARY AND COMPATIBILITY 

CONDITIONS 

The coupling methodology and the necessary conditions to achieve a valid and reliable coupling 

are described below. 

3.1. Initial Conditions 

The NWFS-3D model is spun-up from rest and the ensuing flow develops in response to the 

water elevation, temperature and salinity initialization fields. The NWFS-3D water elevation 

initialization field is derived via bilinear interpolation from the NGOM domain and the 

temperature and salinity fields are created through a tri-linear interpolation process. Numerical 

experiments where the model was initialized using also the currents fields from NGOM 

exhibited a high degree of numerical instability which is not unexpected. When the NWFS-3D 

model initialization time does not correspond exactly to a time value in the archived NGOM 

fields, the NGOM fields are first linearly interpolated in time before performing the spatial 

interpolations between the two model domains. 

3.2. Surface and Bottom Boundary Conditions 

The basin-scale NGOM model is forced at the surface using wind stresses and the barometric 

pressure produced by the U. S. Navy’s Coupled Ocean/Atmosphere Mesoscale Prediction 

System (COAMPS). The pressure forcing is carried out using the inverted barometric effect 

method. COAMPS was developed by the Marine Meteorology Division (MMD) of the Naval 

Research Laboratory (NRL). The atmospheric components of COAMPS are used operationally 

by the U.S. Navy for short-term numerical weather prediction for various regions around the 

world. NGOM is also forced with monthly climatological net heat fluxes and Sea Surface 

Temperatures (SST) (developed by Dynalysis of Princeton, Princeton, NJ) the latter of which is 

needed to prevent NGOM SST drift in time. The wind stresses and barometric pressure are 

available hourly and the heat fluxes and SSTs are monthly climatologies. The SST forcing is 

carried out via a surface nudging mechanism (see below). At the ocean bottom, NGOM employs 

a quadratic bottom drag formulation with a drag coefficient, CD of 0.0025 and for the heat fluxes, 

an insulating (zero flux) boundary condition is applied. Both at the surface and bottom, 

insulating conditions are employed for the salinity. Precipitation effects are not included. 

In the coupled NWFS-3D set-up, the surface forcing is carried out by directly imposing the 

bilinearly interpolated NGOM wind stresses and net heat fluxes; barometric pressure forcing is 

brought in using the inverted barometric formulation applied to the bilinear interpolated NGOM 

pressure fields. The NGOM SST values are similarly interpolated on to the NWFS-3D domain 

and are nudged to through a nudging coefficient; this coefficient, α is estimated on the 

assumption that shortwave radiation flux incident upon the ocean surface penetrates to and is 

thus absorbed by 1.5 m (=∆z) of water over a duration of 1 day (ܶௗ௔௬ ൌ 86400 seconds). This is 

also the formulation used in the NGOM model set-up. Hence, ߙ ൌ ܥߩ∆௣ݖ/ܶௗ௔௬ where ρ, Cp are 

the sea water density and the specific heat capacity at constant pressure respectively. This 

nudging coefficient is constant in space. There are other spatially varying coefficient 
10 

formulations in the literature (for example, Young-Molling et al., 1997) which are relatively 

more sophisticated but they can be less straightforward to estimate. 

The SST nudging in ROMS takes the form 

ܪ௦ ൌ ܪ௦ ൅ ߙ · ሺܶ௦ െ ܵܵܶሻ

where ܪ௦ is the surface net heat flux, ܶ௦ is the model computed surface temperature and, SST is 

the NGOM interpolated (climatological) SST. 

The bottom boundary conditions in the NWFS-3D model are the same as those in NGOM with 

also the same value for CD. Again, as in NGOM, at the model surface and the bottom, an 

insulating boundary condition is employed for salinity and precipitation is not included. 

3.3. Lateral Boundary Conditions 

The NWFS-3D model is forced at the lateral open boundaries with water elevations, currents 

(both barotropic and baroclinic), temperature and salinity variables which have been spatially 

interpolated from the NGOM model output fields. These variables are brought in to the NWFS3D model via the various open boundary condition options available within the ROMS model. 

For model coupling the most obvious lateral boundary conditions to use would be the clamped 

conditions. These conditions would ensure all of the boundary data on the NWFS-3D domain 

would be identical to that of the NGOM domain at the corresponding spatial locations. 

However, such boundary conditions are known to be excessively restrictive whereby (i) 

barotropic waves are unable to enter and exit the NWFS-3D domain causing them to get trapped 

and possibly amplifying and (ii) the use of different vertical σ-grid formulations in the two 

model domains would cause a mismatch in the discrete, depth-averaged, barotropic velocities 

between them resulting in errorneous volume/mass transport in and out of the NWFS-3D 

domain. In order to address (ii), it was decided to re-compute the barotropic velocities on the 

NWFS-3D domain from the baroclinic velocities interpolated from the NGOM domain. To 

satisfy the first statement, (i), a numerical experiment was performed to investigate the 

propagation of barotropic waves within the NWFS-3D domain with the intention of discovering 

an ideal set of coupling boundary conditions. 

