FOUR CLOSURE STRUCTURES PROJECT Summary Report of Findings and Recommendations

Transcription

1 FOUR CLOSURE STRUCTURES PROJECT Summary Report of Findings and Recommendations Prepared For: Coastal Protection and Restoration Authority Iberia and Vermilion Parishes January 2013 Lafayette 135 Regency Square Lafayette, LA P. O. Box (70505) phone fax New Orleans 1100 Poydras, Suite 1550 New Orleans, LA P. O. Box ( phone fax Baton Rouge 445 North Blvd, Suite 601 Baton Rouge, LA phone fax Houston 675 Bering Drive, Suite 260 Houston, TX phone fax Engineers Surveyors Environmental Consultants

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3 Four Closure Structures Table of Contents TABLE OF CONTENTS 1.0 INTRODUCTION PREVIOUS MODEL DATA COLLECTION FENSTERMAKER MODEL Model Validation RESULTS Scenario 1: South Structures with 2010 Tides and 2010 Channel Discharges Scenario 2: South Structures with 2010 Tides, 2010 Channel Discharges, and Large Atchafalaya Discharge Scenario 3: South Structures with 2010 Tides, 2010 Channel Discharges, and 50-year Rainfall Event Scenario 4: Inland Structures with 2010 Tides, 2010 Channel Discharges, and 50-year Rainfall Event DISCUSSION AND CONCLUSION REFERENCES APPENDICES APPENDIX A: Model Input Data APPENDIX B: Water Surface Elevation and Salinity Comparison APPENDIX C: MIKE FLOOD Solver Routines APPENDIX D: MIKE Presentation i

4 Table of Contents Four Closure Structures LIST OF FIGURES Figure 1-1: Four Closure Structures Project Map... 1 Figure 2-1: Chenier Plain Model Domain... 2 Figure 4-1: Fenstermaker Model... 4 Figure 4-2: Channel Bathymetry Collection Effort... 5 Figure 4-3: Channel Cross-sections Comparison at Locations North of the GIWW... 5 Figure 4-4: Validation Locations... 6 Figure 4-5: CRMS-531 Hourly Water Surface Elevation Validation... 7 Figure 4-6: CRMS-531 Daily Salinity Validation... 7 Figure 4-7: CRMS-532 Hourly Water Surface Elevation Validation... 7 Figure 4-8: CRMS-532 Daily Salinity Validation... 8 Figure 4-9: NOAA Hourly Water Surface Elevation Validation... 8 Figure 4-10: NOAA Daily Salinity Validation... 8 Figure 5-1: Closure Structure Locations... 9 Figure 5-2: Scenario 1 GIWW Discharge Comparison Figure 5-3: Scenario 1 Water Level Comparison Figure 5-4: Scenario 1 Salinity Comparison Figure 5-5: Scenario 2 GIWW Discharge Comparison Figure 5-6: Scenario 2 Water Level Comparison Figure 5-7: Scenario 2 Salinity Comparison Figure 5-8: Scenario 3 GIWW Discharge Comparison Figure 5-9: Scenario 3 Water Level Comparison Figure 5-10: Scenario 3 Salinity Comparison Figure 5-11: Scenario 3 Maximum Water Level Comparison over 15 Days Figure 5-12: Scenario 3 Maximum Salinity Comparison over 15 Days Figure 5-13: Scenario 4 Closure Structure Locations Figure 5-14: Scenario 4 Water Level Comparison Figure 5-15: Scenario 4 Maximum Water Level Comparison over 15 Days LIST OF TABLES Table 3-1: Chenier Plain Model Inputs... 3 Table 4-1: Gage Attributes... 7 ii

