NOAA Technical Report NOS OCS 12

_____________________________________________________________________

Hydrodynamic Model Development for the Port of

New York/New Jersey Water Level and Current

Nowcast/Forecast Model System

Eugene Wei

Manchun Chen

Silver Spring, Maryland

July, 2001

noaa National Oceanic and Atmospheric Administration

----------------------------------------------------------------------------------

U.S. DEPARTMENT OF COMMERCE

National Ocean Service

Office of Coast Survey

Coast Survey Development Laboratory
Office of Coast Survey

National Ocean Service

National Oceanic and Atmospheric Administration

U.S. Department of Commerce

The Offic of Coast Survey (CS) 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 CS:

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 collects marine navigational data to construct and maintain nautical

charts, Coast Pilots, and related marine products for the United States.

The Hydrographic Surveys Divisions directs programs for ship and shore-based hydrographic

survey units and conducts general hydrographic survey operations.

The Navigation Services Division is the focal point for Coast Survey customer service activities,

concentrating predominantly on charting issues, fast-response hydrographic surveys and Coast

Pilot updates.

Notice

Mention of a comercial company or product does not constitute an

endorsement by NOAA. Use of publicity or advertising purposes of

information from this publication concerning proprietary products or the

tests of such products is no authorized.
iii

TABLE OF CONTENTS

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

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

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

2. HYDRODYNAMIC MODEL ..................................................3

2.1. Governing Equations ....................................................3

2.2. Split Mode ............................................................5

2.3. Time Step Constraints ...................................................5

2.4. Model Grid ...........................................................5

3. MODEL COUPLING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1. Grid Comparison .......................................................9

3.2. Coupling Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.2.1. Interface Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.2.2. Noise Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2.3. Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2.4. Programing Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.3. Coupling Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.4. Two-Way Coupling Finite Difference Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4. TIDE SIMULATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.1. Water Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.1.1. Harmonic Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.1.2. Skill Assessment for Tidal Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.1.3. Skill Assessment for High and Low Tidal Level . . . . . . . . . . . . . . . . . . . . . . . 25

4.2. Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.2.1. Harmonic Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.2.2. Skill Assessment for Tidal Current Speed and Direction . . . . . . . . . . . . . . . . 28

4.2.3. Skill Assessment for Tidal Current Slack Time . . . . . . . . . . . . . . . . . . . . . . . 28

5. MODEL HINDCASTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.1. Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.2. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.3. Skill Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.3.1. Skill Assessment for Water Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.3.2. Skill Assessment for High and Low Water Levels . . . . . . . . . . . . . . . . . . . . . 33

5.3.3. Skill Assessment for Current Speed and Direction . . . . . . . . . . . . . . . . . . . . . 33

5.3.4. Skill Assessment for Current Slack Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
iv

6. SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
v

LIST OF FIGURES

Figure 1.1. Map showing New York Harbor and The Port of New York/New Jersey including

PORTS stations and major tributaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Figure 2.1. New York/New Jersey Harbor model grid showing locations of water level gages

and current meter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Figure 2.2. New York/New Jersey Harbor model bathymetry, contours in meter. ............7

Figure 2.3. Nested fine grid ......................................................8

Figure 3.1. Schematic diagram for an uncoupled three-dimensional barotropic POM. . . . . . . . . 13

Figure 3.2. Schematic diagram for a one-way coupled 3-dimensional barotropic POM. . . . . . . 14

Figure 3.3. Schematic diagram for a two-way coupled 3-dimensional barotropic POM. . . . . . . 15

Figure 3.4. Nested grid coupling schematic representation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Figure 4.1. Harmonically predicted and simulated tide (top) and tidal current (bottom) from fine

and coarse grids at Bayonne Bridge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Figure 5.1. Observed water surface elevations at Sandy Hook, NJ and Willets Point, NY for

January, 1997, and surface wind stresses and atmospheric pressure from Buoy 44025.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Figure 5.2. Monthly averaged flow at Raritan, Passaic, Hackensack, and Hudson Rivers, based

on USGS daily averaged flow from 1988 to 1997. . . . . . . . . . . . . . . . . . . . . . . . . . 36

Figure 5.3. Simulated water levels from coarse and fine grids and one- and two- way coupling

models compared with observations at Bayonne Bridge (top) and The Battery

(bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Figure 5.4. Current meter locations at Bergen Point and Bayonne Bridge for 1997 simulation.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Figure 5.5. Simulated current speed from coarse and fine grids and one- and two- way models

compared with observations at Bayonne Bridge. Layer 2 (top) and 3 (bottom) are

about 3 m and 5 m below water surface, respectively. . . . . . . . . . . . . . . . . . . . . . . . 37

Figure 5.6. Simulated current speed from coarse and fine grids and one- and two- way models

compared with observations at Bergen Point. Layer 2 (top) and 3 (bottom) are about

3 m and 5 m below the water surface, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . 38

Figure 5.7. Monthly mean (for 1997) water level for observations at Sandy Hook, Willets Point, 

Bayonne Bridge, and The Battery and for the model at the Bayonne Bridge, The

Battery, and the entire coarse grid domain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
vi

LIST OF TABLES

Table 4.1. Harmonic constants at Sandy Hook and Willets Point for yearly tidal simulation . . . 21

Table 4.2. Comparison of modeled and NOS accepted harmonic constants at Bayonne Bridge 22

Table 4.3. Comparison of modeled and NOS accepted harmonic constants at The Battery . . . . 23

Table 4.4. Tide simulation water level skill assessment standard statistics for entire time series at

Bayonne Bridge and The Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Table 4.5. Tide simulation high and low water level skill assessment standard statistics at Bayonne

Bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Table 4.6. Tide simulation high and low water level skill assessment standard statistics at The

Battery. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Table 4.7. Comparison of Model-Based and NOS-Accepted Current Harmonic Constants at Bayonne

Bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Table 4.8. Tide simulation current speed and direction skill assessment standard suit statistics for

the entire time series at Bayonne Bridge. Note: Predicted: at bin 8, simulated at layer 4, na

= not applicable. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Table 4.9. Skill assessment standard suite statistics for tidal current beginning and end time of SBE

(slack before ebb) and SBF (slack before flood) differences between harmonically predicted

(at bin 8) and simulated currents (at layer 4) at the Bayonne Bridge. Note: na = not applicable

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Table 5.1. Water level hindcast skill assessment standard statistics for complete time series at

Bayonne Bridge and The Battery. (Note: na = not applicable) . . . . . . . . . . . . . . . . . . . . 38

Table 5.2. High and low water level hindcast skill assessment standard suite statistics at the Bayonne

Bridge. (Note: na = not applicable) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Table 5.3. High and low water level hindcast skill assessment standard suite statistics at The Battery.

(Note: na = not applicable) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Table 5.4. Current speed and direction hindcast skill assessment standard suite statistics at Bayonne

Bridge, based on 29,806 six minutes interval data. (Note: na = not applicable)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Table 5.5. Current speed and direction hindcast skill assessment standard suite statistics at Bergen

Point, based on 14,158 six minutes interval data. (Note: na = not applicable) . . . . . . . . 41

Table 5.6. Skill assessment standard suite statistics for begin and end times of SBE (slack before

ebb) and SBF (slack before flood) differences between observed (at bin 7) and simulated

currents (at layer 3) at Bayonne Bridge. (Note: na = not applicable) . . . . . . . . . . . . . . . . 42
1. INTRODUCTION

A New York/New Jersey (NY/NJ) Harbor water level and current nowcast/forecast model system

is under development at NOAA’s National Ocean Service (Wei, et. al. , 1998). The hydrodynamic

model of the system has been developed based on the Princeton Ocean Model (POM) (Blumberg and

Mellor, 1987). Utilizing the near real-time water level and current information from NOS Physical

Oceanographic Real-Time System (PORTS) (Bethem and Frey, 1991), the model system will

provide the water level and current nowcasts and forecasts to mariners to promote navigational safety

and to support oil and hazardous materials spill response activities. Reliable current and water level

information is very important in preventing vessel collisions in a heavy traffic port such as NY/NJ

Harbor, where the U.S. Coast Guard manages vessel traffic based upon tidal current predictions. In

the event of a hazardous materials spill, the real-time and forecast information becomes critical for

predicting the spill movement, thus minimizing the environmental damage (Parker, 1996).

The Harbor and Port of New York and New Jersey (Figure 1.1) has a complex geometry with narrow

navigation channels interconnecting the regional bays, for example, the Kill Van Kull between the

Upper Bay and Newark Bay, the East River between the Long Island Sound and the Upper Bay, the

Arthur Kill between the Newark Bay and the Raritan Bay. These channels are important for both

safe navigation and hydrodynamics in the Harbor. Current shears and eddies, generated by lateral

inertial effects at the junction of channels (e.g., at Bergen Point) and other locations, are important

to pilots and ship captains trying to maneuver large oil tankers and cargo ships. Very high horizontal

resolution is required for a numerical model to accurately predict the occurrence of eddies and

current shears.

Four major river systems provide freshwater to each of the three regional bay; the Raritan River to

the Raritan Bay, the Passaic and Hackensack Rivers to the Newark Bay, and the Hudson River to the

Upper Bay. Discharges from these rivers, ranging from 3 m3

 s-1 in the Hackensack River to 400 m3

s

-1 at Hudson River, not only play the major role in the vertical and horizontal density stratification

but also contribute to the estuarine circulation throughout this hydrodynamically connected system.

