# MISSISSIPPI RIVER WATER REINTRODUCTION INTO BAYOU LAFOURCHE HYDRODYNAMIC MODELING

March 9, 2006MISSISSIPPI RIVER WATER REINTRODUCTION INTO BAYOU LAFOURCHE HYDRO DYNAMIC MODELING

Prepared for the

Louisiana Department of Natural Resources, Coastal Restoration Division

under subcontract with CH2M Hill 1515 Poydras, Suite 2110 New Orleans, LA 70112

Prepared by

FTN Associates, Ltd. 3 Innwood Circle, Suite 220 Little Rock, AR 72211

March 9, 2006March 9, 2006

i 

### EXECUTIVE SUMMARY

The areas benefited by the Bayou Lafourche Divi sion project as identified in “Evaluation of Bayou Lafourche Wetlands Restoration Projec t” (United States Environmental Protection Agency (USEPA) 1998) (Figure 1.5) were re-evalu ated to compensate for limitations of the previous modeling. Marsh surveys required for accu rate determination of salinity reductions for

the identified benefit areas woul d have been cost prohibitive. Consequently, a new model that more accurately represented the forces driving flows in the Terrebonne and Barataria Basins was developed to determine the benefit areas. This work was done using a two-phase approach that allowed project funds to be used judiciously. In Phase 1 of the study, it was shown that tides peak higher and earlier from west to east along the Terrebonne and Barataria Ba sin coastline (Figures 1.2 and 1.3). This causes flow in the Gulf Intracoastal Waterway (GIW W) to flow from west to east, except during storms when the normal tidal forcing can be reversed. During the 13-month period over which hourly data was collected, the flow was in an eas terly direction more than 90% of the time (Figure 1.4). This observation coupled with the flow , stage, and salinity record available at the only connection between the two basins (int ersection of the GIWW and Ba you Lafourche) allowed the computational mesh to be reduced to repres ent only the Terrebonne basin, thus reducing simulation times from weeks to days. This al lowed the model to be quickly calibrated to observed flow, water surface elevation (WSEL), and salinity data from May to June 2004.

Several tracer simulations were run in Ph ase 1 that showed the movement of Bayou Lafourche water through the Terrebonne Basin. These simulations showed that very little of the

tracer moved south of the GIWW. Flow moving south down Company Canal or Bayou Lafourche is largely captured by the GIWW and moved eastward due to the larger conveyance capacity and eastward momentum of the GIWW. In Phase 2, the model was expanded to include the Barataria Basin so that it could be

used to evaluate the effects of 15 operational and channel improve ment scenarios on salinities, water surface elevations, and benefit areas (Table 7.2). The model was improved by collecting additional survey data, refining portions of the grid, and re-calibrating model coefficients.March 9, 2006

ii The channel improvement scenarios that were simulated included five different dredging plans in Bayou Lafourche; the widening of Company Canal between the GIWW and Bayou Terrebonne; and the widening of the end of Bayou L’eau Bleu south of the GIWW that connects to Grand Bayou. The results from these simulations show that:

• Bayou Lafourche Alternative 47 (8-ft av erage dredging upstream of Lockport with a 2,000 cfs diversion) (R un 10) results in the largest reduction of salinities of all the Bayou Lafourche dredging alte rnatives, but primarily in the upper Barataria Basin and with almost no bene fit to the Terrebonne Basin south of the GIWW.

• Widening Company Canal between Bayou Terrebonne and the GIWW in conjunction with Bayou Lafourche Alternat ive 47 (Run 14) incr eases freshwater flows only marginally in southern Bayou Terrebonne and allows saline Gulf water to be more readily transported northward and into the GIWW. This alternative would also require replacing the cons tricting Highway 24 bridge crossing.

• Increasing flows to Grand Bayou via wi dening Bayou L’eau Bleu south of the GIWW and Bayou Lafourche Alternative 47 (Run 12) increases freshwater flows significantly in all channels modeled s outh of the GIWW in the Terrebonne basin (the Houma Navigation Canal, Bayou Te rrebonne, Bayou Lafourche, and Grand Bayou).March 9, 2006

iii 

### TABLE OF CONTENTS

1.0 INTRODUCTION ........................................................................................................... 1-1 1.1 Description of the Project Area............................................................................ 1-1 1.2 Study Approach ................................................................................................... 1-3 1.3 Report Content Overview and Organization........................................................ 1-9 2.0 MODEL DESCRIPTION ................................................................................................ 2-1 2.1 Model Selection ................................................................................................... 2-1 2.2 Assumptions and Limitations .............................................................................. 2-1 3.0 MODEL INPUT............................................................................................................... 3 -1 3.1 Finite Element Mesh............................................................................................ 3-1 3.2 System Topography ............................................................................................. 3-3 3.3 Boundary Conditions ........................................................................................... 3-4 3.4 Model Coefficients............................................................................................... 3-5 3.5 Model Options ..................................................................................................... 3-5 3.5.1 1D Channels............................................................................................. 3-5 3.5.2 Channel Junctions .................................................................................... 3-8 3.5.3 Channel and Marsh/Swamp Interconnections ......................................... 3-8 3.5.4 Mesh Wetting/Drying .............................................................................. 3-8 4.0 MODEL TESTING AND SENSITIVITY ANALYSES................................................. 4-1 4.1 Model Testing ...................................................................................................... 4-1 4.1.1 Convergence ............................................................................................ 4-1 4.1.2 Channel Geometry Representation .......................................................... 4-1 4.1.3 1D Junction Formulation ......................................................................... 4-2 4.1.4 Lateral Weir 1D-2D Connections ............................................................ 4-3 4.1.5 Continuity ................................................................................................ 4-4 4.2 Sensitivity Analyses............................................................................................. 4-5 4.2.1 Computational Time Step ........................................................................ 4-6 4.2.2 Terrebonne Basin Marsh Elevations........................................................ 4-6 4.2.3 1D Junction Nodes................................................................................... 4-6 5.0 MODEL MESH MODIFICATION................................................................................. 5-1 5.1 Phase 1 Mesh Refinement.................................................................................... 5-1 5.2 Mesh Truncation / Addition................................................................................. 5-1 5.2.1 Upper Bayou Lafourche Truncation ........................................................ 5-1March 9, 2006 

### TABLE OF CONTENTS (CONTINUED)

iv 5.2.2 Phase 1 Barataria Basin Truncation......................................................... 5-1 5.2.3 Phase 2 Barataria Basin Addition ............................................................ 5-1 5.3 Phase 2 Mesh Refinement.................................................................................... 5-1 6.0 MODEL RE-CALIBRATION AND VERIFICATION .................................................. 6-1 6.1 RMA-2 Calibration and Verification................................................................... 6-1 6.2 RMA-11 Calibration and Verification................................................................. 6-8 7.0 MODEL APPLICATION ................................................................................................ 7-1 7.1 Phase 1 Truncated Model Preliminary Simulations............................................. 7-1 7.1.1 RMA-2 Simulations................................................................................. 7-1 7.1.2 RMA-11 Simulations............................................................................... 7-5 7.2 Phase 2 Simulations ............................................................................................. 7-6 7.2.1 RMA-2 Simulations................................................................................. 7-6 7.2.2 RMA-11 Simulations............................................................................. 7-18 8.0 CONCLUSIONS.............................................................................................................. 8- 1 8.1 Bayou Des Allemands Boundary Condition Investigation.................................. 8-1 8.1.1 Boundary Condition Development .......................................................... 8-4 8.1.2 Discussion................................................................................................ 8-4 8.2 Future Mesh Improvements ................................................................................. 8-9 9.0 REFERENCES ................................................................................................................ 9 -1



