NOAA Technical Report NOS CS 29

THE SECOND GENERATION CHESAPEAKE BAY 

OPERATIONAL FORECAST SYSTEM (CBOFS2): MODEL 

DEVELOPMENT AND SKILL ASSESSMENT 

Silver Spring, Maryland 

March 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 29 

THE SECOND GENERATION CHESAPEAKE BAY 

OPERATIONAL FORECAST SYSTEM (CBOFS2): MODEL 

DEVELOPMENT AND SKILL ASSESSMENT 

Lyon W. J. Lanerolle, Richard C. Patchen and Frank Aikman III 

Office of Coast Survey, Coast Survey Development Laboratory, 

Silver Spring, MD 

March 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 ....................................................................................................................... viii 

EXECUTIVE SUMMARY ........................................................................................................... xi 

1. INTRODUCTION ......................................................................................................................1 

2. CBOFS2 MODEL DOMAIN, GRID AND BATHYMETRY ...................................................3 

3. CONSTANT DENSITY TIDAL SIMUALTION ......................................................................7 

 3.1 Water Level Comparisons and Skill Assessments .....................................................9 

 3.2 Currents Comparisons and Skill Assessments .........................................................15 

4. SYNOPTIC HINDCAST SIMULATION ................................................................................23 

 4.1 Initial Conditions and Model Forcings ....................................................................24 

 4.2 Water Level Comparisons ........................................................................................27 

 4.3 Currents Comparisons ..............................................................................................31 

 4.4 Temperature and Salinity Comparisons ...................................................................36 

5. SEMI-OPERATIONAL NOWCAST/FORECAST SIMULATION .......................................43 

 5.1 Water Level Comparisons ........................................................................................43 

 5.2 Currents Comparisons ..............................................................................................45 

 5.3 Temperature Comparisons .......................................................................................45 

 5.4 Salinity Comparisons ...............................................................................................45 

6. SUMMARY AND CONCLUSIONS .......................................................................................47 

ACKNOWLEDGMENTS .............................................................................................................49

REFRENCES .................................................................................................................................51 

APPENDIX A: CBOFS2 CONSTANT DENSITY WATER LEVEL HARMONIC 

 CONSTITUENTS AND SKILL ASSESSMENTS ............................................55 

APPENDIX B: CBOFS2 CONSTANT DENSITY CURRENTS HARMONIC 

 CONSTITUENTS AND SKILL ASSESSMENTS ............................................57 

APPENDIX C: CBOFS2 SYNOPTIC HINDCAST TEMPERATURE AND 

 SALINITY SKILL ASSESSMENTS .................................................................61 

APPENDIX D: CBOFS2 SEMI-OPERATIONAL NOWCAST/FORECAST 

 SKILL ASSESSMENTS ....................................................................................75 
iv 

LIST OF FIGURES 

Figure 1. CBOFS2 model domain and orthogonal, curvilinear grid (left) and model 

 Bathymetry (right) ........................................................................................................3 

Figure 2. CBOFS2 water level stations archive locations (and the NOS/CO-OPS 

 identification numbers) for comparison with tidal predictions in the constant 

 density simulation .........................................................................................................9 

Figure 3. Amplitude differences (CBOFS2-observations in cm) for M2, N2, K1, O1, P1 

 and L2 harmonic constituents in the constant density CBOFS2 simulation ...............10 

Figure 4. Phase differences (CBOFS2-observations in hours) for M2, N2, K1, O1, P1 and 

 L2 harmonic constituents in the constant density CBOFS2 simulation .....................11 

Figure 5. RMS water level errors (in cm) for the constant density CBOFS2 simulation .........12 

Figure 6. Splitting methodology of the RMS error into an amplitude component and a 

 phase component. Here, x-axis annotation of phase variation or difference is 

 equivalent to the amount by which the who water level time-series have been 

 translated relative to each other ..................................................................................13 

Figure 7. CBOFS2 RMSE translation curves for the comparison stations given in 

 Figure 2 .......................................................................................................................14 

Figure 8. The amplitude error (in cm) and phase error (in hours) components of the RMS 

 errors associated with the water levels for the constant density CBOFS2 

 simulation ....................................................................................................................15 

Figure 9. CBOFS2 currents stations archive locations for comparison with tidal predictions 

 in the constant density simulation ...............................................................................16 

Figure 10. CBOFS2 currents stations archive locations for comparison with tidal predictions 

in the constant density simulation ..............................................................................17 

Figure 11. M2, N2 and K1 constituent CBOFS2 amplitude (in cm/s) and phase (in hours) 

 errors (CBOFS2 minus prediction) for the true northward current component in 

 in the constant density simulation ...............................................................................18 

Figure 12. RMS current speed (left, cm/s) and current direction (right, degrees) errors (from 

 the CSDL skill-assessment software package) at a depth of 15 feet (4.6m) for 

 the CBOFS2 constant density simulation at the NOS/CO-OPS/CMIST 

 observational stations ..................................................................................................19 
v 

Figure 13. RMSE translation curves for the CBOFS2 major current component for the 

comparison stations ....................................................................................................20 

Figure 14. The amplitude (left, cm/s) and phase error (right, hours) components of the 

 RMS errors associated with the major current in the constant density 

 CBOFS2 simulation ....................................................................................................21 

Figure 15. Vertical structure of major-direction currents for the constant density 

 CBOFS2 simulation (black – NOS/CO-OPS/CMIST prediction, blue – CBOFS2, 

 red – CBOFS2 with 1 hr. phase lead, green – CBOFS2 with 1 hr. phase lag) ...........22 

Figure 16. Total river volume discharge for the CBOFS2 model domain spanning 

 2003-2005 ...................................................................................................................23 

Figure 17. Wind speed plot for August-October, 2003 at Chesapeake Light, VA NOAA/ 

 National Data Buoy Center (NDBC) station showing hurricane Isabel .....................23 

Figure 18. NARR (blue circles) and NDBC (red squares) data points used in the creation of 

 the wind, air temperature, relative humidity/dew point and net shortwave 

 radiation fields; the thick black line is the southern open boundary of the 

 CBOFS2 computational domain .................................................................................25 

Figure 19. CFL number time-history for the synoptic hindcast simulation ..................................26 

Figure 20. Water level and currents stations archive locations for the synoptic hindcast 

 CBOFS2 simulation for comparison with observations .............................................27 

Figure 21. RMS water level errors (in cm) for the synoptic hindcast CBOFS2 simulation .......28 

Figure 22. CBOFS2 synoptic hindcast RMSE translation curves for the comparison stations ....29 

Figure 23. The amplitude error (cm) and phase error (hours) components of the RMS errors 

 associated with the water levels for the synoptic hindcast CBOFS2 simulation ........30 

Figure 24. RMS current speed (left, cm/s) and current direction (right, degrees) errors at a 

 depth of 5m for the CBOFS2 synoptic hindcast simulation at the NOS/CMIST 

 observational stations (from the CSDL skill-assessment software package) .............32 

Figure 25. CBOFS2 synoptic hindcast RMSE translation curves for the major-current 

 component at the comparison stations ........................................................................33 

Figure 26. The amplitude (left, cm/s) and phase error (right, hours) components of the RMS 

 errors associated with the major current in the synoptic hindcast CBOFS2 

 simulation ...................................................................................................................34 
vi 

Figure 27. Vertical structure of the major-direction currents for the synoptic hindcast 

 CBOFS2 simulation ( black – NOS/CO-OPS/CMIST obs., blue – CBOFS2, red – 

 CBOFS2 with 1 hr. phase lead, green – CBOFS2 with 1 hr. phase lag) ...................35 

Figure 28. Temperature and salinity stations archive locations for the CBOFS2 synoptic 

 hindcast simulation. Locations in red are stations at which local and global 

 error analyses were performed (Figures C1-C10 in Appendix C) ..............................36 

Figure 29. Plot of the RMS and mean errors for T and S as listed in Tables C1 and C1 in 

 Appendix C ..................................................................................................................39 

Figure 30. Plot of the RMS and mean errors for T at the surface, at 15-feet and at the 

 bottom .........................................................................................................................40 

Figure 31. Plot of the RMS and mean errors for S at the surface, at 15-feet and at the 

 bottom .........................................................................................................................41 

Figure 32. Locations of the stations where water level (blue circles) and currents (red 

 squares) skill assessments were performed. The temperature and salinity 

 comparison stations are demarcated with a box next them .........................................44 

Figure 33. Salinity time-series at station 8638863 (CBBT) ..........................................................46 

Figure C1. Observed Bay Program T/S, CBOFS2 predicted T/S and their differences at 

 station CB7.4..............................................................................................................61 

Figure C2. Observed Bay Program T/S, CBOFS2 predicted T/S and their differences at 

 station CB5.4..............................................................................................................62 

Figure C3. Observed Bay Program T/S, CBOFS2 predicted T/S and their differences at 

 station CB4.2C ...........................................................................................................63 

Figure C4. Observed Bay Program T/S, CBOFS2 predicted T/S and their differences at 

 station CB2.1..............................................................................................................64 

Figure C5. Observed Bay Program T/S, CBOFS2 predicted T/S and their differences at 

 station RET5.2 ...........................................................................................................65 

Figure C6. Observed Bay Program T/S, CBOFS2 predicted T/S and their differences at 

 station LE3.1 ..............................................................................................................66 

Figure C7. Observed Bay Program T/S, CBOFS2 predicted T/S and their differences at 

 station RET2.4 ...........................................................................................................67 

Figure C8. Observed Bay Program T/S, CBOFS2 predicted T/S and their differences at 

 station LE1.3 ..............................................................................................................68 
vii 

Figure C9. Observed Bay Program T/S, CBOFS2 predicted T/S and their differences at 

 station EE3.4 ..............................................................................................................69 

Figure C10. Observed Bay Program T/S, CBOFS2 predicted T/S and their differences at 

 station ET5.2 ............................................................................................................70 

Figure C11. Histograms of local errors (in time and depth) for T and S corresponding to 

 Figures C1-C10. The T and S histogram bin widths are 0.5 o

C and 0.5 PSU 

 respectively ...............................................................................................................71 
viii 

LIST OF TABLES 

Table 1. Water level error summary for the synoptic hindcast CBOFS2 : Tidal range (cm), 

 RMS error (cm) and its Central Frequency (CF), high water amplitude error 

 (AHW_err, cm) and its CF, low water amplitude error (ALW_err, cm) and its CF 

 (all from the CSDL skill-assessment software package), amplitude component of 

 the RMSE (cm) and the phase component of the RMSE(hours) ..................................31 

Table 2. Current speed error summary for CBOFS2 synoptic hindcast simulation: RMS of 

 current speed error (cm/s) and its Central Frequency (CF), maximum flood current 

 amplitude error (AFC_err, cm) and its CF, maximum ebb current amplitude error 

 (AEC_err, cm) and its CF (all from the CSDL skill-assessment software package) ....32 

Table 3. Current direction error summary for CBOFS2 synoptic hindcast simulation: RMS 

 of current direction error (degrees) and its Central Frequency (CF), maximum 

 flood current direction error (DFC_err, degrees) and its CF, maximum ebb 

 current direction error (DEC_err, degrees) and its CF (all from the CSDL 

 skill-assessment software package) .............................................................................33 

Table 4. Major current error summary for the synoptic hindcast simulation: raw RMS error 

 (cm/s), the amplitude component of the RMSE (cm/s) and the phase component 

 of the RMSE (hours) .....................................................................................................34 

Table A1. Water level harmonic constituents summary for CBOFS2; amplitudes are in 

 meters and phases are in hours .....................................................................................55 

Table A2. Water level harmonic constituents summary from observations (NOS/CO-OPS 

 Database); amplitudes are in meters and phases in hours ............................................55 

Table A3. Water level error summary: Tidal range (cm), RMS error (cm) and its Central 

 Frequency (CF), high water amplitude error (AHW_err, cm) and its CF, low 

 water amplitude error (ALW_err, cm) and its CF (all from the CSDL skill- 

 assessment software package), amplitude component of the RMSE (cm) and 

 the phase component of the RMSE (hours) .................................................................56 

Table B1. True eastward current harmonic constituents summary for CBOFS2; amplitudes 

 are in m/s and phases are in hours ...............................................................................57 

Table B2. True northward current harmonic constituents summary for CBOFS2; amplitudes 

 are in m/s and phases are in hours ...............................................................................57 

Table B3. True eastward current harmonic constituents summary from observations 

 (NOS/CO-OPS/CMIST database and NOS survey); amplitudes are in m/s and 

 phases are in hours .......................................................................................................58 
ix 

Table B4. True northward current harmonic constituents summary from observations 

 (NOS/CO-OPS/CMIST database and NOS survey); amplitudes are in m/s and 

 phases are in hours .......................................................................................................58 

Table B5. Current speed error summary: RMS of current speed error (cm/s) and its Central 

 Frequency (CF), maximum flood current amplitude error (AFC_err, cm) and its 

 CF, maximum ebb current amplitude error (AEC_err, cm) and its CF (all from 

 the CSDL skill-assessment software package) ...........................................................58 

Table B6. Current direction error summary: RMS of current direction error (degrees) and its 

 Central Frequency (CF), maximum flood current direction error (DFC_err, degrees) 

 and its CF, maximum ebb current direction error (DEC_err, degrees) and its CF 

 (all from the CSDL skill-assessment software package) .............................................59 

Table B7. Major current error summary: raw RMS error (cm/s), the amplitude component 

 of the RMSE (cm/s) and the phase component of the RMSE (hours) .........................59 

Table C1. The RMS and mean errors (calculated in time) for temperature at the surface, at 

 15-feet below the surface and at the bottom ................................................................72 

Table C2. The RMS and mean errors (calculated in time) for salinity at the surface, at 

 15-feet below the surface and at the bottom ................................................................73 

Table D1. RMSE (m) values for the water levels for the semi-operational nowcast/forecast 

 CBOFS2 (from the CSDL skill assessment software package) ...................................75 

Table D2. CF(15cm) values for the water levels for the semi-operational nowcast/forecast 

 CBOFS2 (from the CSDL skill assessment software package) ...................................75 

Table D3. RMSE (m/s) values for the current speed at 15 feet for the semi-operational 

 nowcast/forecast CBOFS2 (from the CSDL skill assessment software package) .......76 

Table D4.CF(26cm/s) values for the current speed at 15 feet for the semi-operational 

 nowcast/forecast CBOFS2 (from the CSDL skill assessment software package) ........76 

Table D5. RMSE (degrees) values for the current direction at 15 feet for the semi-operational 

 nowcast/forecast CBOFS2 (from the CSDL skill assessment software package) .......76 

Table D6. CF(22.5o) values for the current direction at 15 feet for the semi-operational 

 nowcast/forecast CBOFS2 (from the CSDL skill assessment software package) .......76 

Table D7. RMSE (o

C) values for temperature at a 1m depth for the semi-operational 

 nowcast/forecast CBOFS2 (from the CSDL skill assessment software package) .......77 

Table D8. CF(3o

C) values for temperature at a 1m depth for the semi-operational 

 nowcast/forecast CBOFS2 (from the CSDL skill assessment software package) .......77 
x 

Table D9. RMSE (PSU) values for salinity at a 1m depth for the semi-operational 

 nowcast/forecast CBOFS2 (from the CSDL skill assessment software package) .......77 

Table D10. CF(3.5 PSU) values for salinity at a 1m depth for the semi-operational 

 nowcast/forecast CBOFS2 (from the CSDL skill assessment software package) .....77 
xi 

EXECUTIVE SUMMARY 

The National Ocean Service presently has an Operational Forecast System for the Chesapeake Bay 

(CBOFS) which generates only water levels and depth-integrated currents. As a next generation system, 

a fully three-dimensional, baroclinic forecast system (CBOFS2) was developed, calibrated and validated; 

this system will produce water levels, currents, temperature and salinity predictions. CBOFS2 covers the 

whole of the Chesapeake Bay up to and including Reedy Point, DE along the Chesapeake & Delaware 

canal and also includes Ocean City, MD and Duck, NC along its southern boundary which extends as far 

as the 100m isobath on the shelf. 