The model set-up for the numerical experiment consisted of replacing the NWFS-3D bathymetry 

and coastline with those from NGOM model, generating (a) a set of initial conditions as explain 

in Section 3.1, (b) surface and bottom forcing fields as explained in Section 3.2 and (c) lateral 

boundary forcing variables by interpolating them from the NGOM domain on to the NWFS-3D 

boundary grid points. Thereafter, a pulse in the water elevation was introduced in (a) and the 

model was run to see how this pulse would propagate within NWFS-3D domain and also beyond 

it. The results are shown in Figure 6. Figure 6 (a) shows the initial condition where the pulse, 

located on the WFS is 16 cm higher than the surrounding water elevation level. It was found 

that using a higher pulse amplitude leads to model blow-up and a smaller amplitude did not show 

the reflected barotropic waves with sufficient clarity. The evolution of this pulse prior to 

impinging upon the model boundaries (both open ocean and land boundaries) is shown in Figure 
11 

6 (b). Further time evolution of the water elevation pulse, with the use of purely clamped 

boundary conditions, after impinging upon the model boundaries is shown in Figure 6 (c); it 

shows the reflected waves off the land and open ocean boundaries and they (roughly) have an 

amplitude half of the original pulse amplitude. Finally, in Figure 6 (d), where the elapsed time is 

the same as that for Figure 6 (c), the propagated pulse with the boundary conditions tabulated in 

Table 1 is shown. The wave pulse in Figure 6 (d) is quite similar to that in Figure 6 (c) in terms 

of the wave reflections from the land boundaries but it does not contain wave reflections from 

the open boundaries nor the wave “hot spots” at the open boundaries. Hence, in Figure 6 (d), the 

barotropic waves have been freely transmitted out through the open boundaries without them 

getting trapped within the computational domain which is unphysical. 

In the boundary condition set given in Table 1, it is the use of the Flather conditions for the 

normal components of the barotropic velocity which renders the momentum boundary conditions 

non-reflecting. These boundary conditions have been employed by other investigators too (for 

example, see Korres and Lascaratos, 2003). Although Korres and Lascaratos use clamped 

conditions for temperature and salinity, in the present research, it was decided to use radiation 

conditions when there is outflow at lateral boundaries thereby allowing the tracers to evolve 

more naturally in time and space. 

 

Flow variable name Optimal lateral boundary condition 

Water elevation Clamped 

Baroclinic velocities Clamped 

Tangential barotropic velocity Clamped 

Normal barotropic velocity Flather 

Temperature/Salinity Inflow – Clamped and Outflow - Radiation 

Table 1 : Optimal non-reflection open ocean coupling boundary conditions. 

3.4. Other Coupling Compatibility Conditions 

In addition to the above forcings, the NGOM model is also forced with rivers to include their 

volume discharges, water temperatures and salinities. Frequently, river salinity is assumed to be 

zero. In the coupled system, when there is overlap between the two model domains, the rivers 

from NGOM are included in the NWFS-3D model using the same river volume discharges, 

temperatures and salinities but at refined grid point locations (which are physically closest to the 

NGOM grid point locations). When however there is no overlap between the two domains – as 

in the Tampa Bay and Charlotte Harbor regions, additional rivers, if they exist, are included in 

the NWFS-3D model where their locations on the model grid match their actual geographical 

locations and their volume discharges, temperatures and salinities are prescribed from observed 

data which usually is from the US Geological Service (USGS). If the rivers are specified on the 

model grid at locations where tides are pronounced then, they are assumed to be tidal rivers and 

appropriate algorithmic changes have been made to the ROMS code to facilitate their effects. 
12 

 

 

 

Figure 6. Water elevation (m) time evolution : propagation of a pulse in the NWFS-3D 

domain and the effect of lateral boundary conditions. 

As explained in Section 2.0, it is necessary to reconcile the NWFS-3D bathymetry along the 

open ocean lateral boundaries with that of NGOM in order to ensure that the volume transport 

into NWFS-3D matches that exiting NGOM (that is, volume conservation). Therefore, even 

though the NWFS-3D model may have a higher resolution bathymetry which is more accurate 

than that of NGOM, the outer coupling model (NGOM) dictates the resolution and accuracy of 

the near-lateral-boundary bathymetry. 

If the coupling system is driven purely with barotropic currents and water elevations then it is 

possible to maintain the correct transport between the two domains by scaling the normal 

barotropic velocity components by the bathymetric depth ratios at the lateral boundary grid 

points in the nested domain. However, when baroclinic velocities, temperature and salinity are 

involved too, this method fails to maintain : (i) the correct balance between the barotropic and 

baroclinic velocities and (ii) the heat and salt conservation between the two coupled model 

domains. 