### LIST OF ATTACHMENTS

ATTACHMENT 1: RMA-2 Calibration a nd Verification Simulations Results ATTACHMENT 2: RMA-2 Observed vs. Pred icted Water Surface and Velocity Data ATTACHMENT 3: RMA-11 Calibration and Verification Simulation Results ATTACHMENT 4: RMA-11 Observed vs. Predicted Salinity Data ATTACHMENT 5: Week 6 Salinity IsohalinesMarch 9, 2006

v 

### LIST OF TABLES

Table 3.1 Data collection stations and th eir sampling durations and intervals....................3-7

Table 6.1 Final RMA-2 calibration parameters ................................................................... 6-6 Table 6.2 Error Statistics for RMA-2 Water Surface Elevation Calibration ....................... 6-7 Table 6.3 Error Statistics for RMA-2 Velocity Calibration................................................. 6-7 Table 6.4 Error Statistics for RMA-2 Wa ter Surface Elevation Verification......................6-9 Table 6.5 Error Statistics for RM A-2 Velocity Verification ............................................... 6-9 Table 6.6 Final RMA-11 calibration parameters ............................................................... 6-11 Table 6.7 Error statistics for RMA-11 salinity calibration ................................................6-13 Table 6.8 Error statistics for RMA-11 salinity verification...............................................6-13

Table 7.1 Tracer simulation conditions................................................................................ 7-5 Table 7.2 Dredging and operati onal scenarios modeled......................................................7-7 Table 7.3 Average flows at key intersections over the 9-week simulation period .............. 7-8



### LIST OF FIGURES

Figure 1.1 Vicinity map showing major wa terways within the system modeled.................. 1-2 Figure 1.2 Tidal gage locations ............................................................................................. 1-4 Figure 1.3 Tidal cycles with peaks occurr ing earlier and higher at the western tidal stations ......................................................................................................... 1-5 Figure 1.4 Cumulative frequency distribution of hourly flows in the GIWW at Larose from January 2004 through January 2005 ........................................................... 1-6 Figure 1.5 Benefit areas from USEPA (1998) ...................................................................... 1-8

Figure 3.1 Initial finite elemen t mesh for the study area....................................................... 3-2 Figure 3.2 Data collection locations...................................................................................... 3-6

Figure 5.1 Extent of type 999 elem ents used in model mesh................................................ 5-2 Figure 5.2.a Phase 1 truncated model mesh............................................................................. 5-3 Figure 5.2.b Detail from the dense mesh area shown in Figure 5.1.a ...................................... 5-4 Figure 5.3 Boundary condition locations for Phase 1 truncated model mesh....................... 5-5 Figure 5.4 Final Phase 2 finite el ement mesh for the study area........................................... 5-6 Figure 5.5 Boundary condition locations for Phase 2 model mesh....................................... 5-7 Figure 5.6 Final Phase 2 model mesh bathymetry ................................................................ 5-8March 9, 2006 

### LIST OF FIGURES (CONTINUED)

vi Figure 6.1 25-hour average of observed water su rface elevations from May-June 2004 ..... 6-2 Figure 6.2 Location of RMA-2 el ement types in the mesh................................................... 6-5 Figure 6.3 Location of RMA-11 el ement types in the mesh............................................... 6-10

Figure 7.1 Average flow distribution resu lting from 1,000 cfs Bayou Lafourche tracer simulations ........................................................................................................... 7-3 Figure 7.2 Average flow distribution re sulting from 2,000 cfs Bayou Lafourche diversion flow tracer simulations......................................................................... 7-4 Figure 7.3 Average flows in Bayou Lafourch e, Company Canal, Bayou L’eau Bleu, and the GIWW for key simulations ................................................................... 7-10 Figure 7.4 Average flows in Company Cana l, Bayou Terrebonne, St. Louis Canal, and Humble Canal for key simulations .................................................................... 7-11 Figure 7.5 Average flows in the GIWW and Grand Bayou for key simulations ................ 7-12 Figure 7.6 Average flows in the GIWW and the Houma Navigation Canal for key simulations ......................................................................................................... 7-13 Figure 7.7 Location and cross section of Company Canal improvement ........................... 7-15 Figure 7.8 Computed flows in Company Canal north of junction with Bayou Terrebonne for Run 5 and Run 14 ..................................................................... 7-16 Figure 7.9 Location and cross secti on of Grand Bayou improvement................................ 7-17

Figure 8.1 Predicted flow and stag e at Bayou des Allemands boundary.............................. 8-2 Figure 8.2 Period-averaged estimated and predicted flows through Bayou des Allemands boundary .............................................................................................................. 8-7 Figure 8.3 Predicted and observed flow in the GIWW at Larose ......................................... 8-8March 9, 2006

1-1 

### 1.0 INTRODUCTION

The Coastal Wetlands Planning Protection a nd Restoration Act (CWPPRA) Program is assessing the benefit of dive rting Mississippi River flow s into Bayou Lafourche while maintaining or potentially increasing current wa ter levels in the bayou. Numerical modeling was

used to evaluate the different alternatives for this project, the Mississippi River Water Reintroduction into Bayou Lafour che Project (Louisiana Department of Natural Resources (LDNR) “Project”). This report de scribes that modeling effort.

1.1 Description of the Project Area Bayou Lafourche divides the portions of the tw o basins that compri se the study area: the

Barataria and Terrebonne basins (Figure 1.1). The Barataria Basi n lies to the east of Bayou

Lafourche with the Terrebonne Basin to the west. The study area boundaries are roughly the Mississippi River to the north a nd east, Bayou duLarge to the west , and the Gulf of Mexico to the south. The only hydrologic interconnections be tween the Terrebonne and Barataria basins are

at the Gulf Intracoastal Waterw ay (GIWW) and Company Canal. The forces that drive flow within the system are:

• Gulf tides,

• Mississippi River diversion flows at the Davis Pond Diversion Structure,

• Flow that is pumped into th e headwater of Bayou Lafourche,

• Wind,

• Precipitation, and

• Atchafalaya River flows that move into the system via the GIWW.

Direct precipitation was include d for model calibration; runoff from areas adjacent to the mesh is negligible and was not included.1-2Figure 1.1. Vicinitymapshowingmajor waterways within the system modeled.March 9, 2006

1-3 Examination of the tide records for stations in the area (Figure 1.2) showed that tides peak higher and earlier in the west ern part of the study area than in the east (Fi gure 1.3). This

causes flow in the GIWW to flow from west to east, except during storms when the normal tidal forcing may be reversed. During the 13-month period over which hourly data was collected (January 2004 through January 2005) the flow in the GIWW was in an easterly direction more than 90% of the time (Figure 1.4). The GIWW acts as an interceptor for the five main waterways that convey flow north and south within the Terrebonne basin (the Ho uma Navigation Canal (HNC), Grand Bayou, Bayou Petit Caillou, Bayou Grand Caillou, and Bayou Terrebonne). Forced drainage areas (leveed areas unde r pump) are common in the Terrebonne basin and are generally attached to th e natural levees along the bayous and extend into the adjacent marsh. As such, they are hydraulically isol ated and were not included in the study. Relatively shallow marshes and channels domin ate both basins. The marshes exhibit little vertical variation in velocity, density and salinity and can be considered two-dimensional (2D). The channels in the Terrebonne basin generally can be considered one-dimensional (1D) since no significant vertical or late ral variation occurs hydrodynamically except in their southern-most reaches where salt wedges move upstream in deeper channels (e.g., the HNC) causing a vertically stratified flow regime. In the Barataria basin the main nor th-south flow path is a series of wide interconnected lakes and generally can be considered 2D with only small variations vertically.