The astronomical tide (predominated by the principal semidiurnal component M2) enters the Bay

from the Atlantic Ocean through the entrance, between Sandy Hook and Rockway Point. It brings

salty water that passes through The Narrows (the deepest water, 25 m) and the Upper Bay to the

Hudson River and reaches up to Albany, New York, more than 100 km from the river mouth.

Another branch of water flows past the bend to the Kill Van Kull at Constable, producing a shear

flow around the bend, and then into Newark Bay, mixing with fresh water from the Passaic and

Hackensack Rivers.

The model is a homogeneous three-dimensional version of Princeton Ocean Model (POM) to resolve

water level and three-dimensional velocity. A finer sub-grid model, covering channels and bays

critical to navigation, including the Kill van Kull and Bergen Point, has been developed, embedded

within and dynamically connected to the coarse grid with a coupling technique. This coupled model

has been implemented to produce hourly nowcasts including the near-real-time water level and

current information in the Harbor. The model also produces 36 hour forecasts forced with water

level forecasts at Sandy Hook and Willets Point from a shelf model and wind forecasts from an

atmospheric model.
2

Chapter 2 describes the hydrodynamic model including governing equations and model grid

generation. Coarse and fine grid model coupling techniques are introduced in Chapter 3. Chapter

4 describes one year tidal simulation as a model calibration. Model validation simulations with

observed water levels and river flows as the boundary conditions are presented in Chapter 5. A

summary is given in Chapter 6. 

Figure 1.1. Map showing New York Harbor and The Port of New York/New Jersey including

PORTS stations and major tributaries.
3

2. HYDRODYNAMIC MODEL

2.1. Governing Equations

The hydrodynamic model used in the Port of New York/New Jersey water level nowcast/forecast

system is developed based on the three-dimensional barotropic version of POM (Blumberg and

Mellor, 1987). Since the hydrodynamics of New York Harbor are tidally dominated and the primary

goal of the nowcast/forecast system is to focus on the water levels and the currents for navigation

safety purposes, the density effect has been neglected in the present model development stage. The

governing equations in a sigma coordinate are briefly given as follows. Detailed formulations are

contained in Blumberg and Mellor (1987) or Mellor (1998).

, (1) ∂η

∂

∂

∂

∂

∂

∂ω

t ∂σ

UD

x

VD

y

+ + += 0

, (2) ∂

∂

∂

∂

∂

∂

∂ ω

∂σ

∂η

∂

UD

t

U D

x

UVD

y

U Fx fVD gD

x

+ + + −− + =

2

( ) ∂

∂σ

∂

∂σ ρ

τ τ

K

D

U

sx bx

 M



 



 + −

1

, (3) ∂

∂

∂

∂

∂

∂

∂ ω

∂σ

∂η

∂

VD

t

UVD

x

V D

y

V Fy fUD gD

y

+ + + −+ + =

2

( ) ∂

∂σ

∂

∂σ ρ

τ τ

K

D

V

sy by

 M



 



 + −

1

, (4) ∂

∂

∂

∂

∂

∂

∂ω

∂σ

∂

∂σ

∂

∂σ

q D

t

Uq D

x

Vq D

y

q K

D

q q

2 222 2

+ + +=















 + 



 



 + 



 









	

	










− +

2 2 2 2 3

1

K

D

U V Dq

B

F M

q

∂

∂σ

∂

∂σ 

, (5) ∂

∂

∂

∂

∂

∂

∂ω

∂σ

∂

∂σ

∂

∂σ

q D

t

Uq D

x

Vq D

y

q K

D

q q 2 22 2 2   

+ + +=

















+





 



 +





 









	

	








 E − +

K

D

U V

W Dq

B

F M

1

2 2 3

1

2 2

 

∂

∂σ

∂

∂σ

~

where σ = (z-η)/(H+η), H is the mean sea level water depth, U and V are horizontal velocities, KM

and KH are vertical kinematic viscosity and diffusivity, Kq is vertical turbulence mixing coefficient,

q2

 is twice the turbulence kinetic energy, is the turbulence length scale, =1+E2  ( /k L), k = 0.4 ~

W 

is the von Karman constant, L-1=(η-z)-1+(H+z)-1, B1, E1, and E2 are constants, τs and τb are wind

stress and bottom friction, D=H+η is the total water depth, g is the acceleration due to gravity, f is

the Coriolis parameter, ρ is the water density, and ω is the transformed vertical velocity normal to

a sigma surface. The relationship of ω with Cartesian vertical velocity w is

W U . (6) D

x x

V D

y y

D

t t

=+ + 



 



 + +





 



ω σ  + +

∂

∂

∂η

∂

σ

∂

∂

∂η

∂

σ

∂

∂

∂η

∂

And the horizontal viscosity and diffusion terms Fx and Fy are defined as

F (7) x x

HAM

U

x y

HAM

U

y

V

x = 



 



 + +





	 




 















∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

2
4

F , (8)

y

HA

V

y x

HA

U

y

V

x yM M = 



 



 + +





	 




 















∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

2

where AM, the vertically integrated horizontal eddy viscosity, is defined by the Smagorinsky formula

A Cxy V V M , (9) T = ∇ +∇ ∆ ∆

1

2 ( )

where C, a non-dimensional parameter, is set to be 0.2 in this study; u, ∆x and v, ∆y are the

vertically-integrated velocities and grid spacings in the x and y directions for each grid cell;

∇ +∇ = ( ) . (10) 



 



 + +





 



 +





 









	

	








 V V T u

x

v

x

u

y

v

y

/ /

/

2

2 2

2

2 1 2

∂

∂

∂

∂

∂

∂

∂

∂

The vertical boundary conditions for (1), (2), and (3) are

ω ω () ( ) 0 10 = −= , (11)

[ ] , (12)

K

D

U V

CU V UV M z

∂

∂σ

∂

∂σ , ( , ),σ





 



 = + →− 2 2

1/2

1

where

, (13)

{ } ( )

C MAX

k

H z

z

kb

=

+ 

 

























− 

2

1 0

2

1

0025

ln /

,0.

σ

k = 0.4 is the von Karman constant, z0 is the roughness parameter, and kb is the bottom layer. The

boundary conditions for the turbulence closure equations (4) and (5) are

( )( ) q q Bu , (14) 2 2

1

23 2 ( ), ( ) ( ), 0 0 00 /  = τ

( )( ) q q Bu , (15) 2 2

1

23 2 ( ), ( ) ( ), 1 1 10 / − −= −  τ

where B1 is one of the turbulence closure constants and uτ is the friction velocity at the top or bottom

as denoted.
5

2.2. Split Mode

For computational economy, the split mode is used in the model in which the vertically integrated

equations (external model) are separated out to calculate the free surface elevation (due to fast

moving external gravity waves) from the vertical structure equations, where the vertical velocity

shear (slow moving internal gravity waves) are calculated.

2.3. Time Step Constraints

The external mode of the model time step is limited by the Courant-Friedrichs-Levy (CFL)

computational stability condition

∆ (16)

∆ ∆

t

C x y

E

t

≤ +

−

11 1

2 2

1 2/

where Ct = 2(gH)1/2 + Umax; Umax is the expected maximum velocity. The internal mode time step

(∆tI) criteria is analogous to, however much less stringent than, that for the external model. Typical

ratio of the time steps, ∆tI

/∆tE, for an estuarine is on the order of 10.

2.4. Model Grid

A coarse model grid has been constructed to cover the New York Harbor and vicinity estuarines

from 74° 10' W to 73° 45' W and from 40° 24' N to 40° 52' N including the East River, Hudson River

up to Poughkeepsie, the Newark Bay, the Hackensack and Passic Rivers, Arthur Kill, the Raritan

River, and Raritan Bay (Figure 2.1). The grid itself is orthogonal and is sufficiently fine to minimize

truncation errors. The horizontal resolution varies spatially and ranges from 150 to 1000 m, resulting

in 134 by 73 grid points in the cross- and along- harbor direction. The model water depth ranges

from 3 m in the shallow shoals to 25 m in the navigation channel near The Narrows (Figure 2.2).

The Hudson River north of Spuyten Duyvil has been “bent” to take into account the river effect and

to save on computational cost.

A fine grid, dimensioned 126 by 38 (shaded area in Figure 2.1 and Figure 2.3) and covering the

critical navigation waterways of Kill van Kull and Newark Bay, has been developed and embedded

within the original (coarse) grid. The grid resolution for the nested grid is double that of the coarse

grid. The fine grid takes hydrodynamic information at the interface between the coarse and fine

grids. Due to the a higher spatial resolution, the fine grid is then capable of resolving small scale

eddies in more detail. 