(a) Initial condition (b) Before contact with boundaries 

(c) Clamped boundary conditions (d) Optimal boundary conditions 
13 

Finally, it is possible to implement the NGOM-NWFS-3D coupling in two ways : with or 

without volume conservation within the NWFS-3D domain. Some investigators, for example, 

Korres and Lascaratos, (2003) have chosen the former. Numerical experiments were conducted 

to test both options and it was discovered that during hurricanes and extreme meteorological 

phenomena, the conservation of volume led to a dampened response in the water elevations 

whereby the simulated elevations were not as high as prescribed by observations. The NWFS3D water elevation predictions without the volume conservation constraint matched observations 

significantly more closely. As the WFS region is known to experience hurricanes regularly, it 

was decided not to force volume conservation within the NWFS-3D model. 
14 
15 

4. COUPLING VALIDATION 

The validity of the NGOM-NWFS-3D coupling was tested by running the NWFS-3D domain 

with the initial, boundary and compatibility conditions as stated in Sections 3.1 – 3.4 for the time 

period spanning June 15, 2005 to June 30, 2005. Therefore, the NGOM model was run first for 

this time period and thereafter, its model output fields were employed to generate the model 

initialization and forcing fields necessary for the NWFS-3D simulation. To make the two 

systems entirely compatible, (i) the NGOM bathymetry was also used for the NWFS-3D domain 

not only along the open boundaries but also throughout the domain and (ii) the NWFS-3D 

coastline was modified to emulate that of NGOM (thus deleting Tampa Bay and Charlotte 

Harbor). For (i), the NGOM bathymetry was interpolated on to the NWFS-3D domain via 

bilinear interpolation. 

For the NWFS-3D ROMS model configuration, the Mellor-Yamada 2.5 vertical eddy-viscosity 

scheme was employed and the advection terms associated with the momentum and tracer 

equations were discretized using the third-order, upstream-biased discretization option. The 

latter option alleviated the need for using explicit numerical viscosity in the horizontal to remove 

spatial oscillations in the model solution fields. The baroclinic time step used was 240 seconds 

and the corresponding barotropic time step was 12 seconds. The adjustment process of the 

NWFS-3D model which was spun-up from rest was seen to occur over a period of approximately 

7 simulation days. 

The results of the 15-day model simulation are given in Appendix A. The (thin) black line in the 

plots associated with the NGOM fields is the open ocean boundary perimeter of the NWFS-3D 

domain. Figure A1 shows a comparison of the barotropic flow variables (water elevations, true 

east barotropic current and true north barotropic current) of NWFS-3D with those of NGOM. 

The comparison is seen to be close, in particular, for the currents. As expected, due to the finer 

model grid resolution, the NWFS-3D fields are seen to include small-scale details not contained 

in the NGOM fields. A comparison of the true eastern and true northern currents at a depth of 

5m (approximate nominal ship draft depth) is given in Figure A2. Here too the comparison 

between the fields of NWFS-3D and those of NGOM is close and the currents fields of the 

former reflect the characteristics of the latter but with greater fine-scale detail. Finally, the 

potential temperature and salinity comparisons at a depth of 5m are shown in Figure A3 and the 

fields of NWFS-3D reflect the characteristics of those of NGOM whilst also including fine-scale 

details. Comparisons of currents, temperatures and salinities between the two models at other 

depths show a similar degree of agreement as well. 

Therefore, these coupling initial, boundary and compatibility conditions have yielded a robust 

(numerically stable), accurate and reliable mechanism to couple the NWFS-3D model to the 

NGOM model. The fields of the former show the characteristics of the latter but with a greater 

content of small-scale detail as expected. 
16 
17 

5. COUPLING APPLICATION TO A SYNOPTIC HINDCAST SIMULATION 

This section describes the application of the NGOM-NWFS-3D coupled system to perform a 

realistic 6-month synoptic, hindcast simulation from June 15, 2005 to December 15, 2005 and 

the evaluation of the model outputs. The NGOM model was again run first for this time period 

and thereafter, its model output fields were employed to generate the model initialization and 

forcing fields necessary for the NWFS-3D simulation. The simulation period was chosen due to 

(a) the availability of NGOM model fields to provide initialization and forcing data for NWFS3D, (b) the availability of observations to evaluate the output solution fields of NWFS-3D and 

NGOM and, (c) the occurrence of five hurricanes (Dennis, Emily, Katrina, Rita and Wilma) in 

the Gulf of Mexico which will severely test the robustness, reliability and accuracy of the 

coupled set-up. In this NWFS-3D configuration, the high resolution NOS sounding bathymetry 

and the NGDC medium resolution coastline are employed as described in Section 2.0 and it 

includes both Tampa Bay and Charlotte Harbor. Along the lateral open boundaries, the 

bathymetry has been matched with that of NGOM as also explained in Section 2.0. 

The ROMS model configuration was identical to that for the coupling validation experiments in 

Section 4.0 but with the exception that, due to the long duration of the hindcast simulation (6-

months), the ROMS perfect restart mechanism was employed and the simulation was continued 

in 1-month segments. The model was run on an IBM RS1000 platform using MPI parallelization 

with 96 processors. A single day of simulation consumed 2.53 minutes of wall clock time 

thereby giving a computational efficiency ratio of 1:568 which is highly efficient. Due to the 

fine grid resolution within the Tampa Bay and Charlotte Harbor regions, the baroclinic time step 

needed to be reduced to 90 seconds in order to maintain numerical stability which was ensured 

by monitoring the Courant-Lewy-Friedrichs (CFL) parameter. 

