7. SEA SURFACE TOPOGRAPHY

The sea surface topography defines the difference between the elevation of NAVD88 and local
mean sea level (LMSL). The sea surface topography is based on the relationship between these
datums at NOAA tide gauges. Only one tide station with benchmark ties to NAVD88 exists in
the Lake Charles VDatum area: Lake Charles (NOAA station #8767816). At this station, the
difference between NAVD88 and LMSL is — 0.354 m (i.e. NAVD88 is 0.354 m below MSL).
Since there is only one station, the sea surface topography was defined as a constant value of —
0.354 m over the entire domain. Based on other estuaries, one would expect some variation in
the NAVD88 to MSL difference as one progresses up the system from the Gulf of Mexico
entrance up into Lake Charles, but with no other published data, no adjustments to the sea
surface topography constant can be made. Recent GPS work at the East Jetty suggests a
NAVD88 to LMSL difference of -0.254, but this is based only on a GPS occupation of one
benchmark for a short time period. NGS is continuing to refine the NAVD88 reference system
for all of Louisiana by taking into account rates of vertical movement using repeat GPS surveys
over time (Tronvig et al, 2003). Changes to the VDatum sea surface topography field may be
made in the future when studies of the NAVD88 reference system in Louisiana are completed.

ACKNOWLEGEMENTS

Kurt Hess of CSDL provided support in evaluating ADCIRC model results and generating the
VDatum marine grids. Bathymetric data was supplied by Adeline Wong of CSDL. The tide
datum information used for model validation and interpolation of the errors was supplied by
NOS’ CO-OPS.

REFERENCES

Hess, K.W., 2002: Spatial interpolation of tidal data in irregularly shaped coastal regions by
numerical solution of Laplace’s equation. Estuarine, Coastal and Shelf Science, 54(2), 175-
192.

Hess, K.W, and S. K. Gill, 2003: Puget Sound Tidal Datums by Spatial Interpolation.
Proceedings, Fifth Conference on Coastal Atmospheric and Oceanic Prediction and
Processes. Am. Meteorological Soc., Seattle, August 6-8, 2003. Paper 6.1, 108 - 112.

Hess, K.W, and S. A. White, 2004: VDatum for Puget Sound: Generation of the Grid and
Population with Tidal Datums and Sea Surface Topography. U.S. Department of Commerce,
National Oceanic and Atmospheric Administration, Silver Spring, Maryland, NOAA Technical
Memorandum NOS CS 4, 27 pp

Luettich, R.A., and J.J. Westerink, 1992: ADCIRC: An advanced three-dimensional circulation

model of shelves, coasts, and estuaries, Report 1: theory and methodology of ADCIRC-2DDI
and ADCIRC-3DL. Department of the Army Technical Report, DRP-92-6.

19


1. INTRODUCTION

The National Ocean Service (NOS) of the National Oceanic and Atmospheric Administration
(NOAA) requires tidal datum information such as Mean High Water (MHW) and Mean Lower
Low Water (MLLW) to support nautical charting, navigational safety, shoreline
photogrammetry, and marine boundary determination. In addition, tidal datum information is
needed for referencing NOS’ bathymetric data (which is typically referenced to MLLW) to any
one of the other vertical elevation reference systems. A software tool under development at NOS
called VDatum (Milbert, 2002; Parker, 2002) is designed to transform among approximately 30
vertical reference datums. To be applicable over coastal waters, VDatum requires tidal datum
fields, where the field describes the two dimensional, horizontal variability of the datum
elevation. This paper chronicles the continuing work on the VDatum software for southwestern
Louisiana. The work for this project work was originally conducted for and partially funded by
the FY’03 NOS Partnership, “Determining Accurate Elevations for Hurricane Evacuation Route
Planning in Subsidence-threatened southern Louisiana using Integrated GPS, Inertial
Measurement, and Distance Measurement Systems”.