Although the New York Harbor is hydrodynamically connected with Long Island Sound and the NY

Bight, for the operational nowcast/forecast model system to fully utilize information from NOS’s

Physical Oceanographic Real Time System (PORTS) as lateral boundary conditions, the model grid

open boundary has been set at Willets Point, New York, and Sandy Hook, New Jersey.
6

Figure 2.1. New York/New Jersey Harbor model grid showing locations of water level gages and

current meter.
7

Figure 2.2. New York/New Jersey Harbor model bathymetry, contours in meter.
8

Figure 2.3. Nested fine grid.
9

3. MODEL COUPLING

The curvilinear coordinate system used in the model allows fine grids in regions near the Narrows

and the navigation channel approaching Kill Van Kull and Port Elizabeth. This gives us the ability

to provide detailed water level and current information where water currents change dramatically,

however, the placement of the fine grid is constrained by the orthogonality requirement. This means

that refined grid resolution in one part of the model region is often done at the expense of grid

resolution in other subregions. Thus the choice of where in the modeled coastal ocean one can put

more grid points is not completely arbitrary. The information given by the coarse model is not able

to satisfy mariners and Coast Guard requirements for the purposes of safe navigation, efficient oilspill cleanup and managing vessel traffic, especially for the region of the tidal eddy in the west

entrance of the Kill Van Kull, which was confirmed by a towed ADCP survey conducted in 1993

(Parker, 1996). In order to provide more accurate detailed current information in these areas, a fine

grid (FG) model has been developed and nested in the coarse grid (CG). The spatial resolution of

the fine grid is twice that of the coarse grid. There are 7 sigma levels in the vertical in both the CG

and the FG, although extension to cases with different sigma levels is conceptually not difficult but

does require extensive coding. There are two coupling methods that exchange fluxes across the grid

interface (Oey and Chen, 1992) : one-way and two-way couplings. In the one-way coupling, the FG

is driven by fluxes from the CG through the grid interface, and the FG does not feedback any

information to the CG. In the two-way coupling, in addition to providing open boundary conditions

for FG model, CG model also receives flux feedback information from FG model. For convenience,

the model is coded such that a common block was set up to communicate field variables at interface

between two model grids. Both the CG and the FG models are independent and compiled separately

before being coupled, however, the two models run in parallel. At present, the model uses the oneway coupling approach in which the FG model obtains the water elevations and fluxes from the CG

model through the common block.

The evaluation of one- and two- way coupling results is summarized in Chapter 4, Model Hindcasts.

3.1. Grid Comparison

Key features of the two model grids are listed below for comparison:

(1) Coarse Grid

Dimension : 73x134x7

Horizontal Resolution: from 170 to 1000 m

Nested Area: I, from 7 to 71 

J, from 65 to 85 

(2) Fine Grid

Dimension : 26x38x7

Horizontal Resolution: from 70 to 150 m, half of the corresponding coarse grid cell.
10

(3) Vertical Structure: 

The CG and nested FG have same number of vertical sigma levels.

Kcoarse-grid=Kfine-grid=7

(4) Grid Generation

The FG coordinates are interpolated from the CG with half of the corresponding CG cell

size. 

(5) Water Depth Setup

The FG water depths are bilinearly interpolated from the FG.

(6) Nested Grid Model Initialization

The FG is initialized with parameters (velocity flux and water level) interpolated from the

CG when the FG model starts.

(7) Interaction Between CG and FG

Set up a common block between the CG model and FG model so that the two models can

only interact with each other through this common block. Thus, the parameter name remains

the same in the same function subroutines of two models.

(8) Time stepping

The CG model’s external time step is N times the FG model’s external time step, while the

two models have the same internal time step.

(9) Boundary Forcing

The boundary conditions in the FG are interpolated from their overlapped CG cells at each

external time step.

(10) Model Spin-up

The CG model starts first and the FG model can start at any time once the CG model is

started.

3.2. Coupling Considerations

Many factors such as model physics, grid interaction, conservation properties, computational

expense and model applications are taken into account to design a nested model.

3.2.1. Interface Conditions

The interface conditions are designed to maintain continuity and compatibility of solutions between

the two model grids. Following computation of variables in the CG model domain, all flux and field

variables at the input dynamic interface are saved and then interpolated along input interfaces as the

FG model boundary solution. Because of the nature of the staggered grid, the spatial relationships

between CG model and FG model points are different for the flux and field variables. It is important
11

to point out that the flux and the mass at the interface between the CG model and FG model must

be conserved. 

In the two-way coupling, the feedback from the FG model to CG model is obtained at every second

time step of the FG model (i.e., when both FG model and CG model are at the same time level) by

satisfying the flux conservation at the feedback dynamic interface, where a CG model flux location

coincides with corresponding FG model flux locations. All other field variables are obtained from

this specification.

The preceding specification of interface conditions allows two-way interaction of physical processes

to be accomplished. The CG model system provides the FG model with the larger scale forcing

through the dynamic interface and then the FG model affects the larger scale through the feedback

interface. However, it is noted that the FG model values at the boundary are specified externally

from the CG model values and do generate some numerical noise. Therefore, values at points next

to the FG model boundary must not be included in the feedback process. On the other hand, it is

better to place the feedback interface as close as possible to the dynamic interface in order to

maximize the use of information about the FG model variables in the CG model solution (see

Section 3.4 for detail formulation and schematic representation).

3.2.2. Noise Control

Most nested grid models exhibit a compatibility problem at the interface where the two grid systems

meet due to the nonuniform nature of the grids. For instance, a disturbance propagating from the CG

model to the FG model may induce false reflection back to the CG model and scattering into the FG

model. Likewise, a disturbance propagating from the FG model to the CG model may also

experience false reflection back onto the FG model. These interface generated problems may lead

to numerical instabilities that can seriously affect the simulated results over the entire domain. This

is known as the interface condition problem. As Zhang and Chang (1986) pointed out, an optimal

interface procedure which has the following two properties could eliminate this problem: 1) all

resolvable waves propagate across the interface smoothly with only minimal changes in amplitude

and minimum reflection of energy, and 2) mass, momentum and total energy exchanged between the

two grid systems are conserved.

To satisfy the first condition, which is important to allow the nested grid system to operate

effectively, special noise control techniques must be used. Many methods have been employed for

two-way nesting system. Jones (1977) found that the spatial smoother is the most effective method

of noise control compared to other methods tested. In our model, a flow relaxation scheme, similar

to that of Oey and Chen (1992), is applied to the dynamic interface and feedback interface between

FG model and CG model. For the x component depth-averaged velocity, for example, that is
12

UC=aUF +(1-a)UC (17)

where the subscript F denotes the values interpolated from the FG model to the corresponding CG

model, the subscript C indicates the values from the CG model, and a is the weight parameter (ranges

from zero at FG model feedback row to 1 at the two grid systems interface).

For the second condition, the exact conservation of momentum flux at the interface of two grid

systems is satisfied in our model.

3.2.3. Initialization

It is highly desirable that the initial conditions of the FG model and the CG model be determined in

such a way that the fields in the overlap region are compatible when the integration begins. The

procedure for obtaining the grid points values starts with the CG model and then interpolated to the

FG model corresponding points by a bilinear interpolation. These data include flux and threedimensional field variables. In order to attain better quality interface conditions, the bathymetry

between the dynamic interface and feedback interface are specified as the same. So both the FG

model and CG model will have the same variable in this area.

3.2.4. Programing Considerations

In constructing the nested New York/New Jersey model, the interface between the CG model and

FG model has been placed parallel to the CG model axis. When the CG information and its field

variables and the FG information are given, all the necessary information for the FG model

integration such as surface forcing, and field variables, are automatically generated by bilinear

interpolation. The information over the interface zone shared by the FG model and CG model are

stored in the special common blocks, thus minimizing coding errors and simplifying the coupling

procedure coding.

3.3. Coupling Procedures

Figure 3.1 shows a schematic diagram illustrating the procedure of a typical barotropic POM run

without coupling. With the nested grid one-way coupled, the diagram is shown as in Figure 3.2

where the right side is the FG model procedure. The process underlined in Figure 3.3 indicates the

two-way coupling procedure, in addition to the one-way coupling procedure.
13

Figure 3.1. Schematic diagram for an uncoupled three-dimensional barotropic POM.
14

Figure 3.2. Schematic diagram for a one-way coupled 3-dimensional barotropic POM.
15

Figure 3.3. Schematic diagram for a two-way coupled 3-dimensional barotropic POM.
16

3.4. Two-Way Coupling Finite Difference Equations

The one-way coupling algorithm is simple and straight forward for computer program coding. Here

the finite difference form of the feedback from the FG model to CG model for the two-way coupling

at the southern and northern boundary interface (east and west can be derived following similar

notation) are listed as follows. Figure 3.4 illustrates the schematic representation of the nested grid

coupling.