1.2 Study Approach The original LDNR Scope of Services for the Project was based on the previous modeling which showed that some of the benefit areas were in the southernmost portions of the

Barataria and Terrebonne basins. Th e survey effort to develop the detailed bathymetry required to accurately model an area that larg e would have been cost-prohibitive.1-4Figure 1.2. Tidal gage locations.1-5Figure 1.3. Tidal cycles with peaks occurring earlier and higherat the western tidal stations.1-6Figure 1.4. Cumulative frequency distribution of hourly flows in the GIWW at Larose from January 2004 through January 2005.March 9, 2006

1-7 In addition, a review of the modeling upon wh ich the benefits were based (LDNR 1999) revealed that the 1D dynamic wave model UNET (HEC 2001) simulations were made in steady state mode without any represen tation of the interaction between the channels and marsh areas and without any water quality transport. By running only steady state flows and constant boundary elevations in the model, the effect of tid es that move water in and out of the system on

a diurnal basis were not accounted for. The mode l also excluded complex interactions of flow

between the channels and marshes in the area th at affect the distribution of flows in the interconnecting canals. The net effect of not including these components in the model was an inaccurate representation of the movement of the freshwater in the channels that biased the interpretation of benefit areas. The benefit ar eas identified by the prev ious modeling (United States Environmental Protection Agency (USEPA) 1998) are shown in Figure 1.5. Without including water quality transport, bene fits were assumed to occur wherever flow increases were predicted. However, flow increas es could be due to displaced ambient or Gulf water, not to the transport of freshwater. The previous modeling did not show where the freshwater was transported. Consequently, an alternative Scope of Services was developed. The modeling was divided into two phases in order to “creep up on the solution” - i.e ., gain insight in to the system behavior with a model where complexity is gradually added. In Phase 1, only the Terrebonne

basin was modeled because the simulation times for the entire Terrebonne–Barataria system proved to be about one-fourth of the prototyp e time. By removing the Barataria basin, the simulation times were reduced by more than 50 %. Reducing the simulation times allowed for many more simulations to be made to learn where mesh refinements were needed, what coefficients were appropriate, where new surveys might be require d, and to gain insight into the system in general. What made the reduction in simulation area possible wa s the fact that flow into the Barataria Basin is predominantly one-way in an eastward dire ction (Section 1.1). This flow passes through the Bayou Lafour che ridge near Larose, LA wh ere a recording water surface and salinity gage were placed. The gage pr ovided boundary condition data for calibration and

verification of the truncated model.1-8Figure 1.2. ?Figure 1.5. Benefit areas from USEPA (1998).March 9, 2006

1-9 The limitation of the smalle r Terrebonne basin model was that a boundary condition would need to be synthesized at Larose when it came time to simulate conditions associated with proposed management alternatives; however, any synthesized boundary condition there would

have a tremendous influence on the model results due to its close proximity to the study area. Consequently, in Phase 2, the Barataria Basin was added back to the model to eliminate the Larose boundary condition and cap ture the true inte raction of flow between the basins. The Phase 2 modeling effort also involved refi nement of the model a nd its application to evaluate several proposed dredging and operation al scenarios. The re finements included the addition of new survey data to the model, refine ment of the mesh, and verification of the mesh boundaries against more current di gital ortho-quarter-quadrangle im ages (DOQQs). A total of 15 operational and channel improvement scenarios we re simulated to determine their effects on salinities, water surface elev ations, and benefit areas.

1.3 Report Content Over view and Organization This report is an update to “Phase 1 Modeli ng Preliminary Results”, which was included as Appendix 1 in the Phase 1 Design Report (C H2M HILL 2004). Sections of that Appendix 1 are repeated herein for the conve nience of the reader but it shoul d be noted that many of these

sections have been revised to reflect the addi tional data and insight gained in Phase 2. The description of the calibration and verification efforts for the Phase 1 study is not repeated since

the model was re-calibrated in Ph ase 2 because the mesh was incr eased to include the Barataria basin. The description of the tracer simulation re sults from the Phase 1 modeling effort are only summarized in Section 7.1; for a complete desc ription of tracer simu lation results from the Phase 1 modeling effort, the reader is referre d to Section 7.0 of Appendix 1 in the Phase 1 Design Report. This report is organized in the following sections:

• Section 1 – Introduction

• Section 2 – Model Description

• Section 3 – Model Input

• Section 4 – Model Testing and Sensitivity Analysis

• Section 5 – Model Mesh ModificationMarch 9, 2006

1-10 • Section 6 – Model Re-Ca libration and Verification

• Section 7 – Model Application

• Section 8 – Conclusions and Future Mesh Improvements

• Section 9 – ReferencesMarch 9, 2006

2-1 

### 2.0 MODEL DESCRIPTION

2.1 Model Selection A 2D vertically-averaged hydrodynamic trans port model was deemed appropriate for representing the Terrebonne and Barataria Basins (Section 1.2). A lthough, at times, portions of the system may be three-dimensiona l (3D), they are the exception rather than the rule and are not representative of the co nditions to be modeled. Modeling was initiated using the TABS-MD modeling system (RMA-2 and RMA-4) (US Army Corps of Engineers (USACE) Engin eering Research and Development Center (ERDC) 2000) and the Surface Water Modeling System (SMS) (Brigham Young University 2004). TABS-MD is distributed by the ERDC (forme rly the Waterways Experiment Station) of the USACE. SMS is a pre/post-pr ocessing interface deve loped by ERDC and the Environmental Modeling Research Laboratory at Brigham Young University. However, this study required that several unique features be added that were not in the ERDC version of TABS-MD. Consequently, Dr. Ian King’s ve rsion of the RMA modeling suite (RMA-2 hydrodynamic and RMA-11 water quality models) (King 2005) was used. Dr. King was coauthor of the code the ERDC version of TABS-M D is based on. His latest version was selected

because:

• Dr. King was available to add the necessary project-specific features (Section 3.2) to the model code in a short time frame (he is one of the original model’s developers), and

• Dr. King’s version had other enhancements that promoted model stability and allowed greater flexibility in mode ling the system (Sections 3.5.3 and 3.5.4).

2.2 Assumptions and Limitations

RMA-2/RMA-11 is a finite element model de signed for simulation of flow and water quality in rivers, estuaries, and coastal systems. RMA-2 solves th e vertically averaged equations of continuity and momentum using the Galerkin Method of weighted residuals to calculate timevarying velocities, elevations, a nd flows. A 1D representation of system geometry is also accommodated using the area-integrated 1D shallo w water equations. Flow is assumed to beMarch 9, 2006

2-2 subcritical with a free water su rface, and vertical accelerati ons are assumed negligible. The model incorporates a fully non-linear solution of the governing equations including terms for bed friction, turbulent viscosity, wi nd stresses, pressure gradient, and Coriolis forces. This means that the model cannot represent:

• Stratified flows (e.g., sa lt wedge movement),

• Supercritical flows (high velocity, sha llow depth flows that may occur near spillway outlets, in steep sloped channels, or in some areas where large constrictions in the channel may occur),

• Flows in long culverts or tunnels flowing full, or

• Flows in the immediate vicinity (near-field ) of a pump station intake as well as other situations where the flow varies significantly with depth.

It also means that observed water surface el evation, velocity, and salinity data are required to calibrate the va rious model coefficients.

The finite element solution method allows th e user to specify an irregular mesh of quadrilateral and triangular elements of varying si zes over the 2D areas of the system so spatial resolution may vary. In contrast, a finite difference grid for the same system would have many

more elements to achieve the same resolution in the area of interest by the requirement that the grid be of uniform size, which results in a larger computational bur den and longer simulation

times. One-dimensional elements (usually channels) may be connected to 2D elements to allow

a transition from riverine to estuarine environm ents and to allow the representation of overbank flooding into areas where depth-averaged 2D circulation patterns are needed. In this application, the followi ng assumptions were also made:

• Winds are accounted for implicitly in the boundary conditions.

• The calibration data collected (Section 3.3) is representative of conditions to be evaluated in future simulations.