First, a two-month tides-only simulation was conducted to validate the tidal water levels and currents and 

thereafter, a synoptic hindcast simulation from June 01, 2003 – September 01, 2005 was performed to 

validate water levels, currents, temperature and salinity. The synoptic hindcast simulation included a 

diverse range environmental conditions in the Bay including very high and very low river volume 

discharges and a hurricane (Isabel, in September of 2003). Finally, CBOFS2 was run in a semioperational, nowcast/forecast mode to validate these model outputs. 

The simulations showed that both the constant density and synoptic hindcast CBOFS2 configurations 

were numerically stable and highly efficient under a MPI parallelization environment. A computational 

effort ratio of 1:144 resulted when employing 96 parallel processors. The numerical stability of the 

computations was accounted for by monitoring the Courant-Friedrichs-Lewy (CFL) stability parameter 

during model simulations. 

As for the quality of the CBOFS2 predictions, when compared with observations, it was found that: (i) the 

water level amplitude errors were less than 22 cm and phase errors generally less than 0.5 hours and, both 

the amplitude and phase errors increase in magnitude when moving up the Bay and for the latter, this is 

also true when moving up tributaries, (ii) currents speed errors were less than 26 cm/s and the direction 

errors less than 22.5o

 which are the NOS skill criteria and for the major-direction components, the phase 

errors were also less than 0.5 hours, (iii) the temperature Root Mean Square (RMS) errors were generally 

less than 2 o

C and the mean errors were in the range [-1°C, 1°C] and near the ocean surface CBOFS2 was 

cooler and near the bottom warmer relative to observations and (iv) the salinity RMS errors were 

generally less than 4 PSU and the mean errors were in the range [-2 PSU, 3 PSU] and CBOFS2 was 

saltier near the surface and fresher near the bottom when compared with observations. The accuracy of 

the semi-operational, nowcast/forecast predictions are as good as and if not better than those from the 

synoptic hindcast and in general meet the NOS skill criteria; furthermore, the forecasts are valid for up to 

a 24-hour period without deterioration of their accuracy. 

This report also describes a RMS error splitting (into an amplitude and phase component) procedure 

which was found to be very reliable for both water level and current comparisons (with observations) and 

for both the constant density and synoptic hindcast simulations. 

Therefore, the predictive accuracy for water level, currents, temperature and salinity associated with 

CBOFS2 warrants it being accepted as a NOS Operational Forecast System (OFS) upgrade to the 

presently available CBOFS set-up. It is expected that the predictions from this modeling set-up may be 

further enhanced in the future by experimenting with: (a) spatially variable bottom friction formulations, 

(b) various shapes and extents of the shelf open ocean boundaries, (c) other model constants in the 

General Length Scale (GLS) vertical eddy-viscosity scheme and (d) the possibility of coupling the open 

ocean boundaries to a basin-scale model to better account for the shelf dynamics and its influence on the 

Chesapeake Bay. 
xii 
1 

1. INTRODUCTION 

Presently, there exists an operational model for the Chesapeake Bay named the Chesapeake Bay 

Operational Forecast System (CBOFS), which runs routinely at the Center for Operational 

Oceanographic Products and Services (CO-OPS) of the National Ocean Service (NOS) of 

NOAA (Gross et al., 2000). This model set-up, since being two-dimensional and barotropic in 

nature, only generates water levels (elevations) and barotropic (depth-integrated) currents for 

Chesapeake Bay. The navigational and ecological communities in particular are increasingly 

demanding not only water levels and depth-integrated currents but also the full three-dimensional 

currents, salinity and temperature fields. Therefore, a second generation three-dimensional 

Chesapeake Bay Operational Forecast System (CBOFS2) has been developed, calibrated, 

implemented and vetted which will provide these additional physical fields. This model is based 

on the Rutgers University’s Regional Ocean Modeling System (ROMS). 

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, terrainfollowing, 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 

(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 CBOFS2 model domain was designed to include the whole of the Chesapeake Bay and a 

piece of the shelf to allow a realistic interaction between the shelf and the entrance to the Bay. 

The domain therefore included Washington, DC to the west, Reedy Point, DE (along the 

Chesapeake & Delaware (C & D) canal) to the east, the Susquehanna River (near the river 

reservoir) to the north and in the south out to the 100m isobath with Ocean City, MD and Duck, 

NC as the end points. The inclusion of the C &D canal is necessary in order to account for the 

interaction with the Delaware Bay, but it forces the use of a particular set of open ocean 

boundary conditions which required a smaller model time step in order to maintain numerical 
2 

stability. The model grid is curvilinear and orthogonal in nature in the horizontal and in the 

vertical, it was of a terrain-following, sigma-coordinate nature. 

The calibration and validation of the CBOFS2 set-up was performed in three stages. First, a 

constant density, three-dimensional baroclinic simulation was run to validate the accuracy of the 

tides (water levels and currents). Once this simulation was validated, a synoptic hindcast 

simulation spanning June, 2003 to September, 2005 was carried out where the initialization 

fields and the model forcings (rivers, meteorology, etc.) were based on both synoptic 

observations and climatological fields; this period included very high and very low river 

discharges and a hurricane (Isabel). This second set-up was employed to validate the accuracy of 

the full suite of model outputs – water levels, currents, temperature and salinity against 

observations. Finally, CBOFS2 was run in a semi-operational, nowcast/forecast model and the 

model outputs (same as those for the hindcast) were validated to ensure its suitability for being 

an Operational Forecast System (OFS); the model forcing were from model-generated forecast 

products. All of these scenarios also served to examine the numerical stability properties 

associated with the CBOFS2 set-up. 

This report is arranged as follows: In section 2, the model domain, grid and bathymetry are 

described and in section 3, the constant density simulation and its results are described. In 

section 4 the synoptic hindcast simulation is discussed together with the validation efforts of the 

model output fields. Section 5 describes the semi-operational, nowcast/forecast CBOFS2 system 

and the validation of its outputs. Finally, in section 6, a summary of the findings in this paper 

and the conclusions pertaining to its research are provided. 
3 

2. CBOFS2 MODEL DOMAIN, GRID AND BATHYMETRY 

The CBOFS2 model domain and the model grid are given in Figure 1. The domain extends from 

the 100m isobath in the south to the Susquehanna River (at the river reservoir) in the north and 

from Washington, DC in the west to Reedy Point, DE in the east. There are two open ocean 

(lateral) boundaries in this domain with the first situated on the shelf between Duck, NC and 

Ocean City, MD and the second at Reedy Point, DE where the C & D canal exits to Delaware 

Bay. The C & D canal was included to ensure a realistic interaction between the two Bays and 

its termination at Reedy Point, DE was selected since water level observations are available at 

this location and a nearby US Geological Survey (USGS) gauge in Delaware Bay can be used to 

provide the temperature and salinity values. Along the southern open boundary, the end points 

Figure 1. CBOFS2 model domain and orthogonal, curvilinear grid (left) and model bathymetry 

 (right). 
4 

of Duck, NC and Ocean City, MD were selected because water level observations are available 

at these locations (temperature and salinity boundary values are from climatological fields). The 

above mentioned observations for water levels, temperature and salinity are required for model 

open boundary conditions/forcings in the synoptic hindcast simulation. 

The CBOFS2 model grid was generated using the DELFT3D grid generator (Delft3D, 2008) and 

is curvilinear and orthogonal in nature. It was produced within the generator as multiple smaller 

curvilinear, orthogonal grid segments (so as to fit the local coastline segments as accurately as 

possible) and thereafter pasted together seamlessly within the grid generator but still maintaining 

continuity and global orthogonality. This grid generator only outputs the grid point locations of 

the wet-points and its output was converted to a ROMS-compatible grid file (in Matlab) by 

generating a pseudo land-mask and yet preserving a matrix structure for the grid file variables 

(eg. land-sea mask, bathymetry, etc.) with fixed dimensional limits. The grid has 332 x 291 

points in the horizontal. The finest grid resolutions in the x- and y- directions are 34m and 29m, 

respectively, and the coarsest resolutions are 4895m and 3380m, respectively. For this CBOFS2 

grid, unfortunately, due to the presence of many near-radial (as opposed to near-axial) tributaries, 

only 20.5% of the grid points are wet, implying that the vast majority of the points are land 

points and ROMS computes solutions on both sets of points without any discrimination. 

The vertical grid is a terrain following, sigma coordinate system (Song and Haidvogel, 1994) 

consisting of 20 model levels. The true vertical depth z (in meter) is related to the sigma level, σ 

for a given bathymetric water depth, h (relative to model datum) through the following 

formulation: 

z = z0 + η(t)·[1 + z0/h] with z0 = σ hC + (h - hC) Cσ ,

where σ lies within the interval [-1,0] and is equally spaced. In the above formula, 

hC=min(hmin,Tcline) with hmin, Tcline being the globally minimum bathymetric depth and a guessed 

depth of the thermocline, respectively and, η(t) is the time-dependent water level/free-surface 

elevation (at the horizontal geographical location associated with the depth, h). The stretching 

function Cσ is given by 

Cσ = (1 - θb) P(σ) + θb R(σ) 

where P(σ) = sinh(θs σ)/sinh(θs) and R(σ) = tanh(θs(1⁄2 + σ))/2tanh(θs/2) – 1⁄2 with θb, θs being 

grid stretching parameters associated with the ocean bottom and ocean surface vicinities 

respectively. Numerical experiments showed that for the constant density (Section 3), synoptic 

hindcast (Section 4) and semi-operational (Section 5) CBOFS2 set-ups, the optimal values for 

the parameters θb, θs and Tcline were 0.95, 4.5 and 10m respectively. 

The CBOFS2 bathymetry was formed by numerically interpolating National Ocean Service 

(NOS) bathymetric soundings on to the model grid nodes via an inverse square distance 

weighted interpolation. When unsmooth bathymetry related numerical instabilities occurred in 

the CBOFS2 simulations, the bathymetry was smoothed locally (as opposed to globally). This 

approach was adopted to maintain the true bathymetry of the Chesapeake Bay whenever 

possible. A plot of the model bathymetry is shown in Figure 1. 
5 

A comparison of the water levels with and without the ROMS wetting/drying algorithms showed 

that they were quite similar to each other. However, in order to generate the former, it was 

required to use significantly smaller time steps to maintain numerical stability. Hence, the 

CBOFS2 was run without the use of wetting/drying and the model bathymetry was truncated at a 

minimum depth of 2m globally which also improved computational efficiency. 
6 
7 

3. CONSTANT DENSITY TIDAL SIMULATION 

As the primary use of CBOFS2 will be to support the marine navigational community, tidal 

water levels and currents must be accurately modeled. Therefore, in order to validate these 

fields, a constant density tidal simulation from January 01, 2000 – February 29, 2000 was 

performed. This simulation was run without specifying river forcing, 

meteorological/atmospheric forcing or any non-tidal open ocean boundary forcing (for 

temperature, salinity and non-tidal water levels). The initial fields of temperature and salinity 

were defined to be 15 °C and 35 PSU, respectively, and these values were maintained throughout 

the simulation. The only model forcing employed was the tidal forcing at the open ocean 

boundaries. 

 

The tidal forcing at the southern open boundary was enforced via the use of water level and 

barotropic current harmonic constituents from an ADCIRC model (Luettich et al., 1992) 

database generated at NOAA/NOS/Office of Coast Survey (OCS)/ Coast Survey Development 

Laboratory (CSDL) (Feyen, 2008) using the EC2001 grid, (EC2001, 2009). This database 

consisted of 37 harmonics including the long-term SA and SSA constituents which were not 

employed in the simulations as these include the effects of meteorology. The harmonic 

constituents were bilinearly interpolated (using Matlab) from the EC 2001 grid on to the 

CBOFS2 grid. For the C & D canal, the water level harmonic constituents were prescribed 

using those at Reedy Point, DE from the NOS/CO-OPS database (NOAA Tides & Currents, 

2009a); the currents harmonic constituents were from a harmonic analysis of observed currents 

associated with NOS station 154 located at the Delaware Bay entrance to the C & D canal 

(Browne and Fisher, 1988). The currents were first rotated to be in alignment with the axis of 

the C & D canal and the major component was harmonically analyzed using the T_Tide Matlab 

software package (T_Tide, 2007). The cross-axis component of the barotropic current was 

assumed to be zero. The observed data was at an approximately 6m depth which is midway 

down the water column in the C & D canal the averaged depth of which is approximately 12m. 

It was attempted to examine the sensitivity of the CBOFS2 tide predictions for water levels to 

two factors: 

(1) any mismatch in the harmonic constituents between those from the ADCIRC database and 

observations for water levels (corresponding observed harmonics for barotropic currents are 

not available) and, 

(2) the various open ocean boundary condition options available in ROMS for the inclusion of 

tides. 

To examine the effects of (1), the ADCIRC database water level harmonics were forced to match 

those from NOS/CO-OPS observations at Duck, NC and Ocean City, MD via a linear and an 

exponentially damped matching function on the southern open boundary. The independent 

variables in these functions were the two arc distances (of a particular CBOFS2 grid point along 

the open boundary) from Duck, NC and Ocean City, MD. Hence, if L is the total arc distance 

along the CBOFS2 southern open boundary (for wet-points only) and x is the distance of a 

particular grid point from Duck, NC, then the matching functions for the linear formulation 

respectively are 1-x/L and x/L and, the corresponding ones for the exponential formulation are ℮-
8 

Ax and ℮-A(L-x) where A is a user-defined exponent. Therefore, at these extreme locations, the 

water level harmonics exactly matched the observed values and thereafter they gradually 

asymptoted towards the (interpolated) values from the ADCIRC database. 

