# Presentation: 056170

## WMO/NOAAHydrologic Forecasting Course(NWS FLDWAV Model)NWS Training CenterKansas City, MOOctober 27, 2003Janice SylvestreNOAA/NWS/Office of Hydrologic DevelopmentSilver Spring, MD

## 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

## 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

## Flood Waves and Routing Methods

-  Routing Methods
-  Hydraulic
-  Hydrologic

## Movement of a Natural Flood Wave

## 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

## Types of Channel Systems

- Single Channel

- River & Tributaries

- Canal & Distributaries

- River Delta

- Network

- Dendritic (tree-type) System

## 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

## 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

## 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

## 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  = sin . ( =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.

## Continuity Equation

- Where:
- 	Q = Discharge
- 	A = Cross Sectional Area
- 	 x = Distance
- 	  t = Time
- 	qL = Lateral Flow
- 	  I = Inflow
- 	O = Outflow
- 	S = Storage

## Momentum Equation

- Conservation form

- Dynamic wave equation

- Diffusion wave equation
- (less inertial terms)

- Kinematic wave equation
- (less pressure term)

- Solving for Sf

- Where:
-      V = Velocity
-      y = flow depth
-      t = time
-      x = distance
-      g = acceleration due to gravity
-      So = bottom slope
-      Sf = friction slope

## Dynamic Wave Routing Method

- Based on the complete 1-D equations of unsteady flow
- (St. Venant equations)

- Where:   h = water surface elevation and

- Continuity

- Momentum

- 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.

## Solution of the St. Venant Equations

- Weighted four-point finite difference scheme

- Continuity

- Momentum

## Solution of the St. Venant Equations

- Weighted, four-point implicit, finite difference equations

- Continuity

- Momentum

- Continuity

- Momentum

## Dynamic Wave Routing Method

**7 GRIDS x 2 EQUATIONS = 14 EQUATIONS + 2 BOUNDARY EQNS = 16 EQNS**
**                    ****(7 + 1) NODES * 2 **_**UNKNOWNS**_** = 16 UNKNOWNS**
**                                                       ****NODES**

**UPSTREAM BOUNDARY**
**Flow or WSEL T.S. **

**DOWNSTREAM BOUNDARY**
**Flow, WSEL, or tide T.S or Rating Curve**

**INITIAL CONDITIONS**
**Initial flow & elevation at each cross section location; **
**Lateral Flow, pool elevation, gate control switch at each location **

- x

**1**

**2**

**3**

**4**

**5**

**6**

**7**

**i**

**i+1**

- t

**j**

**j+1**

**DETERMINATE**

**t=0**

## Dynamic Wave Routing Method

- 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

- UB ...
- C1 ...
- M1 ...
- C2 ...
- M2 ...
- C3 ...
- M3 ...
- DB ...

- -UB
- -C1
- -M1
- -C2
- -M2
- -C3
- -M3
- -DB

- =

- h1

- Q2

- Q1

- h2

- h4

- h3

- Q3

- Q4

- 1

- 2

- 3

- 4

## Matrix Form

- 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

- 2N-1
- 2N

- 2N-1 2N

- [A] X = R
- [A] – 2N x 2N SQUARE MATRIX (BANDED)
- X – COLUMN VECTOR
- R – COLUMN VECTOR

- Required Storage: 4N
- Required Computaion: 38N

-  1   2   3   4

- 1
- 2
- 3
- 4

## Momentum Equation

- Conservation form

- Dynamic wave equation

- Diffusion wave equation
- (less inertial terms)

- Kinematic wave equation
- (less pressure term)

- Solving for Sf

- Where:
-      V = Velocity
-      y = flow depth
-      t = time
-      x = distance
-      g = acceleration due to gravity
-      So = bottom slope
-      Sf = friction slope

## Diffusion Wave Routing 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

- Continuity

- Momentum

## Local Partial Inertia (LPI) Method

-  Retains the essential accuracy     associated with dynamic routing models    and provides stable, accurate numerical    solutions for mixed flows.

| Fr |  |
| --- | --- |
| 0.70 | 100% |
| 0.80 | 90% |
| 0.90 | 65% |
| 0.95 | 50% |
| 1.00 | 0% |

## Kinematic Routing Method

- Continuity

- Momentum

-  The inertial terms

-  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

## 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)

## 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

## Rating Curve

## Channel Properties

- h

- 1

- B

- B

- B

- B

- BO4

- 1

- 2

- 3

- 4

- Embayment

- Dead Storage

- Tributary

- River

- Plan View

- Datum

- B5

- BO5

- Active

- Dead Storage

- Cross Section A-A

- Plan view of river with active and dead storage areas, and cross section view.