A numerical tide model was employed to determine the tidal datums along the Calcasieu River
from Lake Charles, Louisiana, to the mouth of the river, and out into the Gulf of Mexico. The
two-dimensional finite element hydrodynamic model, ADCIRC (Luettich et al., 1992; Luettich
and Westerink, 2004) was used to calculate these datums. An unstructured mesh was developed
for the tidal modeling efforts and a regular grid was developed for the final VDatum results. The
unstructured mesh incorporates bathymetric data from several sources and the land-water
boundary of the mesh is based on NOAA’s Medium Resolution Coastline. The tidal datum
results from the hydrodynamic model (on the unstructured mesh) were interpolated onto the
‘Datum marine grid. The VDatum marine grid was developed based on the same coastline,
using programs discussed by Hess and White (2004), and is a regular, structured grid. The final
tidal datum results are presented. The Topography of the Sea Surface, which relates local Mean
Sea Level (MSL) to the North American Vertical Datum 1988 (NAVD838) is a spatially constant
value, based on the National Geodetic Survey geodetic benchmark connections to tidal
benchmarks at Lake Charles, Louisiana.


4. ADCIRC MODEL RESULTS

Fifteen different model runs were conducted for this study. These runs were conducted on three
meshes (each with the same node and element configuration, but with different bathymetric
depths at the nodes) for five different values of Cfnin (0.002, 0.0025, 0.003, 0.0035, and 0.004).
The different meshes will be referred to as the initial mesh, the second mesh, and the third mesh.
While the combined final mesh, described in the above Section 3.1, is referenced to MLLW, the
initial, second and third meshes are all referenced to the ADCIRC “model zero” (MZ) elevation,
which is an equipotential surface.

For the initial model set up, the depths at every node in the final combined mesh were adjusted
from MLLW to MSL based on a spatial interpolation of the MSL-MLLW differences at Lake
Charles (-20.5 cm) and the East Jetty station (-37.3 cm) using the before mentioned TCARI
model. The local MSL can vary from MZ, but for the initial mesh, MSL and MZ were assumed
to be equal. The model was run using all five of the different Cjmm, values with the initial mesh.
The absolute average error between the model results and the station data at Lake Charles
(station #8767816) and the East Jetty (station #8768094) for four datums (MHHW, MHW,
MLW, and MLLW all relative to MSL) was calculated for each run. These results are shown in
Figure 3 and are listed as “initial mesh” results. The best run (i.e. the lowest absolute average
error) was with Cnn = 0.003, producing an absolute average error of 1 19 cm.

Absolute Avgerage Error
(for 2 stations and 4 datums) vs C_fmin

2
1.9 + 3 — —
1.8 - — —= —

1.7 J— - — 3
1.6
1.5}
1.4
1.3
1.24
14
1 ¥ Ys
0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045

Cfmin

-il— initial mesh
a second mesh

Abs Avg Err (cm)

Figure 3. Absolute Average Error for modeled MHHW, MHW, MLW, and MLLW datums at
the location of the Lake Charles station #8767816 and the East Jetty station #8768094.

The results from the best run with the initial mesh were used to make the second mesh. Instead
of using the TCARI interpolation of data at the NOAA tide gauges, the MSL-MLLW results

11


3. ADCIRC MODEL SET UP AND TESTING

For this modeling effort, the two-dimensional, depth-integrated, barotropic version of the finite
element model ADCIRC was employed (Luettich et al., 1992; Luettich and Westerink, 2004).
This model solves the shallow water equations for water elevation and velocity on an
unstructured, triangulated mesh. The following sub-sections outline the steps taken to set-up and
test the ADCIRC model for this domain. First, the creation of the unstructured mesh will be
outlined. Discussion of the bathymetric data and the process used to populate the mesh with
depths at the nodes will follow. The model allows for a variety of hydrodynamic conditions,
including wetting and drying, that are implemented through several user-specified parameters.
The parameters used for this study along with details of tests done to find the best bottom friction
parameters will be discussed. Finally, a description of the series of runs conducted to determine
model convergence towards a physically realistic answer will conclude this section.