The following are the equations at the southern boundary:

Vflux ic jc Vflux in jn Vflux in jn

V ic jc av H in jn V in jn av H in jn V in jn H ic jc

H ic jc H ic jc H ic jc

H in jn H in jn H in jn

av

x in jn

x ic jc

x in jn

( , ) ( , ) ( , ),

( , ) ( ( , ) ( , ) ( ) ( , ) ( , ))/ ( , ),

( , ) ( ( , ) ( , ))/ ,

( , ) ( ( , ) ( , ))/ ,

(, )

(, )

( ,

= ++

= +− + +

= +−

= +−

= =

1

1 11

1 2

1 2

where

∆

∆

∆ ) (, )

(, ) (, ) ,

( , ) ( , )( , ) ( , )( , )

( ), ) ( , ) ( , ) ( , ))/ ( , ),

(, ) ((, ) (, )

+ −

+ −

−= − − + + − + − +

+ − + −+ − − −

+ == − − +

∆

∆ ∆

∆

x in jn

x ic jc x ic jc

ic jc in jn S in jn in jn S in jn

in jn S in jn in jn S in jn S ic jc

U ic jc U in jn y in jn U

1

1

1 2 2 12 12

1 1 11 1 1 1

1 11

ηη η

η η

( , ) ( , ))/ ( , ),

( , ) ( ( , ) ( , ) ( ) ( , ) ( , ))/ ( , ),

( , ) ( ( , ) ( , ))/ ,

( , ) ( ( , ) ( , ))

in jn y in jn y ic jc

U ic jc auH in jn U in jn au H in jn U in jn H ic jc

H ic jc H ic jc H ic jc

H in jn H in jn H in jn

−− +

+= − − +− + − − +

+= − ++ +

−= − −+ −

22 1

1 2 21 1 1 1 1

1 1 1 12

2 12 2

∆ ∆

or

where

/ ,

(, )

(, )

(, ) ( , )

(, ) ( , )

, ;, ;

2

2

1

2 12

1 11

13 2 3

au

y in jn

y ic jc

y in jn y in jn

y ic jc y ic jc

i il ir j jb i IMn j c cn n

= −

+ = −+ − −

++ − +

= =+ = − =

∆

∆

∆ ∆

∆ ∆ ,

 ...... ; 

where subscripts c and n denote coarse and fine grids, au and av are the weigh parameter for U and

V, il and ir are interface i-index of CG model, S is the surface area (equivalent to art(ic,jc) for coarse

grid and art(in,jn) for fine grid), IMn and JMn are the dimensions of the FG model.
17

The following are the equations at the northern boundary:

Vflux ic jc Vflux in jn Vflux in jn

V ic jc av H in jn V in jn av H in jn V in jn H ic jc

H ic jc H ic jc H ic jc

H in jn H in jn H in jn

av

x in jn

x ic jc

x in jn

( , ) ( , ) ( , ),

( , ) ( ( , ) ( , ) ( ) ( , ) ( , ))/ ( , ),

( , ) ( ( , ) ( , ))/ ,

( , ) ( ( , ) ( , ))/ ,

(, )

(, )

( ,

= ++

= +− + +

= +−

= +−

= =

1

1 11

1 2

1 2

where

∆

∆

∆ ) (, )

(, ) (, ) ,

( , ) ( , )( , ) ( , )( , )

( ), ) ( , ) ( , ) ( , ))/ ( , ),

(, ) ((, ) (, )

+ −

+ −

−= − − + + − + − +

+ − + −+ − − −

− == − − +

∆

∆ ∆

∆

x in jn

x ic jc x ic jc

ic jc in jn S in jn in jn S in jn

in jn S in jn in jn S in jn S ic jc

U ic jc U in jn y in jn U

1

1

1 2 2 12 12

1 1 11 1 1 1

1 11

ηη η

η η

( , ) ( , ))/ ( , ),

( , ) ( ( , ) ( , ) ( ) ( , ) ( , ))/ ( , ),

( , ) ( ( , ) ( , ))/ ,

( , ) ( ( , ) ( , ))

in jn y in jn y ic jc

U ic jc auH in jn U in jn au H in jn U in jn H ic jc

H ic jc H ic jc H ic jc

H in jn H in jn H in jn

−− −

−= − − +− + − − −

−= − −+ −

−= − −+ −

22 1

1 2 21 1 1 1 1

1 1 1 12

2 12 2

∆ ∆

or

where

/ ,

(, )

(, )

(, ) ( , )

(, ) ( , )

, ;, ;

2

2

1

2 12

1 11

13 2 2

au

y in jn

y ic jc

y in jn y in jn

y ic jc y ic jc

i il ir j jt i IMn j JM c c n nn

= −

− = −+ − −

−+ − −

= =− = − = −

∆

∆

∆ ∆

∆ ∆ ,

 ...... ; 
18

Figure 3.4. Nested grid coupling schematic representation.
19

4. TIDE SIMULATIONS

The barotropic three-dimensional barotropic model described in Chapter 2 was calibrated with

astronomical tide simulation. NOS accepted harmonic constants (Table 4.1 referenced to UTC) at

Sandy Hook and Willets Point were used to generate astronomical tide as open boundary conditions

predictions for the year of 1997. Winds, atmospheric pressure, and river discharge were turned off.

The internal and external time steps were specified as 12 and 6 seconds, respectively.

After several test simulations, key hydrodynamic parameters are determined based on the comparison

between simulated and harmonically generated tides at the Bayonne Bridge and The Battery, the two

locations inside the model grid with long term water level records qualified for NOS to provide

accepted harmonic constants. Among other parameters, the roughness depth is specified as 0.1 cm

and the horizontal diffusivity constant C in Equation 8 as 0.1. Water depth and the land-water

boundary are also adjusted, especially along the Kill Van Kull navigational channel, based on the

most recent nautical charts and 1996 USACE dredging plan map. The yearly simulation starts on

January 1, 1997 after 10 days of spin up. The simulated tide and tidal current at Bayonne Bridge,

and tide at The Battery, are saved at 6 minute intervals for analysis. Figure 4.1shows two days of

tide predictions and simulated tides from the fine and coarse grids at the Bayonne Bridge and The

Battery (see Figure 2.1 for locations), and tidal currents at Bayonne Bridge in layers 2 and 4.

Overall, the simulated tidal water levels have a better accuracy than tidal currents and the simulated

currents from the fine grid are more accurate than those of the coarse grid.

4.1. Water Level

4.1.1. Harmonic Constants

The least square program used by the NOS tidal analysis programs (Zervas, 1999), based on

Schureman (1971) has been applied to obtain 37 harmonic constants by analyzing 6 minute interval

simulated tides at the Bayonne Bridge and The Battery for the entire 1997 year. Tables 4.2 and 4.3

show the comparison of NOS accepted and model simulated amplitude and epoch for each

constituent at two locations. It can be seen that M2 is the predominate tide component in New York

Harbor. At the Bayonne Bridge, the M2 amplitude and epoch differences between NOS accepted and

model values are 1.7 cm and 3.3 degrees, respectively. The values are derived from the embedded

fine grid model results. Values derived from the coarse grid model results shows slightly greater

errors (4.4 cm and 3.9 degrees) than that from the fine grid, indicating that model accuracy increases

slightly with grid resolution. Amplitude and epoch differences appear to be greater at The Battery

(5.9 cm and 7.6 degrees for M2). This is probably due to the location of The Battery outside the fine

grid domain. Differences for other tide components are insignificant both in amplitude and epoch.
20

19 20 21

Time in Julian Day (1997)

0

0.5

1

1.5

Current Speed (M/S)

Simulated Tidal Current Speed (Coarse Grid)

Simulated Tidal Current Speed (Fine Grid)

Harmonically Predicted Tidal Current Speed

19 20 21

Time in Julian Day (1997)

−1.5

−1

−0.5

0

0.5

1

1.5

Water Surface Elevation (M, MSL)

Bayonne Bridge

(Astronomical Tide)

Simulated Tide (Coarse Grid)

Simulated Tide (Fine Grid)

Harmonically Predicted Tide

Figure 4.1. Harmonically predicted and simulated tide (top) and tidal current (bottom) from fine

and coarse grids at Bayonne Bridge.
21

Table 4.1. Harmonic constants at Sandy Hook and Willets Point for yearly tidal simulation.

 Sandy Hook Willets Point

 Name Amp. Epoch Amp. Epoch

 (m) (degree) (m) (degree)

 1 M2 0.693 7.5 1.091 118.1 

 2 S2 0.137 35.4 0.189 144.4 

 3 N2 0.157 349.7 0.240 97.9 

 4 K1 0.105 175.3 0.094 194.7 

 5 M4 0.015 266.3 0.036 152.2 

 6 O1 0.054 171.2 0.065 221.5 

 7 M6 0.017 90.7 0.076 166.4 

 8 MK3 0.005 57.9 0.010 208.7 

 9 S4 0.010 14.0 0.000 0.0 

 10 MN4 0.007 276.0 0.022 126.2 

 11 NU2 0.030 349.9 0.054 96.3 

 12 S6 0.000 0.0 0.000 0.0 

 13 MU2 0.026 14.9 0.000 0.0 

 14 2N2 0.022 333.0 0.024 81.3 

 15 OO1 0.004 203.6 0.000 0.0 

 16 LAM2 0.009 356.1 0.021 138.9 

 17 S1 0.010 136.9 0.000 0.0 

 18 M1 0.004 173.2 0.009 225.5 

 19 J1 0.004 177.4 0.005 181.2 

 20 MM 0.000 0.0 0.039 233.8 

 21 SSA 0.030 56.1 0.027 42.3 

 22 SA 0.064 126.5 0.060 135.7 

 23 MSF 0.000 0.0 0.020 215.9 

 24 MF 0.000 0.0 0.018 268.7 

 25 RHO 0.002 169.3 0.000 0.0 

 26 Q1 0.010 177.4 0.014 202.5 

 27 T2 0.011 16.4 0.011 144.3 

 28 R2 0.001 36.5 0.000 0.0 

 29 2Q1 0.001 167.0 0.000 0.0 

 30 P1 0.032 175.5 0.032 206.1 

 31 2SM2 0.000 0.0 0.000 0.0 

 32 M3 0.011 61.2 0.000 0.0 

 33 L2 0.028 9.1 0.092 136.3 

 34 2MK3 0.007 37.2 0.009 193.5 

 35 K2 0.036 35.1 0.051 141.9 

 36 M8 0.000 0.0 0.000 0.0 

 37 MS4 0.011 235.4 0.009 174.1 
22

Table 4.2. Comparison of modeled and NOS accepted harmonic constants at Bayonne Bridge.