• The assumed bathymetry for the mars h areas in the Terrebonne basin is representative (Section 3.2).March 9, 2006

3-1 

### 3.0 MODEL INPUT

The data required for model input are the finite element mesh, topography of the study area, salinities, flows, or wate r surface elevations at the e dges of the stud y area (boundary condition data), and model coefficients. In additi on, several model options must be specified to properly represent the system.

3.1 Finite Element Mesh

The finite element mesh defines where results will be calculated and reported spatially within the system. The finite element mesh used for the project area is shown in Figure 3.1. This is the largest and most complex TABS model that has ever been constructed 3

. The finite element mesh for the Baratari a basin was obtained from the New Orleans District (NOD) office of the US ACE. It was developed for a TA BS-MD model to evaluate the Myrtle Grove Siphon Project.

The finite element mesh for the Terrebonne basin was developed by FTN Associates, Ltd. (FTN) using 1998 georeferenced DOQQ aerial photos as a guide to marsh boundaries and

channel centerlines. It should be noted that num erous large forced drainage areas are excluded from the mesh because they are separated from the marsh by levees and are drained by pump stations (Section 1.2).

3 Personal Communication, Ian King, PhD, author of RMA-2 and RMA-11, based on number of computational nodes, degree of wetting and drying of mesh, and length of marsh-channel exchange zones.3-2Figure 3.1. Initial finite element mesh for the study area.March 9, 2006

3-3 3.2 System Topography In terms of topography, the system has two dist inct features, namely canals and marshes. In the model the canals are represented using over 130 newly surveyed cross sections for Bayou Lafourche, Company Canal, the GIWW, and por tions of Grand Bayou. Topography for the rest of the channels was represented using 740 survey ed cross sections from the USACEs’ Morganza to the Gulf Feasibility Study (USACE NOD 2000) UNET model. These sections from the UNET model were adjusted vertically as necessary to tie them into the Louisiana Coastal Zone Primary

GPS network. Previously in RMA-2, 1D cha nnels could only be represente d by certain regular shapes (e.g., trapezoidal, triangular, rectangular). In this study, however, preliminary testing (Section 4.1.2) showed that improved computed wa ter surface elevations and flows would result from refined representation of the channels. Repr esenting the channels with 2D elements would add considerable computational overhead and stability problems. Th erefore, RMA-2 was

modified to read in tables of elevation versus cross-sectiona l area and top width that were computed using detailed cross se ction points for 1D elements. Th e tables were computed using the same algorithms used in HEC-RAS (HEC 2002) and in the UNET (HEC 2001) preprocessor program CSECT. The only available useful topographic data for the marsh areas was in the Barataria Basin. This consisted of bathymetry from another RMA-2 model created by the NOD to evaluate the Myrtle Grove Siphon Project. LDNR collected eight transects in th e large open water areas of the basin for the Barataria Basin Feasibility Study and the NOD Barataria basin model bathymetry was updated in these areas. The only available topographic data for the Terrebonne basin marsh areas was the National Oceanic and Atmospheri c Administration (NOAA) National Geophysical Data Center’s (NGDC) compendium of various hydrographic, topographic, and other surveys that proved to be inaccurate in many areas. This was not unexpected since none of the data were tied to a common reference datum. Consequent ly, marsh topography had to be assumed. A sensitivity analysis was performed to determine the effect of this assumption on model results (Section 4.2.2).March 9, 2006

3-4 3.3 Boundary Conditions The hydrodynamics and the salinity transport in a modeled system are driven by the forces applied to the system via flow and sa linity entering or leav ing it at the boundaries. Continuous readings of water surf ace elevations and salinity data were collected over a period of

13 months at several locations in and around the study area. Fi gure 3.2 shows the locations and station identifiers of the gages where data was collected. Table 3.1 summarizes characteristics of

the collected data sets. The recorded data from the boundary gage s (10, 11, and 19) were used to provide boundary input to the model. Water surface eleva tions at the GIWW at Minor’s Canal gage (Gage 18) initially was used as a boundary c ondition, but during model ca libration (Section 6.1), the data was found to be questionable, and th e GIWW at Houma gage data (Gage 17) was applied instead. Data recorded at the internal gages (1 through 8, 12 through 17, and 20 through 21) were not part of the input to the model but were used to compare against simulated values produced by the model. Most of the newly inst alled gages were active during the period from February 2004 through January 2005. The remainde r were active during the whole period except for a few days or hours. With exception to th e upstream end of Bayou Lafourche where the diversion flow was applied, the upstream ends of all other 1D channels were assumed to have

zero flow because of little runoff contribution from upland areas. Before processing the observed data into the format readable by the RMA-2 modeling program, it was visually inspected to identify any ar tificial or err oneous values, revealed in most cases by spikes in plots of th e data. Any spikes that were unrealistic were smoothed out. Daily rainfall data were obtained from the L ouisiana State University (LSU) Agricultural Center in Houma, Louisiana. These data were used as time-varying input to the model. The original tidal gage locations were at Cocodrie, Dulac, and Grand Isle. However, it

was determined that the recorded water surface el evations at the Cocodrie and Dulac gages (data collection location 15 and 16 respec tively) did not accurately repr esent the tidal fluctuations along the Gulf of Mexico boundary in the Terreb onne Basin. After inves tigating potential new sources of tidal gage data, gage data at Isle Dernieres and Port F ourchon provided by the LSU

Coastal Studies Institute and the NOAA National Data Buoy Center, resp ectively, were obtainedMarch 9, 2006

3-5 for use in the model instead. The locations of the tidal stations used for the model are shown in Figure 1.2. The Isle Dernieres elevat ions were applied at the west ernmost point of the southern boundary. Port Fourchon data were applied near the outlet of Bayou Lafourche. The Grand Isle data were applied at the easternmost point. RMA-2 linearly interpolated between the three locations along the southern boundary. These inte rpolated data proved to provide the best available representation of tidal forcing along the southern boundary. Figure 1.3 shows that the tides p eak earlier and higher from west to east. This differential drives flows in the GIWW from west to east, and is the reason why more than 90% of the observed hourly data over the 13-month data collection period shows eastward flows in the GIWW (Figure 1.4).

3.4 Model Coefficients Three important coefficients must be specified that affect model results. First, bottom and bank friction within the protot ype is represented using Manni ngs ‘n’ roughness coefficients. Second, eddy viscosity represents th e resistance of flow to change s in applied force. Third, the dispersion coefficient defines the spreading of a constituent due to differe ntial shear within the water column. Values for these coefficients vary spatially and were assigned initially based on engineering judgment and adjusted through the calibration process.

3.5 Model Options 3.5.1 1D Channels As described in Section 3.2, a new capability was added to RMA-2 that used irregular cross sections instead of trapez oidal approximations to represent channel geometry. This allowed

