Agenda

1. WMO/NOAAHydrologic Forecasting Course(NWS FLDWAV Model)NWS Training CenterKansas City, MOOctober 27, 2003Janice SylvestreNOAA/NWS/Office of Hydrologic DevelopmentSilver Spring, MD

2. Agenda 1:00pm - 2:45pm Introduction Describe channel routing Review the principles of hydraulic modeling 2:45pm - 3:00pm Break 3:00pm - 5:00pm FLDWAV Overview Describe FLDWAV Capabilities Tuesday, Feb 25, 2003 8:00am - 9:45am Describe FLDWAV features using examples 9:45am-10:00am Break 10:00am - Noon Describe FLDWAV features using examples (cont.) Noon - 1:00pm Lunch 1:00pm - 2:45pm FLDWAV Input/Output Example Problem 1 2:45pm - 3:00pm Break 3:00pm - 5:00pm Example Problem 2 Wednesday, Feb 26, 2003 8:00am - 9:45am Example Problem 3 9:45am - 10:00am Break 10:00am - Noon Example Problem 4 Noon -1:00pm Lunch 2

3. Objectives • Describe channel routing • Theoretical review of hydraulic routing methods • FLDWAV Overview • Review FLDWAV features using examples • Discuss operational use of FLDWAV • Future FLDWAV Enhancements • Introduce FLDWAV Utilities 3

4. Flood Waves and Routing Methods • Routing Methods • Hydraulic • Hydrologic 4

5. Movement of a Natural Flood Wave 5

6. Flood Waves and Channels Types of Flood Waves • Floods – Rainfall/ Snowmelt Runoff • Dam-Break Wave • Reservoir Releases for Power, Flood Control • Tidal-Generated Waves • Earthquake-Generated Tsunami (tidal waves) • Irrigation Releases, Diversions, etc. • Wind-Generated Seiches in Lakes • Landslide-Generated Reservoir Wave • Mud-Debris Floods • Hurricane-Generated Storm Surges • Volcanic Mud Flows • Glacier Dam Outbreaks • Types of Channels • Rivers • Réservoirs • Lakes • Estuaries • Canals • Ditches • Sewers/Drains 6

7. Types of Channel Systems Single Channel Dendritic (tree-type) System River & Tributaries Canal & Distributaries River Delta Network 7

8. Hydrologic vs. Hydraulic Routing • Hydrologic Routing • Lumped routing method • Uses continuity equation only • Examples: Lag & K, Tatum • Hydraulic Routing • Distributed routing method (need cross sections) • Uses continuity and momentum equations • More accurately describes flood wave movement • Examples: FLDWAV, UNET 8

9. Hydraulic Routing • Advantages • Most accurate method • Accounts for many hydraulic conditions including backwater effects, hydraulic structures, and unsteady effects • Disadvantages • May become unstable under some conditions • Requires extensive data input • More difficult to update results than with simpler methods 9

10. Hydraulic Routing Equations(St. Venant Equations) Continuity equation preserves the water volume in channel Momentum equation physical relationship describing the actual physics of the movement of the water 10

11. Assumptions of St. Venant Equations • Flow is 1-D: flow characteristics (depth, velocity, etc.) vary only in the longitudinal x-direction of the channel. • Water surface is horizontal across any section perpendicular to the longitudinal axis. • Flow is gradually varied with hydrostatic pressure prevailing at all points in the flow. • Longitudinal axis of the channel can be approximated by a straight line. • Bottom slope of the channel is small, i.e., tan h = sin h. (h =10 yields 1.5% variation). • Bed of the channel is fixed, i.e., no scouring or deposition is assumed to occur. • Resistance coefficient for steady uniform turbulent flow is considered applicable and an empirical resistance equation such as the Manning equation describes the resistance effect. • Flow is incompressible and homogeneous in density. 11

12. or Continuity Equation Where: Q = Discharge A = Cross Sectional Area x = Distance t = Time qL = Lateral Flow I = Inflow O = Outflow S = Storage 12

13. Momentum Equation Conservation form Solving for Sf Dynamic wave equation Diffusion wave equation (less inertial terms) Where: V = Velocity y = flow depth t = time x = distance g = acceleration due to gravity So = bottom slope Sf = friction slope Kinematic wave equation (less pressure term) 13

