1. WMO/NOAA Hydrologic Forecasting Course (NWS FLDWAV Model) NWS Training Center Kansas City, MO October 27, Janice Sylvestre NOAA/NWS/Office of Hydrologic Development Silver Spring, MD

2. Agenda 2 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
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
Hydraulic
Hydrologic 4

5. Movement of a Natural Flood Wave5

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 Disadvantages 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. Continuity Equation or Where: Q = Discharge A = Cross Sectional Area
x = Distance
t = Time
qL = Lateral Flow
I = Inflow
O = Outflow
S = Storage or 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. 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 X t
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. Solution of the St. Venant Equations
Momentum
Continuity
Weighted four-point finite difference scheme Dx j
j+1 i
i+1 x t
Time derivative: Dt h
Spatial derivative:
Other terms: 15

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

17. 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 Dt
UPSTREAM BOUNDARY
Flow or WSEL T.S.
Flow, WSEL, or tide T.S or Rating Curve
DOWNSTREAM BOUNDARY
j+1
Momentum
Continuity j
t=0 x Dx 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. Dynamic Wave Routing Method1 2 3 1 2 3 4
Q,h
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 = 18

19. Matrix Form Required Storage: 4N Required Computaion: 38N [A] X = R
[A] – 2N x 2N SQUARE MATRIX (BANDED)
X – COLUMN VECTOR
R – COLUMN VECTOR
2N-1 2N 1 2 3 4
a a
a a a a
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. Diffusion Wave Routing Method
Continuity
Momentum
The inertial terms
have been removed from the
Momentum equation. The solution procedure is the same as for the Dynamic Wave method.
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. 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. Fr r
0.70
100%
0.80
90%
0.90
65%
0.95
50%
1.00 0%
subcritical flow; dynamic routing
supercritical flow; diffusion routing 22

23. Kinematic Routing Method
Continuity
Momentum
and the pressure term
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)
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. Channel Properties 27 Plan View Dead Storage Cross Section A-A River
Embayment
Tributary
Dead Storage B5
BO5 B
BO4 4 B
Active 3 B 2
Dead Storage h BO
= 0 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 Parameters28

29. Channel Roughness Parameter, n29

30. NWS Hydraulic Routing Models30

31. Dynamic Wave Operational Model DWOPER
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. Dam Break 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 Flood Wave Routing Model FLDWAV
Combines the capabilities of DWOPER and DAMBRK
All future capabilities will be added to this model 33

34. Expanded Form of St. Venant Equations
Momentum
Continuity
Basic
DWOPER
DAMBRK
FLDWAV
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. NWS - FLDWAV Model SchematicB LQ RC Q t L
Tidal Boundary
LEGEND
B - bridge
RC - rating curve
- reservoir and dam
- lateral inflow
- levee overtopping and/or failure
L - lock and dam manually operated

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 Selection46

47. Breach starts forming when
Dam Breach Formation
Front View
BREACH
DAM b h o bm 1 z
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
QI = f(t) HF h o g dm s
Breach starts forming when
h > HF 47

48. Dam Breach Shapes Triangular Breach Z > 0 BB = 0 Rectangular Breach1 z
hdm hb
Triangular Breach
Z > 0
BB = 0
hdm hb BB
Rectangular Breach
Z = 0
BB = 0 1 z
hdm hb BB
Trapezoidal Breach
Z > 0
BB > 0 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
Type of Dam
Avg. Breach Width (b)
Time of Failure (tf ) hrs.
EARTH (well constructed) 2H d
< b < 5H tf d
0.1 # #
0.5
EARTH 2H d
< b < 5H tf d
0.1 # #
0.5
SLAG PILE b $
0.8 w tf # .2 tf
CONCRETE (gravity) b #
0.5 w # .2
CONCRETE (arch) b $
0.8 w tf # .1 W
Earth K
= 1 (piping) o H K
= 1.2 (overtopping) d o 50