ROMS has a suite of open boundary conditions for tidal applications and here, three of the most 

common options have been examined; they are (i) Chapman-Flather (traditional, Chapman, 1985 

and Flather, 1976), (ii) Clamped-Reduced Flather and (iii) Clamped-Reduced for water levels 

and the barotropic currents respectively. For choices (ii) and (ii) it is not necessary to supply 

any barotropic currents. 

The tides in ROMS are ramped-up using a hyperbolic tangent function so that they reach 99.0% 

of their full strength after 2.65 days. The bottom drag was prescribed via a quadratic formulation 

and its coefficient was taken to be 0.005 (although several values in the range 0.001-0.010 were 

examined), which gave the best overall water level predictions. Spatially variable bottom 

friction coefficients/formulations were not examined. The momentum and tracer advection 

terms were numerically discretized using the ROMS upstream-biased advection schemes which 

alleviated the need for artificial/numerical horizontal viscosity and diffusivity to eliminate 

spurious spatial numerical oscillations. The vertical eddy-viscosity was prescribed by the 

Mellor-Yamada 2.5 closure scheme and its background value was set to 1.0 x 10-8 m

2

/s. For the 

baroclinic currents, temperature and salinity, the standard radiation open ocean boundary 

conditions were applied both along the southern and C & D canal boundaries. The model was 

run with a 30 second baroclinic time step and a 1.5 second barotropic time step in a Message 

Passing Interface (MPI parallelization environment using 96 processors. 

The outcome of the above numerical experiments was measured by examining the Root-MeanSquare (RMS) differences in the water levels at one grid point into the domain from the southern 

open boundary grid nodes corresponding to Duck, NC and Ocean City, MD on the southern 

boundary. The differences taken were between the ROMS-generated water levels and those 

predicted from the harmonic constituents associated with the open boundary grid nodes. The 

eastern open boundary at Reedy Point, DE was treated with Flather-Chapman boundary 

conditions and no matching of tidal harmonic constituents was necessary. The use of other 

boundary condition options available within ROMS for the C & D canal open boundary did not 

yield numerically stable computations and even with the present choice, a reduced global time 

step needed to be adopted in order to maintain stability. The RMSE differences clearly showed 

that the Flather-Chapman option generated the largest differences and the Clamped-Reduced 

option generated the least differences; furthermore, for each choice of boundary condition, the 

exponentially damped matching of harmonic constituents produced smaller errors than those 

with either no matching or with linear matching. The optimal exponent, A for the exponential 

matching function was found to be -5.0. Therefore, it was decided to adopt the ClampedReduced option for the southern open boundary together with the exponentially damped 

harmonic constituent matching. These reduced boundary conditions however were developed 

ideally for two-dimensional, barotropic ROMS applications (Ocean Modeling Discussion, 2008) 

and their validity for and effects on three-dimensional baroclinic ROMS applications are not yet 

fully known. 
9 

3.1. Water Level Comparisons and Skill Assessments 

The water level predictions from CBOFS2 were compared with tidal predictions (from the 

NOS/CO-OPS harmonic constituents (NOAA Tides & Currents, 2009a)) at the station locations 

(corresponding to those maintained by NOS/CO-OPS) shown in Figure 2. The 

differences/discrepancies between the CBOFS2 predictions and the tidal predictions will 

hereafter be referred to as errors. 

First however, the CBOFS2 water level time-series at each of the stations in Figure 2 was 

harmonically analyzed using the NOS harmonic analysis software (Zervas, 1999) and compared 

with those from NOS/CO-OPS for the M2, N2, K1, O1,P1 and L2 constituents (as they are the 

most dominant). The outcome of the harmonic analysis is provided in Tables A1 and A2 in 

Appendix A where the constituent amplitudes are in meters and the phases in hours. The errors 

in constituent amplitudes and phases are plotted in Figures 3 and 4. The amplitude errors show 

that (i) as expected, the largest errors are for the M2 constituent, (ii) the largest errors are at the 

extremeties of the wet-point computational domain (in the C & D canal, entrance to the Bay and 

 

Figure 2. CBOFS2 water level stations archive locations (and the NOS/CO-OPS identification 

 numbers) for comparison with tidal predictions in the constant density simulation. 
10 

at the beginnings of the tributaries) and (iii) there is no strong pattern to the spatial distribution of 

the errors and they assumed both positive and negative values. The phase errors too show both 

positive and negative values but their magnitudes are not clearly correlated with any particular 

constituent(s) and the largest errors tend to be at the extremeties of the Potomac and York River 

tributaries where they show that CBOFS2 lags the predicted phase values. As with the 

amplitudes, the phase errors do not show a strong pattern to their spatial distribution within the 

Bay. 

Figure 3. Amplitude differences (CBOFS2-observations in cm) for M2, N2, K1, O1, P1 and L2 

 harmonic constituents in the constant density CBOFS2 simulation. 

The Root Mean Square Errors (RMSE) for the water levels are given in Table A3 of Appendix A 

and they have also been plotted in Figure 5. Table A3 also provides the high and low water 

amplitude errors and the Central Frequency (CF) associated with each of these three errors. 
11 

These metrics were computed using the NOS/OCS/CSDL ocean model skill-assessment software 

package (Zhang, et al., 2009). The NOS skill-assessment criteria for water level error is that (a) 

their RMSE be less than 15cm at least for 90% of the time (that is, with CF(15cm) > 90%) and 

(b) their phase difference be less than 15 minutes also for at least 90% of the time. 

Figure 4. Phase differences (CBOFS2-observations in hours) for M2, N2, K1, O1, P1 and L2 

 harmonic constituents in the constant density CBOFS2 simulation. 

Table A3 shows that only about half of the stations satisfy the RMSE error criterion although 

eleven out of fifteen stations satisfy the criterion for the high and low water amplitude errors. It 

is also seen that whenever the RMSE and the high and low water amplitude errors are well below 

the 15 cm limit, the CF parameter assumes values above 90%. 
12 

For oscillatory/periodic signals such as tidal water level and current time-series, the use of 

RMSE provides only a limited picture of the error content. What would be more pertinent would 

be to split the RMSE into an amplitude component and a phase component. Given say two water 

level time-series, it is possible to split the error by translating one series relative to the other (as a 

pair of autocorrelation functions) and estimating a RMSE for each translation and examining its 

structure. If this RMSE (a) forms a smooth curve and (b) has a single, unique, global minimum 

then at this minimum, as shown in Figure 6, the x-abscissa is the phase component of RMSE 

(phase error) and the y-abscissa is the amplitude component of the RMSE 

Figure 5. RMS water level errors (in cm) for the constant density CBOFS2 simulation. 

(amplitude error). Conditions (a) and (b) also ensure that the two sets of time-series are 

composed of the same set of tidal harmonic constituents. Such RMSE translation curves were 
13 

calculated for each of the water level archive stations given in Figure 2 using a translation 

interval of 1-minute and the resulting curves are given in Figure 7 and each of them satisfies both 

conditions (a) and (b). The resulting amplitude and phase error components are also given in 

Table A3 of Appendix A and are plotted in Figures 8. 

Figure 6. Splitting methodology of the RMS error into an amplitude component and a phase 

component. Here, x-axis annotation of phase variation or difference is equivalent to 

the amount by which the two water level time-series have been translated relative to 

each other. 

Although the raw RMSE (Figure 5) shows that it is frequently above the allotted 15 cm limit, 

when decomposed into its amplitude and phase components, it is seen that a significant 

contribution to it comes from the phase error and that the amplitude component is below 15 cm. 

The phase error components tend to be mainly positive implying that CBOFS2 leads the tidal 

prediction. The raw RMSE, amplitude and phase error components are smallest in the vicinity of 

the mouth of the bay. It is seen that the requirement of the phase error to be less than 15 

minutes/0.25 hours (for at least 90% of the time) is rarely met and perhaps this requirement is 

excessively stringent. Furthermore, the raw RMSE is seen to increase when moving up the bay 

and up the (James and Potomac) tributaries but their amplitude components only show a similar 
14 

trend for the former (up the Bay) and not for the latter (up the tributaries) ; the phase error 

component however, while showing a similar trend, also grows rapidly when moving up the 

tributaries due to an expected rapid growth in tidal phase between stations 8638433 and 8638489 

and stations 8635150 and 8594900 as documented, for example, in Browne and Fisher (1988) 

and, which CBOFS2 is incapable of capturing. The physical reason for this rapid growth in 

phase could be due to the curvature of the tributaries and/or the bottom roughness (sediment type 

for example) and/or the local bathymetric features. 

Figure 7. CBOFS2 RMSE translation curves for the comparison stations given in Figure 2. 
15 

Figure 8. The amplitude error (in cm) and phase error (in hours) components of the RMS errors 

 associated with the water levels for the constant density CBOFS2 simulation. 

3.2. Currents Comparisons and Skill Assessments 

The stations locations for comparison of currents are shown in Figure 9. These stations 

correspond to (i) those maintained by the NOS/CO-OPS/Currents Measurements Interface for 

the Study of Tides program (CMIST, 2009) at which currents at high vertical (< 1.0 m) and 

temporal (usually 6-minute) resolution are observed and archived and (ii) those from the 1981-

1983 NOS Chesapeake Bay Circulation Survey (Browne and Fisher (1988)) which are usually 

available only at a few vertical depths. The currents comparisons were performed at 4.6m (15 ft) 

which is considered to be the nominal ships draft. The predicted tidal currents were obtained by 

using the harmonic constituents at these station locations derived by running the NOS harmonic 

analysis software on the CMIST and the 1981-1983 NOS observed current time-series data. 

As with the water levels, the amplitude and phase errors associated with the M2, N2, K1 

harmonic constituents (as they are the most dominant) for the true eastward (U) and true 

northward (V) currents are plotted in Figures 10 and 11 and are listed in Tables B1-B4 in 

Appendix B (which also contain the O1, P1 and L2 constituents). 
16 

Figure 9. CBOFS2 currents stations archive locations for comparison with tidal predictions 

in the constant density simulation. 

The greatest current amplitude errors are seen for the M2 constituent which is the most dominant 

and there is no strong pattern to the spatial distribution of the amplitude or phase errors. The 

errors however for stations cb0601 and cb1301 are excessively large because the former is in a 

narrow channel which the CBOFS2 grid cannot resolve and the latter is within the C & D canal 

the dynamics of which are modeled in a limited manner due to the use of open ocean boundary 

conditions and the inability to account for the full interaction with Delaware Bay. 
17 

Figure 10. M2, N2 and K1 constituent CBOFS2 amplitude (in cm/s) and phase (in hours) errors 

 (CBOFS2 minus prediction) for the true eastward current component in the constant 

density simulation. 
18 

Figure 11. M2, N2 and K1 constituent CBOFS2 amplitude (in cm/s) and phase (in hours) errors 

 (CBOFS2 minus prediction) for the true northward current component in the constant 

density simulation. 
19 

Figure 12. RMS current speed (left, cm/s) and current direction (right, degrees) errors (from the 

 CSDL skill-assessment software package) at a depth of 15 feet (4.6m) for the 

 CBOFS2 constant density simulation at the NOS/CO-OPS/CMIST observational 

 stations. 

The CBOFS2 versus predicted tidal currents comparisons are summarized in Tables B5-B7 in 

Appendix B. The NOS target skill-assessment criteria for currents comparisons is for (a) the 

speeds to agree to within 26 cm/s for at least 90% of the time (that is, CF(26cm/s) > 90%) and 

(b) the directions of the major currents components to agree within 22.5o for at least 90% of the 

time (that is CF(22.5o

) > 90%). The metrics in these tables too were generated using the CSDL 

skill-assessment package. Only the CMIST stations were employed for the comparisons as they 

had better quality data, for longer durations in time and which was also better resolved with 

depth. 

Table B5 shows that the RMSE of the currents speeds satisfy the NOS criteria except for those at 

stations cb1301 (Chesapeake City, MD located within the C & D canal) and station cb0601, 

which is located within a narrow channel which the CBOFS2 model grid is unable to resolve. 

This also true for the maximum flood and ebb current amplitude errors. 
20 

Table B6 shows that the RMSE of the currents directions including those at maximum flood and 

maximum ebb and all of them meet the NOS criteria stated above. 

Plotted in Figure 12 are the RMS currents speed and direction errors given in Tables B5 and B6. 

As explained above, the largest errors are at stations cb0601 and cb1301 and with the exception 

of these two stations, the errors remain well below the critical limit throughout the Bay; and, 

there is not a strong pattern to their spatial distribution and there is no growth in their magnitudes 

when moving up the Bay - although they show somewhat of a decrease in value. 

The major current component (in the Principal Current/Flood Direction) RMSE, its amplitude 

contribution and its phase contribution comparisons are given in Table B7 and they are plotted in 

Figure 14. The corresponding RMSE translation curves for the comparison stations are shown in 

Figure 13 and they again exhibit smooth behaviors and each contain a unique, global minimum 

thus rendering the RMSE splitting method valid. 

 

Figure 13. RMSE translation curves for the CBOFS2 major current component for the 

comparison stations. 

The greatest amplitude error components are at the same stations mentioned above (cb1301 and 

cb0601), which miss the NOS criteria although not by very much whereas the other stations meet 

the NOS criteria quite well. The phase error component is not only largest at these two stations 

but also at station CHB0301 and the examination of other depths at this station showed similar 

trends throughout the water column. The data itself was found to be of good quality, and the 

CBOFS2 bottom depth was also in close agreement with the observed depth. The phase errors 

indicate that the CBOFS2 currents lag relative to the predicted currents. This is opposite to the 

phase error trend seen in the water level comparisons. 

Plotted in Figure 15 are the CBOFS2 major-direction current components against depth at three 

separate time snapshots and their profiles ± 1 hour relative to these times (in order to account for 
21 

tidal phase errors in CBOFS2). Station cb1301 was excluded as it is based on Side Scan Sonar 

measurements. The predicted curve is the thick black line and it was generated using harmonic 

constituents extracted from observations (via the NOS software) at each of the observational 

stations and depths. They show in general that CBOFS2 profiles without a time shift are the 

ones that are best correlated with the predictions and that the predictions contain much more 

vertical stratification specially in the near-surface and near-bottom regions. The reason for the 

lack of stratification in CBOFS2 is not known but it may be due to the use of the algebraic 

Mellor-Yamada 2.5 vertical eddy-viscosity closure scheme. 

Figure 14. The amplitude (left, cm/s) and phase error (right, hours) components of the RMS 

 errors associated with the major current in the constant density CBOFS2 simulation. 
22 

 

Figure 15. Vertical structure of major-direction currents for the constant density CBOFS2 simulation (black – NOS/CO- OPS/  CMIST prediction, blue – CBOFS2, red – CBOFS2 with 1 hr. phase lead, green – CBOFS2 with 1 hr. phase lag). 