14. t X Dynamic Wave Routing Method Based on the complete 1-D equations of unsteady flow (St. Venant equations) Continuity Momentum Where: h = water surface elevation and The discharge (Q) and water surface elevation (h) at each location along the river is computed using an algebraic representation of the St. Venant equations. Q and h are determined for the river system at each time step. 14

15. Dx j+1 Dt Time derivative: t h j Spatial derivative: i i+1 x Other terms: Solution of the St. Venant Equations Momentum Continuity Weighted four-point finite difference scheme 15

16. Solution of the St. Venant Equations Momentum Continuity Weighted, four-point implicit, finite difference equations Continuity Momentum 16

17. Dt Momentum Continuity Dx Dynamic Wave Routing Method 7 GRIDS x 2 EQUATIONS = 14 EQUATIONS + 2 BOUNDARY EQNS = 16 EQNS (7 + 1) NODES * 2 UNKNOWNS = 16 UNKNOWNS NODES t DETERMINATE 1 2 3 4 5 6 7 DOWNSTREAM BOUNDARY Flow, WSEL, or tide T.S or Rating Curve UPSTREAM BOUNDARY Flow or WSEL T.S. j+1 j x t=0 i i+1 INITIAL CONDITIONS Initial flow & elevation at each cross section location; Lateral Flow, pool elevation, gate control switch at each location 17

18. 1 2 3 Q,h Q,h Q,h Q,h Dynamic Wave Routing Method 1 2 3 4 Dh1 DQ1 Dh2 DQ2 Dh3 DQ3 Dh4 DQ4 UB … C1 … M1 … C2 … M2 … C3 … M3 … DB … -UB -C1 -M1 -C2 -M2 -C3 -M3 -DB X X X X X X X X X X X X X X X X X X X X X X X X X X X X = 18

19. Matrix Form [A] X = R [A] – 2N x 2N SQUARE MATRIX (BANDED) X – COLUMN VECTOR R – COLUMN VECTOR 1 2 3 4 2N-1 2N a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a 1 2 3 4 Required Storage: 4N Required Computaion: 38N 2N-1 2N 19

20. Momentum Equation Conservation form Solving for Sf Dynamic wave equation Diffusion wave equation (less inertial terms) Where: V = Velocity y = flow depth t = time x = distance g = acceleration due to gravity So = bottom slope Sf = friction slope Kinematic wave equation (less pressure term) 20

21. The inertial terms have been removed from the Momentum equation. The solution procedure is the same as for the Dynamic Wave method. Diffusion Wave Routing Method Continuity Momentum • Advantages: • More stable than Dynamic Wave Method near critical flow • As accurate as Dynamic Wave Method for supercritical flow • Limitations: • Wave propagation is in the downstream direction only • Not applicable where backwater effects are significant • Not applicable for dam break-type waves on mild slopes 21

22. subcritical flow; dynamic routing supercritical flow; diffusion routing Local Partial Inertia (LPI) Method • The r factor filters the inertial terms such that the Momentum equation fluctuates between the dynamic and diffusion equation based on the Froude number. • Retains the essential accuracy associated with dynamic routing models and provides stable, accurate numerical solutions for mixed flows. 22

23. and the pressure term Kinematic Routing Method Continuity Momentum • The inertial terms have been removed from the momentum equation. The friction slope is estimated as the channel bottom slope. • Advantage: Robust • Limitations: • Wave propagation is in the downstream direction only • Not applicable where backwater effects are significant • Not applicable for fast-rising waves on mild slopes 23

24. Dynamic Routing Methods • Dynamic Wave Method • Includes inertial and pressure terms • Wave may move in both the upstream and downstream directions • LPI capability provides stability when modeling mixed flows • Examples: DAMBRK, DWOPER, FLDWAV, UNET, HEC-RAS (unsteady component) • Diffusion Method • Excludes the inertial effects • Wave will move in the downstream direction only • Wave is allowed to attenuate as it moves downstream • Example: Muskingum-Cunge • Kinematic Wave Method • Excludes the influence of mass and force (inertial and pressure terms) • Wave will move in the downstream direction only • Examples: Manning’s equation, HEC-2, HEC-RAS (steady component) 24

25. Key Parameters for Hydraulic Modeling • Stage-Discharge Relationship • Channel Properties • Channel Geometry • Channel Slope • Channel Roughness • Hydrograph Properties • Peak Flow • Time to Peak Flow • Average Flow 25