51. Dam Breach Parameters Dam Type Codes Rule of Thumb DAMCAT Catalog
SMPDBK
TFH (hrs) BW
TFH (min)
Earth ER
2HD-5HD
HD/10
3HD
3HD<CL
Concrete Gravity PG
<=0.5CL
HD/40
5HD
5HD<CL
Concrete Arch VA
>=0.8CL
HD/50
0.9CL
Rockfill RE
HD/5
4HD
4HD<CL
Buttress CB
Multi-Arch MV
Other OT CL
Slag Pile
Min(CL,10HD)
Concrete CN
Masonry MS
Stone ST
Timber Crib TC 51

52. Topography 52

53. Topography B5 B4 B3 B2
HS5
HS4
HS3
HS2
HS1
Actual Cross Section
FLDWAV converts each cross section into a series of top width vs. elevation curves. The shape of the actual cross section is not retained.
Top Width vs. Elevation Curve
Symmetrical Cross Section
Elevation (HS)
Top Width (B) 53

54. Topography Meandering River with Floodplain Illustrating Sinuosity1
Left Floodplain L x 2
Main Channel
Actual Cross Section
BL5 B5
BR5
Right Floodplain
HS5
BL4 B4
BR4
HS4
BL3 B3
BR3
HS3 B2
HS2
HS1
With the floodplain option, the actual cross section is divided into three components: main channel, left floodplain and right floodplain. Each component is modeled in FLDWAV as a separate channel using sinuosity and conveyance.
Sinuosity Coefficient:
s1 = L1/x1 54

55. Expansion/Contraction Coefficients
Type of
Expansion/Contraction
Expansion
0.8
0.5
0.3
Contraction
0.4
0.2
0.1 55

56. 56

57. 57

58. 58

59. 59

60. Computed Lateral Flowsh w ) X 60

61. 61

62. Dynamic Tributaries
1st order tribs
2nd order tribs
3rd order tribs
4th order trib
Main stem
Rivers may be read into FLDWAV in any order. They will be automatically reordered from lowest to highest order tributary. The order is then reversed to allow initial flows to be generated. Later, backwater computations are done to obtain the initial water elevations. 62

63. FLDWAV Enhancements 63

64. Recent Enhancements to FLDWAV Model
Stand-Alone model
- Ability to model channel networks including bifurcations
- Ability to handle floodplain compartments (network + levee options)
- Ability to model mudflows
- Ability to export information for FLDVIEW and FLDAT applications
- Muskingum-Cunge Routing method
Operational model
- Added ability to blend observed and NOS tide time series
- Added ability to blend observed adjust computed stage time series
- Tested several internal boundary options including rating curves &
bridges
+ Ability to export information for FLDVIEW and FLDAT applications 64

65. Future Enhancements to FLDWAV Operation
Verify that all options working in stand-alone model are working in NWSRFS
- Make sure all current DWOPER segments run in FLDWAV
- Debug options as they are utilized by the field
- Add new enhancements in the stand-alone model
Develop/Test new enhancements to FLDWAV operation
- Initial conditions when cross sections are interpolated
- How to handle irregular time-dependent variables (e.g., turbines, gates)
- Easier method to obtain initial conditions
Compare NWSRFS reservoir capabilities to FLDWAV capabilities
- Add reservoir rules to FLDWAV 65

66. Future Enhancements to FLDWAV Stand-Alone Model
Add new capabilities
+ Sediment transport
+ Pollutant transport
+ Routing flow thru culverts
- Channel losses
- Practical Updating Techniques
+ Ice Jams
Add DWOPER/DAMBRK capabilities not currently in FLDWAV
- Landslide generated waves
- Multiple movable gates
- Improved method of modeling wind effects 66

67. FLDWAV Features Unique to NWSRFS
Carryover (Initial conditions)
No values read in ( ICOND=0)
Stored values – all values read in and stored (ICOND=1)
Interpolated values – read in gaged values and zeroes everywhere where else; these values will be interpolated (ICOND=1)
Steady State (all zeroes) – normal depth backwater computations will be done (ICOND=1).
Save carryover for specified dates
Adjust tide
Adjust time series
Output time series
Minimum stage/discharge at upstream boundary
More warning and error messages
FLDGRF 67

68. River Mechanics Contact Information
Web address
address
River Mechanics Forum 68

69. 69