3.1. Creating the Unstructured Mesh

The placement of nodes in the unstructured triangulated mesh used for the ADCIRC model runs
was based on the NOAA’s Medium Resolution Coastline (see Figure 1). The nodes and
elements in the grid were placed to follow this shoreline as closely as possible. The entire finite
element mesh is shown in Figure 2(a). This mesh contains 20,575 nodes and 36,931 elements.
One advantage of flexible, finite clement meshes is that they easily allow different levels of
resolution within one domain. Fewer nodes are needed in deeper waters in the Gulf of Mexico,
but when advection begins to dominate the flow regime as the waters channel into the Calcasieu
Pass at the mouth of the Calcasieu River, more nodes are needed to accurately capture the
hydrodynamics. Two zoomed views of the Calcasieu Pass area (connecting Calcasieu Lake to
the Gulf of Mexico) are shown in Figures 2(b) and 2(c). These figures illustrate the increasing
resolution through the Calcasieu Pass area. The largest elements in the grid are just over 4
kilometers (measured as the average distance between nodes in an element) in the Gulf of
Mexico and the smallest elements are about 30 meters wide in the Calcasieu River.

3.2. Adjusting and Combining Bathymetric Data

Even before the bathymetric data could be incorporated in the unstructured mesh, the depths
needed to be converted to a common vertical datum. The common datum chosen was MLLW,
which is NOAA’s chart datum.

The USACE data are referenced to MLG. No exact relationship between MLG and MLLW has
been established but the estimated relationship is that MLG is 1.2 feet below MLLW at the Port
of Lake Charles and 0.8 feet below MLLW near the mouth of the Calcasieu River at Calcasieu
Pass (Steve Gill, NOAA/NOS/CO-OPS, personal communication). The MLG-to-MLLW
difference was assumed to be a linear function of the latitude between the station at Lake Charles
and the station at Calcasieu Pass, and this relationship was used to transform from USACE data
so that all sounding depths were referenced to MLLW.


2. DATA SOURCES
2.1. Coastline Data

NOAA’s Medium Resolution Digital Vector Shoreline was used for this project. The shoreline
was compiled by digitizing NOAA charts. Charts with a scale of 1:80,000 were used where
available, and in the few places where those charts were unavailable, higher resolution 1:60,000
scale charts were used. This coastline accurately delineates the Mean High Water (MHW)
shoreline as depicted on NOAA nautical charts as a solid dark line. The coastline in the Lake
Charles Calcasieu River, Louisiana, area is shown in Figure 1.

2.2. Water Level Stations

For purposes of model validation, the NOAA tide stations that exist in the region were examined.
Three tide stations were found in the area. These stations are listed in Table 1 along with the
location, tidal datums, and epoch. The Lake Charles station (#8767816) and the East Jetty station
(#8768094) are also shown in Figure 1.

The only tide station in the survey area with a published tie between tidal datums and geodetic
datum of North American Vertical Datum 1988 (NAVD88) is at Lake Charles. While the tidal
epoch for the data at the Calcasieu Pass Light station is not known, the age of the data is known
— it was collected from May 12, 1924 until May 16, 1924. Due to the short duration and the old
date of this deployment, the data from this station was not used for this project. The station at
East Jetty has had a GPS tie to one bench mark which is insufficient to produce a published tidal
datum to NAVD88 relationship. GPS connections are also only accurate to 2-5 cm, where the
direct leveling connections are accurate to sub-centimeter levels. Given the uncertainty, this
value was also not used for this project at this time. Future repeat leveling will narrow the
uncertainty. Tidal datums will also become more accurate as the data are now being collected
over a long time period and the datums will be updated using a longer time series.

Table 1. List of NOAA water level stations and vertical datums in the Lake Charles Calcasieu
River, Louisiana, area.