In the generation of the NWFS-3D model initialization and surface forcing fields (wind stress, 

net heat flux, barometric pressure and SST fields), for the non-overlapping near shore, Tampa 

Bay and Charlotte Harbor regions (not present in the NGOM domain), a Nearest-Neighbor (NN) 

interpolation technique was employed. This interpolation method therefore, extended the 

NGOM model fields into these non-overlapping areas. For the initialization temperature and 

salinity fields, the interpolation was carried out along constant geopotential surfaces. 

In the coupling validation exercise described in Section 4.0, the river forcing (volume transport, 

temperature and salinity) employed in the NWFS-3D model was identical to that of the NGOM 

model which involved only the Peace River. However, in the present application, due to the 

inclusion of Tampa Bay and Charlotte Harbor, a total of nineteen rivers are included in order to 

simulate the WFS temperature and salinity more realistically. The geographical locations of the 

river volume transport (blue circles) and river temperature/salinity (red triangles) data sources 

are shown in Figure 7 all of which are from the USGS; the river discharge locations themselves 

within the NWFS-3D model domain are shown as heavy black dots. Due to the relative sparsity 

of the temperature/salinity data sources, several rivers share the same temperature/salinity 

values. If multiple volume transport sources are available for each of the tributaries, their 

transports are combined together when generating the river forcing fields. 
18 

Figure 7. USGS river data source and river discharge locations in the NWFS-3D model. 

5.1. Coupling Calibration Experiments 

Numerical calibration experiments were performed in order to discover the optimal 

configurations for the meteorological forcing (possible further improvements to that described in 

Section 3.2), the vertical eddy-viscosity parameterization and the inclusion of tidal effects. 

These experiments are described below. 

5.1.1. Calibration of the Surface Forcing 

It was attempted to blend the COAMPS wind stresses, barometric pressure and the 

climatological net heat fluxes with values computed over the WFS from possible observational 

data sources. Such a blending would yield physically more realistic wind stress, barometric 

pressure and heat flux fields possibly also at a higher temporal frequency. An exhaustive search 

of observations yielded little usable data and they were sparsely spread in space and contained 

large gaps in their time-series. Hence, the forcing fields mentioned in Section 3.2 were 

employed. 
19 

5.1.2. Calibration of the Vertical Eddy-Viscosity Parameterization 

Numerical calibration experiments in the Chesapeake Bay using ROMS showed that the vertical 

temperature and salinity stratification was quite sensitive to the vertical eddy-viscosity scheme 

employed (Lanerolle et al., 2011). The effect of the closure scheme on the water elevations and 

currents was minimal. The GLS k-ω scheme produced the best temperature and salinity values 

and stratification relative to observed data. 

Similar experiments to examine the influence of the ROMS eddy-viscosity schemes on the 

temperature and salinity vertical stratification associated with the NWFS-3D model were 

performed. As before, the effect of the closure scheme on the water elevations and currents was 

negligible. Two 6-month synoptic hindcasts were run one with the Mellor-Yamda 2.5 scheme 

and the other with the GLS k-ω scheme. The vertical temperature and salinity profiles at 30 

stations on the WFS were compared with each other and with observed data. These stations are 

plotted in Figure 8. 

Figure 8. NWFS-3D model temperature and salinity comparison stations on the WFS. 

Unlike in the Chesapeake Bay numerical experiments (Lanerolle et al., 2011), here, the model 

solutions were seen to be much less sensitive to the choice of eddy-viscosity closure scheme 

employed. Therefore, it was decided to adopt the Mellor-Yamada 2.5 scheme which also is 

computationally less expensive. 

5.1.3. Calibration of the Tides 

The NGOM model and hence also the NWFS-3D model inherently do not contain tides. It was 

therefore decided to investigate whether or not tides should be included in the latter to generate 

physically more realistic simulations for the WFS. 
20 

An ADvanced CIRCulation Model (ADCIRC, (Luettich et. al., [1992])) generated tidal harmonic 

constituent database has been created at NOAA/NOS/Office of Coast Survey (OCS)/ Coast 

Survey Development Laboratory (CSDL) (Feyen, 2008) using the EC2001 grid (EC2001, 2009). 

It contains the 37 standard NOS harmonic constituents (Tides & Currents, 2009) for water 

elevations and barotropic velocities (east and north components). These tidal constituents were 

bilinearly interpolated on to the NWFS-3D open boundary grid nodes and thereafter, predicted 

water elevation and barotropic velocity time-series were generated for the synoptic hindcast 

simulation time period (at each boundary node). Finally, these tidal time-series were added to 

their non-tidal counterparts generated previously (from the NGOM model fields as explained in 

Section 3.3) to get the full water elevation and barotropic velocity forcing fields at lateral 

boundaries. 

