# Presentation: 056158

## HEC-RAS Version 3.1

***HEC-RAS Version 3.1***
***Unsteady Flow***

**Presented by:**
**slides adapted from HEC**
** ****Unsteady Flow Course**

- Feb 2003

## Unsteady Flow Documentation

- Technical/theoretical - Chapters 2 and 5 from EM 1110-2-1416
- http://www.hnd.usace.army.mil - click on TECHINFO, then Engineering Publications, then Engineering Manuals, scroll for manual
- HEC-RAS User’s Manual - Chapter 8 (data input and window operations)
- HEC-RAS Application Guide - Chapter 17 (example application)

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
There is also a difference in our institutional experience with steady vs. unsteady model applications.  We have a much larger experience, knowledge and data base with use of the steady flow approach.  Keep in mind that finely tuned steady flow data sets may not be optimal for unsteady flow modeling of the same physical setting.  Indeed, some of the hydraulics that were folded into that fine tuning may now be modeled directly with the unsteady flow equations.

## When to use Unsteady Flow

- Tidal/estuary fluctuation
- Off-channel storage
- Dam breach routing
- Channels with flat slopes
- Levee overtopping
- Hydraulic structures affected by changing backwater
- Large amounts of storage behind roads or culverts

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
There is also a difference in our institutional experience with steady vs. unsteady model applications.  We have a much larger experience, knowledge and data base with use of the steady flow approach.  Keep in mind that finely tuned steady flow data sets may not be optimal for unsteady flow modeling of the same physical setting.  Indeed, some of the hydraulics that were folded into that fine tuning may now be modeled directly with the unsteady flow equations.

## Steady vs. Unsteady

- Difference in handling boundary friction and other losses
- Difference in numerical solution algorithm
- Difference in handling non-flow areas
- Difference in flow and boundary condition data requirements
- Difference in calibration strategy
- Difference in application strategy

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
There is also a difference in our institutional experience with steady vs. unsteady model applications.  We have a much larger experience, knowledge and data base with use of the steady flow approach.  Keep in mind that finely tuned steady flow data sets may not be optimal for unsteady flow modeling of the same physical setting.  Indeed, some of the hydraulics that were folded into that fine tuning may now be modeled directly with the unsteady flow equations.

## Unsteady Flow Equations

- Momentum Equation:

- Continuity Equation:

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
Where:		Q = Flow (water discharge)
		  = velocity distribution coefficient
		A  = cross-sectional flow area
		t  = time
		x  = distance in the flow direction
		h  = depth
		So = bed slope
		Sf = friction slope, from Manning’s equation:

		v  = flow velocity

## Steady Flow Equations

- Energy (momentum) Equation:

- Continuity Equation:

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
Where:		Q = Flow (water discharge)
		  = velocity distribution coefficient
		A  = cross-sectional flow area
		x  = distance in the flow direction
		h  = depth
		So = bed slope
		Sf = friction slope, from Manning’s equation:

		v  = flow velocity

## Distance vs Time Solution Grid

- X = distance, feet
- t = time, seconds

- t

- x

- 1,1

- 2,1

- 1,2

- 2,2

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- Feb 2003

## Finite Difference Term

-    Q              Q (2,2)  -  Q(1,2)                   Q(2,1)  -  Q(1,1)
-  -----   =       -----------------------  + ( 1 -     )  ---------------------
-    X                           X                                           X

-   = theta weighting factor  0.5 <      < 1.0

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## Pre-Computation of Hydraulic Properties

- Steady – Compute exact hydraulic properties at a section for each trial water surface elevation from the elevation/station points, *n-*values.
- Unsteady – Hydraulic properties are pre-computed for all possible water surface elevations at each cross section (hydraulic table)

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
Step-backwater programs compute the cross section properties exactly from the GR points for every trial water surface elevation.  For computational efficiency, all unsteady flow models represent cross sections as tables of hydraulic properties vs. elevation that are pre-processed from the GR data. In RAS (UNET) these tables are comprised of elevation, conveyance, and storage.  The hydraulic values used at any time at any cross section during the solution are interpolated from the table values.  Rating curves for hydraulic structures have always been pre-computed in HEC-RAS; what is new in unsteady RAS is the development of these tables for cross sections.  The structure of these tables affects both the accuracy and stability of the unsteady flow solution.