Station | Station | Longitude | Latitude | MHHW | MHW | MLW | MLLW| MSLto | Tidal
ID# Name | (degrees) | (degrees) (m) (m) (m) (m) NAVD88 | Epoch
Lake 1983 -
8767816 Charles -93.3450 29.7783 0.1630 | 0.1310 | -0.1580 | -0.2050 0.354 2001
Calcasiew 1983 -
8768094 Pass, -93.3417 29.7583 0.2420 | 0.1940 | -0.2170 | -0.3730 | -0.254* 2001
East Jetty
Calcasieu
8768106 Pass, -93.3450 29.7783 0.3050 | 0.2440 | -0.1530 | -0.3050 NA NA
Light

* Note — this value is preliminary based on recent GPS surveys. ‘The entire region is undergoing readjustment using predicted vertical velocities
of bench marks and the vertical time dependent positioning(VTDP) model. This value does not take into account VTDP and the estimate that
matches how the value was computed at Lake Charles.



Boulder, Colorado. It took approximately 4 wall-clock hours to complete the 37-day run
utilizing 36 processors.

3.4. Bottom Friction Formulation

The ADCIRC model allows for several different methods of implementing bottom stress.
Generally, bottom stress is expressed as %,=Ut and ty=Vt, where U and V are the velocity
terms and tis the bottom friction coefficient. For the linear friction option, t= Cy, where Cris
the user-specified bottom friction coefficient, and that term is constant in time, but may vary in
space. For the quadratic friction option, a more complex formula is used for a such that
c,ur +7? ; ; ;
Te = where H is the bathymetric depth at the node. For the so-called hybrid
friction option, the same formula for t+ as in the second option is used, but Cy is not assigned by

oye
the user, but is calculated in the code by the following formula: C, =Cyni, [ (4) In

this equation, H is again the bathymetric depth at a specified mesh node and Horeax (the so-called
break depth) is a depth specified by the user such that in waters deeper than Hp;eqx (where H >
Horet), Cy approaches Cynin, and in shallower waters (where H < Horeak) Cr approaches
Chnin(Horeai/H)” The exponent, 6, determines how quickly Cy approaches the asymptotic limit and
y determines how quickly the friction coefficient increases as the water depth decreases. The
user is required to specify Chnin, Horeak, 8 and ¥ This formulation allows for increased bottom
stress in very shallow water.

For the bottom friction test discussed here, the Hpreat, 6, and yvalues were set to relatively low
values so that the value specified for Cfnin would approximately equal Cy even in very shallow
waters. (Basically, the parameters were set to mimic quadratic bottom friction.) These
parameters were: Hpreqk = 1m, 6= 10, and y= 1/3. With these parameters held constant, the
differences in changing Cymin could be examined, Runs were conducted using Cfnin = 0.002,
0.0025, 0.003, 0.0035, and 0.004. These Cyn, values fall in the range of the generally accepted
values for a bottom friction drag coefficient and are near the ADCIRC recommended valued of
0.0025 (Luettich and Westerink 2004). Although the ADCIRC model is much more sensitive to
changes in bathymetry and node configuration, this study of bottom friction parameters was
conducted to confirm that the bottom friction coefficients generally chosen for large scale deep
ocean to shelf water scale models are also appropriate for this near-shore coastal water model.


NOAA Technical Report NOS CS 19

VDATUM FOR THE CALCASIEU RIVER FROM
LAKE CHARLES TO THE GULF OF MEXICO,
LOUISIANA: TIDAL DATUM MODELING AND
POPULATION OF THE GRID

Silver Spring, Maryland
March 2005

n @Gaa National Oceanic and Atmospheric Administration

U.S. DEPARTMENT OF COMMERCE
National Ocean Service
Coast Survey Development Laboratory


5. INTERPOLATION OF ERRORS

Even though the model results very closely matched the tide gauge data and appeared to
converge to the correct hydrodynamic solution throughout the domain, it was important to ensure
that the final results used in the VDatum marine grid matched the NOAA tide gauge data
exactly. This match was guaranteed by using the finite element implementation of TCARI to
spatially interpolate the error between the tide gauge data and the ADCIRC model results. This
error field (for each datum) was then added to the ADCIRC model results, which produced an
exact match of the datums at the tide gauge stations. Figure 5 shows the TCARI interpolation of
the MSL-MLW errors and the final corrected MSL-MLW tidal datum results (chosen since that
was the datum with the highest errors). From the corrected MHHW, MHW, MLW and MLLW
tidal datum fields, the Mean Tide Level (MTL) and Diurnal Tide Level (DTL) were computed
such that MTL = %(MHW+MLW) and DTL = % (MHHW+MLLW). These six final tidal datum
fields were used for the population of the VDatum marine grid and are shown in Appendix B.