Initial tidal simulations with the NWFS-3D model showed that the water elevations on the WFS 

were sufficiently accurate in terms of their phases but their amplitude comparisons with 

observations were somewhat poor. A comparison of the EC2001 and NWFS-3D model grid 

bathymetries along the NWFS-3D open boundaries showed that there were appreciable 

differences in value. Hence, the amplitudes of the interpolated harmonic constituents were 

scaled by the local bathymetric ratios to ensure that the tidal volume transport entering and 

exiting the NWFS-3D domain was consistent with that of ADCIRC. The resulting NWFS-3D 

model predicted water elevations showed a significant improvement in their agreement with 

observations. A comparison of water elevations at the entrance to Tampa Bay is shown in Figure 

9. It can be inferred that the non-tidal NGOM and non-tidal NWFS-3D model water elevations 

are closely correlated with each other attesting to the validity of the coupling between the two 

models. The plot however also shows that it is the tidal-NWFS-3D model prediction which is 

able to follow the observed data and, the comparison between the two time-series is good both in 

terms of amplitude and phase. The non-tidal water elevations emulate a time-averaged 

counterpart of the tidal water elevations. Therefore, the inclusion of tides in the NWFS-3D 

model set-up is a necessity. 

Figure 9. Water elevation comparison at the entrance to Tampa Bay with and without tides. 
21 

The model-observation comparison of the vertical temperature and salinity profiles conducted in 

Section 5.1.2 was now repeated by also including tides in the simulated results (still with the 

Mellor-Yamada 2.5 vertical eddy-viscosity scheme). It showed that the best overall comparisons 

were obtained by the model predicted profiles which contained tides. Hence, in addition to the 

water elevation comparisons, the temperature and salinity comparisons too clearly indicate the 

need for the inclusion of tides in the NWFS-3D model. 

5.2. Comparison of Model Predictions with Observations 

The NWFS-3D model results from the 6-month synoptic hindcast were evaluated against 

observations for water elevations, currents, temperature (T) and salinity (S) at the locations 

shown in Figure 10. The water elevation and currents data were from the University of South 

Florida’s Coastal Ocean Monitoring and Prediction System (COMPS) (USF, 2010). The T and 

S data were from observations made by the Mote Marine Laboratory, Sarasota, FL (Mote, 2010). 

5.2.1. Water Elevation Comparisons 

The water elevation predictions from NWFS-3D and NGOM models are compared with 

observed data in Figure B1 (Appendix B) and some evaluation metrics are provided in Table 2. 

In these metrics, the raw Root Mean Square Error (RMSE) associated with the water elevations 

is split in to an amplitude and phase component following the method described in Lanerolle et. 

al, (2011) which is more pertinent for wave-like phenomena such as water elevation time-series. 

Comparison stations WL1 and WL4 (Figures 10 and B1) were selected as the former is 

representative of the three stations in the vicinity of Tampa Bay and the latter is the only other 

station available for comparison and is in a different region of the model domain. The water 

elevation time-histories in Figure B1 (panels 1 and 3) show that the NWFS-3D model predictions 

follow the observations closely specially at station WL1. The predictions at station WL4 clearly 

show amplitude errors and the model predominantly over-predicts the water elevations relative to 

observations. The predictions from NGOM are seen to be devoid of tides and they emulate a 

temporally averaged version of the NWFS-3D predictions as expected. Table 2 shows that 

water elevation model errors are small in and around Tampa Bay and they satisfy the 

NOAA/NOS water elevation skill assessment limit of being under 15 cm in amplitude and 15 

minutes in phase (Zhang et. al, 2009). With regards to station WL4, both the amplitude and 

phase errors are bigger than those near Tampa Bay and this could be due to it being in a marshy 

area within an embayment which is not adequately resolved in the NWFS-3D model grid (and 

the sediment dominated dynamics not accounted for). The amplitude error at WL4 however is 

still within the acceptable NOAA/NOS skill assessment limit. To get a clearer understanding of 

the water elevation model predictions for extreme events (the hurricanes), they were filtered 

using a 39-hour low pass filter (Figure B1, panels 2 and 4) to de-tide them. They show that : (i) 

the NGOM and NWFS-3D model predictions are practically coincident thus attesting to the 

validity of the model coupling and (ii) the model predictions are able to discern the hurricane 

water elevations, although some amplitude and phase errors are apparent. The unfiltered water 

elevations (panels 1 and 3) also confirm (ii). The water elevation time-series also prove that both 

models are able to transition in to and recover from hurricanes correctly which is evidence that 

the NGOM-NWFS-3D coupled system is numerically stable, robust and reliable during both 
22 

when meteorological events are present and when they are not. The coupled system was not 

developed exclusively as a hurricane modeling system. 

 Figure 10. Water elevation (WL1-WL4), current (C1-C5) and T/S (TS1-TS8) 

 model-observation comparison stations in the NWFS-3D model domain. 