more accurate water surface profiles and flow distri butions to be calculated.3-6Figure 3.2. Data collection locations.Table 3.1. Data collection stations and their samplingdurations and intervals.StationNoStation DescriptionStartingDateEndingDateSamplingIntervalCollectedParameter3Agency Station Number1 Bayou Lafourche north of Company Canal 02/19/04 01/10/05 15 min ZSV New installation2 Company Canal at Highway 1 near Lockport 01/01/04 01/30/05 15 min ZS USGS ID 73813503 Lake Fields 02/16/04 01/10/0515 min/1hr ZS New installation4 GIWW east of Bayou Lafourche at Larose02/15/04 01/11/05 15 min ZSVNew installation5 Bayou Lafourche south of GIWW 02/12/04 01/11/05 15 min ZSV New installation6 GIWW west of Bayou Lafourche at Larose 01/01/04 01/30/05 15 min ZSVQ USGS ID 73812357 Grand Bayou Marsh 02/16/04 01/10/05 15 min ZS New installation8 Bayou Terrebonne southeast of Houma 02/13/04 01/11/05 15 min ZSV New installation9 Bayou Lafourche at Donaldsonville01/01/04 10/01/04 15 min ZSVQ USGS ID 738040110 Bayou Lafourche at Thibodaux 01/01/04 01/30/05 15 min ZVQ USGS ID 738100011 Davis Pond Freshwater Diversion 01/01/04 01/30/05 15 min ZSVQ USGS ID 9019040012 Lake Cataouatche 01/01/04 01/30/05 15 min S USGS ID 9090121713 Lake Salvador 01/26/04 01/30/05 15 min ZS USGS ID 7380237514 Barataria Pass east of Grand Isle01/01/04 01/30/05 15 min ZSQ USGS ID 7380251515 Houma Navigation Canal at Dulac 01/01/04 10/01/04 15 min ZSV USGS ID 738132816 Bayou Petit Caillou at Cocodrie01/01/04 01/31/05 1 hr ZSV LUMCON17 GIWW at Houma 01/01/04 01/30/05 15 min ZSVQ USGS ID 738133118 GIWW at Minors Canal 02/19/04 01/25/05 15 min/1 hr ZS USACE19 Bayou des Allemands at Highway 9001/01/04 06/28/04 15 min ZS LDNR ID BAFS-0320 Barataria Bay Waterway north of Mud Lake 01/01/04 09/30/04 1 hr ZSV DNR ID BA-0621 South end of Little Lake 01/01/04 07/07/04 1 hr ZS DNR ID BA-073Key: Z=Water Surface ElevationS=Salinity ConcentrationV=VelocityQ=Discharge

3-7March 9, 2006

3-8 3.5.2 Channel Junctions At channel intersections, junc tion elements were coded to use matching water surface elevations (element type 901) since the mome ntum conservation method (element type 903) proved to produce unrealistically large water su rface elevation and flow differences at the intersections. This was due to the tendency for ch annel flows to change directions in response to

the tidal influence of the Gulf.

3.5.3 Channel and Marsh/Swamp Interconnections In the ERDC version of RMA-2, connections between 1D (channe l) and 2D (marsh) elements are modeled using special “Transi tion Elements.” For the dozens of miles of connectivity within this system, these elemen ts proved to be time-consuming to code and introduced stability and mass conservation problems in preliminary simulations. Consequently, for this study, a new type of 1D to 2D connection technique was used in RMA-2 as described in King and Williams ( 1999). This technique forces water surface elevations to match along the li ne of the 1D channel nodes and th en treats these water levels as water surface elevation boundary conditions for th e 2D portion of the mesh. The advantages of this technique are that the bounding 1D nodes are connected to the 2D nodes with a new quadrilateral element that:

• Significantly reduces the mass conserva tion problems that can occur with Transition Elements (sharp element angles), and

• Allows the full length of the ove rflow area to be represented.

3.5.4 Mesh Wetting/Drying The Marsh Porosity option was used for handl ing element wetting and drying issues. This is a technique that allows a smooth transition computationally when s horeline elements vary between wet and dry states. This was used inst ead of the Element Elimination Method that requires much more refinement of the mesh in the shoreline areas in order for the solution to converge, which would result in sign ificantly longer simulation times.March 9, 2006

4-1 

### 4.0 MODEL TESTING AND SE NSITIVITY ANALYSES

4.1 Model Testing Model testing has been an integral and c ontinuous part of the model development, starting with small simplified test cases duri ng the initial model deve lopment and continuing through to initial calibration si mulations with the full model mesh. Just a few of the many purposes for model testing are:

1. Checking model convergence, 2. Evaluating the implications of repres enting the 1D channel geometry with a simplified shape, 3. Testing newly added model capabilities, 4. Comparing different modeling me thodologies or formulations, and 5. Revealing problems with the mesh that cause mass not to be conserved locally.

4.1.1 Convergence Since the model uses the Newton-Raphson iter ative solution tec hnique, convergence criteria must be specified that define when to stop the iterations and move to the next computational time step (i.e., the maximum accep table change between computed values of depth and velocity components between iterations ). For all the model simulations, convergence criteria of 0.005 ft were used for depth and 0.001 ft/sec for both the x- and y-velocity components. Using a 15-minute timestep, the solu tion usually converged within 20 iterations initially and then within 8 to 10 iter ations as the simulations progressed.

4.1.2 Channel Geometry Representation

Some of the earliest model te sting conducted for this project involved testing the effects of the trapezoidal shape to approximate the chan nel cross sections in RMA-2. A simplified test case was developed consisting of a small networ k of 1D channels and interconnected storage areas. The UNET model was used for compari ng flows and water surface elevations using irregular cross section geometry from Bayou Lafourche along w ith vertical-walled storage areas.March 9, 2006

4-2 Lateral weir (UNET “LA” and “WD”) records were used to represent th e connections between the 1D channels and the storage areas with UNET. For RMA-2, the geometry included 1D trapezoid al representations of the irregular cross

sections for the channels and si mplified 2D meshes re presenting the same storage areas defined in the UNET input test case. Transition Elements we re first used to connect the 1D channels to

the 2D mesh to allow for the interaction of flow between the channels and storage areas; however, these proved problematic and a new me thod for connecting the channels and marsh was used (Section 4.1.4). The same boundary conditions were specifi ed for both models. Various runs were performed with both steady state and dynamic bounda ry conditions, and the results from the two models were compared at selected locations. Co mputed water surface elev ations typically were within 0.5 ft or less, and computed flows were within 20%. However, this was not deemed accurate enough, which gave rise to the need fo r the representation of irregular channels in RMA-2 (Section 3.2). After adding the irre gular channel capabil ity to RMA-2, RMA-2 computed water surface

elevations matched those from UNET to within 0.2 ft with flows ma tching within 5%.

4.1.3 1D Junction Formulation Another example of model te sting conducted with a simp le test case involved the comparison of available 1D junction node types in RMA-2. RMA-2 includes the following three types of junction nodes:

• Type 901 - Forces equal water surface elev ation at the ends of all the reaches forming the junction;

• Type 902 - Matches total head (water su rface elevation + velo city head) at the ends of all the reaches forming the junction; and

• Type 903 - Conserves momentum at the junction.

For the type 903 junction, it is necessary to specify which reaches represent the “main channel” at the junction. It s eems reasonable to assume that any differences between these formulations would be highly dependent upon the magn itudes of flow velociti es in the reaches atMarch 9, 2006

4-3 the junction and upon the differences in velocity among the reaches forming the junction. These expectations were confirmed with a small test case consisting of three 1D reaches creating a simple T-shaped junction. The different formul ations were tested by comparing the flow distribution and computed water surface elevations at the junction. When velocities in the reaches were low, th ere was practically no difference between the three formulations. For higher velocities, more pronounced differences were observed. These

results confirmed that the momentum cons ervation method (type 903) produced unrealistic

results under some flow conditions.