Figure 5. (a) TCARI MSL-MLW error correction results (m) using two forcing stations (Lake
Charles station #8767816 and East Jetty station #8768094) and (b) the final corrected MSL-
MLW model results (m).

15


While the results from the model runs could be compared to the NOAA tide gauge records, the
modeled datums (at locations other than the Lake Charles and East Jetty stations) had no
reference data. The change in the MSL-MLLW difference was evaluated between the different
model runs to look for a general pattern of convergence. The initial MSL-MLLW difference
field, developed from a TCARI spatial interpolation of the datum records at the Lake Charles and
East Jetty stations, is shown in Figure 4(a). This field does not reflect the hydrodynamics that the
ADCIRC model simulates. The first ADCIRC model run produced a MSL-MLLW field that
showed more realistic variations in that datum field with smaller values in very shallow regions
(like the West Cove) and larger values in deep channels (like the main Calcasieu River channel).
These results are shown in Figure 4(b). The spatially interpolated MSL-MLLW difference field
and the MSL-MLLW results from the initial model run were compared on a node by node basis
and the maximum absolute difference and the average absolute difference were calculated. These
comparisons are listed in Table 3. The model results from the second model run are shown in
Figure 4(c). The results from the second model run were compared to the first model run and the
maximum absolute difference and the average absolute differences are listed in Table 3. The
MSL-MLLW model results from the third model run are shown in Figure 4(d). The maximum
absolute difference and the average absolute difference between the MSL-MLLW fields from the
second model run the and third model run are listed in Table 3.

Table 3. Maximum absolute and average absolute difference between MSL-MLLW results from
two sources.

MSL-MLLW MSL-MLLW Maximum Average
Source 1 Source 2 Difference (cm) | Difference (cm)
TCARI Spatial Interpolation | Initial Mesh Model Run 20.77 6.65
Initial Mesh Model Run Second Mesh Model Run 2.11 0.62
Second Mesh Model Run Third MeshModel Run 1.01 0.02

Two conclusions can be made from this analysis. First, it can be seen in Figure 4 that the
hydrodynamic model results reflect a more physically accurate picture of the tidal datum fields
compared to a TCARI interpolation. Second, the average and maximum differences between the
model runs decreases not only between the TCARI interpolation and the ADCIRC model results,
but also between modeled outputs over the iteration process. The average difference between the
last two model runs is negligible: only two-hundredths of a centimeter. This leads one to believe
that the model results are converged to a physically accurate solution.

13


30.2

30.1

30.0

29.9

29.8

29.7

29.4

-94.0 93.5 -93.0 -92.1 a

el
ne

i
I
<I

segeee
es
stan Vay,

Figure 2. Finite element mesh for (a) the entire model domain following the Calcasieu River
from Lake Charles to the Gulf of Mexico, and zoomed views of (b) the Calcasieu Pass, and (c)
the mouth of the Calcasieu River.

The second individual mesh was created using NOS sounding data. This bathymetric data
(which were all adjusted to MLLW) were incorporated into a mesh using the cluster averaging
approach. Null values of -9999 were listed at the locations where no NOS data were available.
Unlike the CRM data mesh, the null value nodes were not eliminated.