## Expansion/Contraction Coeffs.

-  Not used in the momentum formulation (RAS-unsteady)
-   Should be in the data, however, for use with steady flow analysis

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
The momentum approach integrates forces acting over the surfaces and ends of a control volume; therefore, impacts of flow expansions/contractions are captured in the forces on the upstream and downstream ends of that control volume.   Of course, proper selection of the flow areas needs to be done here.  The energy approach integrates work/energy for the control volume; so, these coefficients are needed to describe the losses associated with the turbulent energy expenditure associated with flow expansion/contraction.

## Data Requirements(Flow and Boundary Conditions)

- Steady:  Discharge (Q) at each cross section.
- Unsteady:  Inflow hydrograph(s) which are routed by the model.

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
For steady flow the discharges are usually peak flows derived from statistical analysis.  The development and routing of these flows throughout the system is done externally to the steady flow model.  When using unsteady flow, developing a complete hydrologic scenario becomes an important part of the application.

##           Prepare hydrographs 

-         (boundary   conditions)
- 	Upstream flows
- 	Tributary (local flows)
- 	Ungaged/unmodeled flows
- 	Downstream (rating curve?)

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## HEC-RAS Main Window

- HEC-RAS Version 3.1

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## Entering Geometric Parameters

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
The Geometric Data Editor is shown in the above figure.  From this editor, select the button labeled Cross Section to view and edit the cross section geometry.

## Cross Section Table Properties

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
The Geometric Data Editor is shown in the above figure.  From this editor, select the button labeled Htab Param. to view and edit the cross section table parameters.

## Pre-processing Geometry

- For unsteady flow, geometry is pre-processed into tables and rating curves
- Cross sections are processed into tables of area, conveyance, and storage
- Bridges and culverts are processed into a family of rating curves for each structure
- Weirs and gated structures are calculated on the fly during unsteady flow calculations
- Pre-processor results can be viewed in graphs and tables

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
The pre-processor is used to process the geometric data into a series of hydraulic properties tables and rating curves.  This is done in order to speed up the unsteady flow calculations.  Instead of calculating hydraulic variables for each cross-section during each iteration, the program interpolates the hydraulic variables from the tables.  The preprocessor must be executed at least once, but then only needs to be re-executed if something in the geometric data has changed. 

## Cross Section Properties Plot

- 0

- 1000

- 2000

- 3000

- 4000

- 5000

- 6000

- 7000

- 650

- 660

- 670

- 680

- 690

- 700

- Property Table

- RS = 138154.4

-   Conveyance/1000 (cfs)  Storage (cu ft)

- Elevation (ft)

**Legend**

- Conv. Channel

- Conv. Valley

- Conv. Total

- Storage

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
Cross sections are processed into tables of elevation versus hydraulic properties of areas, conveyances, and storage.  Each table contains a minimum of 21 points (a zero point at the invert and 20 computed values).  The user is required to set an interval to be used for spacing the points in the cross section tables.  The interval can be the same for all cross sections or it can vary from cross section to cross section.  This interval is very important, in that it will define the limits of the table that is built for each cross section.  On one hand, the interval must be large enough to encompass the full range of stages that may be incurred during the unsteady flow simulations.  On the other hand, if the interval is to large, the tables will not have enough detail to accurately depict changes in area, conveyance, and storage with respect to elevation.

## Geometry Preprocessor

- What does it do?
- Processes geometric data into a series of hydraulic tables and rating curves.
- Why do we use it for unsteady flow?
- Instead of calculating hydraulic variables for each cross-section during each iteration, the program interpolates the hydraulic variables from the tables.