 January 20, 2000 0000 hrs. 

 February 05, 2000 0000 hrs.  February 20, 2000 0000 hrs. 
23 

4. SYNOPTIC HINDCAST SIMULATION 

The synoptic hindcast simulation to validate the full suite of CBOFS2 output fields (water levels, 

currents, temperature and salinity) was run from June 01, 2003 – September 01, 2005. This time 

period was selected because: (i) it is sufficiently long (27 months) to show seasonal variations; 

(ii) it has both very dry (low river discharge) and wet (high river discharge) periods as seen 

from the total river discharge plot in Figure 16; and (iii) it includes an extreme meteorological 

event (that is, Hurricane Isabel) as shown in Figure 17. These diverse conditions will not only 

serve to validate the physics of the model, but will also test the numerical stability associated 

with the CBOFS2. 

Figure 16. Total river volume discharge for the CBOFS2 model domain spanning 2003-2005. 

Figure 17. Wind speed plot for August-October, 2003 at Chesapeake Light, VA NOAA/National 

 Data Buoy Center (NDBC) station showing hurricane Isabel. 
24 

4.1. Initial Conditions and Model Forcings 

The model was spun-up from rest and the initial temperature (T) and salinity (S) fields were 

generated by (a) interpolating the World Ocean Atlas 2001 (WOA 2001, Conkright, et al., 2002) 

monthly climatological T and S values on to the CBOFS2 grid in the horizontal and the vertical 

for the mid-lower part of the Bay (below the Patuxent River), (b) interpolating the Chesapeake 

Bay Program (CBP, 2009) T and S values for the upper part of the Bay (above the Patuxent) and 

then (c) melding (a) and (b) in a smooth and continuous way through bilinear interpolation. The 

reason for using Bay Program T, S values for the upper segment of the Bay was that in this 

region, unlike in the mid-lower Bay, significant differences were seen between the Bay Program 

and WOA 2001 T, S values (which had good coverage in the lower Bay). 

For the river forcing, the volume discharges were obtained from the US Geological Survey 

(USGS) historical data (USGS, 2009) and the river T, S values were obtained from the Bay 

Program stations closest to the corresponding USGS gauge locations. 

The meteorological forcing fluxes (wind stresses and net heat flux) in CBOFS2 were computed 

within ROMS using its bulk flux formulation and the input fields of the wind speed components, 

air temperature, air pressure, air relative humidity, net shortwave radiation and downward 

longwave radiation were primarily taken from the 32 km resolution North American Regional 

Re-analysis products (NARR, 2009). These 3-hourly NARR fields for winds, air temperature, 

air pressure and relative humidity (via the dew point) were enhanced by spatio-temporally 

blending them with hourly observed historical data within the Bay and on the shelf from the 

following NOAA/NDBC stations (NDBC, 2009): TPLM2 (Thomas Point, MD), CHLV2 

(Chesapeake Light, VA), 44014 (east of Virginia Beach, VA), 44009 (Delaware Bay southeast 

of Cape May, NJ) and DUCN7 (Duck Pier, NC). These stations together with the NARR grid 

points used for the generation of the meteorological fields are plotted in Figure 18. In order to 

increase the influence of the NDBC stations in the creation of these fields (via spatial 

interpolation), some NARR data points in the vicinity of the former were removed from the 

process as also depicted in Figure 18. Furthermore, in the creation of the wind, air temperature, 

dew point/relative humidity and net shortwave radiation fields, only water points on the NARR 

grid were employed as pronounced differences in them were seen between on-land points and insea points. 

In addition, upon comparison with observations at NDBC station 44009, it was found that the 

optimal level of net shortwave radiation to use was 80% of the value provided by NARR and 

therefore a global scaling factor of 0.8 was applied to the radiation flux employed in CBOFS2. 

Similar comparisons for air temperature and dew point with this NDBC station yielded minor 

global adjustment factors/offsets which were applied to the fields before being used within 

CBOFS2. 

For the open ocean boundary conditions along the southeastern boundary, the T and S values 

were taken from the WOA 2001 monthly climatology. The non-tidal water levels were those 

extracted from the NOS/CO-OPS Ocean City, MD and Duck, NC stations. These values were 

then distributed along the boundary nodes via linear interpolation using the arc distances from 

the two end points as also described in Section 3. The tidal component of the forcing was 
25 

generated in exactly the same manner as for the constant density simulation and thereafter the 

two contributions were combined at each of the boundary grid points. For the C & D canal open 

boundary, the T, S values were derived from the USGS station 01482800 which lies within 

Delaware Bay, the full (tidal plus non-tidal) water levels were prescribed using the observations 

at the NOS/CO-OPS Reedy Point, DE station and the barotropic currents were obtained from a 

prediction using the analyzed tidal harmonic constituents from NOS station 154 as also 

explained in Section 3. 

Figure 18. NARR (blue circles) and NDBC (red squares) data points used in the creation of the 

 wind, air temperature, relative humidity/dew point and net shortwave radiation fields; 

 the thick black line is the southeastern open boundary of the CBOFS2 computational 

 domain. 

The model was run with a 15 second baroclinic time step and a 0.75 second barotropic time step; 

this time step was half of that used for the constant density simulation. This reduction in its 

value was necessary to maintain the numerical stability of CBOFS2 (due to the fine grid 

employed to resolve the C & D canal when density effects were included). The model was run 

with MPI parallelization using 96 processors and in 15-day segments, each of which took 
26 

approximately 150 minutes to complete thereby yielding a highly efficient computational effort 

ratio of 1:144. The ROMS model configuration for this case was identical to that for the 

constant density simulation with exception that (i) for the vertical eddy-viscosity model choice, 

the GLS k-ω model was employed as it generated the best overall vertical T and S stratification; 

(ii) several additional model forcings (for example, river forcing, etc.) were included; and (iii) as 

described previously, a realistic T-S field was employed in the model initialization. In the 

application of the model forcings, the river volume discharges, winds in the meteorological 

forcing and the non-tidal water levels in the open boundary forcing were ramped up linearly in 

time during the first five days past model initialization. 

CBOFS2 ran successfully for the entire 27-month period without experiencing any numerical 

instabilities thereby illustrating that this modeling set-up is capable of withstanding a diverse 

range of environmental conditions observed in the Bay. During the computations, the maximum 

u-component, v-component, w-component of the Courant-Freidrichs-Lewy (CFL) numbers as 

well as the maximum of their sum were monitored to examine their numerical stability. Due to 

the (i) use of the upstream-biased advection schemes in the horizontal in ROMS and hence the 

lack of a need for the use of explicit horizontal viscosity to control spatial numerical oscillations 

and the (ii) use of an implicit vertical viscosity formulation in ROMS (solved locally via a tridiagonal solver), the CFL number alone is an adequate measure of the numerical stability 

associated with the overall model algorithm. Plotted in Figure 19 are the time-series for each of 

the CFL number components and it shows that (a) the total maximum CFL number is well below 

unity for the vast majority of the time and when it exceeds this limit, it does so for very brief 

intervals in time and in highly localized regions in the model grid (hence, not rendering CBOFS2 

numerically unstable and causing model blow-ups), (b) the largest contribution to the total CFL 

number comes from the w-component and (c) the u-component and v-component are 

significantly smaller than the w-component. It has also been found that the largest CFL numbers 

usually occur within the C & D canal where the mesh is quite fine. 

Figure 19. CFL number time-history for the synoptic hindcast simulation. 
27 

4.2. Water Level Comparisons 

The water levels were compared with observed values at the NOS gauges shown in Figure 20. 

Figure 20. Water level and currents stations archive locations for the synoptic hindcast CBOFS2 

simulation for comparison with observations. 

The raw RMS water level errors plotted in Figure 21 have been evaluated using observations 

from the NOS/CO-OPS database (NOAA Tides & Currents, 2009b). They show that the errors 

are greater in magnitude than those for the constant density case (at coincident locations) and the 

largest ones are in the upper bay and up the Potomac River tributary at Washington DC. 

As before, employing the translational curve method, these RMS errors were split into their 

amplitude and phase components and they are plotted in Figure 23. The RMSE curves 

themselves are plotted in Figure 22 and they satisfy the error splitting validity requirements of 

being smooth in space and having a single, unique global minimum. 
28 

Figure 21. RMS water level errors (in cm) for the synoptic hindcast CBOFS2 simulation. 

The distribution of the amplitude and phase errors in space show that they grow when moving 

towards the northern extent of the Bay and the smallest errors are in the vicinity of the Bay 

mouth. In addition, the phase error grows in magnitude when moving up the Potomac River 

tributary towards Washington DC. Similar inferences were made regarding the water level 

errors in the constant density simulation. 
29 

Figure 22. CBOFS2 synoptic hindcast RMSE translation curves for the comparison stations. 
30 

Figure 23. The amplitude error (cm) and phase error (hours) components of the RMS errors 

associated with the water levels for the synoptic hindcast CBOFS2 simulation. 

The errors associated with the CBOFS2 water levels are summarized in Table 1. The raw RMS 

water level errors indicate both an improvement and a degradation relative the corresponding 

errors for the constant density simulation. For the stations where the RMS errors violate the 

NOS criterion (stations 8574070, 8574680, 8594900 and 8573927), generally, the synoptic 

hindcast errors exceed those of the constant density simulation. In particular, the amplitude 

components of the errors still remain above 15 cm whereas for the constant density tidal 

simulation, practically all of the stations generated errors less than 15 cm. The phase 

components of the errors however show a marked improvement over their constant density 

counterparts (although still failing to meet the stringent 15 minute/0.25 hour NOS skill 

assessment criterion). These CBOFS2 phase errors are always positive and hence produce a 

phase lead relative to observations. In terms of the Central Frequency, CF for the RMSE, only 

about five stations satisfy the CF(15cm) > 90% criterion and for the high and low water 

amplitudes, they are five and ten stations respectively. Therefore, the synoptic hindcast 

CBOFS2 water level predictions have a bias such that the low water amplitudes are predicted 

better than the high water amplitudes and such a bias was not seen in the constant density case 

(where the proportion of high and low water amplitudes satisfying CF(15cm) > 90% was the 

same). As expected, it is the stations with the smallest errors that are most likely to have 

CF(15cm) > 90%. 
31 

Table 1. Water level error summary for the synoptic hindcast CBOFS2: Tidal range (cm), RMS 

 error (cm) and its Central Frequency (CF), high water amplitude error (AHW_err, cm) 

 and its CF, low water amplitude error (ALW_err, cm) and its CF (all from the CSDL 

 skill-assessment software package), amplitude component of the RMSE (cm) and the 

 phase component of the RMSE (hours). 

Station Range RMSE CF AHW_err CF ALW_err CF Amp_err Phs_err 

8574070 57.9 23.2 37.2 25.9 7.0 18.5 39.9 22.0 0.65 

8632200 79.2 6.8 96.5 7.3 96.1 5.5 98.4 6.7 0.07 

8577330 35.7 9.1 91.2 10.4 88.4 6.7 96.1 8.7 0.38 

8573364 36.9 13.1 76.2 16.1 60.6 8.2 93.4 12.7 0.45 

8575512 29.6 10.3 87.4 10.7 85.5 8.5 92.7 10.1 0.35 

8571559 62.5 11.0 85.9 13.2 79.0 7.8 93.9 9.7 0.45 

8636580 34.7 7.5 95.0 6.7 95.9 7.2 95.3 7.3 0.02 

8638610 74.1 9.5 88.3 12.0 81.5 6.1 97.8 8.1 0.37 

8574680 34.7 17.9 54.5 21.0 30.7 12.5 79.1 17.8 0.33 

8635750 37.8 8.0 93.7 9.3 91.5 6.3 96.6 8.1 0.20 

8638863 77.7 7.5 95.3 9.6 91.4 7.1 96.3 7.3 0.13 

8571892 49.4 12.2 80.5 11.3 85.7 8.3 93.0 10.0 0.75 

8594900 85.0 31.1 48.5 20.2 34.3 18.1 47.6 20.2 1.60 

8573927 87.2 19.1 55.7 14.7 67.8 16.8 53.9 16.6 0.63 

4.3. Currents Comparisons 

The accuracy of the CBOFS2 currents was evaluated at the NOS/CO-OPS/CMIST stations 

shown in Figure 20. The Chesapeake Bay Observing System (CBOS) station had time-series 

data but it was of poor quality and different data segments were inconsistent with each other. 

These CMIST stations were selected because they contained observed data in the 2003-2005 

period of acceptable quality. The currents comparisons are summarized in Tables 2 and 3 and 

plotted in Figure 23. 

Table 2 shows that the current speed RMS errors satisfy the NOS skill criterion (CF(26 cm/s) > 

90%) at all of the stations and except at station cb1301 (Chesapeake City, MD along the C & D 

canal), where it is an improvement over its constant density counterpart. The same could be 

said for the current direction RMS errors given in Table 3 in that all of the stations satisfy the 

NOS skill criterion (CF(22.5o

) > 90%). The current speed amplitudes and directions at flood and 

ebb too satisfy the NOS criteria for a majority of the stations and that maximum ebb amplitude 

errors are in general greater than those for the maximum flood amplitude. The RMS speed and 

direction errors are plotted in Figure 24 and for the former, the largest error is at station cb1301 

and these errors do not show any particular spatial distribution pattern or behavior. 

Figure 25 shows the RMSE translational curves for the major-current component and again, they 

are smooth in space and they each contain only a single, unique and well defined global 

minimum thus allowing the RMS errors to be split into their amplitude and phase components in 

a reliable manner. The amplitude and phase error components are plotted in Figure 26 and are 

listed in Table 4. 
32 

Figure 24. RMS current speed (left, cm/s) and current direction (right, degrees) errors at a depth 

 of 5m for the CBOFS2 synoptic hindcast simulation at the NOS/CMIST observational 

stations (from the CSDL skill-assessment software package). 

Table 2. Current speed error summary for CBOFS2 synoptic hindcast simulation: RMS of 

current speed error (cm/s) and its Central Frequency (CF), maximum flood current 

amplitude error (AFC_err, cm) and its CF, maximum ebb current amplitude error 

 (AEC_err, cm) and its CF (all from the CSDL skill-assessment software package). 