ABSTRACT

The goal of the VDatum, vertical datum transformation tool, project is to provide
transformations between tidal, orthometric and three-dimensional datums for all areas of the
contiguous United States. This paper chronicles the continuing work on this project in the Lake
Charles and Calcasieu Lake area of Louisiana. A VDatum marine grid was created and populated
for this area. The tidal datum fields were created using a two-dimensional finite element
hydrodynamic model of the area. The tidal datum results from this model were corrected to
match existing NOAA tide gauge data in the region using a spatial interpolation scheme. The sea
surface topography, or difference between local mean sea level and the NAVD 88 geopotential
surface, was defined as a constant over the domain based on data at one tide gauge.

Key Words: tides, tidal datums, Lake Charles, Lake Calcasieu, finite element model,
hydrodynamic model, ADCIRC, bottom friction, North American Vertical Datum of 1988, mean
sea level, spatial interpolation, coastline


APPENDIX A. RESULTS FROM BOTTOM FRICTION TESTING

Table A.1. Model run tidal datum results compared to NOAA datums at Lake Charles, Louisiana
(Station #8767816) for a series tests using three meshes (with different bathymetry) and five
different bottom friction parameters. Negative error values mean that the model was
underpredicting and positive error values mean the model was overpredicting.

MHHW MHW MLW MLLW

Mesh/Run Name ___Cfmin (cm) (cm) (em) (em)

16.30 13.10 “15.80 -20.50 NOAA

i 17.37 15.09 “14.26 24.86 Model
Tita MeshRuns| | 4.002 1.07 1.99 “1.54 4.36 Difference
6.36% 14.12% 10.25% 19.22% % Diff

16,30 13.10 -15.80 -20.50 NOAA

16.15 14.07 "13.23 23.29 Model

ome 0.15 0.97 2.57 2.19 Difference

0.92% 7.14% 17.1% 12.74% % Diff

16.30 13.10 “15.80 -20.50 NOAA

003 15.12 13.23 -11.90 21.50 Model

“1.18 0.13 3.90 1.00 Difference

751% 0.99% 28.16% 4.16% % Diff

16.30 13.10 “15.80 -20.50 NOAA

0.0035 14.30 12.55 “11,24 20.43 Model

-2.00 0.55 4.56 -0.07 Difference

13.07% 4.29% 33.73% 0.34% % Diff

16.30 13.10 -15.80 -20.50 NOAA

0054 13.87 11.96 =10.69 =19.10 Model

2.43 “1.14 “5.1 “1.40 Difference

16.11% 9.10% 38.58% 7.07% % Diff

16.30 13.10 -15.80 20.50 NOAA

17.02 1481 “13.94 “24,32 Model

Second MestiRung ji! 1050 0.72 LT “1.86 3.82 Difference
4.32% 12.25% 12.51% 17.05% % Diff

16.30 13.10 -15.80 -20.50 NOAA

Pn 15,82 13.79 “12.93 22.19 _ Model

0.48 0.69 -2.87 2.29 Difference

2.99% 5.13% 19.98% 10.58% % Diff

16.30 13.10 “15.80 -20.50 NOAA

as 14.81 12.96 “11.63 21.08 Model

“1.49 -0.14 “4.17 053 Difference

9.58% 1.07% 30.40% 2.55% % Diff

16.30 13.10 “15.80 -20.50 NOAA

14.01 12.30 710.98 719.99 Model

10083 2.29 0.80 4.82 0.51 Difference
15.11% 6.30% 36.00% 2.52% ‘% Diff

21


APPENDIX B. FINAL, CORRECTED TIDAL DATUM FIELDS

MHHW-MSL (m) MHW-MSL (m)
0.300
0.280
0.260
0.240
0.220
0.200
0.180
0.160
0.140
0.120
0.100

MSL-MLLW (m) MSL-MLW (m)
0.080

-0.120
0.160

-0.110
0.130

-0.150
-0.200

0.240
-0.280

-0.170
0.190
» -0.320 0.210

-0.360 0,230

0.400 -0.250



TABLE OF CONTENTS

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

LIST OF TABLES

ABSTRACT... sccsssvscssvcasconssssssaseasiansesipessapentbooracecensanenseennstecosnssosensseaceeescrssvoseypasasscesedooseercinsastotcicisivit v

2. DATA SOURCES .....sssssssssssssssssssnsesnssssssssennsnsttisssssssisssssnstssensssstesssssstesasesessssseseessssusseseuunansavvesse 3

2.3. Bathymetric Data...

3. ADCIRC MODEL SET UP AND TESTING

3.1. Creating the Unstructured Mesh
3.2. Adjusting and Combining Bathymetric Data..
3.3. ADCIRC Model Parameters...
3.4. Bottom Friction Formulation.

