1. A SURFACE WATER MODEL OF THE MIAMI RIVER

2. CONTENTS Background HEC-RAS Model’s Assumptions Methodology
Project Objective
HEC-RAS
Model’s Theory
Model’s Assumptions
Methodology
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3. CONTENTS (Cont.) Model’s Results Conclusion Recommendations References
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4. BACKGROUND Miami River: Estuary Navigation and storm drainage relief
5.5 miles long
Tamiami Canal
Comfort Canal
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Estuary=affected by tidal flows
Provides a waterway for navigation and storm drainage relief for surrounding areas within its drainage basin
Approximately 5.5 miles long, from S-26 to the Biscayne Bay
Two tributaries: Tamiami and Comfort

5. PROJECT OBJECTIVE Predict surface profiles
Average flow conditions from 1986 to 1999
HEC-RAS
Hydrologic Engineering Center River Analysis Software
One-dimensional steady flow analysis
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Flows that were used were those provided in Nahum Fernandez’s Master Project: A Basic Study on the Hydraulics of the Miami River, Miami Dade County
HEC-RAS was created by US Army Corps of Engineers. It is part of the next generation models.

6. HEC-RAS Applicable to steady gradually varied flow
Natural channels
Constructed channels
Supercritical, subcritical, and mixed flow regimes
Energy or Momentum equations
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7. HEC-RAS (Cont.) Software limitations: Flow must be steady
Flow must be gradually varied
Flow must be one-dimensional
River/channel must have small slopes
Channel must have a fixed bed
Energy losses must be definable by the energy head loss equation
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Does not accept time dependent variables
For the energy equation, program assumes that the pressure is hydrostatic. At hydraulic structures, where flow can rapidly vary, the momentum equation or an applicable empirical equation is used.
3. Because the energy equation is based on the premise that the total energy head is the same for all points in a cross section
4. Because the pressure head is represented by a vertical measurement of the water depth
5. Because the program does not have the capability to deal with movable boundaries; for example sediment transport
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None of these limitations affect the application of this software to this project

8. ENERGY EQUATION Standard Step Method Layla
1.      The user must assume a water surface elevation at the downstream cross section for a subcritical profile, or at the upstream cross section for a supercritical profile.
2.      Based on the assumed water surface elevation, the software determines the corresponding total conveyance and velocity head.
3.      With results from step 2, the software computes Sf and solves equation 2 for he.
4.      With results from steps 2 and 3, the program solves equation 1 for WS2.
5.      The software then compares the computed value of WS2 with the value assumed in step 1; it then repeats steps 1 through 5 until the values agree to within 0.01 feet or the user-defined tolerance.

9. CRITICAL DEPTH Calculated: 1. Supercritical flow regime
2. Requested by the user
3. User entered boundary condition
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3. To make sure that the selected flow regime for the external boundary condition is correct

10. CRITICAL DEPTH (Cont.) Flow regime identification
Program cannot balance the energy equation
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4. For subcritical profiles in order to verify the flow regime associated with the balanced elevation
5. Within the specified tolerance before reaching the maximum number of iterations.

11. Found through iterations of the total energy equation:
CRITICAL DEPTH (Cont.)
Found through iterations of the total energy equation:
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Values of WS are assumed and corresponding values of H are determined, until a minimum value for H is reached

12. MOMENTUM EQUATION Applicable when: Water surface at critical depth
Rapidly varying flow
HEC-RAS applies the momentum equation for the following:
Hydraulic jumps
Stream junctions
Flow obstructions
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Rapidly varying flow situations, such as: where a bridge constricts the channel, at a drop structures, at a weirs, at a stream junctions, or where the changes in the channel slope are significant

13. STREAM JUNCTIONS
Analyzed by HEC-RAS using energy or momentum equations
Cross sections placed close to the stream junction
Cross sections perpendicular to the flow before and after the junction
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14. STREAM JUNCTIONS Momentum vs. Energy
Six different possible flow conditions
Flow combining, subcritical flow
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For water surface elevations at stream junctions, HEC-RAS defaults to the energy equation.
In the event that the angles of the entrance into the junction play a significant role, the momentum equation may be used.
The smaller the angle of entrance, the larger the specific force at the junction.
The more perpendicular the flows are, the larger the disturbance of the flow of the main channel
Six different possible flow conditions:
Flow combining, subcritical flow
Flow combining, supercritical flow
Flow splitting, subcritical flow
Flow splitting, supercritical flow
Flow combining, mixed flow
Flow splitting, mixed flow

15. STREAM JUNCTIONS Energy equation at a stream junction
Momentum equation at a stream junction
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Energy Equation Method:
Backwater calculations are performed separately across the junction for each of the upstream reaches.
The surface is calculated by computing the energy balance between cross sections.
Friction losses are based on the length between cross sections.
Contraction and expansion losses are also calculated across these cross sections.
Momentum Equation Method:
Same logic as the energy method, except the momentum equation is used.
The momentum equation is formulated to account for the angles at which reaches connect.
The computations of subcritical flow are computed by standard step backwater calculations.
Then a momentum balance is performed across the junction.