5 Four Closure Structures January INTRODUCTION Fenstermaker teamed with the Coastal Protection and Restoration Authority (CPRA) and ARCADIS to examine water level and salinity impacts due to channel closure structures placed in Vermilion and Iberia Parishes. The goal of this Four Closure Structures project was to develop numerical simulations to evaluate impacts of the closure structures during storm events. Fenstermaker refined an existing MIKE FLOOD model to analyze the Vermilion Bay vicinity (Figure 1-1). This area is influenced by tides in Vermilion Bay and freshwater inflows from the inland riverine network. Figure 1-1: Four Closure Structures Project Map 2.0 PREVIOUS MODEL Fenstermaker refined an existing MIKE FLOOD model of coastal Louisiana developed under the Louisiana Coastal Area (LCA) Science and Technology Office in conjunction with the University of Louisiana at Lafayette. This Chenier Plain model analyzed regional tidal and salinity circulation patterns along the Chenier Plain in southwest Louisiana. Development of the Chenier Plain 1

6 January 2013 Four Closure Structures model began in 2006 examining water levels, salinity, and velocity patterns on a daily and monthly scale along the Louisiana coastal zone from Freshwater Bayou to Sabine Lake (Figure 2-1). The Chenier Plain model is a living model that has been calibrated and validated over multiple years (Meselhe and Miller 2007), and is regularly updated with improved data and modeling techniques. The most recent version of the Chenier Plain model was expanded to include Vermilion Bay and 5,100 square kilometers of additional open water in the Gulf of Mexico, in addition to hydrologic data from The 2010 model was validated and calibrated using gage data collected by CPRA and the National Oceanic and Atmospheric Administration (NOAA). In addition to the reasons stated above, Fenstermaker selected the 2010 Chenier Plain model for the Four Closure Structures study because of Fenstermaker s familiarity of the model setup and outputs. Figure 2-1: Chenier Plain Model Domain (Meselhe and Miller 2007) The MIKE FLOOD software suite developed by the Danish Hydraulic Institute (DHI) was selected for the Four Closure Structures study because of its coupled one- and two-dimensional capabilities and ability to capture time varying hydraulic structures such as locks. MIKE FLOOD is an ideal software suite for analyzing channel, open water, and overland flow in conjunction with 2

7 Four Closure Structures January 2013 salinity transport. Please see Appendix C for a detailed discussion on the MIKE FLOOD solver routines (Meselhe and Miller 2007). 3.0 DATA COLLECTION The Chenier Plain model was developed in 2007 using data from 2002 through As a living model, it has been continuously expanded and updated as more data becomes available. The data types and sources listed in Table 3-1 were collected as boundary conditions for the 2010 Chenier Plain model. Time series of select data are located in Appendix A. Table 3-1: Chenier Plain Model Inputs Type Bathymetry Evapotranspiration Hydraulic Structures Precipitation Riverine Discharge Salinity Topography Water Level Wind Source National Geophysical Data Center (NGDC) NOAA & Louisiana State University (LSU) AgCenter United States Army Corps of Engineers (USACE) & Coastal Wetlands Planning and Protection Act (CWPPRA) USACE, National Climatic Data Center (NCDC), & United States Geological Survey (USGS) USGS & NOAA USGS, Coastal Protection and Restoration Authority (CPRA) Coastwide Reference Monitoring System (CRMS), & USACE LSU Atlas USACE, CPRA CRMS, NOAA, & USGS National Data Buoy Center (NDBC) 4.0 FENSTERMAKER MODEL Fenstermaker was tasked with analyzing impacts to water levels and salinity in Vermilion Bay and surrounding project area due to placement of closure structures along several channels during typical conditions such as daily tide cycles and large rainfall events. ARCADIS analyzed storm surge impacts using the coastal circulation and storm surge model ADCIRC. The eastern portion of the 2010 Chenier Plain model was used to develop the Four Closure Structures model. Approximately 470 kilometers of channel and 5,600 square kilometers of model domain were added to capture water levels and salinities north of Vermilion Bay (Figure 4-1). Model inputs and extents are shown in Appendix A. 3