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
The preprocessor is used to process the geometric data into a series of hydraulic property tables and rating curves.  This is done in order to speed up the unsteady flow calculations.  Instead of calculating hydraulic variables for each cross-section during each iteration, the program interpolates the hydraulic variables from the tables.  The preprocessor must be executed at at least once, but then only needs to be re-executed if something in the geometric data has changed.

##  Conveyance Calculations

-             Manning Equation
-                                    1/2
-                    Q =  K  Sf
-                    K = Conveyance
-                    Sf = friction/energy slope

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
Conveyance is calculated from the above form of Manning’s equation (based on English units):

where:	
K	=  conveyance for subdivision
n	=  Manning's roughness coefficient for subdivision
A	=  flow area for subdivision
R	=  hydraulic radius for subdivision (area / wetted perimeter)
Sf	=  friction slope

## Conveyance Calculations

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
The determination of total conveyance and the velocity coefficient for a cross section requires that flow be subdivided into units for which the velocity is uniformly distributed.  The approach used in HEC-RAS is to subdivide flow in the overbank areas using the input cross section n-value break points (locations where n-values change) as the basis for subdivision.

The program sums up all the incremental conveyances in the overbanks to obtain a conveyance for the left overbank and the right overbank.  The main channel conveyance is normally computed as a single conveyance element.  The total conveyance for the cross section is obtained by summing the three subdivision conveyances (left, channel, and right).

##      Cross Section Example

- HEC-RAS Version 3.1

- Feb 2003

##     Geometry Preprocessor

- HEC-RAS Version 3.1

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**Notes:**
The geometric preprocessor is located in the Unsteady Flow Analysis Window, found from the main program window under the Run menu.

##     Hydraulic Property Plot

- HEC-RAS Version 3.1

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**Notes:**
Output can be viewed in graphical form.  Viewing the graphical output is a good diagnostic tool for examining cross section geometry.  The relationship of area, storage, and conveyance should be examined for abrupt changes with elevation.  Any abrupt changes should be reviewed to determine the overall significance within that particular model. 

## Cross Section Properties Table

- HEC-RAS Version 3.1

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##      Conveyance Subdivisions

- HEC-RAS Version 3.1

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**Notes:**
As shown in the figure above, there is a distinct increase in elevation located at station 2000.  The entire left bank is being modeled with one Manning’s n value.  Remember that RAS computes the left and right overbank conveyances using subdivision of Manning’s n.

##       Conveyance Subdivisions

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
As seen in the figure, there is a hitch in the increase of conveyance with elevation at just above 75 feet.  This corresponds to the steep increase in elevation located at station 2000 on the previous figure.

HEC-RAS uses Manning’s equation to calculate conveyance.  Imbedded in this equation are relationships for channel depth, channel area, and wetted perimeter.  In this example, when the calculations go just above the elevation of 75 feet, Manning’s equation sees an enormous increase in wetted perimeter for a minute increase in water depth.  The conveyance answer found from this calculation is dramatically different from the conveyance answer found at the previous calculation below 75 feet.

##      Conveyance Subdivisions

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
To account for this situation, a subdivision made by inserting another Manning’s n value must be added at the point of discontinuity.  The value does not need to be different, as long as the subdivision is present, RAS will calculate separate conveyances for the geometry.

##      Conveyance Subdivisions

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
As seen on the figure, this subdivision for the left overbank smoothed the relationship between conveyance and elevation.

## Boundary andInitial Conditions

- Objectives:
-  Know boundary condition options
-  Know initial condition requirements
-  Sources of data for both

**Notes:**
References:

HEC-RAS River Analysis System, User’s Manual, Chapter 8, Performing an Unsteady Flow Analysis, January 2001.

## Unsteady Flow Data

- External Boundaries required
- Upstream and Downstream ends of the river
- Typically flow or stage hydrograph upstream
- Typically rating or “normal depth” downstream
- Internal Boundaries can be added
- Add flow within the river system
- Define gate operation
- Initial Conditions - at the start of simulation

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
     As with steady-flow applications, the Unsteady Flow data define flow and starting conditions for the simulation.  The models a dynamic hydraulic process on an segment of a river system network.  To perform the hydraulic calculations within the segment, the “Boundary Conditions” must be defined for the “External Boundaries.”