## Cross Section Parameters

## Channel Roughness Parameter, n

## NWS Hydraulic Routing Models

## 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

## 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

## Generalized Flood Wave Routing ModelFLDWAV

- Combines the capabilities of DWOPER and DAMBRK
- All future capabilities will be added to this model

## Expanded Form of St. Venant Equations

- Continuity

- Momentum

- sm : sinuosity
-    : momentum correction factor
- Se : expansion/contraction effect
- Si  : mud/debris flow
- L     : Lateral Inflow/Outflow
- WfB : wind effect

- sc : sinuosity
- Ao : inactive area

- Where

## NWS FLDWAV Model

## 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

## NWS - FLDWAV Model Schematic

## 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.

## 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.

## 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.

## 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.

## 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.
-  ___t 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.

## 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

## FLDWAV Features

## Routing Options in FLDWAV

- Dynamic
- - Implicit
- - Explicit (Upwind)
- Implicit Local Partial Inertia (LPI)
- Implicit Diffusion
- Muskingum-Cunge (stand-alone only)
- Level Pool

## Breach Parameter Selection

## Dam Breach Formation

- 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

- Front View

- Breach starts forming when
- h > HF

## Dam Breach Shapes

## 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

## Breach Characteristics

- H

- d

- W

- Type of Dam

- Avg. Breach Width (b)

- Time of Failure (tf ) hrs.

- EARTH (well constructed)

- EARTH

- SLAG PILE

- CONCRETE (gravity)

- CONCRETE (arch)

- 2H

- d

- <  b  <  5H

- d

- 2H

- d

- <  b  <  5H

- d

- b

- 

-   0.8  w

- b

- 

-   0.5  w

- b

- 

-   0.8  w

- 0.1

- 

- tf

- 

-   0.5

- tf

- tf

- tf

- 

-   .2

- 

-   .2

- 

-   .1

- 0.1

- 

- tf

- 

-   0.5

- K

- o

-  = 1 (piping)

- K

- o

-  = 1.2 (overtopping)

- _Earth_

## Dam Breach Parameters

| Dam Type | Codes | Rule of Thumb |  | DAMCAT Catalog |  | SMPDBK |  |
| --- | --- | --- | --- | --- | --- | --- | --- |
|  |  | TFH (hrs) | BW | TFH (min) | BW | TFH (min) | BW |
| Earth | ER | 0.1-0.5 | 2HD-5HD | HD/10 | 3HD | HD/10 | 3HD<CL |
| Concrete Gravity | PG | 0.0-0.2 | <=0.5CL | HD/40 | 5HD | HD/40 | 5HD<CL |
| Concrete Arch | VA | 0.0-0.1 | >=0.8CL | HD/50 | 0.9CL | HD/50 | 0.9CL |
| Rockfill | RE |  |  | HD/5     | 4HD | HD/5 | 4HD<CL |
| Buttress | CB |  |  | HD/40 | 5HD | HD/40 | 5HD<CL |
| Multi-Arch | MV |  |  | HD/50 | 0.9CL | HD/50 | 0.9CL |
| Other | OT |  |  | HD/10 | CL | HD/10 | CL |
| Slag Pile |  | 0.0-0.1 | >=0.8CL |  |  | HD/10 | Min(CL,10HD) |
| Concrete | CN |  |  |  |  | HD/50 | 0.9CL |
| Masonry | MS |  |  |  |  | HD/5 | 4HD |
| Stone | ST |  |  |  |  | HD/5 | 4HD |
| Timber Crib | TC |  |  |  |  | HD/5 | CL |

## Topography

## Topography

- Symmetrical Cross Section

- Top Width (B)

- Elevation (HS)

- Top Width vs. Elevation Curve

- FLDWAV converts each cross section into a series of top width vs. elevation curves.  The shape of the actual cross section is not retained.

## Topography

- Meandering River with Floodplain Illustrating Sinuosity

- Sinuosity Coefficient:
-     s1 = L1/x1

- Right Floodplain

- Main Channel

- B5

- B4

- B3

- B2

- HS5

- HS4

- HS3

- HS2

- HS1

- Actual Cross Section

- BL3

- BR3

- BL4

- BR4

- BL5

- BR5

- 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.

## Expansion/Contraction Coefficients

- Type of
- Expansion/Contraction

- Expansion
- 0.8
- 0.5
- 0.5
- 0.3

- Contraction
- 0.4
- 0.2
- 0.2
- 0.1

## Slide 56

## Slide 57

## Slide 58

## Slide 59

## Computed Lateral Flows

## Slide 61

## Dynamic Tributaries

- 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.

## FLDWAV Enhancements

## 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 model channel networks including bifurcations
-    - Ability to handle floodplain compartments (network + levee options)
-    + Ability to export information for FLDVIEW and FLDAT applications

## 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

## 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

## 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

## River Mechanics Contact Information

- Web address
- _[http://www.nws.noaa.gov/oh/hrl/rvrmech/](http://www.nws.noaa.gov/oh/hrl/rvrmech/)_
- Email address
- _[River.Mechanics@noaa.gov](mailto:River.Mechanics@noaa.gov)_
- River Mechanics Forum
- _[http://hydrology.nws.noaa.gov/oh/discus/](http://hydrology.nws.noaa.gov/oh/discus/)_

## Slide 69