8 January 2013 Four Closure Structures Several closure structures were placed within the model domain along Vermilion River, Boston Canal, Oaks Canal, and Delcambre-Avery Canal to reduce inland inundation due to storm surge. These closure structures would be closed before storm events reached the Vermilion Bay area and re-opened as soon as possible after the storm event to reduce flooding Figure 4-1: Fenstermaker Model Accurate channel dimensions were an important component of the Four Closure Structures model. Discharge is highly sensitive to channel geometry, and salinity transport is predicated on discharge. As such, a handheld depth finder was used to record water depth at locations shown in Figure 4-2. These water depths were related to observed water levels from the USGS gage at Cypremort Point and converted to an elevation. Figure 4-3 shows a comparison of channel cross-sections north of the Gulf Intracoastal Waterway (GIWW). Due to the absence of a complete survey, channels dimensions were adjusted for several channels during the validation process (orange channels in Figure 4-2). These channel dimensions differ from the ADCIRC model and were selected during the validation process because they showed optimal salinity transport compared to gage data. 4

9 Four Closure Structures January 2013 Figure 4-2: Channel Bathymetry Collection Effort Figure 4-3: Channel Cross-sections Comparison at Locations North of the GIWW 5

10 January 2013 Four Closure Structures As with the 2010 Chenier Plain model, the Four Closure model is intended to output daily and monthly average water levels and salinities; however, the model adequately captures hourly water levels as shown in Section Model Validation The Four Closure model was validated using three gage locations which collected water level and salinity data. One NOAA gage is located at Cypremort Point and two Coastwide Reference Monitoring System (CRMS) gages are located in Vermilion Bay and near Delcambre-Avery Canal. Gage locations are shown in Figure 4-4, and Table 4-1 lists the gage attributes. Water level and salinity outputs from the Four Closure model compare favorably with observed gage data. Figures 4-5 through 4-10 compare observed water levels and salinity to the Four Closure model outputs. During January and February of 2010, the Four Closure model showed bi-directional discharge in the GIWW typically flowing to the east as it runs along Vermilion Bay (yellow arrows in Figure 4-4). Figure 4-4: Validation Locations 6

11 Four Closure Structures January 2013 Table 4-1: Gage Attributes Station Latitude Longitude Location CRMS Marsh CRMS Channel NOAA Open Water CRMS Average: 0.32 CHF Average: 0.19 RMSE: 0.16 Figure 4-5: CRMS-531 Hourly Water Surface Elevation Validation CRMS Average: 0.79 CHF Average: 1.36 RMSE: 0.36 Figure 4-6: CRMS-531 Daily Salinity Validation CRMS Average: 0.18 CHF Average: 0.29 RMSE: 0.18 Figure 4-7: CRMS-532 Hourly Water Surface Elevation Validation 7

12 January 2013 Four Closure Structures CRMS Average: 0.49 CHF Average: 2.12 RMSE: 0.74 Figure 4-8: CRMS-532 Daily Salinity Validation CRMS Average: 0.06 CHF Average: 0.29 RMSE: 0.27 Figure 4-9: NOAA Hourly Water Surface Elevation Validation CRMS Average: 0.38 CHF Average: 1.86 RMSE: 0.64 Figure 4-10: NOAA Daily Salinity Validation 8

13 Four Closure Structures January RESULTS Several scenarios were analyzed to determine water level and salinity impacts due to closure structure placement. Four scenarios were analyzed with Inland closure structures or closure structures south of the GIWW (Figure 5-1). The southern structures were placed across Vermilion River, Boston Canal, Oaks Canal, Delcambre-Avery Canal, and Weeks Bay. The inland structures were placed across Delcambre-Avery Canal and Bayou Tigre. Scenario 1: South Structures (shown in yellow in Figure 5-1) with 2010 Tides and 2010 Channel Discharges Scenario 2: South Structures with 2010 Tides, 2010 Channel Discharges, and Large Atchafalaya River Discharge Scenario 3: South Structures with 2010 Tides, 2010 Channel Discharges, and 50-year Rainfall Event Scenario 4: Inland Structures (shown in orange in Figure 5-1) with 2010 Tides, 2010 Channel Discharges, and 50-year Rainfall Event Figure 5-1: Closure Structure Locations 9