 NOS Model

 Amp. Epoch Amp. Epoch

 (m) (degree) (m) (degree)

 1 M2 0.745 21.2 0.728 24.5

 2 S2 0.143 51.3 0.142 54.8

 3 N2 0.166 5.1 0.161 7.6

 4 K1 0.106 182.9 0.103 182.2

 5 M4 0.036 292.4 0.028 324.9

 6 O1 0.053 179.3 0.052 177.7

 7 M6 0.021 174.3 0.029 140.8

 8 MK3 0.010 72.8 0.007 99.9

 9 S4 0.014 44.5 0.012 57.5

 10 MN4 0.017 291.5 0.012 319.4

 11 NU2 0.034 1.6 0.031 6.9

 12 S6 0.000 0.0 0.000 0.0

 13 MU2 0.029 38.1 0.027 41.3

 14 2N2 0.021 345.0 0.022 354.7

 15 OO1 0.003 204.5 0.004 221.5

 16 LAM2 0.013 2.3 0.012 7.8

 17 S1 0.013 139.7 0.010 143.7

 18 M1 0.007 245.9 0.004 182.7

 19 J1 0.005 204.0 0.003 195.4

 20 MM 0.000 0.0 0.005 204.3

 21 SSA 0.031 58.4 0.029 56.7

 22 SA 0.074 129.2 0.061 127.2

 23 MSF 0.000 0.0 0.005 199.5

 24 MF 0.000 0.0 0.002 219.7

 25 RHO 0.003 181.5 0.002 175.7

 26 Q1 0.011 191.3 0.009 185.9

 27 T2 0.013 30.4 0.012 34.7

 28 R2 0.005 270.2 0.001 60.4

 29 2Q1 0.001 175.7 0.000 0.0

 30 P1 0.033 181.8 0.031 183.4

 31 2SM2 0.000 0.0 0.002 225.1

 32 M3 0.012 86.6 0.013 90.3

 33 L2 0.026 10.2 0.032 25.1

 34 2MK3 0.009 46.1 0.010 58.4

 35 K2 0.040 47.9 0.037 54.8

 36 M8 0.000 0.0 0.006 106.4

 37 MS4 0.018 284.9 0.012 290.1
23

Table 4.3. Comparison of modeled and NOS accepted harmonic constants at The Battery.

 NOS Model

 Amp. Epoch Amp. Epoch

 (m) (degree) (m) (degree)

 1 M2 0.671 19.4 0.730 27.0

 2 S2 0.133 45.3 0.141 55.0

 3 N2 0.149 0.9 0.162 9.0

 4 K1 0.102 180.4 0.107 181.5

 5 M4 0.025 252.3 0.022 252.8

 6 O1 0.054 177.1 0.056 179.0

 7 M6 0.028 153.1 0.030 154.3

 8 MK3 0.009 85.1 0.006 83.1

 9 S4 0.012 17.4 0.012 46.1

 10 MN4 0.010 263.9 0.006 258.6

 11 NU2 0.028 0.8 0.032 10.8

 12 S6 0.000 0.0 0.000 0.0

 13 MU2 0.025 9.2 0.024 30.9

 14 2N2 0.018 346.2 0.022 352.1

 15 OO1 0.002 183.6 0.004 218.9

 16 LAM2 0.011 19.4 0.010 17.7

 17 S1 0.012 133.8 0.010 143.1

 18 M1 0.004 178.7 0.004 181.9

 19 J1 0.004 182.0 0.004 190.9

 20 MM 0.000 0.0 0.004 212.2

 21 SSA 0.030 54.6 0.030 55.7

 22 SA 0.077 131.8 0.063 126.8

 23 MSF 0.000 0.0 0.003 207.5

 24 MF 0.000 0.0 0.002 257.6

 25 RHO 0.002 175.7 0.002 174.0

 26 Q1 0.012 189.8 0.010 185.0

 27 T2 0.011 28.2 0.011 34.4

 28 R2 0.001 45.3 0.000 0.0

 29 2Q1 0.002 173.7 0.001 169.6

 30 P1 0.031 182.2 0.033 183.0

 31 2SM2 0.000 0.0 0.001 224.0

 32 M3 0.010 81.4 0.012 85.2

 33 L2 0.015 21.6 0.031 39.8

 34 2MK3 0.006 61.1 0.008 58.4

 35 K2 0.036 44.0 0.037 54.8

 36 M8 0.004 329.7 0.002 29.4

 37 MS4 0.016 250.8 0.017 261.2
24

4.1.2. Skill Assessment for Tidal Level

A standard suit of assessment statistics is defined in NOS (1999). Parameters in the suite calculated

based on the time series of harmonically predicted and model simulated tidal water levels (hourly)

at the Bayonne Bridge and The Battery are derived. Defining the error as the predicted tide minus

the simulated tide, these parameters are (NOS, 1999):

1. SM: Series mean.

2. SD: Standard deviation of the error.

1. RMSE: Root mean squared error.

2. CF(x): Central Frequency. Percentage of errors that lie within the limit ±x

3. POF(x): Positive Outlier Frequency. Percentage of errors that are greater than x.

4. NOF(x): Negative Outlier Frequency. Percentage of errors that are less than x.

5. MDPO(x): Maximum Duration of Positive Outliers. A positive outlier event is two or more

consecutive occurrences of an error greater than x. MDPO is the length (number of consecutive

occurrences) of the longest event.

6. MDNO(x): Maximum Duration of Negative Outliers. A negative outlier event is two or more

consecutive occurrences of an error less than -x. MDNO is the length (number of consecutive

occurrences) of the longest event.

Table 4.4 lists these parameters at Bayonne Bridge and The Battery. The criteria accepted by NOS

are also included in the table. All model statistical parameters pass the criteria.

Table 4.4. Tide simulation water level skill assessment standard statistics for entire time series at

Bayonne Bridge and The Battery.

Bayonne Bridge The Battery NOS

Accepted

Predicted Model Difference Predicted Model Difference Criteria

SM (cm) 0.04 -1.43 -1.47 0.04 -2.53 -2.56 na

SD (cm) na na 4.68 na na 8.87 na

RMSE (cm) na na 4.91 na na 9.23 na

CF (15 cm) % 99.1 92.1  90

POF (30 cm) % 0 0 1

NOF (30 cm) % 0 0 1

MDPO (30 cm) (Hour) 0 0 24

MDNO (30 cm) (Hour) 0 0 24
25

4.1.3. Skill Assessment for High and Low Tidal Level

A standard suit of assessment statistics for the amplitude and time at high and low water time series

is computed. This subset time series for high and low water is derived from the entire 6 minute

interval model simulated and harmonically predicted tide time series. Differences of amplitude and

time between the subset time series are computed and the standard suit of statistical parameters are

derived and listed in Tables 4.5 and 4.6. All model parameters pass the criteria.

Table 4.5. Tide simulation high and low water level skill assessment standard statistics at Bayonne

Bridge.

Bayonne Bridge

NOS Accepted

Criteria

High Water Low Water

Amplitud

e

Time Amplitude Time

Difference SM (cm) (min) 0.9 14.5 0.4 7.2 na

Difference SD (cm) (min) 1.9 5.9 2.2 4.7 na

RMSE (cm) (min) 2.1 15.7 2.2 8.6 na

CF (15 cm) (30 min) % 100 99.7 100 100  90

POF (30 cm) (60 min) % 0 0.3 0 0 1

NOF (30 cm) (60 min) % 0 0 0 0 1

MDPO (30 cm) (#) 0 0 0 0 3

MDNO (30 cm) (#) 0 0 0 0 3
26

Table 4.6. Tide simulation high and low water level skill assessment standard statistics at The

Battery.

The Battery

NOS Accepted

Criteria

High Water Low Water

Amplitud

e

Time Amplitude Time

Difference SM (cm) (min) 4.9 18.6 -9.9 11.7 na

Difference SD (cm) (min) 1.5 5.8 1.7 6.2 na

RMSE (cm) (min) 5.1 19.5 10.1 13.2 na

CF (15 cm) (30 min) % 100 96.1 100 100  90

POF (30 cm) (60 min) % 0 0 0 0 1

NOF (30 cm) (60 min) % 0 0 0 0 1

MDPO (30 cm) (#) 0 0 0 0 24

MDNO (30 cm) (#) 0 0 0 0 24
27

4.2. Current

4.2.1. Harmonic Constants

The longest consecutive ADCP current meter record available within New York Harbor are about

4 months at Bayonne Bridge from January 1 to April 30, 1998. Harmonic constants at bin 8, derived

by NOS and at layer 2, derived from the model in the principal current direction (257 degrees true)

are listed in Table 4.7. Difference for M2 amplitude is about 7 cm s-1, however, the model-based

phase lags by 13 degrees, equivalent to about 28 minutes.