Station RMSE CF AFC_err CF AEC_err CF 

 cb0801 10.3 98.3 10.8 100.0 8.3 100.0 

CHB0303 10.4 98.6 11.8 100.0 12.4 95.6 

 cb1001 15.6 90.6 12.7 97.1 14.0 94.3 

CHB0305 12.0 97.3 11.0 100.0 18.9 84.8 

 cb1301 20.8 78.6 13.0 95.3 27.8 54.5 

Table 3. Current direction error summary for CBOFS2 synoptic hindcast simulation: RMS of 

 current direction error (degrees) and its Central Frequency (CF), maximum flood current 

 direction error (DFC_err, degrees) and its CF, maximum ebb current direction error 

 (DEC_err, degrees) and its CF (all from the CSDL skill-assessment software package). 
33 

Station RMSE CF DFC_err CF DEC_err CF 

 cb0801 10.0 94.0 12.8 93.1 19.8 77.8 

CHB0303 4.9 99.6 10.9 93.3 9.7 97.1 

 cb1001 11.2 96.9 8.7 100.0 10.4 95.6 

CHB0305 2.8 99.7 16.6 81.5 18.2 84.8 

 cb1301 6.9 99.9 0.6 100.0 0.5 100.0 

Figure 25. CBOFS2 synoptic hindcast RMSE translation curves for the major-current component 

at the comparison stations. 

Table 4 shows that the major current component errors (both its RMSE and amplitude 

component) satisfy the NOS acceptable limit of being less than 26 cm/s. For cb0801, the 

amplitude error is larger than its constant density counterpart but the phase component is much 

smaller and the error at this station is purely based on the amplitude. At station cb1301, both the 

amplitude and phase errors are an appreciable improvement over their constant density 

counterparts. With the exception of station CHB0303, the phase errors are almost always in 

compliance with the NOS acceptable limit of being less than 15 minutes/0.25 hours and unlike 

for the constant density case, here the phase errors are primarily positive implying that CBOFS2 

exhibits a phase lead relative to the observations. 

A plot of the major current amplitude and phase errors are given in Figure 26. The amplitude 

error plot contains a weak and non-monotonic trend showing an increase in error when moving 

up the Bay but the phase errors do not show a perceivable pattern in their spatial distribution. 
34 

Figure 26. The amplitude (left, cm/s) and phase error (right, hours) components of the RMS 

 errors associated with the major current in the synoptic hindcast CBOFS2 simulation. 

Table 4. Major current error summary for the synoptic hindcast simulation: raw RMS error 

 (cm/s), the amplitude component of the RMSE (cm/s) and the phase component of the 

 RMSE (hours). 

 Station RMSE Amp_err Phs_err 

 cb0801 12.6 12.6 -0.02 

 CHB0303 11.5 9.2 0.63 

 cb1001 18.6 18.5 0.17 

 CHB0305 15.6 15.4 0.35 

 cb1301 22.3 20.8 0.25 

Figure 27 shows the major direction current vertical profiles at four different time snapshots (and 

± 1 hour relative to them) for some of the currents comparisons stations. Stations cb1301 and 

cb1001 were excluded as its data is based on Side Scan Sonar measurements. It is seen that 

unlike for the constant density case, there is significantly more stratification associated with the 

CBOFS2 predictions and that they are generally in agreement with observations. This could be 

due to the inclusion of T and S in the computations and the use of the GLS k-ω vertical eddyviscosity turbulence closure scheme. Observations still however show a greater degree of 
35 

vertical stratification than the model predictions. The least agreement with observations is seen 

to be for station CHB0305. In most cases, it is the non-displaced (in time) CBOFS2 predictions 

that are in closest agreement with the observations (as also was the case in the constant density 

simulation). 

Figure 27. Vertical structure of the major-direction currents for the synoptic hindcast CBOFS2 simulation ( black – NOS/CO-  OPS/CMIST obs., blue – CBOFS2, red – CBOFS2 with 1 hr. phase lead, green – CBOFS2 with 1 hr. phase lag). 
36 

4.4. Temperature and Salinity Comparisons 

The CBOFS2 temperature and salinity predictions were evaluated against Bay Program 

observations at the locations shown in Figure 28. At each of these stations, the Bay Program 

database provides temperature and salinity (in addition to other biogeochemical variables such as 

Dissolved Oxygen, Phosphorous, Nitrogen, etc.) both in time and in depth; the temporal 

resolution of the observations is roughly bi-weekly and they are well resolved in the vertical. 

The comparison of the CBOFS2 T, S values with those from the Bay Program were carried out 

for the period January 01, 2004 – September 01, 2005 where the first seven months of the 

simulation was discarded to allow for the model adjustment/spin-up. 

Figure 28. Temperature and salinity stations archive locations for the CBOFS2 synoptic hindcast 

simulation. Locations in red are stations at which local and global error analyses 

were performed (Figures C1-C10 in Appendix C). 
37 

At each of the stations in Figure 28, the errors/differences in T and S between CBOFS2 and the 

Bay Program values were evaluated as a function of both space and time (encompassing the 

same spatiotemporal extent as the T/S fields themselves); the CBOFS2 fields were interpolated 

in space and time on to the Bay Program locations using Matlab. Comparisons were made at 

common depths only. For measurement depths greater than model depths, no comparisons were 

made. Hence, these error fields show how the CBOFS2 T and S values evolve (relative to 

observations) spatio-temporally and can thus be considered to be the “local errors” and they also 

yield information about the vertical structure/stratification of the errors and are useful in 

distinguishing systemic errors or inconsistencies associated with modeling set-ups. Error fields 

at ten stations from Figure 28 (shown as red filled circles) are plotted in Appendix C (Figures 

C1-C10). The plots are arranged so that the top most panel gives the observed T values followed 

by the CBOFS2 T values followed by the difference in T between CBOFS2 and observations; 

this sequence is then repeated in the next three panels for S. Generation of these error fields at ± 

1.0 hours to account for tidal phase errors did not alter them in any significant way. The 

following information can be extracted from these ten figures: (1) they clearly show the seasonal 

variations particularly in T and also in S as for example seen in panels one and four in Figure C1, 

(2) the T and S difference plots show both positive and negative values in both time and depth 

and are devoid of systemic trends implying that the CBOFS2 implementation is valid, (3) not 

only the stratifications associated with the T and S fields themselves (for example, strong 

stratification for S in panel four of Figure C3 (panel six) and minimal stratification for T in panel 

one of Figure C4) but those of T and S differences are also clearly seen from these plots – for 

example, in the third panel of Figure C2 it is seen that between December 2004 and February 

2005, the differences in T in the vertical are somewhat constant (that is, a constant shift in 

CBOFS2 T values relative to observations) whereas around July 2005 in Figure C3, strong 

stratification in the S differences are seen where near the surface CBOFS2 is much saltier than 

observations whereas near the bottom, CBOFS2 is much fresher than observations, (4) sporadic 

and intermittent differences in T and S are also captured as shown in panel six of Figure C4 and 

(5) they show the depth differences between the CBOFS2 bathymetry and the Bay Program 

observed bathymetry as for example seen in Figure C8 and the spatio-temporal density 

differences in the number of observations made by the Bay Program as for example seen 

between Figures C8 (higher density) and C9 (lower density/more sparse). 

Plotted in Figure C11 (Appendix C) are the Probability Density Functions (PDF) of the T and S 

errors associated with the above mentioned ten Bay Program stations (Figure 28). The errors for 

T are restricted to be in the interval [-2 o

C, +2 oC] and those for S in [-4 PSU, +4 PSU] and the 

bin widths for the PDF are respectively 0.5 oC and 0.5 PSU. As no discrimination is made 

between the temporal and spatial (vertical) error variations, these histograms therefore display 

the global T and S error structure as opposed to the local structure seen from Figures C1-C10 of 

Appendix C. These PDFs show that: (1) there are stations (for example, T differences of CB7.4, 

CB4.2C T) where the error spread is evenly within the full range ([-2 oC, +2 oC]) and also 

stations (for example, S differences of ET5.2, LE1.3, RET5.2) where their spread is highly 

skewed in either a positive or negative direction; (2) there are stations where the error spread is 

broad (for example, RET 2.4) and also those where the spread is highly localized (for example, S 

differences for RET5.2 and CB2.1); (3) while the T errors normally occupy both positive and 

negative values, there are S errors which are purely negative (for example, RET5.2) or positive 

(for example, LE1.3 and ET5.2); (4) in general the T errors are negative implying CBOFS2 is 
38 

excessively cool and S errors are positive implying CBOFS2 is excessively salty; and, (5) along 

the stem/axis of the Bay, T differences have a broad spread about 0 o

C with a negative bias and 

the S differences have a positive bias implying excessive saltiness on the part of CBOFS2 

predictions but along the tributaries, while the T differences still have the same bias, S 

differences could have either a negative or a positive bias. 

 The local spatio-temporal errors (i) at or near the ocean surface; (ii) at 15-feet (of importance to 

NOS for navigational mariners); and (iii) at or near the ocean bottom were extracted and their 

RMS and mean values were evaluated. The RMS values provide a measure of the average 

deviation of the CBOFS2 predictions relative to the Bay Program data and the mean errors (ME) 

show their bias which is important in discriminating whether the CBOFS2 T and S are either 

warmer/cooler or saltier/fresher respectively than the observations. The CBOFS2 T, S errors are 

summarized in Tables C1 and C2 respectively (in Appendix C) and to identify patterns or trends 

they are also plotted in Figure 29. These errors at the surface, 15-feet depth and bottom for T 

and S are plotted in space in Figures 30 and 31 which are useful for discerning error distributions 

and trends in space within the CBOFS2 computational domain. 

For temperature, Table C1 and Figures 29 and 30 show that: (a) the RMSE T values are between 

0 and 3 °C although the majority of them are between 0 and 2 °C; (b) the ME T values are 

between -1 and 1.5 °C although the majority of them are between -1 and 1 °C; (c) the errors at 

the surface and at 15-feet (4.6m) are similar in magnitude and sign; (d) the largest errors are at 

the ocean bottom (or near it); (e) at the surface and at 15-feet, CBOFS2 is cooler than the 

observations but at the bottom CBOFS2 is warmer relative to the observed values; and (f) there 

is not a strong pattern to the horizontal distribution of errors in space (at any of the three depths) 

but the largest values tend to lie at or near the Bay axis. 

For salinity, Table C2 and Figures 29 and 31 show that: (a) the RMSE S values are between 0 

and 5.5 PSU, although the majority of them are between 0 and 4 PSU; (b) the ME T values are 

between -5 and 4 PSU, although the majority of them are between -2 PSU and 3 PSU; (c) the 

errors at the surface and at 15-feet are similar in magnitude and sign with the exception of 

stations #1 - #9 (that is, those along the Bay axis), where errors at 15-feet exceed those at the 

surface; (d) the largest errors, as for temperature, are at the ocean bottom (or near it); (e) at the 

surface and at 15-feet, CBOFS2 is saltier than the observations but at the bottom, CBOFS2 is 

somewhat fresher relative to the observed values; and, (f) a strong pattern to the horizontal 

distribution of errors in space is not seen but for the surface and 15-foot errors, the largest values 

tend to be along the axis of the Bay. 
39 

Figure 29. Plot of the RMS and mean errors for T and S as listed in Tables C1 and C1 in Appendix C. 
40 

Figure 30. Plot of the RMS and mean errors for T at the surface, at 15-feet and at the bottom. 
41 

Figure 31. Plot of the RMS and mean errors for S at the surface, at 15-feet and at the bottom. 
42 
43 

5. SEMI-OPERATIONAL NOWCAST/FORECAST SIMULATION 

In order to test its viability and accuracy as an OFS, CBOFS2 was run in a nowcast/forecast 

mode and the resulting water levels, currents, temperature and salinity were skill-assessed 

against observations. 

The model initialization fields were from a previous simulation segment brought in via the 

ROMS perfect restart algorithm. For the nowcast, the river forcing (discharges and temperature 

with river salinity assumed zero) was from USGS gauge data, open boundary non-tidal water 

levels were from the Extra-Tropical Storm Surge (ETSS) model products, the open boundary 

temperature and salinity variables were from Navy Coastal Ocean Model (NCOM) and the 

meteorological forcing viable (to be taken as inputs to the ROMS Bulk Flux formulation) were 

from NOAA/NWS/NCEP’s Real Time Mesoscale Analysis (RTMA) model products. For the 

forecast, the river forcing was a persistence from the nowcast values, open boundary non-tidal 

water levels were from ETSS, open boundary temperature and salinity from were NCOM and the 

meteorological forcing variables were from the 12km spatial resolution NOAA/NWS/NCEP’s 

North American Mesoscale (NAM) model. Otherwise, the ROMS model configuration was 

identical to that for the synoptic hindcast simulation. 

The evaluation period was three months from April 20, 2010 to July 20, 2010. The water level 

observations were extracted from NWLON stations, the currents from NOS/CO-OPS/CMIST 

array of stations and the temperature and salinity were from the PORTS stations. Described 

below are the details pertaining to the skill assessment of each of these four physical parameters. 

5.1. Water Level Comparisons 

The water levels were skill-assessed at each of the locations shown in Figure 32 and the derived 

RMSE and CF(15cm) skill metrics (from the CSDL skill-assessment software package) are 

summarized in Tables D1 and D2 respectively of Appendix D. The stations listed in the tables 

span from the south to the north of Chesapeake Bay. 

Table D1 shows that with the exception of station 8594900 (Washington, DC) and station 

8573927 (Chesapeake City, MD) all of the others satisfy the NOS skill criterion of being below 

15 cm for 90% of the time. As in the synoptic hindcast simulation, there is a large error at 

Washington, DC due to poor phase accuracy. The RMSE values at Washington, DC and 

Chesapeake City are similar in values to their synoptic hindcast counterparts. It is seen that the 

nowcast and the 00h, 06h, 12h, 18h and 24h forecast RMSE values are similar in magnitude to 

each other with the latter frequently showing an improvement over the former. 

The Central Frequencies in Table D2 also reflect the inferences made regarding Table D1. The 

lowest CF values are at Washington, DC and Chesapeake City, MD as expected and this metric 

maintains its value (at each comparison station) when moving from a nowcast to a forecast and 

all the way up to a 24-hour forecast. As with the synoptic hindcast simulations, stations with the 

lowest RMSE values tend to possess the highest CF values. 
44 

In summary, the water level RMSE and CF metrics for this semi-operational set-up are as good 

as and if not better (at stations 8577330, 8636580, 8574680, 8635750) than their hindcast 

counterparts. Furthermore, these CBOFS2 water level forecasts are reliable up to 24 hours. 

Figure 32. Locations of the stations where water level (blue circles) and currents (red squares) 

 skill assessments were performed. The temperature and salinity comparison stations 

 are demarcated with a box next them. 

T 

T, S

T, S

T, S 

T

T

T
45 

5.2. Currents Comparisons 

The corresponding currents comparisons (for speed and direction) at the stations locations 

plotted also in Figure 32 are given in Tables D3-D6 (Appendix D). They show that the RMSE of 

the speeds and their CF values are comparable with the corresponding stations for the hindcast 

simulations. Moreover, they maintain their values during the 24-hour forecast period and any 

deterioration of accuracy relative to that of the nowcast is not significant. This is also true for 

the RMSE and CF values associated with the currents directions but here, as the forecast 

progresses in time, a lowering of accuracy relative to the nowcast, although not drastic, is seen. 