14 January 2013 Four Closure Structures 5.1 Scenario 1: South Structures with 2010 Tides and 2010 Channel Discharges Scenario 1 examined the impacts of closure structures placed south of the GIWW with tides and channel discharges from The purpose of this scenario was to determine if placement of the closure structures would impact salinity transport in the Vermilion Bay vicinity. Figures 5-2 through 5-4 compare discharge, water level, and salinity at hourly and ten day increments through January The yellow and green values shown in Figures 5-2 and 5-3 are areas of minimal impact. The addition of closure structures tended to damp discharge variability along the GIWW and increase the bi-directional discharge to the east. The water levels showed minimal impacts due to closure structures south of the GIWW, but there was a slight shift in the tidal cycle. Salinities increased in Vermilion Bay due to freshwater routed through the GIWW around Vermilion Bay. The water level impacts do not appear substantial enough to affect the Vermilion Bay ecosystem. Salinity levels increase over time and would require further analysis to determine ecosystem impacts if this scenario was selected for storm surge reduction benefits. Figure 5-2: Scenario 1 GIWW Discharge Comparison 10

15 Four Closure Structures January day Water Level Difference 20 day Water Level Difference Abbeville Delcambre 30 day Water Level Difference WSE (m) (Transparent) Figure 5-3: Scenario 1 Water Level Comparison 11

16 January 2013 Four Closure Structures 10 day Salinity Difference 20 day Salinity Difference Abbeville Delcambre 30 day Salinity Difference Salinity (ppt) (Transparent) Figure 5-4: Scenario 1 Salinity Comparison 12

17 Four Closure Structures January Scenario 2: South Structures with 2010 Tides, 2010 Channel Discharges, and Large Atchafalaya Discharge Scenario 2 examined the impacts of closure structures placed south of the GIWW with tides and channel discharges from 2010, but introduced high freshwater discharge from Atchafalaya River and Wax Lake Outlet during the flood of 2011 (see Appendix A for discharge data). The purpose of this scenario was to examine how the structures would impact salinity with abnormally high levels of freshwater inflow from the east. The majority Atchafalaya River and Wax Lake discharge exits the GIWW before reaching the project area. The bi-directional discharge in the GIWW tended to the east with the increased discharge from Wax Lake Outlet and the Atchafalaya River. Figures 5-5 through 5-7 compare discharge, water level, and salinity at hourly and ten day increments for January 2010 (yellow and green values are areas of minimal impact). The results for Scenario 2 are similar to Scenario 1: damped GIWW discharge, minimal impacts to water levels, and increased Vermilion Bay salinity. Further analysis of long term salinities and discharges would be required is if this scenario was selected for storm surge reduction benefits. Figure 5-5: Scenario 2 GIWW Discharge Comparison 13

18 January 2013 Four Closure Structures 10 day Water Level Difference 20 day Water Level Difference Abbeville Delcambre 30 day Water Level Difference WSE (m) (Transparent) Figure 5-6: Scenario 2 Water Level Comparison 14

19 Four Closure Structures January day Salinity Difference 20 day Salinity Difference Abbeville Delcambre 30 day Salinity Difference Salinity (ppt) (Transparent) Figure 5-7: Scenario 2 Salinity Comparison 15

20 January 2013 Four Closure Structures 5.3 Scenario 3: South Structures with 2010 Tides, 2010 Channel Discharges, and 50- year Rainfall Event Scenario 3 analyzed the impacts of closure structures south of the GIWW during a 50-year, 24- hour rainfall event with tides and channel discharges from The purpose of this scenario was to examine water level impacts and salinity impacts during a large rainfall event. The 50- year, 24-hour rainfall event was applied uniformly over the model domain. As shown in Figures 5-8 through 5-12, the closure structures damped GIWW discharge, caused localized ponding, slightly decreased Vermilion Bay water levels, and increased Vermilion Bay salinity. The yellow and green values shown in Figures 5-9 and 5-10 are areas of minimal impact. Placement of the closure structures during a 50-year, 24-hour rainfall event increased easterly discharge along the GIWW. Figure 5-11 shows the maximum water levels over the 15 day period. Ponding due to the closure structures is most pronounced around Delcambre-Avery Canal and the Weeks Bay closure structure. Similar to the other scenarios, Scenario 3 increased salinity in Vermilion Bay (Figure 5-12). Figure 5-8: Scenario 3 GIWW Discharge Comparison 16