Table 4.7. Comparison of model-based and NOS accepted current harmonic constants at Bayonne

Bridge.

Note: Harmonic constants are in principal current direction 257 degree True.

 NOS Model

 Amp. Epoch Amp. Epoch

 Name (m s-1) (degree) (m s-1) (degree)

 1 M(2) 0.789 285.6 0.851 299.0

 2 S(2) 0.150 329.8 0.179 338.7

 3 N(2) 0.142 269.8 0.186 287.3

 4 K(1) 0.051 79.5 0.063 96.4

 5 M(4) 0.082 185.5 0.116 268.9

 6 O(1) 0.023 74.7 0.026 90.5

 7 M(6) 0.066 64.9 0.084 74.7

 8 MK(3) 0.000 0.2 0.000 0.2

 9 S(4) 0.005 46.3 0.025 18.5

 10 MN(4) 0.377 37.6 0.030 18.3

 11 NU(2) 0.325 83.7 0.472 58.0

 12 S(6) 0.557 65.9 0.362 76.4

 13 MU(2) 0.160 60.5 0.000 0.0

 14 2N(2) 0.035 4.7 0.543 37.6

 15 OO(1) 0.000 0.3 0.000 0.3

 16 LAMDA(2) 0.078 33.9 0.021 27.2

 17 S(1) 0.299 68.1 0.222 62.3

 18 M(1) 0.000 0.0 0.006 53.1

 19 J(1) 0.042 34.2 0.021 36.5

 20 MM 0.006 98.1 0.021 36.0

 21 SSA 0.000 0.0 0.023 52.3

 22 SA 0.000 0.4 0.000 0.4

 23 MSF 0.000 0.0 0.000 0.0

 24 MF 0.000 0.0 0.004 4.0

 25 RHO(1) 0.000 0.0 0.000 0.0

 26 Q(1) 0.021 1.4 0.000 0.0

 27 T(2) 0.093 48.4 0.051 0.0

 28 R(2) 0.000 0.0 0.153 18.4

 29 2Q(1) 0.000 0.5 0.000 0.5

 30 P(1) 0.016 79.9 0.000 0.0

 31 2SM(2) 0.024 98.6 0.019 98.6

 32 M(3) 0.010 48.5 0.061 36.5

 33 L(2) 0.022 4.9 0.028 29.0

 34 2MK3(3) 0.546 75.6 0.592 73.5

 35 K(2) 0.156 11.0 0.283 35.5

 36 M(8) 0.000 0.6 0.000 0.6

 37 MS(4) 0.197 97.2 0.017 25.1
28

4.2.2. Skill Assessment for Tidal Current Speed and Direction

Similar to the tide water level skill assessment, the modeled astronomical tidal current speed and

direction are compared with predictions from NOS harmonic constants listed in Table 4.7 at the

Bayonne Bridge. The entire year 6-minute interval speeds and directions are used in the analysis.

Table 4.8 lists the standard suite of skill assessment parameters required by NOS (1999). Only

directions with harmonically predicted and modeled speed greater than 26 cm s-1 are included in the

skill assessment analysis. Tidal current speed has a central frequency of 81.8 %, which is below the

NOS accepted criterion of 90%. This is due to the fact that the modeled tidal current lags the

predictions, as appeared in the M2 epoch (Table 4.7). This will also show in the time of SBE (slack

before ebb) and SBF (slacks before flood), listed in Table 4.9. Besides the speed central frequency,

other skill parameters meet NOS accepted criteria by a large margin. 

Table 4.8. Tide simulation current speed and direction skill assessment standard suit statistics for

the entire time series at Bayonne Bridge. Note: Predicted: at bin 8, simulated at layer 4, na = not

applicable.

Speed Direction NOS

Accepted

Predicted Model Difference Predicted Model Difference Criteria

SM (cm/s) (deg) 54.1 59.9 5.9 159.1 170.5 11.4 na

SD (cm/s) (deg) na na 18.9 na na 4.9 na

RMSE (cm/s) (deg) na na 19.8 na na 12.4 na

CF (26 cm/s) (22.5 deg)% 81.2* 98.9  90

POF (52 cm/s)(45 deg) % 0.6 0 1

NOF (52 cm/s) (45 deg)% 0.2 0.03 1

MDPO (52 cm/s) (45 deg)(Hour) 0 0 24

MDNO (52 cm/s)(45 deg) (Hour) 0 0 24

4.2.3. Skill Assessment for Tidal Current Slack Time

Important information regarding the tidal current in terms of navigation safety is the start and end

time of the slack water. This information is important for vessels navigating in a high current

channel since it is easier to maneuver during the slack water. The beginning and end times of SBE

and SBF time series are obtained from the original uniform-interval harmonically predicted and

model-based time series. Two sets of standard NOS suite statistics are then computed based on the

differences of SBE and SBF beginning and end times between harmonically predicted and modelbased tidal currents.
29

Table 4.9 indicates that, in general, the simulated time of SBE and SBF lags behind the tide

prediction. This can also be seen clearly in the current speed time series, Figure 4.1. Because of the

phase lag, many skill statistics do not meet NOS accepted criteria. These statistics are noted with

asterisks in the table. The phase lag is much greater for the time of slack before the flood. A

possible reason for missing the target is discussed below.

NOS accepted harmonic constants at the Bayonne Bridge are based on data collected between

January 1 and April 30, 1998. Due to the complex shallow water interaction in the vicinity of

measurement and the flow regimes between Newark Bay, Kill Van Kull, and Arthur Kill, a phase

lag during SBF exists in the harmonically predicted tidal current when compared with observations.

The model simulated tidal current accuracy could be improved by adjusting the shoreline location

or other model parameters without increasing grid resolution. However, this process could be very

time consuming since many sensitivity tests would be needed. At present, we continue to work on

this improvement in order to be closer to the NOS accepted criteria.

Table 4.9. Skill assessment standard suite statistics for tidal current beginning and end time of SBE

(slack before ebb) and SBF (slack before flood) differences between harmonically predicted (at bin

8) and simulated currents (at layer 4) at the Bayonne Bridge. Note: na = not applicable

SBE SBF NOS Accepted Criteria

SM (minutes) 30.7 35.4 na

SD (minutes) 20.6 12.5 na

RMSE (minutes) 36.9 37.5 na

CF (15 minutes) % 27.5* 2.9*  90

POF (30 minutes) % 47.9* 67.6* 1

NOF (30 minutes) % 0 0.2 1

MDPO (30 minutes) (#) 0 33* 24

MDNO (30 minutes) (#) 0 0 24

31

5. MODEL HINDCASTS

Results reported in Chapter 4 show good comparisons between model-simulated and harmonically

predicted tides and tidal currents. The model is then validated with observed total water levels and

currents over a period from January 1 to December 31, 1997. The purpose of this simulation is twofold; validating hydrodynamic parameters used in the model and assessing the model skill at

handling the meteorological and hydrological effects. Both the one- and two-way coupled models

described in Chapter 3 are used for the simulation in order to evaluate if there is an accuracy

improvement in the nested grid and the two-way coupling technique. However, the skill assessment

is performed based on the results from the one-way coupled model.

5.1. Boundary Conditions

Water level observations at Sandy Hook, NJ, and Willets Point, NY, are used as model lateral open

boundary conditions. The model is also forced at the surface with surface winds and atmospheric

pressure from Buoy 44025 near the harbor entrance. Figure 5.1 shows the water levels at Sandy

Hook and Willets Point and the hourly buoy wind stresses and atmospheric pressure for January,

1997. The water level time series show that the semidiurnal tide dominates, with more than 1.7 m

spring tide range at Sandy Hook and 2.0 m at Willets Point. In addition to the astronomical tide, the

meteorological effects on the water level are clear during a storm moving through the area around

January 7. Mean water level decreased at both locations due to the eastward wind blowing offshore.

On January 10, the atmospheric pressure dropped to 991 mb due to the storm center moving into the

area. Mean water levels increased due to strong westward winds (up to 16 dyne cm-2) associated

with the low pressure center. Wind direction then returned to eastward after the storm center passed

and the water level was lowered. This illustrates the coastal meteorological effect on the water levels

at Willets Point and Sandy Hook, which in turn influences the water levels in the harbor.

Monthly mean river discharges (Figure 5.2) based on 1988 to 1997 United States Geological Survey

(USGS) daily mean flow at four rivers: Raritan (Sta. No: 01403060, below Calco Dam at Bound

Brook, NJ), Passaic (Sta. No: 01389500, Little Falls, NJ), Hackensack (Sta. No: 01377000, at

Riverdale, NJ), and Hudson Rivers (Sta. No: 01335754, above Lock 1, near Waterford, NY), are

specified as inflow to the model grid. The Hudson River is the major freshwater tributary in this

estuarine system with mean discharges reaching 470 m3

 s-1 in the spring. Discharges from the

Raritan and Passaic Rivers account for only 20% of the Hudson River mean flow. Tests show that

although river discharges may modify the tidal current phase near the eastern entrance to the Kill

Van Kull, the effects on the water levels in the bay are minor when compared to the coastal

meteorological effects.