4.1.4 Lateral Weir 1D-2D Connections A fairly recent addition to King’s version of RMA-2 is the type 999 lateral connection element between 1D and 2D elements (King an d Williams 1999). This capability was added to

the RMA-2 model to simulate the lateral flow exchange between a river channel and leveed overbank areas during flood events. Conceptually, the same type of flow exchange occurs between the channels and adjacent marsh areas in the project area. To use the type 999 lateral flow exchange f eature, the 2D elements along the edge of a

mesh that abuts a 1D channel reach where flow exchange can occur must be aligned and nodes spaced to be adjacent to end nodes of 1D elements on the channel. Internally, the model matches

water surface elevation in the ch annel to the adjacent 2D elemen t and matches flow entering or leaving a 1D element as inflow to or outflow fr om the adjacent 2D element. In effect, the 1D channel becomes a boundary condition for the 2D mesh. This formulation allows for the exchange of flow between 1D and 2D elements in either direction. The connection between a 1D and 2D element is specified by creating a quadrilate ral element from the corner nodes of adjacent 1D and 2D elements with the element type 999. Because accurate representation of the interaction between the channels and adjacent marsh areas is such a critical component of this project, it was decided to prepare a simple test case to test the type 999 lateral flow exchange formulation. The purpose of this test was to determine the effect on computation times. Acco rding to Dr. Ian King, the primary drawback of the type 999 lateral connections is increased computation times. Because manageable simulationMarch 9, 2006

4-4 times are critical to meeting project deadlines, it was essent ial to know how the type 999

elements would affect simulation times to decide whether or not to use them. Two simple test cases were set up with a 1D channel reach connected to a 2D mesh; one

with traditional Transition Elements and one with the type 999 elements. While both formulations gave similar results , the runs with the type 999 elements took about twice as long. The decision was initially made not to use the ty pe 999 lateral connections, and to code all lateral

connections with traditional Transition Elements based on these test results. However, it was later decide d that the best possible formulation for the type of

continuous connection between the channels and marshes in the project area was the type 999 element. At issue was the preservation of lateral weir length along the cha nnel that controlled the exchange between the channel and adjacent marsh areas (too short a length meant that flows into or out of the marsh would be underestimated). Wi th the Transition Elements it was difficult to conserve the weir length due to the discrete nature of the conn ection from a single 1D node to a 2D element. At best, the Transition Elements could give only a rough, di scretized approximation of the weir length. When tests were run with t ype 999 elements implemented in the full model network, it was found that their impact on computation times was minimal. The earlier simplified tests with the type 999 elements led to a biased conclusion about simulation times due to the scale of the original te st. In the original test, only one reach and two adjacent marsh areas were tested. Due to the small number of nodes and elements in the test network, the type 999 elements had a substantial influence on the simulation times. The full model simulation times are more heavily influenced by the very large total number of elements, so the type 999 elements have much less influenc e. For this particular case, the original model testing led to a misleading conclusion.

4.1.5 Continuity

One of the fundamental tests of acceptability for any model is adequate continuity and

conservation of mass. For a model mesh this large, it is critical to ascertain whether mass is being created or lost in the model. Therefore, continuity checks are on e of the most importantMarch 9, 2006

4-5 kinds of model testing. In fact, the goal of having acceptable continuity errors has driven the development and refinement of this mode l more than any other single factor.

4.1.5.1 1D Reach Continuity Due to the density and sheer numbers of 1D nodes in this model, it was originally difficult to quantify continuity in the 1D reaches. The majority of visualization tools for interpreting output data from RMA- 2 are specific to 2D elements (e.g., contouring). To eliminate the laborious task of tracking flows by 1D node numbers in the model output file, Dr. Ian King developed a tool for the RMAPLT program that graphically displa ys flows at 1D nodes. This tool proved invaluable in finding areas of poor continuity in the 1D reaches. These areas typically occurred around bridge s or other significant changes in the channel geometry (e.g., cross-sectional area, invert eleva tion). The solution for these continuity errors in most cases was simply to refine the spacing of the 1D nodes. Th e addition of 1D nodes had a negligible effect on computation times, so the 1D elements could be made very dense at locations where extra

resolution was needed.

4.1.5.2 2D Continuity – Flow Through a Marsh Two-dimensional continuity was tested by establishing continuity lines at inflow, outflow, and interior points of the 2D mesh. The total inflow versus outflow could then be tracked, giving an estimate of the mass created or lost in the mesh. Continuity was tested for

small marsh areas as well as th e entire Barataria Ba sin. Under steady state conditions, the entire mesh showed good continuity at all continuity li nes, with no more than 10% losses at any given

location.

4.2 Sensitivity Analyses Several sensitivity analyses have been performed on the full model. These include investigation of the effects of computational time step, the mars h elevations in the Terrebonne Basin, and the 1D junction node types.March 9, 2006

4-6 4.2.1 Computational Time Step In Phase 1, to test the effect of the comput ational time step for dynamic simulations, three simulations were performed, one with a one hour time step, one w ith a 30-minute time step, and another with a 15-minute time step. While the longe st time step simulation ran faster, results differed from shorter time step simulations during periods of la rge tidal changes. The largest impact of computational time step was obser ved in the RMA-11 simulations where negative salinity concentrations were computed on occasion with time steps larger than 15 minutes. Consequently, all simulations in Phase 1 were made using a 15-minute time step. In Phase 2, with the addition of the Barataria Basin, model run times doubled in duration. In order to meet deadlines, the model was run with a 30-minute time step. Testing showed no changes in the results between usi ng a 15-minute and 30-minute time step.

4.2.2 Terrebonne Basin Marsh Elevations Because of the lack of bathymetry data in the Terrebonne Basin, all marsh invert

elevations north of the Gulf were initially set at –5 ft NAVD88 based on local knowledge. Because of concerns about artificially deep depths affecting flows and velocities in the marshes, a simulation was performed with all marsh bo ttom elevations increased to –2 ft NAVD88. Because this change did not have a significant impact on the computed marsh velocities, it was decided to keep the marsh elevations at –5 ft NAVD88.

4.2.3 1D Junction Nodes As described in Section 3.5.2, RMA-2 allows a choice of 1D junction node types. The model for this project was initia lly developed using the default j unction node type (type 901). In response to questions about the flow distribution at 1D nodes, the junction nodes at the Bayou LaFourche/Company Canal and Bayou LaFourche/GI WW junctions were cha nged to a type that conserved momentum (type 903). This change had a negligible impact on the flow distributions at these junctions due to the low velocities in the channels. Thus, the fl ow distribution was more significantly impacted by head differential than momentum for the conditions tested. Later simulations showed, however, that the moment um junction (type 903) produced unrealisticallyMarch 9, 2006

4-7 large head and flow differential s at the junctions due to the tidally-induced reversing flows. Consequently, all junctions were changed back to equal elevation (type 901) junctions.March 9, 2006

5-1 

### 5.0 MODEL MESH MODIFICATION

After the model testing phase, several sets of modifications were made to the geometry to “creep up on the solution” – i.e., starting with a simplified model and adding complexity as

needed.

5.1 Phase 1 Mesh Refinement As stated in Section 3.5.3 (C hannel and Marsh/Swamp Interconnections), the connections between 1D (channel) and 2D (marsh) elements were modeled using a new quadrilateral element type 999 instead of Transition Elements. The nodal elevations for all 2D elements connected to type 999 elements were held constant so th at there was no slope across the 2D elements. Additionally, a second tier of 2D elements adjacen t to the weir connections was coded with a

constant elevation to create a flat “shelf” at the overbank weir elevation. These shelves were coded to help smooth the transition of flow betw een the 1D channels and 2D marsh areas. As the model development progressed, the 2D marsh areas to which the type 999 elements are

connected were refined further to more accura tely compute the flow exchange between 1D

channels and 2D marsh. For mars hes connected to 1D channels, nodal elevations for perimeter

nodes not included in a weir c onnection were increased to +5.0 ft NAVD88. Figure 5.1 shows the extent of the type 999 elements in the model.