21 Four Closure Structures January day Water Level Difference 6 day Water Level Difference Abbeville Delcambre 9 day Water Level Difference WSE (m) (Transparent) Figure 5-9: Scenario 3 Water Level Comparison 17

22 January 2013 Four Closure Structures 3 day Salinity Difference 6 day Salinity Difference Abbeville Delcambre 9 day Salinity Difference Salinity (ppt) (Transparent) Figure 5-10: Scenario 3 Salinity Comparison 18

23 Four Closure Structures January 2013 Abbeville Delcambre WSE (m) Figure 5-11: Scenario 3 Maximum Water Level Comparison over 15 Days Abbeville Delcambre Salinity (ppt) Figure 5-12: Scenario 3 Maximum Salinity Comparison over 15 Days 19

24 January 2013 Four Closure Structures 5.4 Scenario 4: Inland Structures with 2010 Tides, Channel Discharges, and 50-year Rainfall Event Scenario 4 analyzed the impacts of inland closure structures at Delcambre-Avery Canal and Bayou Tigre during a 50-year, 24-hour rainfall event with tides and channel discharges from 2010 (Figure 5-13). The purpose of this scenario was to examine water level and ponding impacts due to inland structure placement during a large rainfall event. Salinity was not examined. Scenario 4 was examined over 15 days which would be an abnormally long duration for the structures to be closed. Minimal water level impacts were seen in Vermilion Bay; however, the closure structures caused ponding along Delcambre-Avery Canal and Tigre Bayou (Figure 5-14). Figure 5-15 shows maximum water levels over the 15 day period. Pump stations could be used to minimize ponding. Bayou Tigre would require a pump station with a 15 m 3 /s capacity and Delcambre- Avery Canal would require an 8 m 3 /s capacity pump station to relieve upstream ponding due to closure structures. Figure 5-13: Scenario 4 Closure Structure Locations 20

25 Four Closure Structures January day Water Level Difference 6 day Water Level Difference Abbeville Delcambre 9 day Water Level Difference WSE (m) Figure 5-14: Scenario 4 Water Level Comparison 21

26 January 2013 Four Closure Structures Abbeville Delcambre WSE (m) Figure 5-15: Scenario 4 Maximum Water Level Comparison over 15 Days 6.0 DISCUSSION AND CONCLUSION After examining the results from the Four Closure Structures model in the Vermilion Bay area, the modeling team found that Scenarios 1 and 2 showed little impact to water levels, while Scenarios 3 and 4 showed larger impacts. Scenarios 1, 2, and 3 showed impacts to salinity, while salinity was not examined in Scenario 4. Structures south of the GIWW in Scenarios 1, 2, and 3 typically had little impact on water levels in Vermilion bay while increasing salinity. The increase in Vermilion Bay salinity under these scenarios is largely due to freshwater riverine inputs being rerouted through the GIWW and not entering the northern portions of Vermilion Bay. Due to the closure of the four canals and Weeks bay, the freshwater is re-routed and lowered the salinity levels in West Cote Blanche Bay. The inland closure structures in Scenario 4 caused large areas of ponding near Delcambre, Louisiana. Runoff from the 50-year, 24-hour storm event began to pond as it reached the 22

27 Four Closure Structures January 2013 closure structures along Delcambre-Avery Canal and Bayou Tigre. This area did not have enough hydraulic connections to allow for adequate drainage of the area with these two large channels closed. 7.0 REFERENCES Meselhe, Ehab A. and Robert L. Miller Hydrologic Modeling and Budget Analysis of the Southwestern Louisiana Chenier Plain. Louisiana Coastal Area Science and Technology Program Office. USGS Surface-Water Hydrology of the Gulf Intracoastal Waterway in South-Central Louisiana, United States Geological Survey. 23