Station ID Amplitude error (cm) Phase error (hours) 

WL1 9.9 -0.05 

WL2 11.4 -0.08 

WL3 10.4 -0.12 

WL4 14.6 0.83 

Table 2. Amplitude and phase errors for the water elevations at stations shown in Figure 10. 

5.2.2. Currents Comparisons 

The currents time-series for stations C2 and C4 (Figure 10) are plotted in Figure B2 (Appendix 

B) and some evaluation metrics are provided in Table 3. Stations C2 and C4 are University of 

South Florida’s COMPS-ADCP/oldEC4 and COMPS-ADCP/old EC5 stations respectively. 

These two stations were selected because both their tidal and non-tidal components of the 

currents time-series are clearly discernable. For stations on or close to the shelf, the currents 

analyses were performed by rotating them to along-shore and cross-shore components but at 
23 

other stations, they were carried out in their true eastern and true northern directions. All of the 

currents plots and analyses were generated at a depth of 5m (nominal depth of ship’s draft) and 

similar inferences and conclusions can be made for currents at other depths too. 

The currents time-series plots in Figure B2 show that the along-shore component is significantly 

larger in magnitude than its cross-shore counterpart. However, it is the latter (panels 1 and 3) 

which contains most of the tidal signal and the NWFS-3D model predictions are able to follow 

the observations closely and the main error contribution is from amplitude mismatches. As 

expected, the NGOM model predictions are a time-averaged version of those from the NWFS3D model due to the lack of tides. The along-shore currents components (panels 2 and 4) show 

that the NWFS-3D model predictions have a weak tidal signal and are not appreciably different 

to those from the NGOM model and they both in general follow the observations. The observed 

time-series however include a relatively stronger tidal signal. The model predictions account for 

the hurricanes but during them, the currents amplitudes are somewhat over-predicted. 

Stn. ID Current Analysis 

 Orientation

 U-current 

Amp. Err (cm/s) Phs. Err (hrs.)

 V-current 

Amp. Err (cm/s) Phs. Err (hrs.)

 C1 Cross-Along Sh. 4.4 -0.15 6.2 0.07 

 C2 Cross-Along Sh. 2.8 -0.05 5.2 -2.07 

 C3 True East-North 5.9 0.85 5.3 -0.37 

 C4 Cross-Along Sh. 2.7 0.05 5.4 -0.25 

 C5 True East-North 8.9 0.72 8.3 -0.67 

Table 3. Amplitude and phase errors for currents at comparison stations shown in Figure 10. 

Depending on the current analysis orientation, the U-current is either in the true east or 

cross-shore direction and the V-current is either in the true north or along-shore 

direction. 

The error metrics given in Table 3 are for currents which have been de-meaned and filtered via a 

39-hour low-pass time filter so as to expose the tidal signals associated with the along-shore 

current component better. The de-meaning was carried out for both model generated currents 

time-series and also observations. They show that the current amplitude errors are well below 26 

cm/s which is the NOAA/NOS current skill assessment limit (Zhang et. al, 2009). The main 

source of error therefore is in the phases and due to the presence of a relatively stronger tidal 

signal, the errors in the cross-shore currents are smaller than those in the along-shore currents. 

For the latter, at station C2, the amplitude-phase error splitting algorithm (Lanerolle et. al, 2011) 

fails and the resulting phase error is quite large. The algorithm is only valid for comparing two 

oscillatory time-series which are generally similar to each other and are composed of similar 

tidal harmonic constituents and where the tidal signal is discernable. For the stations beyond the 

shelf break (stations C3 and C5) the currents were analyzed in the true eastern and true northern 

directions. Although the amplitude errors are well within the acceptable range (0-26 cm/s), the 

phase errors are quite large. 
24 

5.2.3. Temperature and Salinity Comparisons 

The T and S model-observation comparisons are given in Figures B3-B7 (Appendix B). Figures 

B3 and B4 show the vertical stratification comparisons at discrete dates for stations TS1-TS8 and 

Figures B5-B7 show the comparisons over time at 65 Mote measurement stations (on the WFS 

as shown in Figure 10) but at discrete vertical (geopotential) depths of 5m, 10m and 15m. 

Hence, the former provides a local picture and the latter provides a global picture or general 

assessment of the nature of T, S predictions from the NWFS-3D model. 

In the vertical stratification comparisons in Figures B3 and B4, the T and S profiles predicted by 

NWFS-3D model are given at the exact times and also at an hour before and an hour after them 

so as to account for any errors associated with the tides. The vertical T and S profiles show that : 

(i) the sloshing motion of the tides has a negligible effect on the profiles, (ii) in general, the 

vertical stratification associated with the modeled results and the observations is weak and there 

is no seasonal dependence (also true for the other T/S comparison stations shown in Figure 10) 

over the 6-month simulation period, (iii) the observations show relatively stronger stratification 

than the model predictions (e.g. the salinity profile for station TS3), (iv) the NWFS-3D and 

NGOM model predicted profiles are close to each other and more so than to the observed 

profiles; for T, the model profiles are generally about 0.5 o

C apart with neither model being 

consistently cooler or warmer than the other and for S, they are about 0.5 PSU apart with the 

NWFS-3D model predictions being fresher in general and, (v) neither model convincingly 

compares better with observations than the other; for T, they are 0.5o

C – 1.5oC cooler than the 

observations and for S, model predictions are saltier by 0 PSU – 3 PSU at the near-shore stations 

(TS1-TS4) and are fresher than observations by 0.25 PSU – 1.0 PSU at stations beyond the shelf 

break (TS5-TS8). 