4, ADCIRC MODEL RESULTS........sssssssssssssssesssssssssssssevsssssssssssssssssnssnasestssessaseesnssareeseenesassenvense 11

5. INTERPOLATION OF ERRORS.

6. THE VDATUM MARINE GRID ....scscsscsssssssssssssssssssssssssccsecsssuessssssssesissasissesessessensnsseeeseveee 17
7. SEA SURFACE TOPOGRAPHY.

ACKNOWLEGEMEN TS. ......sssssssssssssssssssssssssnstqesstinsstessssssnsssnsssssssssssensesssssnensssenensensenanecesanenenaneee 19
REFERENCES.

APPENDIX A, RESULTS FROM BOTTOM FRICTION TESTING .....ssscsssssssssssssssssnssssssseece 21
APPENDIX B. FINAL, CORRECTED TIDAL DATUM FIELDS .....ssssssssssssscessssssssssssssnsesesee 25

iti


NOAA Technical Report NOS CS 19

VDATUM FOR THE CALCASIEU RIVER FROM
LAKE CHARLES TO THE GULF OF MEXICO,
LOUISIANA: TIDAL DATUM MODELING AND
POPULATION OF THE GRID

Emily A. Spargo
Office of Coast Survey, NOAA

Jason W. Woolard
National Geodetic Survey

ome

<a.
3
NX

—

n Oaa National Oceanic and Atmospheric Administration

nomen

U.S. DEPARTMENT National Oceanic and National Ocean Service

OF COMMERCE Atmospheric Administration Richard W. Spinrad, Ph.D.

Carlos Gutierrez, Secretary Conrad C. Lautenbacher, Jr., Assistant Administrator
VADM USN (Ret.), Under Secretary

Office of Coast Survey Coast Survey Development

Captain Roger L. Parsons, NOAA Laboratory

Maureen Kenny


6. THE VDATUM MARINE GRID

The VDatum software requires a regularly girded data, so the unstructured mesh used for the
ADCIRC and TCARI model runs could not be used. Therefore, a new VDatum marine grid was
generated with a Ax of 0.0021 degrees and Ay of 0.0018 degrees, resulting in the spacing
between points of about 200 m (0.1 nmi). The grid resulting from this process has a width of
109 points and a height of 501 points, totaling 54,609 points. The grid is bounded between the
latitudes 29.34° in the south and 30.24° in the north, and the longitudes -93.445° in the west and
-93.218333° in the east.

The VDatum marine grid was populated using the Fortran program vpop5.f. This program
interpolates the corrected ADCIRC model results onto the VDatum marine grid. The basic
program is described by Hess and White (2004), but changes to the program were made to
interpolate the final tidal datum results from an unstructured mesh onto the regular VDatum
marine grid. The vpop5.f program finds a value for each marine point by averaging all of the
ADCIRC mesh points within a user-specified radius or the closest user-specified number of
points. The program was set to use the 10 closest points. However, looking only at the 10 closest
points, the program does not account for landforms that affect the hydrodynamics of the model.
For example, the West Cove area (see Figure 1) has a very small tide range, but the main channel
of the Calcasieu River, which is on the other side of a long island separating the two bodies of
water, has a much larger tide range. When selecting only the 10 closest points, the program
averages the high values of the river with the low values in West Cove to get an average datum
value, which makes the values in the West Cove area of the VDatum marine grid too large and
the values of the Calcasieu River area of the VDatum marine grid too small. To remedy this
problem, the area was divided into three separate regions contained within three different
bounding polygons. Three separate VDatum marine grids were created to correspond to these
regions, where all areas outside the associated bounding polygon were designated as land. For
each region, only ADCIRC mesh nodes within the bounding polygon were used to populate the
Datum marine grid. One bounding polygon restricts the selection process to only the West
Cove, another region restricts the selection process to only the main area of the Calcasieu Lake
and the final bounding polygon covers the rest of the domain. The boundary lines that divide the
main area of the Calcasieu Lake and the Calcasieu River were selected so that there are no
discontinuities between the different regions (i.e. the boundary was selected in a region where
the tidal datums are slowly varying). The regional VDatum marine grids and associated
bounding polygons are shown in Figure 6.