28 January 2013 Four Closure Structures This Page Was Intentionally Left Blank 24

29 Four Closure Structures January 2013 APPENDIX A: Model Input Data Figure A-1: Daily Rainfall Total: mm Figure A-2: 50-year, 24-hour Storm Event Rainfall Figure A-3: Freshwater Bayou Lock Schedule (2010) A-1

30 January 2013 Four Closure Structures Figure A-4: Freshwater Bayou Lock Schedule (January March 2010) Figure A-5: Schooner Bayou Lock Schedule (2010) Figure A-6: Schooner Bayou Lock Schedule (January March 2010) A-2

31 Four Closure Structures January 2013 Figure A-7: Atchafalaya River Discharge (January March 2010 and 2011) Figure A-8: Wax Lake Outlet Discharge (January March 2010 and 2011) Figure A-9: Daily Rainfall Evapotranspiration A-3

32 January 2013 Four Closure Structures Figure A-10: Daily Rainfall Evapotranspiration (January March 2010) Figure A-11: Model Inputs and Extents A-4

33 Four Closure Structures January 2013 APPENDIX B: Water Surface Elevation and Salinity Comparisons 0-10 day Average Water Level Difference 0-10 day Average Salinity Difference day Average Water Level Difference day Average Salinity Difference day Average Water Level Difference day Average Salinity Difference Figure B-1: Scenario 1 Average Water Level and Salinity Comparison B-1

34 January 2013 Four Closure Structures 0-10 day Average Water Level Difference 0-10 day Average Salinity Difference day Average Water Level Difference day Average Salinity Difference day Average Water Level Difference day Average Salinity Difference Figure B-2: Scenario 2 Average Water Level and Salinity Comparison B-2

35 Four Closure Structures January day Average Water Level Difference 0-10 day Average Salinity Difference day Average Water Level Difference day Average Salinity Difference day Average Water Level Difference day Average Salinity Difference Figure B-3: Scenario 3 Average Water Level and Salinity Comparison B-3

36 January 2013 Four Closure Structures 0-10 day Average Water Level Difference day Average Water Level Difference day Average Water Level Difference Figure B-4: Scenario 4 Average Water Level Comparison B-4

37 Four Closure Structures January 2013 Figure B-5: Scenario 1 Channel Water Level Comparison B-5

38 January 2013 Four Closure Structures Figure B-6: Scenario 2 Channel Water Level Comparison B-6

39 Four Closure Structures January 2013 Figure B-7: Scenario 3 Channel Water Level Comparison B-7

40 January 2013 Four Closure Structures Figure B-8: Scenario 4 Channel Water Level Comparison B-8

41 Four Closure Structures January 2013 APPENDIX C: MIKE FLOOD Solver Routines The following MIKE FLOOD explanation was copied directly from Meselhe and Miller 2007: Numerical Modeling with MIKE FLOOD MIKE FLOOD by the Danish Hydraulic Institute (DHI) is the modeling software used to simulate the Chenier Plain hydrodynamics. MIKE FLOOD is a commercially-available robust hydrodynamic and advection-dispersion modeling package linking a one-dimensional channel network with a two-dimensional relief grid (Its capability of handling a tidally-driven estuarine system such as the coastal Chenier Plain, and its GIS-based interface, makes it suitable in the present case). Given the proper inputs from the tides, upstream discharge, wind, and bathymetry, the model is capable of capturing the hydrodynamics of the system quite well. In addition, the inclusion of structures, wetting and drying capabilities, and the modeling of lateral outflow from the channels into the surrounding marshes make MIKE FLOOD an attractive modeling option. MIKE FLOOD connects the channel network with the surrounding marsh and open water bodies (Figure B.1). This allows the modeler to represent the small-scale channel details and the floodplain flow separately. This in turn gives the modeler the ability to use a larger grid spacing (hence faster simulations compared to a grid-only representation) without omitting the structures, narrow cross-sections, and other small features affecting the circulation patterns. Figure B-1: Overview of the Chenier Plain Modeling Scheme MIKE11 Hydrodynamic Module C-1