The model-observation comparison of T at constants depths of 5m,10m and 15m given in 

Figures B5-B7 indicate that : (i) a seasonal cooling from July-December is clearly visible in the 

observations and the model predictions, (ii) a cooling behavior is also seen when moving deeper 

down the water column from 5m to 10m and from 10m to 15m, (iii) the general modelobservation comparisons at 5m, 10m and 15m depths are similar, which is consistent with the 

weak vertical stratification seen (Figures B3-B4), (iv) in the warmer months of July-October, the 

model predictions are cooler than the observations with predictions of NGOM being cooler than 

those of NWFS-3D; in the cooler months – for example, December, the converse is true and the 

model predictions are warmer than observations with NGOM being the warmest. The difference 

between model predictions and observations is generally in the range of 1o

C – 2oC and the 

excessive cooling/heating could be attributed to the use of the monthly climatological net heat 

fluxes in the meteorological forcing. This trend may be able to be eliminated or curtailed by 

using the ROMS Bulk Flux formulation with realistic meteorological forcing data (wind speeds, 

air pressure, air temperature, net shortwave radiation flux and downward longwave radiation 

flux). However, then, the meteorological forcing may become inconsistent with the tidesenhanced, open boundary forcing fields from the NGOM model (which is forced with COAMPS 

wind stresses, air pressure; climatological net heat fluxes) and the coupled system could become 

numerically unstable. 
25 

The S model-observation comparisons in Figures B5-B7 at 5m, 10m and 15m depths show that : 

(i) unlike for T, there is no obvious seasonal variation in S, (ii) the greatest spread in values of S 

between NWFS-3D and NGOM model predictions and also between the model predictions and 

observations is at the 5m depth and in the July-August time which is the warmest season, (iii) the 

average S value increases with depth as expected, (iv) at 5m, the spread in values of observed S 

is greater than those of the model predictions and the latter is excessively salty with NGOM 

model predictions being the saltiest; the general discrepancy between predictions and 

observations is about 2 PSU but upon approaching the winter season, the observations and 

predictions show convergence toward each other, (v) at the 10m depth, the spread in the S values 

is significantly less than that at 5m and the model-observation agreement is also better; during 

the fall-winter season, NWFS-3D model predictions are about 0.5 PSU fresher than those of 

NGOM which shows closer agreement with observations and (vi) at 15m, there is close 

agreement between the model predictions and observations with the exception in November, 

when the predictions are seen to be fresher than observations with the NWFS-3D model 

predictions being the freshest by about 1 PSU. 

The NOAA/NOS skill assessment limits state that model predicted and observed T values should 

be within 2 o

C of each other and the corresponding S differences should to be within 3.5 PSU 

(Zhang et. al, 2009). The above T and S validation exercises have shown that the NWFS-3D 

model predictions (and also those of the NGOM model) do satisfy these limits. 
26 
27 

6. SUMMARY, CONCLUSIONS AND FUTURE DIRECTIONS 

Global and basin-scale numerical ocean models run on model grids which are too coarse to 

resolve most bays, estuaries and embayments. Generating bay and estuary resolving grids for 

such models on the other hand would produce grids with prohibitively large numbers of grid 

points and the time step restrictions for running on such grids would also be unacceptably strict. 

Therefore, model coupling (or nesting as also commonly known) is a reasonable way to 

downscale global/basin-scale models to perform spatio-temporally high resolution computations 

in localized regions. Model coupling can be achieved via : two-way nesting within the same 

model or by coupling two separate models (sharing common interfaces) one of which could be a 

global/basin-scale model. Due to the greater degree of flexibility associated with the latter, it is 

preferred over the former and hence is also adopted in the present research. 

In this report, the coupling of a ROMS-based model for the west Florida shelf to a larger, POMbased, basin-scale Gulf of Mexico model is described. The former, named NWFS-3D includes 

both Tampa Bay and Charlotte Harbor which were not contained in the latter which is called 

NGOM. The coupling is effected via the T and S initialization fields, lateral and surface 

boundary condition fields all of which are interpolated on to the NWFS-3D model grid from the 

NGOM grid using bi-linear or tri-linear interpolation techniques. The ideal lateral boundary 

condition set was to use clamped conditions for water elevations and baroclinic velocities, 

Flather-clamped conditions for the normal and tangential barotropic velocities (respectively) and 

a radiation-clamped condition for T and S depending on whether there was outflow or inflow at 

the boundary (respectively). It is this specific boundary condition set which enabled the NWFS3D model to be able to transmit barotropic waves freely in and out of the model domain, while a 

purely clamped set of boundary conditions led to the trapping of these waves resulting in 

unphysical model solutions. Additionally, any NGOM domain river forcing was also 

consistently included in the NWFS-3D domain together with bathymetry matching along the 

open ocean boundaries to ensure consistency in the volume transport between the two domains. 