26. Rating Curve 26

27. BO = 0 Channel Properties Plan View River Embayment Tributary Dead Storage B5 BO5 BO4 B 4 B 3 Active B 2 h Dead Storage 1 B 1 Datum Cross Section A-A Plan view of river with active and dead storage areas, and cross section view. 27

28. Cross Section Parameters 28

29. Channel Roughness Parameter, n 29

30. NWS Hydraulic Routing Models 30

31. Dynamic Wave Operational ModelDWOPER • Developed to model unsteady flow in major rivers where backwater and mild bottom slopes are troublesome for hydrologic routing methods. • Limitations include inability to: • interpolate cross sections • model dam breaks and reservoir outflow controls • handle supercritical or mixed-flow regimes • handle complex levee systems 31

32. DamBreak Model DAMBRK • Developed to model unsteady flow in major rivers where backwater and mild bottom slopes are troublesome for hydrologic routing methods. • Limitations include inability to: • model single rivers only • fixed number of time steps and cross sections 32

33. Generalized FloodWave Routing ModelFLDWAV • Combines the capabilities of DWOPER and DAMBRK • All future capabilities will be added to this model 33

34. Basic DWOPER DAMBRK FLDWAV Expanded Form of St. Venant Equations Momentum Continuity Where sc : sinuosity Ao : inactive area sm : sinuosity b : momentum correction factor Se : expansion/contraction effect Si : mud/debris flow L : Lateral Inflow/Outflow WfB : wind effect 34

35. NWS FLDWAV Model 35

36. NWS FLDWAV Model Description • Routes outflow hydrograph hydraulically through downstream river/valley system using expanded form of 1-D Saint-Venant equations • 2. Considers effects of: downstream dams, bridges, levees, tributaries, off-channel storage areas, river sinuosity, backwater from tides • 3. Flow may be Newtonian (water) or non-Newtonian (mud/debris) • 4. Produces output of: • a. High water profiles along valley • b. Flood arrival times • c. Flow/stage/velocity hydrographs • 5. Exports data needed to generate flood forecast map: • a. Channel location (river mile and latitude/longitude) • b. Channel invert profile • c. Water surface profile for area to be mapped • d. Channel top width corresponding to water surface elevations in profiles 36

37. LQ Q t LQ Q B t B RC RC LEGEND B - bridge RC - rating curve - reservoir and dam - lateral inflow LQ - levee overtopping and/or failure B L - lock and dam manually operated L B Tidal Boundary NWS - FLDWAV Model Schematic

38. NWS FLDWAV Model Capabilities • Variable Dimensioning - The input data structure has been arranged in such that array sizes are determined internally based on the river system. This eliminates the problem of running out of number of available time steps or number of cross sections. • Multiple Rivers - FLDWAV can model river systems that have a dendritic structure (both first and nth order tributaries). Channel networks can also be modeled. • Dam and Bridge/Embankment – Flow through dams (spillway, gate, turbine, etc.) or bridges may be model; overtopping flow and flow due to dam/embankment failure may also be modeled. • Levee Option - Flows which overtop levees located along either or both sides of a main-stem river and/or its principal tributaries can be simulated within FLDWAV. • Simultaneous Method of Computation -FLDWAV can route unsteady flows occurring simultaneously in a system of interconnected rivers. Any of the rivers may have one or more structures (dams, bridges, levees, etc.) which control the flow and which may breach if failure conditions are reached. 38

39. NWS FLDWAV Model Capabilities • Flow Regime - FLDWAV can handle subcritical, supercritical, critical or a combination of each, varying in space and time from one to another. A new computational scheme (LPI) has been developed to model mixed flow. • Boundary Conditions - The upstream boundary may be either a stage or discharge hydrograph for each river. The downstream boundary may be a stage/discharge hydrograph, tide, or a variety of rating curves. • Initial Conditions - The initial conditions include the initial water surface elevations (WSEL) and discharges at each of the read-in cross section locations. FLDWAV can start up in either a steady- state (not changing temporally) or an unsteady-state condition. The operational version also needs initial pool elevations and gate control switches. 39