The metrics for currents directions too are consistent with their counterparts in the synoptic 

hindcast simulations. Both the speed and direction RMSE errors at station cb1101 are seen to be 

somewhat greater than those for stations cb1001 and cb0801 and hence also a corresponding 

degredation of the CF values. 

5.3. Temperature Comparisons 

Temperature comparisons were performed at the locations also shown in Figure 32 and at a 

depth of 1m to avoid the effects of the model surface bulk flux boundary conditions. The RMSE 

and CF values given in Tables D7 and D8 (Appendix D) show that: (i) the RMSE errors are less 

than 2oC, (ii) CF > 90% almost always, (iii) the accuracy associated with (i) and (ii) cover all the 

stations examined (as opposed to drastic accuracy differences between different stations/regions 

within the computational domain) and (iv) the accuracy in terms of the RMSE and CF hold well 

beyond the hindcast and into the 24-hour forecast. As the synoptic hindcast simulations were 

validated against bi-weekly Chesapeake Bay Program (CBP) temperature vertical profiles which 

were not time-series, a direct comparison of the accuracy of these nowcast/forecast predictions 

against the hindcast predictions cannot be made. 

5.4. Salinity Comparisons 

The salinity RMSE and CF values compared at the locations plotted in Figure 32 at a 1m depth 

(to be consistent with the comparisons for temperature) given in Tables D9 and D10 (Appendix 

D) show that: (i) their RMSE errors are less than 2 PSU with the exception of station 8638863 

(CBBT), (ii) CF > 90% again with the exception of the same station and (iii) the accuracy in 

terms of the RMSE and CF hold well beyond the hindcast and into the 24-hour forecast. As the 

synoptic hindcast simulations were validated against bi-weekly Chesapeake Bay Program (CBP) 

salinity vertical profiles which were not time-series, here too a direct comparison of the accuracy 

of these nowcast/forecast predictions against the hindcast predictions cannot be made. The 

reason for the relatively large RMSE and relatively low CF for CBBT is not known and a plot of 

the observed and modeled salinity time-series at a 1m depth are given in Figure 33. To provide a 

second observational data source, the bi-weekly measured, low-resolution S values from CBP 

station CB8.1 are included in the plot for reference. This CBP station is located geographically 

close to the CBBT station and the plotted data is also at a 1m depth.

Figure 33 shows that both the model predicted salinity and the observations have reasonable 

values. The CBP observations are clearly devoid of the high (temporal) resolution information 

contained within the PORTS observations. Both the CBOFS2 predictions and the CBP 
46 

observations show a more tempered behavior relative to the PORTS observations and the two 

sets of observations show large disagreements after (approximately) Julian Day 175; due to the 

lack of sufficient temporal resolution in the CBP observations, the disagreement during Julian 

Days 140-150 cannot be verified. In terms of the trends in the S values, the model predictions 

appear to follow the CPB observations where: (i) the former is almost always saltier than the 

latter and, (ii) the model-observation disagreement is usually within a range of about [-1,3] PSU. 

In the synoptic hindcast simulation too, the model was seen to be saltier than observations for the 

shallower depths. 

Figure 33. Salinity time-series at station 8638863 (CBBT). 
47 

6. SUMMARY AND CONCLUSIONS 

The NOS operational Chesapeake Bay model, (CBOFS), is only capable of generating water 

levels and depth-integrated currents due to its two-dimensional, barotropic nature. Therefore, an 

upgrade to this modeling framework was proposed and as a consequence the fully threedimensional CBOFS2 set-up based on the Rutgers University’s ROMS model was developed. It 

covers the whole of the Chesapeake Bay up to and including Reedy Point, DE along the C & D 

canal and also includes Ocean City, MD and Duck, NC along its southestern boundary which 

extends as far as the 100m isobath on the shelf. 

The evaluation of this new modeling set-up was carried out in three stages. First, a constant 

density three-dimensional baroclinic simulation was performed to ensure the accuracy of the 

tides – water levels and currents. Thereafter, a synoptic hindcast simulation (using observed and 

climatological initialization and forcing fields) spanning June 01, 2003 to September 01, 2005 

was performed to validate the water levels, currents, temperature and salinity. Finally, the 

synoptic hincast CBOFS2 set-up was employed to perform a 3-month as a semi-operational 

nowcast/forecast simulation and its outputs were again skill-assessed. 

A summary of the results are as follows: 

(1) All three configurations of CBOFS2 ran successfully without encountering any numerical 

instabilities. Hence, this modeling set-up is capable of withstanding a diverse range of 

environmental conditions within the Bay (that is, the high and low river discharges and 

potential extreme meteorological events that may pass through the Bay). The CourantFriedrichs-Lewy (CFL) numerical stability parameter was monitored during the synoptic 

hindast simulations and for the most part, it was below unity and its overall value was 

dominated by the contribution from the vertical velocity (w) component. 

(2) Under a MPI parallelization it was found that CBOFS2 was computationally highly efficient 

yielding a computational effort ratio of 1:144 with the use of 96 processors. 

(3) The water level comparisons showed that the constant density simulation produced smaller 

amplitude errors but the synoptic hindcast simulation generated smaller phase errors relative 

to each other. The amplitude errors were less than 22 cm and phase errors at many locations 

were less than 0.5 hours. In general, both the amplitude and phase errors increase in 

magnitude when moving up the Bay and for the latter, this is also true when moving up 

tributaries. 

(4) The currents comparisons show better agreement with predictions and observed data than 

the water levels. The comparisons for the synoptic hindcast simulation were also an 

improvement over those for the constant density simulation and the NOS skill criteria for 

both speed and direction were always met. This is also true for the amplitude of the majordirection current component and for its phase, in most cases, the phase error was less than 

0.5 hours. 
48 

(5) The RMS error splitting (into an amplitude and phase component) method described in this 

report was found to be very robust and reliable for both water levels and currents and for 

both the constant density and synoptic hindcast simulations. In all cases, the two required 

conditions of there being smooth RMSE curves (in space) and each of them having a unique, 

global minimum were met which also implied that the CBOFS2 time-series and the 

observations were both composed of the same set of (at least dominant) tidal harmonic 

constituents. 

(6) The temperature and salinity comparisons showed that at a majority of the locations, their 

RMS errors relative to the Chesapeake Bay Program data were less than 2°C and 4 PSU 

respectively and their mean errors were in the ranges of [-1°C, 1°C] and [-2 PSU, 3 PSU] 

respectively. The errors at the surface and at a 15-foot depth were similar and the largest 

errors were in the vicinity of the ocean bottom, indicating errors in stratification. Closer to 

the ocean surface, CBOFS2 was cooler and saltier than the Bay Program observations and 

closer to the ocean bottom, it was warmer and fresher than the observations. Thus, CBOFS2 

generates less stratification than reality. This could be an attribute of the vertical eddyviscosity model (GLS k-ω model) employed in CBOFS2; however, upon testing the full 

suite of turbulence models available within ROMS, this particular closure model generated 

the most accurate overall T and S stratification (relative to observations). The horizontal 

T/S spatial error distributions do not show pronounced trends although for the shallower 

depths they are mainly along the axis of the Bay. 

(7) The semi-operational nowcast/forecast CBOFS2 simulation showed that the predicted water 

levels, currents, temperature and salinity were as accurate as those from the hindcast 

simulation or better. Furthermore, the accuracy of the predictions were valid for up to and 

including a 24-hour forecast period. 

This report therefore has carefully and thoroughly quantified the model solution errors associated 

with CBOFS2. Its predictive accuracy for water level, currents, temperature and salinity warrant 

it being accepted as a NOS Operational Forecast System (OFS) upgrade to the presently 

available CBOFS. 

Future efforts could be directed towards: (i) reduction of the water level phase errors encountered 

when moving up tributaries; (ii) reduction of the water level amplitude and phase errors 

encountered when moving up the Bay; (iii) improving the salinity predictions near the ocean 

bottom to further reduce salinity errors; (iv) further reduction of both the temperature and salinity 

errors in the vertical; (v) further research into the reduced open boundary conditions for fully 

three-dimensional flow; and, (vi) employing model high-resolution nests for the tributaries in 

Chesapeake Bay and in particular for the Potomac and James rivers in order to better resolve the 

physical processes within them. For (i) and (ii) perhaps the use of a spatially variable bottom 

friction coefficient is conducive and the examination of the effects of the extent and the shape of 

the southern open ocean boundary may also be worthwhile; as for (iii) and (iv) other GLS 

turbulence model constant sets and models themselves may be worth experimenting with. In 

addition to the above, the lateral open ocean boundaries of CBOFS2 could also be coupled to a 

basin-scale model which will provide the full suite of open boundary forcing variables and 

thereby account for the shelf dynamics and its influence on the Bay better. 
49 

ACKNOWLEDGMENTS 

The authors wish to thank Dr. Zizang Yang of CSDL for generating the CBOFS2 grid using the 

DELFT3D grid generator, Dr. Jiangtao Xu for the many illuminating discussions on the physics 

of the Chesapeake Bay and her modeling experience and help with the Chesapeake Bay Program 

database, Mr. Patrick Burke, Mr. Christopher Paternostro, Mr. Armin Pruessner, Ms. Maria Little 

for help with the latest NOS harmonic analysis software, the use of the CMIST website and 

access to CMIST and water level data, and Dr. Aijun Zhang for help with the use of the CSDL 

skill-assessment software package. 
50 
51 

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54 
55 

APPENDIX A: CBOFS2 CONSTANT DENSITY WATER LEVEL HARMONIC 

CONSTITUENTS AND SKILL ASSESSMENTS

Table A1. Water level harmonic constituents summary for CBOFS2; amplitudes are in meters 

 and phases are in hours. 

Stn ID M2 N2 K1 O1 P1 L2 

 Amp Phs Amp Phs Amp Phs Amp Phs Amp Phs Amp Phs 

8571892 0.243 8.022 0.045 7.409 0.051 22.080 0.041 23.926 0.011 21.345 0.010 8.317 

8573364 0.207 11.296 0.040 10.552 0.069 0.339 0.054 -0.021 0.016 23.297 0.009 0.088 

8574680 0.192 11.113 0.038 10.411 0.067 0.412 0.054 0.065 0.016 -0.649 0.007 12.093 

8575512 0.153 9.643 0.030 9.030 0.058 23.496 0.047 -0.681 0.013 22.635 0.004 10.116 

8577330 0.188 6.397 0.036 5.644 0.034 20.697 0.029 22.850 0.008 19.975 0.007 7.230 

8632200 0.386 1.042 0.086 0.415 0.071 13.297 0.050 15.025 0.019 12.708 0.004 1.104 

8638863 0.398 0.638 0.091 0.035 0.073 12.798 0.051 14.516 0.021 12.421 0.003 -0.630 

8638610 0.373 1.290 0.083 0.742 0.066 13.603 0.047 15.269 0.018 13.203 0.005 0.420 

8635750 0.199 5.748 0.040 5.000 0.031 18.948 0.024 21.272 0.007 18.163 0.006 6.753 

8573927 0.363 2.308 0.057 1.554 0.046 25.557 0.033 0.165 0.027 20.523 0.020 2.079 

8637624 0.358 1.573 0.077 1.118 0.055 13.948 0.038 15.635 0.014 13.464 0.008 0.440 

8638433 0.273 4.409 0.054 3.759 0.065 17.193 0.050 18.690 0.014 17.013 0.010 4.866 

8638489 0.478 6.297 0.080 5.928 0.076 18.642 0.056 20.039 0.016 18.845 0.029 6.130 

8636580 0.154 3.809 0.034 3.024 0.033 16.076 0.022 18.210 0.008 15.389 0.003 5.747 

8635150 0.221 7.025 0.047 6.343 0.038 20.211 0.029 22.377 0.008 19.420 0.005 7.989 

8594900 0.387 -1.101 0.067 10.503 0.052 23.403 0.037 -0.423 0.010 -1.036 0.021 -0.109 

8574070 0.298 1.432 0.049 0.499 0.073 1.882 0.055 1.248 0.019 -0.047 0.019 2.015 

8571559 0.350 5.945 0.068 5.362 0.047 18.430 0.034 20.404 0.011 17.642 0.012 6.228 

8571214 0.227 5.324 0.046 4.550 0.038 18.144 0.029 20.304 0.009 17.274 0.007 6.431 

8576363 0.155 8.191 0.029 7.560 0.047 22.665 0.040 24.435 0.011 21.887 0.006 8.541 

8632974 0.207 3.233 0.046 2.489 0.043 15.544 0.030 17.514 0.011 14.747 0.004 4.965 

8573903 0.302 1.677 0.048 0.809 0.064 1.589 0.048 0.703 0.020 -1.758 0.019 1.951 

Table A2. Water level harmonic constituents summary from observations (NOS/CO-OPS 

 database); amplitudes are in meters and phases are in hours. 

Stn ID M2 N2 K1 O1 P1 L2 

 Amp Phs Amp Phs Amp Phs Amp Phs Amp Phs Amp Phs 

8571892 0.239 9.081 0.047 8.460 0.050 22.631 0.039 25.525 0.020 22.482 0.019 9.811 

8573364 0.174 11.958 0.037 11.396 0.069 0.219 0.058 1.004 0.023 23.558 0.008 1.057 

8574680 0.159 11.627 0.034 11.048 0.069 0.532 0.056 1.076 0.022 0.087 0.007 12.046 

8575512 0.139 10.061 0.029 9.511 0.059 23.715 0.048 0.430 0.020 23.317 0.010 10.434 

8577330 0.171 6.859 0.036 6.058 0.027 20.983 0.023 23.840 0.012 21.318 0.012 7.918 

8632200 0.388 1.121 0.088 0.432 0.059 12.858 0.046 15.319 0.019 13.484 0.018 1.605 

8638863 0.380 0.725 0.090 0.049 0.058 12.293 0.045 14.982 0.018 12.574 0.014 0.975 

8638610 0.366 1.611 0.081 0.995 0.049 13.357 0.042 16.108 0.015 13.310 0.012 1.541 

8635750 0.184 6.086 0.040 5.355 0.023 18.363 0.019 21.423 0.009 19.587 0.011 6.885 

8573927 0.434 3.243 0.075 2.679 0.032 22.884 0.014 0.179 0.010 22.127 0.030 3.072 

8637624 0.361 1.849 0.080 1.273 0.051 13.177 0.038 15.850 0.015 12.882 0.015 1.693 

8638433 0.287 4.285 0.058 3.949 0.060 16.149 0.039 19.902 0.020 16.412 0.008 4.609 

8638489 0.422 8.574 0.073 8.467 0.076 19.673 0.059 23.445 0.025 19.935 0.012 8.673 

8636580 0.175 3.561 0.038 2.954 0.030 15.072 0.023 17.636 0.008 15.402 0.005 3.928 

8635150 0.246 7.380 0.050 6.814 0.030 19.566 0.026 22.341 0.011 21.125 0.013 7.864 

8594900 0.407 0.704 0.075 12.535 0.046 23.735 0.035 1.621 0.013 0.294 0.027 1.134 

8574070 0.282 2.481 0.052 1.565 0.084 1.842 0.059 2.309 0.019 1.304 0.021 3.620 

8571559 0.310 6.607 0.066 6.167 0.042 18.762 0.033 21.430 0.014 19.721 0.011 6.736 

8571214 0.203 5.469 0.039 4.800 0.036 17.539 0.024 20.822 0.000 5.000 0.012 5.830 

8576363 0.139 8.585 0.029 7.792 0.045 23.044 0.036 25.247 0.017 22.501 0.010 9.907 

8632974 0.216 3.316 0.052 2.598 0.033 15.731 0.031 17.465 0.000 5.000 0.009 4.692 

8573903 0.274 2.526 0.059 1.600 0.076 1.243 0.049 1.614 0.027 1.116 0.022 3.041 
56 

Table A3. Water level error summary: Tidal range (cm), RMS error (cm) and its Central 

 Frequency (CF), high water amplitude error (AHW_err, cm) and its CF, low water 

 amplitude error (ALW_err, cm) and its CF (all from the CSDL skill-assessment 

 software package), amplitude component of the RMSE (cm) and the phase 

 component of the RMSE (hours). 