      The Unsteady Flow editor provides the options to defined:
  External boundary type and data
  Add internal boundary data
  Set the initial conditions for the start of the simulation

## Unsteady Flow Data Editor

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
     Once all of the geometric data are entered, the modeler can then enter any unsteady flow data that are required.  To bring up the unsteady flow data editor, select Unsteady Flow Data from the Edit menu on the HEC-RAS main window.  The Unsteady flow data editor should appear as shown above.  

Unsteady Flow Data
     The user is required to enter boundary conditions at all of the external boundaries of the system, as well as any desired internal locations, and set the initial flow and storage area conditions in the system at the beginning of the simulation period. 

## Boundary Conditions

- Editor shows required external boundaries
- Boundary Type shows available options
- Upstream options:
- Stage Hydrograph
- Flow Hydrograph
- Stage & Flow Hydrograph

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
   Boundary conditions are entered by first selecting the Boundary Conditions tab from the Unsteady Flow Data Editor.  River, Reach, and River Station locations of the external bounds of the system will automatically be entered into the table.  
   Boundary conditions are entered by first selecting a cell in the table for a particular location, then selecting the boundary condition type that is desired at that location.  Not all boundary condition types are available for use at all locations.  The program will automatically gray-out the boundary condition types that are not relevant when the user highlights a particular location in the table.  
   Users can also add locations for entering internal boundary conditions.  To add an additional boundary condition location, select the desired River, Reach, and River Station, then press the Add a Boundary Condition Location button.

## Boundary Conditions - continued

- Downstream Boundary Options:
- Stage Hydrograph
- Flow Hydrograph
- Stage & Flow Hydrograph
- Rating Curve
- Normal Depth

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
     The downstream boundary can be:
  Stage Hydrograph - e.g., gage data on the stream, or tidal cycle
  Flow Hydrograph - e.g., gage data converted to flow
  Stage & Flow - e.g., combined observed stage and forecasted flow
  Rating Curve - e.g., rating at a gauged location, or steady-flow rating
  Normal Depth - e.g., average slope of stream to estimate energy slope

## Flow Hydrograph

- Read from DSS
- Select DSS file
- Select Pathname
- Enter in Table
- Select time interval
- Select start date/time
- Enter flow data - or cut & paste

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**Notes:**
Flow Hydrograph:
     A flow hydrograph can be used as either an upstream boundary or downstream boundary condition, but is most commonly used as an upstream boundary condition.  When the flow hydrograph button is pressed, the window shown above will appear.  As shown, the user can either read the data from a HEC-DSS (HEC Data Storage System) file, or they can enter the hydrograph ordinates into a table.  
     If the user selects the option to read the data from DSS, they must press the Select DSS File and Path button.  When this button is pressed a DSS file and pathname selection screen will appear as shown on the next page.  The user first selects the desired DSS file by using the browser button at the top.  Once a DSS file is selected, a list of all of the DSS pathnames within that file will show up in the table.  The user can use the pathname filters to reduce the number of pathnames shown in the table.  The last step is to select the desired DSS Pathname and to close the window. 

## Sources of Time-Series Data

- Historic Records (USGS)
- Stage Hydrographs
- Flow Hydrographs
- Computed Synthetic Floods
- Rainfall-runoff modeling
- Peak Discharge with assumed time distribution
- Others?

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
     Unsteady-flow modeling provides a dynamic solution for stage and flow throughout the river network.  The primary boundary data are time-series flow, typically for a flood event.  Where do you get that flow data?