It was discovered that enforcing volume conservation within the NWFS-3D model resulted in a 

dampened response to extreme meteorological phenomena and therefore, this condition was not 

specified. A novel terrain-following σ-coordinate grid was employed in the vertical which 

resolved the bottom boundary layer in shallow regions and both the bottom and surface boundary 

layers in the deeper regions. 

The model coupling was validated by performing a 15-day simulation using the low-resolution 

bathymetry and coastline from the NGOM model in the NWFS-3D model also. This model 

domain did not include Tampa Bay or Charlotte Harbor. A comparison of the water elevations, 

barotroic currents, baroclinic currents, T and S showed that the NWFS-3D model was able to 

faithfully reproduce the corresponding fields from the NGOM model. 

The coupled system was then employed to perform a 6-month synoptic hindcast simulation from 

June 15, 2005 to December 15, 2005 for which NGOM fields and observed data were available. 

This period also included five hurricanes (Dennis, Emily, Katrina, Rita, Wilma) which enabled 

the numerical stability, robustness and reliability of the coupled system to be severely tested. 

Initial calibration exercises allowed the optimal surface forcing fields and vertical eddy-viscosity 

scheme to be isolated and they also showed a need for the inclusion of tides in the computations. 
28 

Furthermore, unlike in the NGOM model where only the Peace River was included, in the 

NWFS-3D model, nineteen rivers were included primarily due to the inclusion of Tampa Bay 

and Charlotte Harbor. Comparison of the NWFS-3D water elevations, currents, T and S with 

observations showed that they were in good general agreement with each other and within the 

NOAA/NOS skill assessment limits (within 15 cm for water elevation amplitudes, 26 cm/s for 

currents speeds, 2oC for T and 3.5 PSU for S). For T and S, the NWFS-3D model predictions 

were consistent with those of the NGOM model and neither model showed a strong advantage 

over the other in its agreement with observed data. 

Future research directions could involve : (i) re-running the synoptic hindcast simulation with a 

range of surface forcing meteorological products (for example, those from the NOAA/National 

Weather Service’s (NWS’s) Global Forecast System (GFS), the North American Regional 

Renalysis (NARR) model, the NWS National Digital Forecast Database (NDFD), etc.) to 

possibly further improve the NWFS-3D model predictions and obtain ensemble predictions and 

(ii) the operationalization of the NWFS-3D model set-up to run in real-time and generate daily 

model forecasts for the WFS region. 

The coupling methodology designed and proven in this report are sufficiently general and 

flexible that they are not restricted to modeling applications in WFS region only but are 

generally applicable to any region around the world. 
29 

ACKNOWLEDGEMENTS 

The authors wish the thank Dr. Frank Aikman III, Branch Chief of the CSDL’s Marine Modeling 

and Analysis Programs (MMAP) for his management support. Professor Robert H. Weisberg of 

the College of Marine Science, University of South Florida (USF) is gratefully acknowledged for 

providing the water elevation and current observations for model validation. The Mote Marine 

Laboratory and Dr. Gary Kirkpatrick are also gratefully acknowledged for providing the 

temperature and salinity observations for model validation. 
30 
31 

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34 
35 

APPENDIX A. COUPLING VALIDATION 

Figure A1. Comparison of the barotropic flow variables (water elevations and currents). 
36 

Figure A2. Comparison of the U- (true east) and V- (true north) currents components at a 

depth of 5m. 
37 

Figure A3. Comparison of the temperature and salinity at a depth of 5m. 
38 

 
39 

APPENDIX B. COUPLING APPLICATION TO A SYNOPTIC HINDCAST 

SIMULATION 

Figure B1. Water elevation model-observation comparisons at Tampa Bay (WL1) entrance and Big Carlos Pass (WL4). 
40 

Figure B2. Model-observation comparison of the 5m depth currents at COMP-ADCP EC4 (C2) and EC5 (C4) stations. 
41 

Figure B3. T/S vertical profile model-observation comparisons at stations TS1, TS2, TS3 and TS4. 
42 

Figure B4. T/S vertical profile model-observation comparisons at stations TS5, TS6, TS7 and TS8. 
43 

Figure B5. T (top, oC) and S (bottom, PSU) comparisons between NWFS-3D (blue), NGOM 

(green) and observations (red) at a 5m depth for 2005. 
44 

Figure B6. T (top, o

C) and S (bottom, PSU) comparisons between NWFS-3D (blue), NGOM 

(green) and observations (red) at a 10m depth for 2005. 
45 

Figure B7. T (top, o

C) and S (bottom, PSU) comparisons between NWFS-3D (blue), NGOM 

(green) and observations (red) at a 15m depth for 2005.