Station Range RMSE CF AHW_err CF ALW_err CF Amp_err Phs_err 

8571892 49.4 15.4 64.4 12.0 96.6 13.4 79.1 12.1 1.03 

8573364 36.9 18.3 43.3 21.3 2.3 13.5 77.9 17.6 0.67 

8574680 34.7 15.3 56.7 18.2 9.2 10.6 94.2 14.8 0.53 

8575512 29.6 14.2 66.0 15.2 37.9 11.5 93.0 14.0 0.45 

8638863 77.7 8.3 97.8 9.2 100.0 5.9 100.0 8.3 0.07 

8638610 74.1 9.2 90.6 8.1 100.0 7.1 100.0 8.2 0.30 

8635750 37.8 12.0 84.8 13.7 73.3 9.6 100.0 11.8 0.32 

8573927 87.2 20.2 53.7 10.7 89.7 16.9 40.2 15.1 0.90 

8637624 72.5 10.4 88.2 9.9 100.0 12.3 82.8 9.8 0.25 

8638433 56.1 10.5 91.4 8.3 100.0 7.3 100.0 10.4 -0.12 

8638489 85.3 38.6 18.1 21.5 2.3 7.6 100.0 12.2 2.22 

8636580 35.4 12.2 87.3 8.5 100.0 13.4 79.3 12.1 -0.25 

8635150 49.7 11.4 84.0 8.1 100.0 14.4 62.1 10.9 0.35 

8594900 85.0 29.5 41.0 8.0 100.0 13.1 75.6 11.7 1.80 

8574070 57.9 15.8 62.3 13.8 70.1 9.9 88.5 11.3 0.98 

8571559 62.5 9.3 91.8 10.0 100.0 2.9 100.0 4.8 0.62 

8577330 35.7 12.5 78.6 13.9 68.6 10.2 100.0 12.1 0.43 

8632200 79.2 9.0 97.5 8.2 100.0 8.9 100.0 8.9 0.07 
57 

APPENDIX B: CBOFS2 CONSTANT DENSITY CURRENTS HARMONIC 

CONSTITUENTS AND SKILL ASSESSMENTS

Table B1. True eastward current harmonic constituents summary for CBOFS2; amplitudes are in 

 m/s and phases are in hours. 

True Eastward Current (U) 

 

Stn ID M2 N2 K1 O1 P1 L2 

 Amp Phs Amp Phs Amp Phs Amp Phs Amp Phs Amp Phs 

LCB9903 0.471 7.000 0.124 6.600 0.111 0.400 0.079 1.700 0.037 0.500 0.018 6.400 

cb0601 0.334 6.600 0.077 6.200 0.048 21.900 0.032 24.500 0.016 22.100 0.011 6.000 

cb0801 0.056 10.400 0.013 10.200 0.016 5.000 0.012 6.100 0.005 5.100 0.002 9.800 

cb0901 0.133 11.200 0.032 10.700 0.021 2.500 0.014 3.100 0.007 2.500 0.005 10.300 

CHB0301 0.146 0.200 0.031 12.100 0.039 4.100 0.026 4.700 0.013 4.100 0.004 11.700 

cb1201 0.030 9.800 0.005 9.300 0.005 17.100 0.003 18.100 0.002 17.200 0.001 9.000 

cb1301 0.917 11.800 0.157 11.300 0.081 5.000 0.150 3.800 0.027 4.900 0.022 10.900 

NOS 68 0.046 8.684 0.009 5.707 0.005 11.761 0.006 5.071 0.002 11.826 0.001 11.548 

NOS 63 0.022 0.262 0.004 9.849 0.004 15.065 0.004 8.298 0.001 15.148 0.001 3.221 

NOS 27 0.118 10.292 0.023 7.303 0.007 11.282 0.007 5.228 0.002 11.344 0.003 0.982 

NOS 174 0.091 0.248 0.018 9.645 0.008 15.644 0.010 9.266 0.003 15.730 0.003 3.390 

NOS 123 0.033 2.143 0.006 11.667 0.004 12.160 0.004 3.729 0.001 12.227 0.001 5.161 

NOS 130 0.041 9.498 0.008 6.477 0.008 6.801 0.009 25.059 0.003 6.839 0.001 0.217 

Table B2. True northward current harmonic constituents summary for CBOFS2; amplitudes are 

 in m/s and phases are in hours. 

 

True Northward Current (V) 

 

Stn ID M2 N2 K1 O1 P1 L2 

 Amp Phs Amp Phs Amp Phs Amp Phs Amp Phs Amp Phs 

LCB9903 0.243 0.800 0.062 0.400 0.054 12.600 0.035 14.300 0.018 12.700 0.009 0.400 

cb0601 0.148 1.000 0.034 0.500 0.022 10.000 0.015 11.200 0.007 10.100 0.005 0.500 

cb0801 0.271 3.300 0.061 2.900 0.059 15.400 0.043 17.400 0.020 15.500 0.009 2.800 

cb0901 0.136 5.000 0.033 4.500 0.022 14.900 0.016 16.900 0.007 15.000 0.005 4.300 

CHB0301 0.220 6.100 0.047 5.600 0.060 15.900 0.039 17.500 0.020 16.100 0.007 5.400 

cb1201 0.267 9.700 0.051 9.100 0.051 18.900 0.034 20.700 0.017 19.000 0.007 8.800 

cb1301 0.116 5.600 0.019 5.000 0.011 17.200 0.019 16.800 0.004 17.200 0.003 4.900 

NOS 68 0.337 9.557 0.065 6.688 0.041 12.213 0.044 5.738 0.013 12.280 0.009 0.125 

NOS 63 0.431 9.443 0.084 6.540 0.045 11.881 0.048 5.250 0.015 11.946 0.012 0.044 

NOS 27 0.032 10.689 0.006 7.609 0.002 12.047 0.002 5.379 0.001 12.113 0.001 1.463 

NOS 174 0.030 0.235 0.006 9.670 0.003 14.833 0.003 8.083 0.001 14.914 0.001 3.343 

NOS 123 0.097 9.050 0.019 6.013 0.016 5.711 0.017 24.155 0.005 5.742 0.003 11.978 

NOS 130 0.037 3.843 0.007 0.693 0.005 16.774 0.004 9.381 0.002 16.866 0.001 6.878 
58 

Table B3. True eastward current harmonic constituents summary from observations (NOS/CO- 

 OPS/CMIST database and NOS survey); amplitudes are in m/s and phases are in hours. 

True Eastward Current (U) 

 

Stn ID M2 N2 K1 O1 P1 L2 

 Amp Phs Amp Phs Amp Phs Amp Phs Amp Phs Amp Phs 

LCB9903 0.459 6.100 0.102 5.400 0.078 1.700 0.033 22.600 0.026 1.400 0.015 5.200 

cb0601 0.678 5.800 0.150 4.800 0.134 22.100 0.087 23.400 0.044 22.200 0.021 4.600 

cb0801 0.087 8.300 0.022 9.600 0.010 23.400 0.004 19.700 0.003 23.100 0.003 9.200 

cb0901 0.155 10.900 0.035 10.200 0.030 3.600 0.022 5.700 0.010 3.800 0.005 9.800 

CHB0301 0.133 11.700 0.026 10.700 0.036 5.400 0.034 1.200 0.012 5.100 0.004 10.300 

cb1201 0.053 6.900 0.019 5.600 0.021 14.900 0.008 12.300 0.007 14.700 0.003 5.400 

cb1301 0.541 11.300 0.084 11.000 0.094 6.000 0.050 3.200 0.031 5.800 0.012 10.600 

NOS 68 0.040 10.575 0.008 9.740 0.020 5.425 0.002 10.055 0.007 5.455 0.001 11.375 

NOS 63 0.061 5.096 0.012 5.418 0.017 20.557 0.023 21.143 0.006 20.670 0.002 4.785 

NOS 27 0.324 4.513 0.063 4.212 0.016 14.175 0.017 16.022 0.005 14.252 0.009 4.802 

NOS 174 0.086 6.424 0.017 6.030 0.020 18.622 0.012 21.244 0.007 18.725 0.002 6.807 

NOS 123 0.008 3.236 0.002 1.308 0.008 3.517 0.005 7.437 0.003 3.536 0.000 5.090 

NOS 130 0.039 1.325 0.008 0.352 0.026 6.948 0.022 9.632 0.009 6.986 0.001 2.266 

Table B4. True northward current harmonic constituents summary from observations (NOS/CO- 

 OPS/CMIST database and NOS survey); amplitudes are in m/s and phases are in hours. 

 

True Northward Current (V) 

 

Stn ID M2 N2 K1 O1 P1 L2 

 Amp Phs Amp Phs Amp Phs Amp Phs Amp Phs Amp Phs 

LCB9903 0.240 12.000 0.048 12.000 0.027 13.800 0.009 8.300 0.009 13.500 0.007 11.500 

cb0601 0.111 11.700 0.050 10.200 0.017 9.200 0.004 4.100 0.006 8.900 0.007 9.800 

cb0801 0.277 3.200 0.047 1.800 0.047 16.600 0.030 17.200 0.016 16.600 0.007 1.700 

cb0901 0.150 4.700 0.029 3.000 0.018 15.800 0.025 18.100 0.006 16.000 0.004 2.900 

CHB0301 0.172 5.300 0.032 4.200 0.053 17.100 0.047 13.200 0.018 16.800 0.005 4.100 

cb1201 0.231 9.900 0.052 8.400 0.064 18.200 0.076 21.500 0.021 18.500 0.007 8.100 

cb1301 0.079 5.100 0.012 4.600 0.014 17.900 0.007 16.300 0.005 17.800 0.002 4.500 

NOS 68 0.304 2.080 0.059 1.002 0.020 13.490 0.029 16.331 0.007 13.564 0.009 3.122 

NOS 63 0.280 12.114 0.054 12.250 0.027 22.093 0.030 1.399 0.009 22.214 0.008 11.985 

NOS 27 0.095 4.423 0.018 4.522 0.005 14.733 0.007 12.429 0.001 14.814 0.003 4.331 

NOS 174 0.010 6.659 0.002 5.721 0.004 1.403 0.005 21.602 0.001 1.411 0.000 7.566 

NOS 123 0.170 2.760 0.033 2.036 0.060 4.694 0.040 7.064 0.020 4.720 0.005 3.461 

NOS 130 0.044 7.494 0.008 6.691 0.023 19.493 0.009 21.918 0.007 19.600 0.001 8.270 

Table B5. Current speed error summary: RMS of current speed error (cm/s) and its Central 

 Frequency (CF), maximum flood current amplitude error (AFC_err, cm) and its CF, 

 maximum ebb current amplitude error (AEC_err, cm) and its CF (all from the CSDL 

 skill-assessment software package). 

 Station RMSE CF AFC_err CF AEC_err CF 

 LCB9903 12.6 96.5 11.1 100.0 11.1 100.0 

 cb0601 30.5 50.6 40.0 9.3 35.7 20.9 

 cb0801 5.9 100.0 4.4 100.0 6.0 100.0 

 cb0901 4.4 100.0 3.5 100.0 6.4 100.0 

 CHB0301 9.2 100.0 10.2 100.0 3.7 100.0 

 cb1201 6.4 100.0 5.4 100.0 6.0 100.0 

 cb1301 31.1 43.8 34.8 14.3 39.7 0.0 
59 

Table B6. Current direction error summary: RMS of current direction error (degrees) and its 

 Central Frequency (CF), maximum flood current direction error (DFC_err, degrees) 

 and its CF, maximum ebb current direction error (DEC_err, degrees) and its CF (all 

 from the CSDL skill-assessment software package). 

 Station RMSE CF DFC_err CF DEC_err CF 

 LCB9903 3.8 100.0 6.3 100.0 2.9 100.0 

 cb0601 11.1 92.4 12.1 100.0 10.3 100.0 

 cb0801 3.7 100.0 8.2 98.8 8.8 100.0 

 cb0901 0.1 100.0 5.8 98.8 5.4 100.0 

 CBB0301 1.6 100.0 5.5 100.0 4.5 100.0 

 cb1201 3.8 100.0 13.4 91.9 5.0 100.0 

 cb1301 8.3 99.8 1.1 100.0 0.5 100.0 

Table B7. Major current error summary: raw RMS error (cm/s), the amplitude component of the 

 RMSE (cm/s) and the phase component of the RMSE (hours). 