40. NWS FLDWAV Model Capabilities • Computational Time Step - The initial computational time step may be read in or generated by the model. The model will determine the time to peak of each inflow hydrograph (upstream boundary) and divide the smallest value by 20. This value will be used throughout the run period until a breach failure mode is activated. The model will use the smallest value between failure time step(s) and the initial time step. • Roughness Coefficients - A Manning n table is defined for each channel reach bounded by gaging stations and is specified as a function of either WSEL (h) or discharge (Q). Linear interpolation is used to obtain n for values of h or Q intermediate to the tabular values. The Manning n reaches are defined by their upstream-most section. The Manning n tables are duplicated internally such that there is a table at each reach between cross sections. 40

41. NWS FLDWAV Model Capabilities • Automatic Calibration - This option allows the automatic determination of the Manning n so that the difference between computed WSELs (stage hydrographs) and observed hydrographs is minimized. In areas where detailed cross sections may not be available, there is an option that will automatically adjusts average sections obtained from topographic maps in addition to the Manning n. • Printer Output - FLDWAV will display an echo print of the input data, hydraulic information for all cross sections at all time steps, summary of peak information, stage and discharge hydrograph plots, and statistics comparing computed/observed data. • Multiple Routing - Multiple routing techniques may be used in a river system. Currently, there are four routing techniques available: dynamic implicit, dynamic explicit, level pool (storage), and diffusion. Each reach between adjacent cross sections is assigned a routing technique by the user via the KRCH parameter. The LPI computational scheme may also be applied to specific reaches. 41

42. NWS FLDWAV Model Capabilities • Kalman Filter - If a river has stage observations for more than two gaging stations, the Kalman filter may be turned on to update the predictions for each time step using observations. This option is applicable for real-time forecasting or when observed stage time series are available. • Dt Time Series - This option allows the user to specify multiple computational time steps throughout the temporal range of the inflow hydrograph. • Mudflow/Debris Flow Option – FLDWAV contains three techniques to determine the mud/debris related friction slope term due to the internal viscous dissipation of non-Newtonian fluids and granular sliding friction of coarse-grained debris surges. 42

43. NWS FLDWAV Model Capabilities • Other Options - The following options are in FLDWAV and have not been altered from the original definitions in DAMBRK or DWOPER. • Low flow filter • Pressurized flow • Cross section interpolation • Floodplain option (sinuosity and conveyance) • Metric option • Off-channel (dead) storage • Robust computational features • Local losses • Wind effects • Hydraulic radius option • Lateral inflow/outflow • Routing channel losses • Automatic time step increase for dam-break waves 43

44. FLDWAV Features 44

45. Routing Options in FLDWAV • Dynamic - Implicit - Explicit (Upwind) • Implicit Local Partial Inertia (LPI) • Implicit Diffusion • Muskingum-Cunge (stand-alone only) • Level Pool 45

46. Breach Parameter Selection 46

47. BREACH DAM 1 1 z z 1 h z o h h b b h bm HF h dm h h s QI = f(t) h o h g Dam Breach Formation Front View z = side slope of breach h = elevation of top of dam ho = water elevation at beginning of breach hb = breach elevation at current time hbm = bottom of breach elevation hdm = top of dam elevation hs = spillway crest elevation hg = centerline of gate opening elevation HF = failure elevation QI = inflow to the reservoir Profile View Breach starts forming when h > HF 47

48. hdm Triangular Breach 1 Z > 0 BB = 0 z hb hdm Rectangular Breach hb Z = 0 BB = 0 BB hdm 1 z hb Trapezoidal Breach Z > 0 BB > 0 BB Dam Breach Shapes 48

49. Dam Breach Computations Given the time of failure (tf) and the final breach elevation (hbm), the time history of the breach elevation and breach width may be obtained. tb = current time of breach tf = time of fine breach elevation bi = breach width at current time b = final breach width ho = water elevation at beginning of breach hb = water elevation at current time hbm = bottom of breach elevation 49

50. Breach Characteristics Time of Failure (tf ) hrs. Type of Dam Avg. Breach Width (b) tf EARTH (well constructed) < b < 5H 2H 0.1 # # 0.5 d d tf EARTH < b < 5H 2H 0.1 # # 0.5 d d tf SLAG PILE b $ 0.8 w # .2 tf # .2 CONCRETE (gravity) b # 0.5 w tf CONCRETE (arch) b $ 0.8 w # .1 W Earth K = 1 (piping) o K = 1.2 (overtopping) H o d 50