42 January 2013 Four Closure Structures MIKE11 is a hydraulic modeling software package that solves the equations of conservation of mass and momentum integrated over the cross section. Collectively, these equations are termed the Saint-Venant equations, and are derived on the basis of the following assumptions: The water is incompressible and homogeneous, i.e. without significant variations in density; The channel bottom slope is small (normal depth is greater than the critical depth); The wavelengths are large compared to the water depth. This ensures that the flow everywhere can be regarded as having a direction parallel to the bottom, i.e. vertical acceleration can be neglected and a hydrostatic pressure distribution along the vertical can be assumed; and The flow is subcritical. The continuity and momentum-conservation equations are as follows: where, Q α t + A x Q x + A t = q Q 2 Q = discharge, A = flow area, q = lateral inflow, h = stage above datum, C = Chezy resistance coefficient, R = hydraulic or resistance radius, and α = momentum distribution coefficient. + ga h x + gq Q C 2 AR = 0 [B.1] [B.2] The Saint-Venant equations in MIKE11 are handled by the method of finite differences using the 6-Point Abbott Scheme after the founder of MIKE11, Mike Abbott. For more information, the interested reader is referred to the MIKE11 Reference Manual (2004 Ed.). Model stability depends on the spacing of grid points (Q and h), cross-section inverts, and the time step. Generally, increasing the number of points with a decreasing time step improves the stability of the simulation. This stability criterion is represented by a Courant number condition. C r = t V + gy x [B.3] C-2

43 Four Closure Structures January 2013 V t x 1 to 2 [B.4] Here C r is the Courant Number, Δt is the time step, V represents the cross-sectional velocity, y is the water depth, g is the gravitational acceleration, and Δx is the spacing between two grid points. MIKE11 Advection-Dispersion Module MIKE11 solves the vertically-integrated equations of mass conservation and transport of a dissolved constituent. The solutions obtained will describe the movement of the salinity in the Chenier Plain. The one-dimensional equation for conservation of mass of a constituent in solution (such as temperature, salinity, etc) can be expressed as follows: AC t + QC x C AD x x = AKC + C 2q [B.5] Here, C is concentration (arbitrary unit), D is the dispersion coefficient, K is a linear decay coefficient, q is the lateral inflow, and C 2 is source/sink concentration. The dispersion coefficient is related to the cross sectional average velocity via the following relationship: D = av b [B.6] where a and b are constants to be specified and they can be considered as additional calibration parameters. More information about the solution schemes and detailed descriptions of the various parameters are available in the MIKE11 DHI Software Reference Manual (2004 Ed.). MIKE21 Hydrodynamic Module The hydrodynamic model in the MIKE21 Flow Model (MIKE21 HD) is a general modeling system for the simulation of water levels and flows in estuaries, bays, and coastal areas. It simulates time-varying two-dimensional flows in one layer (vertically homogeneous) fluids and has been used in a large number of studies. The following depth-integrated equations of mass and momentum conservation describe the flow and water level variation. ς t + p x + q y = d t [B.7] p t + x p2 h + y pq ζ + gh h x + gp p2 + q 2 1 C 2 h 2 ρ w x (hτ xx ) + y hτ xy Ω q f(v)v x + h ρ w x (p a ) = 0 [B.8] C-3