5.2. Results

Figure 5.3 shows the comparison between simulated water levels and observations at the Bayonne

Bridge and The Battery (Fig. 1). Simulated water levels show no significant difference between the

coarse and fine grids at both locations. In addition, simulated water levels at the Bayonne Bridge

from the one- and two-way coupling models are very similar, indicating the model nesting and
32

coupling technique have insignificant impact on simulated water levels. However, the impact of grid

resolution and the coupling technique on the current speed is apparent.

Figure 5.4 shows two current meter locations near the Bayonne Bridge and Bergen Point. The

Bergen Point ADCP (Acoustic Doppler Current Profiler) recorded valid measurements during

January and February 1997while the current meter at the Bayonne Bridge recorded valid

measurements from January to June 1997. There was a period about 40 days when both current

meters were working simultaneously. Figures 5.5 and 5.6 show observed and simulated current

speed time history at Bayonne Bridge and Bergen Point. Model results shown in the figures are at

layers 2 and 3 (about 3 and 5 m from water surface) from 3 cases: coarse grid, one-way coupling fine

grid, and two-way coupling fine grid. Observations are taken from bin 9 and bin 7 at depths

corresponding to model layers 2 and 3. For a better comparison, the observed currents have been

low-pass filtered to smooth out high frequency signals less than 90 minutes. The current speed and

current patterns during flood and ebb are quite different between two locations. The ebb current

speed is much less than the flooding current speed at Bergen Point. In general, simulated maximum

current speed from the coarse grid (dotted line) is less than that from the fine grid at both locations

perhaps due to lack of fine scale resolution, particularly at Bergen Point (Fig. 5.6). Current speeds

from the one- and two-way coupling schemes show insignificant differences at both locations. At

the Bayonne Bridge (Fig. 5.5), the model under-predicts the current during the flood and overpredicts during the ebb.

 

5.3. Skill Assessment

The simulated water levels and currents are compared with observations to evaluate the model skill

according to the procedures and statistic parameter requirements described in NOS (1999). The

purpose is to evaluate if the model is accurate for water level and current predictions. The water

level and current are assessed separately. For water level skill assessment, the complete simulated

and observed hourly time series as well as the high and low water time series, are analyzed to obtain

the standard suite of statistical parameters. For the currents, the simulated and observed 6-minute

interval speed and direction information are used for standard suite of statistical parameters. The

slack time statistics, involving the beginning and end time of the slack current, are also obtained

according to NOS (1999).

5.3.1. Skill Assessment for Water Levels

Table 5.1 lists the standard suite of statistics for water levels at the Bayonne Bridge and The Battery.

Hourly observed and model data at Bayonne Bridge for 12 months in 1997 are used, however, only

four months (January to April in 1997) of data at The Battery are used due to the observed data

quality problem from May to December (William Stoney, NOS, personal communication). The

acceptable criteria recommended by NOS are also included in the table. All the model statistical

parameters are within NOS acceptable range. The simulated mean water level (MWL) is higher than

the observed MWL at the Bayonne Bridge by 2.3 cm, however, lower at The Battery by 1.2 cm.

Monthly MWL at Sandy Hook, Willets Point, Bayonne Bridge, and The Battery are shown in Figure

5.7. Apparently, the high monthly MWL at the Bayonne Bridge and The Battery for April results
33

from MWL at Sandy Hook. However, unusual high observed MWL at The Battery occurs from May

to November due to data error. Average MWL for the entire coarse grid domain is also shown in

Figure 5.7. The entire domain average MWL is very close to the values at Sandy Hook, except in

November, indicating that there is only a small portion of the net inflow influence from Willets Point

through East River to the Harbor.

5.3.2. Skill Assessment for High and Low Water Levels

A standard suite of assessment statistics for amplitude and time of high and low water are computed

for the Bayonne Bridge and The Battery. Simulated water levels at the Bayonne Bridge and The

Battery are taken from the fine grid and coarse grid, respectively. The high and low water time series

subsets are derived from the entire 6-minute interval simulated and observed water level time series

and the differences are computed. The standard suite of statistical parameters are derived and listed

in Tables 5.2 and 5.3. All statistical parameters at the Bayonne Bridge are within NOS accepted

criteria; however, CF (84.9%) and POF (1.3%) of high water time at The Battery are slightly below

the threshold. Simulated high and low water time lag behind the observations about 20 minutes at

both locations. The mean model high and low water amplitudes are higher than the observations,

except for the low water amplitude at The Battery.

5.3.3. Skill Assessment for Current Speed and Direction

Current observations in bin 7 (about 5 m below water surface) are compared with simulated current

speed and direction in layer 3 (also about 5 m below the water surface) at the Bayonne Bridge over

5 months from January 17 to June 19, 1997. Because there are 3 gaps in the observed data over this

5 month period, the entire data set has been separated into 4 continuous data sets, resulting in 29,806

total valid 6-minute interval data, equivalent to about 4 months. The simulated currents are

interpolated to the observed data time to make one-to-one comparisons. The parameters in the

analysis are obtained based on the entire data set except for MDPO and MDNO (maximum duration

of positive/negative outliers), which are based on each continuous data set. 

Current speed and direction skill assessments for the Bayonne Bridge are listed in Table 5.4. The

current speed CF (82.8%) is slightly below the NOS acceptable criterion (90%). Other parameters

are either close to or within the NOS acceptable values. The speed RMS error of about 19 cm s-1 is

mostly due to the phase lag of simulated current speed. This can also be seen in the SBF and SBE

slack time analysis results presented in Table 5.6.

Available current speed and direction observations (bin 7 for observations and layer 3 for simulated)

at Bergen Point were only half of those at Bayonne Bridge. About 14,156 continuous 6-minute

interval data are used in the analysis, and the result is listed in Table 5.5. The skill is not as good

as Bayonne Bridge, probably due to the complicated flow pattern in the area.
34

5.3.4. Skill Assessment for Current Slack Time

Similar to the astronomical simulation, the skill assessment for the beginning and end time of SBE

and SBF series are computed. First, the beginning and end time of SBE and SBF are obtained from

the observed and uniform-interval model based time series. Two sets of standard NOS statistics are

then computed based on the differences of SBE and SBF beginning and end times between observed

and model-based tidal currents. Table 5.6 lists the statistical parameters for Bayonne Bridge.

Although the model performance is below NOS acceptable criteria, the statistics are still better than

the results from the tidal simulation (Table 4.9). The skills of CF, POF, and NOF have been

improved dramatically, although still below the criteria, when the criteria was doubled (relaxed)

(below the double line in Table 5.6). Due to the complex flow patterns and shears near Bergen

Point, it is very difficult to define SBE and SBF based on a single pre-specified current speed.

Therefore, the slack time analysis is not performed at this location.
35

Figure 5.1. Observed water surface elevations at Sandy Hook, NJ and Willets Point, NY for

January, 1997, and surface wind stresses and atmospheric pressure from Buoy 44025.
36

1 2 3 4 5 6 7 8 9 10 11 12

Month

0

100

200

300

400

500

Discharge (m **3/s)

Hudson River

1 2 3 4 5 6 7 8 9 10 11 12 0

10

20

30

40

50

60

Discharge (m **3/s)

Raritan River

Passaic River

Hackensack River

19 20 21

Julian Day (UTC, 1997)

−1.5

−1

−0.5

0

0.5

1

1.5

Water Level (m, MSL)

Observations

Model (one way, coarse grid)

Model (two way, coarse grid)

19 20 21

−1.5

−1

−0.5

0

0.5

1

1.5

Water Level (m, MSL)

Observations

Model (one way, coarse grid)

Model (one way, fine grid)

Model (two way, fine grid)

Bayonne Bridge

The Battery

Figure 5.2. Monthly averaged flow at Raritan, Passaic, Hackensack, and Hudson Rivers, based on

USGS daily averaged flow from 1988 to 1997.

Figure 5.3. Simulated water levels from coarse and fine grids and one- and two- way coupling

models compared with observations at Bayonne Bridge (top) and The Battery (bottom).
37

19 20 21

Julian Day (UTC, 1997)

0

0.5

1

1.5

Current Speed (m/s)

Observations (bin 7)

Model (one way, coarse grid)

Model (one way, fine grid)

Model (two way, fine grid)

19 20 21

0

0.5

1

1.5

Current Speed (m/s)

Bayonne Bridge, New York

Observations (bin 9)

Model (one way, coarse grid)

Model (one way, fine grid)

Model (two way, fine grid)

Layer 2

Layer 3

Figure 5.4. Current meter locations at Bergen Point and Bayonne Bridge for 1997 simulation.

Figure 5.5. Simulated current speed from coarse and fine grids and one- and two- way models

compared with observations at Bayonne Bridge. Layer 2 (top) and 3 (bottom) are about

3 m and 5 m below water surface, respectively.
38

19 20 21

Julian Day (UTC, 1997)

0

0.5

1

1.5

Current Speed (m/s)

Observations (bin 7)

Model (one way, coarse grid)

Model (one way, fine grid)

Model (two way, fine grid)

19 20 21

0

0.5

1

1.5

Current Speed (m/s)

Bergen Point, New York

Observations (bin 9)

Model (one way, coarse grid)

Model (one way, fine grid)

Model (two way, fine grid)

Layer 2

Layer 3

Figure 5.6. Simulated current speed from coarse and fine grids and one- and two- way models

compared with observations at Bergen Point. Layer 2 (top) and 3 (bottom) are about 3

m and 5 m below the water surface, respectively.