16. STREAM JUNCTIONS (Cont.)
Friction force equation at a stream junction
Weight force equation at a stream junction
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17. MODEL ASSUMPTIONS Data Average flow data Data Average flow data
Cross sectional data
Assumption
No tidal flow contributions
Five foot freeboard for the river
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DATA:
Flow data used for the model was average monthly flow, average monthly maximum flow, average annual flow for structures S-26, S-25, and S-25B
Most of the cross sectional data used for the river did not provide the freeboard. Those that did, showed a variation of freeboard from two to five feet.
ASSUMPTIONS:
Flow was assumed to be downstream and not subject to reversals caused by the tides

18. MODEL ASSUMPTIONS Layla Cross section for the Miami River
Pictures depict the variation in the River’s freeboard: a few inches and 2 feet

19. MODEL ASSUMPTIONS Data No cross sections for the South Fork Assumption
Comfort connects directly to the River
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20. MODEL ASSUMPTIONS (Cont.)
Data
No cross sections for areas with marinas
Assumption
River does not have any marinas
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21. MODEL ASSUMPTIONS (Cont.)
Data
No cross sections for bridge crossings
Assumption
River does not have any bridges
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22. MODEL ASSUMPTIONS
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23. MODEL ASSUMPTIONS (Cont.)
Manning’s value of 0.07
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Recommended Manning’s value for natural sluggish rivers, as assumed by Nahum Fernandez
The river has light brush on it banks in various locations
Roughness of other obstructions which were not considered, such as ships

24. MODEL ASSUMPTIONS (Cont.)
River’s flow = S-26 + S25B + S25
Drainage basins were not considered
Assumed water surface elevation at last cross section: -0.6 ft NGVD
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Water surface elevation at the final cross section was assumed to be constant for all flow situations because of the embayment downstream.
The water surface elevation at this cross section was assumed to be at – 0.6 feet based on the National Geodetic Vertical Datum

25. METHODOLOGY
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The Miami River was modeled using the HEC-RAS defined Geometric and Steady flow data variables
The geometric data consisted of the geometric variables of the River, the schematic, cross sectional areas, Manning’s coefficient, distance between cross sections, contraction and extraction coefficients, and junctions
The flow data was originally collected from SFWMD.
The average monthly, the average maximum monthly flow, and the average annual flows from 1986 to 1999, as calculated by Nahum Fernandez, were used.

26. METHODOLOGY
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27. METHODOLOGY
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28. METHODOLOGY (Cont.)
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29. METHODOLOGY (Cont.)
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30. METHODOLOGY (Cont.)
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31. MODEL’S RESULTS
Tabular Results
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32. MODEL’S RESULTS (Cont.)
Energy Method Results
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33. MODEL’S RESULTS (Cont.)
Energy Method Results
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34. MODEL’S RESULTS (Cont.)
Momentum Method Results
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35. Momentum Method Results
MODEL’S RESULTS
Momentum Method Results
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36. MODEL’S RESULTS (Cont.)
Test cross section added downstream of Comfort
Steady flow analysis was performed
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The difference in water surface elevation at junction 2 of was believed to be a result of the large difference in depths between the main channel of the River and the Comfort Canal. (5 feet vs. 15 feet due to elimination of the South Fork)
In order to verify this assumption, the a cross sections at the downstream end of the Comfort Canal were replaced by cross sections similar to the one in the Miami River.

37. MODEL’S RESULTS (Cont.)
Momentum Equation Results
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The drop was eliminated with the addition of the cross section
There is a correlation between this missing data and the drop in the water surface elevation
Slopes gradually, as the energy equation does
The lack of good cross sectional data has affected our results and will not provide an accurate model.

38. MODEL’S RESULTS (Cont.)
Energy Equation Results
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The drop was eliminated with the addition of the cross section
There is a correlation between this missing data and the drop in the water surface elevation
Slopes gradually, as the energy equation does
The lack of good cross sectional data has affected our results and will not provide an accurate model.

39. CONCLUSION Results obtained were expected
Reach Three similar to the mean low water elevations
Depth, slope, and bed roughness changed by sediments
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This model resulted in a reasonable profile for the analyzed flows
The calculated results for the Froude numbers and velocities concur with expected results for subcritical flow in the Miami River.
It was found that the water surface elevations for Reach Three were consistent with the mean low water elevations for the cross sections within this reach
No similarity to the mean low water elevations was noticed for Reaches One or Two; this is because major contributors of flow resistance were not considered. Bridge piers, marinas, canals, and control structures affect the flow of the River. These structures create obstructions in the River, which reduce the flow and increases water surface elevations.
It is possible that sediment deposits have changed the depths, slopes, and roughness of the River. This could create an increase in the backwater effect, leading to an increase in surface water elevation, which this model did not consider.

40. RECOMMENDATIONS Match model to existing conditions
Flow data and corresponding water surface elevations
Sensitivity analysis
Inclusion of the flow from drainage basins
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Sensitivity analysis for assumed parameters

41. RECOMMENDATIONS (Cont.)
More recent cross sectional data
Marinas and bridges
Operation of control structures S-26, S-25, and S-25B
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More resent cross-sections are essential for an accurate interpretation of the River.
Flow restrictions caused by marinas and surface obstructions also need to be included in the model.
Furthermore, the hydraulics properties and the behavior of control structures S-26, S-25, and S-25B should be inputted into the model. Finally differential sloping and resistance of the channel bed along the River should be further studied

42. REFERENCES
Fernandez, Nahum D. A Basic Study on the Hydraulics of the Miami River, Miami-Dade County , Florida. Miami: Florida International University, August 2000.
Metro Dade Department of Environmental Resources Management. Miami River Quality (Metro-Dade DERM Technical Report 93-3). Miami: DERM, March 1993.
US Army Corps of Engineers. HEC-RAS River Analysis System: User Manual, Version Davis: US Army Corps of Engineers, September 1998.
US Army Corps of Engineers. HEC-RAS River Analysis System: Hydraulic Reference Manual, Version Davis: US Army Corps of Engineers, August 1998.
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43. THE END
ANY QUESTIONS?
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