5.2 Mesh Truncation / Addition 5.2.1 Upper Bayou La fourche Truncation The representation of the entire length of Bayou Lafourche proved problematic. First, the flow data record for Bayou Lafourche at Donald sonville had periods of missing and invalid data. Second, initial simulations showed that the tr ansport travel time fr om Donaldsonville to Thibodaux was approximately 1 week. Therefor e, the northern end of Bayou Lafourche was

eliminated from the mesh and the model bounda ry was instituted at Thibodaux instead. The measured flow data for Bayou Lafourche at Thibodaux was then used in, lieu of the Donaldsonville data, as the upstream fl ow boundary condition for Bayou Lafourche.5-2Figure 5.1. Extent of type 999 elements(shown in red) used in model mesh.March 9, 2006

5-1 5.2.2 Phase 1 Barataria Basin Truncation Initial simulations with the complete Terrebonne - Barataria Basin mesh were unacceptably slow (approximately one-fourth of the prototype time) given the number of

simulations that were known to be required to gain insight into how this complex system worked. Consequently, it was decided to reduce the size of the mesh by eliminating the Barataria Basin for the Phase 1 effort (Figures 5.2.a and 5.2.b). The result of using just the Terrebonne Basin

mesh was that more than double the number of simulations could be made, allowing significant insight into the system behavior with a less complex model. The model with only the Terrebonne Basin mesh was considered an allowable approxi mation because the observed data showed flow in the GIWW at Bayou Lafourche moved eastward mo re than 90% of the time for the 13-month period over which data was collected (Figure 1.4) - i.e, the Barata ria Basin received flow more
than 90% of the time and contributed flow into the Terrebonne Basin less than 10% of the time. The GIWW gage near Larose served as th e eastern boundary for the model with only the

Terrebonne Basin mesh. Consequently, only the Isle Dernieres and Port Fourchon tidal records were used with the truncated mesh in Phase 1. Figure 5.3 shows the location of the final boundary condition

locations used in the Ph ase 1 truncated model.

5.2.3 Phase 2 Barataria Basin Addition After the Phase 1 modeling effort was comple ted and insight was gained into how the Terrebonne Basin system worked, the model was modi fied to add the Barataria Basin back in so

that it could be used to evaluate the effects of 15 operational and channel improvement scenarios on salinities, water surface elev ations, and benefit areas.

5.3 Phase 2 Mesh Refinement In addition to adding the Barataria Basin mesh, the Phase 2 mesh was improved in the following ways:

• Grand Bayou was modified to better reflect its connectivity to the adjacent marsh areas and the open water ar ea at its southern end.March 9, 2006

5-2 • New cross sections and bank elevations th at were surveyed in the GIWW east of Bayou Lafourche were incor porated into the model.

• Bush Canal was connected to the mars h on its southern side via type 999 elements.

• Mesh boundaries and elevations were refine d to reflect the location of features such as forced drainage areas, and ot her areas that do not flood that were identified using the 2004 DOQQ imagery.

• Even though the NGDC dataset was not used based on calibration results (Section 6.1), ground elevations from th e NGDC bathymetry data was used to represent several barrier islands that are pr esent in this area could not be refined to the level of detail necessary. This one area where the model could be improved upon in the future.

The resulting final mesh is shown in Figur e 5.4. Figure 5.5 shows the location of the final boundary conditions used in the Phase 2 model. Figure 5.6 shows the final bathymetry used in

the mesh.5-3Figure 5.2.a. Phase 1 truncated model mesh.5-4Figure 5.2.b. Detail from the dense mesh area shown in Figure 5.2.a.5-5Figure 5.3. Boundary condition locations (shown inyellow) for Phase 1 truncated model mesh.5-6Figure 5.4. Final Phase 2 finite element mesh for the study area.5-7Figure 5.5. Boundary condition locations for Phase 2 model mesh.5-8Figure 5.6. Final Phase 2 model mesh bathymetry.March 9, 2006

6-1 

### 6.0 MODEL RE-CALIBRATI ON AND VERIFICATION

Calibration is a process where model coeffici ents are systematically varied through a series of simulations to reproduce observed data. Doing this offers more confidence in the model when it is used in predicting data under different scenarios. In Phase 1, the model was calibrated, and the initial Phase 2 calibration was performed using the Phase 1 coefficients. Verification is the process where a single simula tion is performed usi ng the model coefficients selected during calibration to reproduce values durin g a different period to give fu rther confidence in the model.

6.1 RMA-2 Calibration and Verification Water surface elevation, flows, velocities, and salinity were calibra ted to observed gage

data. An initial RMA-2 simulation was run for a 2-week period to establish a baseline condition

to which other calibration simulations could be compared. After the baseline results were examined, a series of runs were executed us ing different boundary c onditions at the western GIWW boundary at Minor’s Canal in combinati on with different geometry modifications because the results did not show a good co rrelation with the observed data. The boundary conditions were varied because the observed data in the GIWW showed consistently higher water surface elevations at Houma than at Minor’s Canal or at Larose (Figure 6.1). Based on the fact that the observed flow data showed eastward flow in the GIWW 90% of the time, the differences in the observed wa ter surface elevations s eemed to indicate that there was a datum problem associated with one or more of the gages. Consequently, the model was run with modified boundary conditions at the Minor’s Canal boundary. Modification methods used included increasing the water su rface elevations there by a fixed incremental value, and applying the GIWW at Houma ga ge elevation data at Minor’s Canal. The geometry modifications used for calib ration included using the bathymetric sounding data from the NGDC in the Terrebonne marsh, a dding constrictions at fl oodgate locations, and adding 1D channel – 2D marsh connections to re present the known flow exchange between the channel and adjacent marsh.6-2Figure 6.1. 25-hour average of observed water surface elevations from May-June 2004.March 9, 2006

6-3 A series of runs were executed for a 4-w eek period, using different combinations of geometries (NGDC Terrebonne basin bathymetry ve rsus original synthesized Terrebonne basin bathymetry), boundary conditions at Minor’s Ca nal (GIWW at Houma versus GIWW at Minor’s Canal elevation plus 1.0 ft), and Manning’s ‘n ’ values for the 1D ch annels, 2D open water elements, and 2D marsh elements. All the simula tions were carried out with a computational time step of 30 minutes. The NGDC Terrebonne basin bathymetry pr oved problematic. Although it intuitively looked more realistic than the synthesized bathym etry, it proved inaccurate in most but not all areas where survey data or local knowledge we re available for verifi cation. Given that the NGDC data is a compendium of a number of sources, many of which were never tied to a known datum, this was not surprising. Setting Manning’s ‘n ’ values for the different areas yielded little improvement in results. Consequently, the synthesized data was kept in the model. In testing the different Minor ’s Canal boundary conditions, the results showed that using the GIWW at Houma gage elevation data at the Mi nor’s Canal location produced the best results. Of all the locations where computed eleva tions matched observed, the poorest matches were found at HNC at Dulac (Station 15), and Lake Cataouache (Station 12). This may be due to problems with the datum for the gages. This is in dicated by the fact that the computed elevations at Dulac match up quite well with the observed el evations at the Bayou Petit Caillou at Cocodrie gage (Station 16), which is located rela tively close to the gage on the HNC.

The observed water surface elevations for the gages in Lake Cataouache and Lake Salvador did not match well (Figure 6.1). While the computed data matched up fairly closely with the Lake Salvador gage data, the va lues for the observed Lake Cataouache were consistently higher than the computed values . This indicates a pr oblem with the Lake Cataouache gage datum because both lakes are connected and both gages are within a short

distance of each other. The water surface elevation and velocity resu lts from the final calibration run for the various gages are shown in Figures A.1 through A.24 in Attachment 1, and the final calibration parameters are shown in Table 6.1 and Figure 6.2. The computed water surface elevations and velocities showed good agreement with the observed data for most of the observed gageMarch 9, 2006

6-4 locations. In instances where values were not matching in magnitude, the computed results reproduced overall observed trends. When assessing the quality of model calibration, it is a good pr actice to look at the results in a variety of ways, instead of focusing merely on matching observed and predicted time series values. This is especially true in systems such as the one studied here, where topography, hydrodynamics, and collection of repr esentative monitoring data have been complex tasks. Other

calibration assessment methods used included looki ng at scatter plots and error statistics, and how well the model captures overall trends. Figures B.1 through B.17 (Attachment 2) show scatter plots where observed and predicted water surface elevati ons are compared, and Figures B.18 through B.27 (Attachment 2) show plots where observed and predicted veloc ities are compared. Some of the statistical parameters that quantify “reasonab le fit” are shown in Tables 6.2 and 6.3. It should be noted that the uncertainty associated with the measurements should be kept in mind in such an assessment of simulation errors. The equations fo r these statistics are shown below.