A final check was done to compare the final corrected datums in the VDatum marine grid with
the NOAA tide gauge data. The VDatum marine grid used for this analysis was the marine grid
that contains the Gulf of Mexico and Calcasieu River channel since bounding polygon defining
this region contains both the East Jetty and Lake Charles stations. Table 4 lists the station
information for the two stations in the domain and the final root mean square error (RMSE) (cm)
error, which was calculated as the RMSE for MHHW, MHW, MLW, and MLLW at each station.

17


Table A.2. CONTINUED

MHHW MHW MLW MLLW
Mesh/Run Name ___Cfmin (cm) (cm) (em) (cm)

24.20 19.40 21.70 -37.30 NOAA
a 23.79 19.43 “19.50 37.95 Model
Initial Mesh Runs] 0.003. (“oat 0.03 2.20 0.65 Difference
L7I% 0.15% 10.68% 1.73% % Diff
24.20 19.40 21.70 “37.30 NOAA
a003s 24.04 19.55 “19.58 “37.98 ~ Model
0.16 0.15 “2.12 0.68 Difference
0.66% 0.7% 10.27% 1.81% % Diff
24.20 19.40 -21.70 3730 NOAA
004 24.24 19.64 =19.63 “37.98 Model
0.04 0.24 2.07 0.68 Difference
0.17% 1.23% 10.02% 1.81% % Diff
24.20 19.40 “21,70 -37.30 NOAA
23.31 19.34 720.00 37.93 Model
SecondiMesh Runs: jp (01002 0.89 0.06 =1.70 0.63 Difference
3.15% 0.31% 8.15% 1.67% % Diff
24.20 19.40 21.70 “37.30 NOAA
23.73 19.40 “19.50 “37.98 Model
0.0025 -0.47 0.00 -2.20 0.68 Difference
1.96% 0.00% 10.68% 1.81% % Diff
24.20 19.40 21.70 37.30 NOAA
i 24.04 19.55 "19.58 “38.02 Model
“0.16 0.15 2.12 0.72 Difference
0.66% 0.77% 10.27% 1.91% % Diff
24.20 19.40 “21,70 “37.30 NOAA
an035 24.27 19.66 719.65 “38.04 ~ Model
0.07 0.26 2.05 0.74 Difference
0.29% 1.33% 9.92% 1.96% % Diff
24.20 19.40 21.70 “37.30 NOAA
0.004 24.46 19.75 719.69 ~38.04 Model
0.26 035 2.01 0.74 Difference
1.07% 1.79% 9.71% 1.96% %Dife
24.20 19.40 21.70 “37.30 NOAA
; 23.31 19.34 20.00 37.93 Model
ed = -0.89 0.06 =1.70 0.63 Difference
3.15% 0.31% 8.15% 1.67% % Diff
24.20 19.40 21.70 “37.30 NOAA
23.74 19.41 "19.49 “37.97 Model
eo -0.46 0.01 2.21 0.67 Difference
1.92% 0.05% 10.73% 1.78% %” Diff
24.20 19.40 -21.70 -37.30 NOAA
ca 24.04 19.55 “19.59 -38.02 Model
0.16 0.15 “2 0.72 Difference
0.66% 0.77% 10.22% 1.91% % Diff

23