Station RMSE Amp_err Phs_err 

LCB9903 13.9 11.2 -0.38 

 cb0601 32.8 28.6 -0.80 

 cb0801 6.2 5.0 -0.33 

 cb0901 4.7 4.0 -0.30 

CHB0301 10.5 6.7 -0.87 

 cb1201 6.3 6.0 0.18 

 cb1301 32.9 30.2 -0.53 
60 
61 

APPENDIX C: CBOFS2 SYNOPTIC HINDCAST TEMPERATURE AND SALINITY 

SKILL ASSESSMENTS 

Figure C1. Observed Bay Program T/S, CBOFS2 predicted T/S and their differences at station 

CB7.4. 
62 

Figure C2. Observed Bay Program T/S, CBOFS2 predicted T/S and their differences at station 

CB5.4. 
63 

Figure C3. Observed Bay Program T/S, CBOFS2 predicted T/S and their differences at station 

CB4.2C. 
64 

Figure C4. Observed Bay Program T/S, CBOFS2 predicted T/S and their differences at station 

CB2.1. 
65 

Figure C5. Observed Bay Program T/S, CBOFS2 predicted T/S and their differences at station 

RET5.2. 
66 

Figure C6. Observed Bay Program T/S, CBOFS2 predicted T/S and their differences at station 

LE3.1. 
67 

Figure C7. Observed Bay Program T/S, CBOFS2 predicted T/S and their differences at station 

RET2.4. 
68 

Figure C8. Observed Bay Program T/S, CBOFS2 predicted T/S and their differences at station 

LE1.3. 
69 

Figure C9. Observed Bay Program T/S, CBOFS2 predicted T/S and their differences at station 

EE3.4. 
70 

Figure C10. Observed Bay Program T/S, CBOFS2 predicted T/S and their differences at station 

ET5.2. 
71 

 

 

 

Figure C11. Histograms of local errors (in time and depth) for T and S corresponding to Figures 

C1-C10. The T and S histogram bin widths are 0.5 o

C and 0.5 PSU respectively. 
72 

Table C1. The RMS and mean errors (calculated in time) for temperature at the surface, at 15- 

 feet below the surface and at the bottom. 

 Surface 15-feet Bottom 

 # Station RMSE Mean E RMSE Mean E RMSE Mean E 

------------------------------------------------------------------ 

 1 CB7.4 1.2 -0.3 1.4 -0.4 1.4 0.4 

 2 CB6.4 0.9 -0.6 1.3 -0.7 0.9 -0.4 

 3 CB6.3 1.1 -0.8 1.5 -0.9 0.9 -0.3 

 4 CB6.1 1.6 -1.1 1.5 -0.9 0.7 -0.3 

 5 CB5.4 1.3 -0.8 1.2 -0.8 0.7 0.1 

 6 CB5.2 1.2 -0.7 1.1 -0.6 1.2 0.7 

 7 CB4.4 1.1 -0.9 1.3 -0.7 2.9 -0.0 

 8 CB4.2C 1.0 -0.7 1.3 -0.7 1.5 1.1 

 9 CB4.1C 1.6 -1.1 1.3 -0.5 2.0 1.3 

10 CB3.2 0.8 -0.2 1.0 -0.2 1.4 0.4 

11 CB2.2 0.8 -0.2 0.8 -0.1 0.9 -0.1 

12 CB2.1 0.9 -0.2 0.8 -0.1 0.8 -0.1 

13 LE5.4 0.6 -0.1 0.5 0.0 0.7 0.2 

14 RET5.2 0.9 -0.6 0.9 -0.6 0.9 -0.6 

15 LE4.3 0.9 -0.7 1.0 -0.8 2.0 0.1 

16 WE4.1 1.1 -0.7 0.9 -0.6 0.9 -0.6 

17 LE3.4 1.2 -0.8 1.0 -0.7 0.7 0.0 

18 LE3.1 1.1 -0.8 0.6 -0.3 0.5 -0.1 

19 LE2.3 1.4 -0.9 1.3 -0.8 0.9 0.4 

20 LE2.2 1.3 -0.7 1.4 -0.8 1.3 -0.7 

21 RET2.4 1.1 -0.4 1.0 -0.2 0.9 0.2 

22 LE1.4 1.7 -0.3 1.2 -0.9 0.9 -0.2 

23 LE1.3 2.2 -0.5 1.7 -1.3 1.3 -0.9 

24 LE1.1 1.0 -0.6 1.3 0.1 1.3 0.1 

25 WT5.1 1.4 -0.9 1.3 -0.3 2.4 0.9 

26 WT2.1 1.0 -0.7 0.9 -0.6 0.9 -0.6 

27 CB1.1 0.6 -0.4 0.4 -0.1 0.4 -0.2 

28 ET4.2 1.4 -1.0 1.1 -0.8 2.2 0.4 

29 EE1.1 1.2 -0.9 1.0 -0.7 1.0 -0.6 

30 EE2.1 0.7 -0.1 0.7 -0.0 2.7 -1.0 

31 ET5.2 0.7 -0.1 0.7 -0.1 0.7 -0.1 

32 EE3.1 0.8 0.0 0.7 0.3 0.8 0.4 

33 EE3.2 0.9 -0.2 0.9 -0.1 0.6 0.3 

34 EE3.4 1.0 -0.4 0.7 -0.1 1.0 -0.2 

35 EE3.5 1.2 -0.5 1.1 -0.4 1.0 -0.2 

 
73 

Table C2. The RMS and mean errors (calculated in time) for salinity at the surface, at 15-feet 

 below the surface and at the bottom. 

 Surface 15-feet Bottom 

 # Station RMSE Mean E RMSE Mean E RMSE Mean E 

------------------------------------------------------------------ 

 1 CB7.4 4.0 2.1 3.2 2.2 1.5 0.6 

 2 CB6.4 2.5 2.2 3.5 3.0 2.7 2.0 

 3 CB6.3 2.3 1.8 4.1 3.7 2.7 2.2 

 4 CB6.1 2.9 2.5 3.5 3.0 2.1 1.8 

 5 CB5.4 2.5 2.3 3.2 3.0 1.8 1.1 

 6 CB5.2 2.4 1.9 3.2 2.9 2.3 -1.3 

 7 CB4.4 2.1 1.6 3.1 2.9 2.8 -2.3 

 8 CB4.2C 2.2 1.9 3.0 2.8 2.9 -2.2 

 9 CB4.1C 2.5 2.1 2.9 2.7 4.3 -3.9 

10 CB3.2 1.8 1.2 1.7 1.2 3.3 -2.2 

11 CB2.2 1.2 0.0 1.6 0.0 2.3 -0.7 

12 CB2.1 0.2 -0.1 0.4 -0.1 0.4 -0.2 

13 LE5.4 1.6 0.1 1.6 0.5 2.0 -0.1 

14 RET5.2 1.2 -0.7 1.4 -0.8 1.4 -0.9 

15 LE4.3 2.0 1.6 1.8 1.5 3.9 -1.7 

16 WE4.1 2.0 1.9 1.9 1.7 1.9 1.7 

17 LE3.4 1.8 1.6 1.8 1.7 1.2 0.5 

18 LE3.1 1.2 0.5 0.8 -0.2 1.2 -0.7 

19 LE2.3 2.4 2.2 2.5 2.3 1.9 0.4 

20 LE2.2 2.3 1.5 2.9 2.4 2.8 2.3 

21 RET2.4 1.4 -0.2 1.4 0.1 2.0 -1.0 

22 LE1.4 2.1 1.8 2.3 2.1 2.4 1.1 

23 LE1.3 2.8 2.5 2.7 2.6 2.5 2.3 

24 LE1.1 2.9 2.7 2.7 2.5 2.7 2.5 

25 WT5.1 1.8 -1.1 2.8 -2.3 5.5 -4.9 

26 WT2.1 0.8 0.7 0.8 0.7 0.8 0.7 

27 CB1.1 0.0 0.0 0.0 0.0 0.0 0.0 

28 ET4.2 1.0 0.4 1.1 0.2 4.3 -2.8 

29 EE1.1 1.6 1.4 1.6 1.4 1.5 1.2 

30 EE2.1 2.2 2.0 2.0 1.7 1.7 1.1 

31 ET5.2 3.3 3.2 3.0 2.9 3.0 2.9 

32 EE3.1 2.7 2.4 2.3 2.1 1.8 1.4 

33 EE3.2 2.5 2.3 2.5 2.3 2.0 1.5 

34 EE3.4 2.7 2.3 2.3 1.9 2.5 2.0 

35 EE3.5 2.4 2.1 2.3 2.1 2.1 1.7 
74 
75 

APPENDIX D: CBOFS2 SEMI-OPERATIONAL NOWCAST/FORECAST SKILL 

ASSESSMENTS 

Table D1. RMSE (m) values for the water levels for the semi-operational nowcast/forecast 

 CBOFS2 (from the CSDL skill assessment software package). 

Table D2. CF(15cm) values for the water levels for the semi-operational nowcast/forecast 

 CBOFS2 (from the CSDL skill assessment software package). 

Stn ID Nowcast Fcst-00h Fcst-06h Fcst-12h Fcst-18h Fcst-24h 

8638610 85.8 89.5 87.2 89.8 90.1 90.1 

8638863 95.8 91.8 95.1 96.7 96.7 97.7 

8632200 95.6 96.1 95.1 96.7 98.0 96.4 

8636580 99.4 99.7 99.7 99.0 98.4 98.4 

8635750 98.8 99.0 98.7 98.7 98.7 97.7 

8577330 96.5 96.7 96.7 98.0 97.0 96.1 

8571559 83.6 85.2 86.5 86.5 89.1 90.8 

8571892 76.8 77.3 76.3 77.0 81.6 81.6 

8594900 41.8 45.4 46.7 44.7 48.4 47.0 

8575512 91.9 92.1 91.8 92.4 92.8 92.1 

8573364 75.1 74.0 75.7 76.0 76.0 76.3 

8574680 82.9 82.9 83.2 81.9 81.6 82.6 

8573927 58.9 56.6 61.5 58.9 60.2 64.5 

Stn ID Nowcast Fcst-00h Fcst-06h Fcst-12h Fcst-18h Fcst-24h 

8638610 0.100 0.092 0.099 0.090 0.086 0.088 

8638863 0.074 0.086 0.075 0.071 0.067 0.070 

8632200 0.074 0.075 0.072 0.071 0.067 0.070 

8636580 0.049 0.048 0.048 0.054 0.053 0.058 

8635750 0.058 0.057 0.059 0.060 0.059 0.059 

8577330 0.075 0.074 0.075 0.075 0.072 0.073 

8571559 0.107 0.103 0.103 0.099 0.095 0.091 

8571892 0.119 0.119 0.121 0.122 0.110 0.112 

8594900 0.311 0.305 0.299 0.300 0.278 0.280 

8575512 0.086 0.087 0.087 0.087 0.084 0.086 

8573364 0.123 0.121 0.121 0.120 0.120 0.118 

8574680 0.108 0.109 0.108 0.108 0.108 0.106 

8573927 0.170 0.168 0.160 0.166 0.168 0.154 
76 

Table D3. RMSE (m/s) values for the current speed at 15 feet for the semi-operational 

 nowcast/forecast CBOFS2 (from the CSDL skill assessment software package). 

Stn ID Nowcast Fcst-00h Fcst-06h Fcst-12h Fcst-18h Fcst-24h 

cb0801 0.107 0.087 0.086 0.088 0.094 0.087 

cb1001 0.150 0.139 0.145 0.152 0.156 0.150 

cb1101 0.208 0.228 0.230 0.232 0.227 0.228 

Table D4. CF(26cm/s) values for the current speed at 15 feet for the semi-operational 

 nowcast/forecast CBOFS2 (from the CSDL skill assessment software package). 

Stn ID Nowcast Fcst-00h Fcst-06h Fcst-12h Fcst-18h Fcst-24h 

cb0801 98.3 100.0 100.0 100.0 100.0 100.0 

cb1001 90.8 89.3 90.0 88.2 93.9 94.1 

cb1101 76.3 67.8 62.7 65.5 68.5 67.3 

Table D5. RMSE (degrees) values for the current direction at 15 feet for the semi-operational 

 nowcast/forecast CBOFS2 (from the CSDL skill assessment software package). 

Stn ID Nowcast Fcst-00h Fcst-06h Fcst-12h Fcst-18h Fcst-24h 

cb0801 14.267 21.934 23.253 23.061 22.837 23.442 

cb1001 9.619 17.380 18.128 18.424 17.423 18.066 

cb1101 13.578 18.554 25.432 26.423 19.247 19.123 

Table D6. CF(22.5o) values for the current direction at 15 feet for the semi-operational 

 nowcast/forecast CBOFS2 (from the CSDL skill assessment software package). 

Stn ID Nowcast Fcst-00h Fcst-06h Fcst-12h Fcst-18h Fcst-24h 

cb0801 90.1 84.3 82.4 78.4 79.6 71.2 

cb1001 94.8 82.1 80.0 73.5 84.8 82.4 

cb1101 86.3 76.3 71.2 72.4 66.7 76.4 
77 

Table D7. RMSE (o

C) values for temperature at a 1m depth for the semi-operational 

 nowcast/forecast CBOFS2 (from the CSDL skill assessment software package). 

Table D8. CF(3oC) values for temperature at a 1m depth for the semi-operational 

 nowcast/forecast CBOFS2 (from the CSDL skill assessment software package). 

Table D9. RMSE (PSU) values for salinity at a 1m depth for the semi-operational 

 nowcast/forecast CBOFS2 (from the CSDL skill assessment software package). 

Table D10. CF(3.5 PSU) values for salinity at a 1m depth for the semi-operational 

 nowcast/forecast CBOFS2 (from the CSDL skill assessment software package). 

Stn ID Nowcast Fcst-00h Fcst-06h Fcst-12h Fcst-18h Fcst-24h 

8638863 1.797 1.862 1.877 1.836 1.837 1.861 

8635750 1.347 1.350 1.340 1.296 1.283 1.267 

8571892 0.933 0.898 0.895 0.888 0.873 0.865 

8594900 1.616 1.680 1.678 1.678 1.678 1.673 

8573364 1.016 1.035 1.023 1.028 1.016 0.985 

8574680 1.860 1.849 1.847 1.825 1.817 1.797 

8573927 0.834 0.894 0.899 0.890 0.881 0.812 

Stn ID Nowcast Fcst-00h Fcst-06h Fcst-12h Fcst-18h Fcst-24h 

8638863 91.7 91.9 91.2 92.6 92.2 90.9 

8635750 97.2 97.6 98.0 96.6 97.6 97.6 

8571892 99.4 99.3 99.3 100.0 100.0 99.7 

8594900 89.8 88.9 88.9 89.2 88.5 88.5 

8573364 97.8 97.6 98.0 98.0 97.6 98.3 

8574680 90.1 89.5 89.5 89.5 89.5 88.9 

8573927 99.7 99.3 99.3 99.3 99.3 99.7 

Stn ID Nowcast Fcst-00h Fcst-06h Fcst-12h Fcst-18h Fcst-24h 

8638863 4.799 5.406 5.584 5.590 5.577 5.611 

8635750 1.827 1.803 1.802 1.794 1.793 1.792 

8574680 1.910 1.961 1.950 1.938 1.931 1.931 

Stn ID Nowcast Fcst-00h Fcst-06h Fcst-12h Fcst-18h Fcst-24h 

8638863 43.5 43.6 42.2 42.2 42.2 42.2 

8635750 97.2 97.3 97.3 97.0 97.0 97.0 

8574680 97.1 97.0 97.3 97.6 97.6 97.6