44 January 2013 Four Closure Structures p t + y q2 h + x pq ζ + gh h t + gq p2 + q 2 1 C 2 h 2 ρ w y hτ yy + x hτ xy Ω p f(v)v y + h xy (p a ) = 0 where, h(x,y,t) = the water depth (ζ-d) in m, d(x,y,t) = the time-varying water depth in m; ζ(x,y,t) = the surface elevation in m; p and q(x,y,t) = flux densities in the x and y-directions in m 3 /s/m; u and v = depth-averaged velocities in the x and y-directions in m/s; C(x,y) = the Chezy resistance in m 1/2 /s; g = the acceleration due to gravity in m/s 2 ; f(v) = the wind friction factor; V, V x, V y (x,y,t) = wind speed and components in the x and y-directions in m/s; Ω(x,y) = the latitude-dependent Coriolis parameter in units s -1 ; p a (x,y,t) = the atmospheric pressure in kg/m-s 2 ; ρ a = the density of water in kg/m 3 ; x and y = the space coordinates in m; t = the time in s; and τ, τ xx, and τ yy = the components of effective shear stress in N/m 2. ρ w [B.9] MIKE21 HD makes use of a so-called Alternating Direction Implicit (ADI) technique to integrate the equations for mass and momentum conservation in the space-time domain. More information is available in the DHI MIKE21 HD Software Scientific Documentation (2005 Ed.). MIKE21 Advection-Dispersion Module The Advection/Dispersion (AD) module simulates the spreading of dissolved substances subject to advection and dispersion processes in lakes, estuaries and coastal regions. Specifically, MIKE21 is used here to simulate the horizontal circulation of salinity in the near-shore Gulf of Mexico, and Chenier Plain lakes and marsh. Transport of a dissolved substance in MIKE21 is governed by the mass-conservation equation: (hc) + (uhc) + (vhc) = t x y x hd c x x + y hd c y F h c + S y [B.10] Here, c is the compound concentration (arbitrary units); u and v are the depth-averaged horizontal velocity components in the x and y directions (m/s); h is the water depth (m); D x and D y are the dispersion coefficients in x and y directions (m 2 /s); F is the linear decay coefficient (s -1 ); S=Q s *(c s -c); Q s is the source/sink discharge m 3 /s/m 2 ; and c s is the concentration of compound in the source/sink discharge Q s. Information on the velocities u and v are provided from the hydrodynamic module. C-4

45 Four Closure Structures January 2013 Dispersion coefficients represent the combined effect of differential advection and diffusion. The dispersion coefficient is an important salinity calibration parameter as it accounts for the effects of numerical diffusion and depth-integration on the transport equations. More details including a report entitled An Explicit Scheme of Advection-Diffusion Modeling in Two Dimensions are given in the DHI MIKE21 AD Software Scientific Documentation (2005 Ed.). MIKE FLOOD Coupling Program As stated previously, the MIKE FLOOD mass-preserving links connect the MIKE11 channel network with the MIKE21 grid (Figure B.2). Figure B-2: Schematization of the MIKE FLOOD Standard Link The hydrodynamic and advective-diffusive transport equations for standard links are as follows: Q n+1 2 t = ga Hn x + Qn Q n A C 2 R [B.11] Here, Q represents the flow rate (m 3 /s); A is the cross-sectional area (m 2 ); x is the length in m; H is the water depth in m; R represents the hydraulic radius in m; and C is the Chezy resistance (m 1/2 /s). C-5

46 January 2013 Four Closure Structures Concentrations of AD (salinity) components are transferred explicitly between MIKE11 and MIKE21 depending on the direction of the flow. For standard links with flow from MIKE11 and MIKE21, the concentration of the AD-component is imposed as with a standard MIKE21 source, i.e. as a flux of mass into the MIKE21 points: V C n+ 1 2 M21 = Q n+1 2 n C t M11 [B.12] Here, C is concentration, V is the total volume in the linked cells, and Q represents the flow rate. When flow is going from MIKE21 to MIKE11, the modification to the AD-equation in MIKE21 is: V C n+ 1 2 M11 = Q n+1 2 n C t M21 [B.13] In summary MIKE FLOOD simulates the exchange between channel and marsh with links and describes a channel connecting to an open water body. In this way the modeler can describe the fine details (dynamic structures, narrow cross-sections, abrupt changes in channel dimensions) with a 1D channel network, while simulating the floodplain and Gulf of Mexico flow fields with a 2D grid. C-6

47 Four Closure Structures January 2013 APPENDIX D: MIKE Presentation D-1

48 January 2013 Four Closure Structures D-2