Table 5.1. Water level hindcast skill assessment standard statistics for complete time series at

Bayonne Bridge and The Battery. (Note: na = not applicable)

Bayonne Bridge The Battery NOS

Accepted

Observed Model Difference Observed Model Difference Criteria

SM (cm) 7.6 9.9 2.3 8.0 6.8 -1.2 na

SD (cm) na na 8.2 na na 9.2 na

RMSE (cm) na na 8.6 na na 9.3 na

CF (15 cm) % 91.5 90.9  90

POF (30 cm) % 0.7 0.1 1

NOF (30 cm) % 0.1 0.2 1

MDPO (30 cm) (Hour) 7 1 24

MDNO (30 cm) (Hour) 2 3 24
39

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month (1997)

−5

0

5

10

15

20

25

Mean Water Level (cm)

Observations (average: 13.9 cm)

Model (average: 10.0 cm)

The Battery

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month (1997)

−5

0

5

10

15

20

25

Mean Water Level (cm)

Observations (average; 9.7 cm)

Model (average: 11.7 cm)

Bayonne Bridge

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month (1997)

−5

0

5

10

15

20

25

Mean Water Level (cm)

Observation, Sandy Hook (average: 12.0 cm)

Observations, Willets Point (average: 8.4 cm)

Model, entire grid domain (average: 12.7 cm)

Figure 5.7. Monthly mean (for 1997) water level for observations at Sandy Hook, Willets Point,

Bayonne Bridge, and The Battery and for the model at the Bayonne Bridge, The Battery,

and the entire coarse grid domain.
40

Table 5.2. High and low water level hindcast skill assessment standard suite statistics at the Bayonne

Bridge. (Note: na = not applicable)

Bayonne Bridge

NOS Accepted

Criteria

High Water Low Water

Amplitud

e

Time Amplitude Time

Difference SM (cm) (min) 3.0 6.9 5.4 0.8 na

Difference SD (cm) (min) 5 17.5 6.9 17 na

RMSE (cm) (min) 5.8 18.8 8.7 17 na

CF (15 cm) (30 min) % 97.2 90.6 91.9 94.3  90

POF (30 cm) (60 min) % 0.1 0.7 1 0 1

NOF (30 cm) (60 min) % 0 0.1 0 0.6 1

MDPO (30 cm) (#) 1 1 2 0 3

MDNO (30 cm) (#) 0 1 0 1 3

Table 5.3. High and low water level hindcast skill assessment standard suite statistics at The Battery.

(Note: na = not applicable)

The Battery

NOS Accepted

Criteria

High Water Low Water

Amplitud

e

Time Amplitude Time

Difference SM (cm) (min) 5.2 12.5 -6.1 4.5 na

Difference SD (cm) (min) 5.5 18.4 6.5 16.4 na

RMSE (cm) (min) 7.5 22.2 8.9 17.1 na

CF (15 cm) (30 min) % 96.6 84.9* 96.1 92.4  90

POF (30 cm) (60 min) % 0.4 1.3* 0 0 1

NOF (30 cm) (60 min) % 0 0 0 0 1

MDPO (30 cm) (#) 1 1 0 0 24

MDNO (30 cm) (#) 0 0 1 0 24
41

Table 5.4. Current speed and direction hindcast skill assessment standard suite statistics at Bayonne

Bridge, based on 29,806 six minutes interval data. (Note: na = not applicable)

Speed Direction NOS

Accepted

Observed Model Difference Observed Model Difference Criteria

SM (cm/s) (deg) 53.6 56.8 3.2 183.9 174.2 -9.7 na

SD (cm/s) (deg) na na 18.8 na na 23.6 na

RMSE (cm/s) (deg) na na 19.1 na na 25.6 na

CF (26 cm/s) (22.5 deg)% 82.8 93.3  90

POF (52 cm/s)(45 deg) % 1.1 0.4 1

NOF (52 cm/s) (45 deg)% 0.5 1.4 1

MDPO (52 cm/s) (45 deg)(Hour) 1.5 1.4 24

MDNO (52 cm/s)(45 deg) (Hour) 1.7 0.9 24

Table 5.5. Current speed and direction hindcast skill assessment standard suite statistics at Bergen

Point, based on 14,158 six minutes interval data. (Note: na = not applicable)

Speed Direction NOS

Accepted

Observed Model Difference Observed Model Difference Criteria

SM (cm/s) (deg) 31.1 41.5 10.4 278.3 271.9 -6.4 na

SD (cm/s) (deg) na na 18.5 na na 46.4 na

RMSE (cm/s) (deg) na na 21.2 na na 46.8 na

CF (26 cm/s) (22.5 deg)% 83.9 77.3  90

POF (52 cm/s)(45 deg) % 3.6 1.6 1

NOF (52 cm/s) (45 deg)% 0.1 6.1 1

MDPO (52 cm/s) (45 deg)(Hour) 2.5 0.7 24

MDNO (52 cm/s)(45 deg) (Hour) 0.5 1.9 24
42

Table 5.6. Skill assessment standard suite statistics for begin and end times of SBE (slack before

ebb) and SBF (slack before flood) differences between observed (at bin 7) and simulated currents

(at layer 3) at Bayonne Bridge. (Note: na = not applicable)

Bayonne Bridge

SBE SBF NOS Accepted Criteria

SM (minutes) 8.5 24.0 na

SD (minutes) 26.0 26.0 na

RMSE (minutes) 27.4 36.1 na

CF (15 minutes) % 46.0 17.6  90

POF (30 minutes) % 19.3 38.4 1

NOF (30 minutes) % 5.3 3.1 1

CF (30 minutes) % 75.4 58.5

POF (60 minutes) % 1.8 3.8

NOF (60 minutes) % 0.7 1.6
43

6. SUMMARY

The Port of NY/NJ water level and current nowcast/forecast model has been developed based on the

three-dimensional barotropic Princeton Ocean Model. The purpose of developing this model is for

water level and current predictions within the New York Harbor. The model will be the core

component within the nowcast/forecast system which utilizes NOS PORTS information to provide

near real-time nowcast information. With proper water level forecasts at Sandy Hook and Willets

Point such as from NWS’s ETSS (Extra Tropical Storm Surge), wind stress forecasts such as NWS’s

Eta, and river flow forecasts, the system will also provide short term forecasts to mariners including

ship pilots and the Coast Guard for optimizing ship operation, navigation safety, and vessel traffic

control.

The model includes a fine grid, which covers the Upper Bay, the Kill Van Kull, and Newark Bay,

nested within the coarse grid. The coupling technique, developed in this study, allows water levels

and momentum fluxes to be communicated between the two grids through the grid interface. The

model code uses a common block to store the interface information so that no external data files are

required for model information exchange and the two models are running within one executable

code. The model has been calibrated for tidal simulations and assessed with long term observed

water levels and currents spanning over various time scales from tidal to seasonal cycles. The model

simulations show insignificant differences for water levels between the fine grid and the coarse grid.

However, the fine grid is more accurate in simulating currents than the coarse grid due to a higher

grid resolution and more detailed shore and bathymetry representation. Experiments also show that

the simulated current differences between one- and two- way coupling are insignificant. Therefore,

the one-way coupling model will be used in the proposed operational nowcast/forecast model

system.

The barotropic POM model used in the system does not include the effects of density. Therefore,

for the simulated circulation, the bottom friction is the primary factor responsible for the vertical

velocity structure due to lack of density stratification. Industrial ship operation requires the density

information for maximizing the cargo draft. In the near future the barotropic model will be extended

to include the salinity and temperature. The salinity and temperature information will not only be

useful for navigation safety and the economy but also the key information input for water quality and

environmental requirements.

ACKNOWLEDGMENTS

The development of Port of New York/New Jersey water level and current nowcast/forecast model

system has been carried out at Coast Survey Development Laboratory (CSDL) of NOS’s Office of

Coast Survey under the leadership of CSDL’s Chief Dr. Bruce Parker. Dr. Parker suggested the

development of nested grid model in resolving detail current pattern and structure in the Kill Van

Kull for the navigation purpose. The second author Manchun Chen, a visiting scientist at CSDL

from National Marine Data Information Service (NMDIS) of Peoples Republic of China’s (PRC)

State Oceanographic Agency (SOA), developed the nested grid model coupling technique. We thank
44

Dr. Leo Oey of Princeton University for providing guidance in the model nesting technique

development. Dr. Frank Aikman, Chief of CSDL’s Marine Modeling and Analysis Programs

(MMAP) has provided valuable comments to the project. His critical report review is acknowledged.

Dr. Aijun Zhang, also a visiting scientist from NMDIS, is also acknowledged for his assistance in

performing many model sensitivity experiments.

REFERENCES

Bethem, T.D. and H.R. Frey, 1991. Operational Physical Oceanographic Real-Time Data

Dissemination. In Proc. IEEE OCEANS ‘91, 1991, p.864.

Blumberg, A.F., and G.F. Mellor, 1987. A Description of a Three-dimensional Coastal Ocean

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