Average Error = 

# ∑

= − = N

1 i i i a ) S (0 N 1 E

O i = Observed value, and S i = Simulated value

Standard Error RMSE =

N ) S (O N

1 i 2 i i 

## ∑

= −

R squared N O O N S S N OS O S

i i ii ii i i i N

−= − − − 

## ∑ ∑ ∑ ∑ ∑ ∑ ∑

= [ ( ) ][ ( ) ] ( ) ( )( )

2 2 2 2 16-5Figure 6.2. Location of RMA-2 element types in the mesh.Table 6.1. Final RMA-2 calibration parameters.Water BodyElement TypeEV-xu-vel(lb-sec/ft2)EV-yu-vel(lb-sec/ft2)EV-xv-vel(lb-sec/ft2)EV-yv-vel(lb-sec/ft2)Manning's nBayou Lafourche 1 20.0 20.0 20.0 20.0 0.015Bayou Terrebonne 8 20.0 20.0 20.0 20.0 0.015Bayou Petit Caillou 12 20.0 20.0 20.0 20.0 0.045Houma Navigation Canal 17 20.0 20.0 20.0 20.0 0.015GIWW East of Bayou Lafourche 43 20.0 20.0 20.0 20.0 0.045All remaining 1D Channels 2-8,9-11,13-16,18-28 20.0 20.0 20.0 20.0 0.025Overbanks 29 Scaled ScaledScaled Scaled 0.025Marsh areas connected to Gulf 30,32,35,42 Scaled Scaled Scaled Scaled 0.030Isolated marsh areas with connections to channels33, 34,36 Scaled ScaledScaled Scaled 0.200Gulf of Mexico 41 Scaled Scaled Scaled Scaled 0.030

6-6 March 9, 2006Table 6.2. Error Statistics for RMA-2 Water Surface Elevation Calibration.Statistical ParameterGage 1Gage 2Gage 3Gage 4Gage 5Gage 6Gage 7Gage 8Gage 10Gage 12Gage 13Gage 14Gage 15Gage 16Gage 17BA 06BA 07Average Error (ft) 0.01 -0.03 0.04 -0.10 -0.06 -0.11 -0.13 0.11 2.25 -0.51 0.17 0.01 -0.53 -0.20 0.22 -0.34 -0.23RMSE (ft) 0.14 0.14 0.16 0.19 0.18 0.19 0.23 0.22 2.26 0.55 0.25 0.16 0.57 0.32 0.24 0.40 0.27R-squared 0.80 0.79 0.73 0.75 0.22 0.78 0.51 0.74 0.31 0.71 0.73 0.93 0.58 0.79 0.77 0.87 0.86Table 6.3. Error Statistics for RMA-2 Velocity Calibration.Statistical ParameterGage 1Gage 2Gage 4Gage 5Gage 6Gage 8Gage 10Gage 15Gage 16Gage 17Average Error (ft/s) -0.03 0.15 0.01 0.43 -0.06 0.11 0.02 0.26 -0.06 0.04RMSE (ft/s) 0.07 0.24 0.27 0.86 0.37 0.36 0.03 0.57 0.30 0.35R-squared 0.19 0.15 0.32 0.09 0.01 0.66 0.98 0.45 0.34 0.156-7March 9, 2006March 9, 2006

6-8 Average error is a measure of model accuracy, bias or systematic error. Positive values indicate systematic oversimulati ons while negative values indicat e a systematic undersimulation.

The tolerances within which the models are judged to be free of such systematic errors are not well defined. Standard Error, RMSE, determines the precision of a simulation. R-squared is the coefficient of determination, which is a statistical measure of how well predicted values approximate observed data points; an r-squared of 1.0 (100%) indicates a pe rfect fit of predicted

values to observed data. After calibration, the next step is model verification. Verification is the process where a single simulation is performed using the mode l coefficients selected during calibration.

Verification of the model was carried out using observed data for October 2004 through December 2004. Results are shown in Figures A.25 through A.38. The observed values are plotted against the simulated in Figures B.28 th rough B.42. The verification comparison statistics

are shown in Tables 6.4 and 6.5. Based on experience from several modeling stud ies, the statistical parameters tabulated

above indicate satisf actory verification.

6.2 RMA-11 Calibrati on and Verification Several simulations were carried out to calibrate the salinity data at various monitoring gages by systematically vary ing dispersion coefficients. As a first step, specific portions of the s outhern mesh were assi gned different element types to account for the variati on in mixing characteristics of the various marsh regions. The southern segments of the canals were also assi gned different element types than those of the northern portion. This allowed hi gher dispersion coefficients to be set in the southern areas where the primary mechanism of transport is mixing and dispersion. Figure 6.2 shows the various element types of the mesh.Table 6.4. Error Statistics for RMA2 Water Surface Elevation Verification.Statistical ParameterGage 1Gage 2Gage 3Gage 4Gage 6Gage 7Gage 8Gage 10Gage 12Gage 14Gage 17Average Error (ft)0.96 0.04 0.60 0.75 -0.02 0.12 0.98 2.40 2.77 -0.03 0.13RMSE (ft)1.93 0.21 0.63 0.77 0.15 0.28 1.01 2.42 2.79 0.13 0.17R-squared0.94 0.93 0.92 0.91 0.81 0.78 0.81 0.62 0.81 0.96 0.94Table 6.5. Error Statistics for RMA-2 Velocity Verification.Statistical ParameterGage 1Gage 4Gage 5Gage 8Gage 16Average Error (ft/s) -0.08 0.05 0.30 0.09 -0.03RMSE (ft/s) 0.12 0.41 0.82 0.43 0.47R-squared 0.72 0.09 0.11 0.66 0.02

6-9 March 9, 20066-10Figure 6.3. Location of RMA-11 element types in the mesh.March 9, 2006

6-11 In RMA-11, one can either specify the absolute value of the dispersion coefficient or a dispersion coefficient scaling parameter for a gi ven element type. When a scaling parameter is specified, the program computes di spersion coefficients based on th e size of the element and the average velocity at that element. The scaling parameter approach was used for the present calibration; the final values are tabulated in Table 6.6.

Table 6.6. Final RMA-11 calibration parameters.

Water Body Element Type Dispersion scale factor in

X-direction Dispersion scale factor in

Y-direction Minimum Dispersion in X-direction (m 2 /s) Minimum Dispersion in Y-direction (m 2 /s) Bayou Terrebonne 8 5 5 0.5 0.5 Bayou Petit Caillou 12 5 5 0.5 0.5 Grand Bayou 28 5 5 0.5 0.5 Marsh south HNC-Bayou Dularge junction 30 10 10 0.5 0.5 Barataria Bay near inlet 31 500 500 0.5 0.5Marsh south Point-auxChenes canal 32 10 10 0.5 0.5

Marsh to the east of Grand Bayou 34 20 20 0.5 0.5 Western part of Barataria Bay 35 100 100 0.5 0.5 Rigollets, Little Lake area 37 10 10 0.5 0.5 Upper Terrebonne Bay 38 10 10 0.5 0.5 Terrebonne Bay 39 10 10 0.5 0.5 Gulf of Mexico 41 500 500 0.5 0.5 Open Water in Barataria Bay 42 2 2 0.5 0.5 Southern segment of Bayou Dularge 44 100 100 0.5 0.5

HNC between Cocodrie and B. Grand Caillou 45 100 100 0.5 0.5

HNC south of Cocodrie 46 100 100 0.5 0.5 Lower Bayou Terrebonne 47 100 100 0.5 0.5Southern part of Pointe-auChenes 48 10 10 0.5 0.5 Lower Grand Bayou 49 10 10 0.5 0.5 Barataria Waterway 50 2 2 0.5 0.5 Southern 2D portions of canals 51-57 500 500 0.5 0.5

All other marshes and channels 1-7, 9-11, 12-27, 33-

36,43 1 1 0.5 0.5