     For most program user’s, the simulation will route an upstream flow hydrograph, using a downstream rating curve or normal depth.  The upstream hydrograph can be: 
  Historic, like those obtained from the US Geologic Service.  
  Synthetic, often, prior studies have computed and published synthetic floods like the Corps’ Standard Project (SPF) or the Probable Maximum Flood (PMF).  
  Modeling, using rainfall-runoff models like the Corps’ Hydrologic Modeling System (HEC-HMS).
  Peak Discharge, and a time to peak estimate, can be used to provide a crude hydrograph using the HEC-RAS interpolation routine (Triangle hydrograph).  If a Unit Hydrograph is available, that distribution can be used to develop a flow hydrograph.

## Normal Depth

- Enter Friction (energy) Slope
- Program uses Manning’s equation to compute stage
- Provides semi-dynamic downstream boundary

- HEC-RAS Version 3.1

- Feb 2003

## Initial Conditions

- Requires an initial flow for all reaches
- Restart file can be read from DSS
- Enter steady-flow at upstream boundary
- Can add a flow-change location
- Pool elevation for storage areas

- HEC-RAS Version 3.1

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## File and Options Menus

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
     The Unsteady Flow Window has the standard File Menu options.  It is a good idea to save the data before going on to the next step.

     The Options Menu has two options:
  Delete an added Boundary Condition.  You cannot delete external boundaries; they are required.
  Add Observed Data in DSS - this option would be helpful when calibrating a model to simulate an historic flood event.

## Unsteady Flow Simulation Simulation Manager

- 1. Define a Plan

- 2. Select which programs to run

- 3. Enter a starting and ending date and time

- 4. Set the computation settings

- 5. Press the Compute button

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
Once all of the geometry and unsteady flow data have been entered, the user can begin performing the unsteady flow calculations.  To run the simulation, go to the HEC-RAS main window and select Unsteady Flow Analysis from the Run menu.

The unsteady flow computations within HEC-RAS are performed by a modified version of the UNET (Unsteady NETwork model) program, developed by Dr. Robert Barkau (Barkau, 1992).  The unsteady flow simulation is actually a three step process.  First a program called RDSS (Read DSS data) runs.  This software reads data from a HEC-DSS file and converts it into the user specified computation interval.  Next, the UNET program runs. This software reads the hydraulic properties tables computed by the preprocessor, as well as the boundary conditions and flow data from the interface and the RDSS program.  The program then performs the unsteady flow calculations.  The final step is a program called TABLE.  This software takes the results from the UNET unsteady flow run and writes them to a HEC-DSS file.  

## Output Selection

- Unsteady Flow Output
- Stage and Flow Hydrographs
- Log File Output
- Post Processor
- Detailed output
- Max Stage
- Selected Time Intervals

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
The output from an unsteady flow run are stage hydrographs,  flow hydrographs, and basic stage profiles.  These hydrographs and profiles are stored in DSS.

For more detailed output you must run the post processor.  The  post processor reads the hydrograph and profile information in the DSS file and creates detailed output data for the maximum stage computed and series of snap shots in time on a selected “Detailed Output Interval”.

## Stage and Flow Hydrographs User Selected Locations

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## Viewing Unsteady Flow Results

- All of the output that was available for steady flow computations is available for unsteady flow (cross sections, profile, and 3D plots and tables).
- Stage and flow hydrographs
- Time series tables
- Animation of cross section, profile and 3-dimensional graphic

- HEC-RAS Version 3.1

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## Stage and Flow Plot

- Stage

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
The stage and flow plotter is opened from the main RAS window.  “Stage and Flow Hydrographs” can be selected from under the “View” menu of the button highlighted above can be pressed to open the window.

Data can be viewed graphically or in table form by selecting the desired tab.   By default, both stage and flow are plotted.  When there are both stage and flow on the plot, a second Y axis is displayed.

## Unsteady Flow Rating Curve

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
The stage and flow hydrograph plotter allows the user to plot flow hydrographs, stage hydrographs, or both simultaneously.  Additionally, if the user has observed hydrograph data, that can also be plotted at the same time.  The plot can be printed or sent to the windows clipboard for use in other software.

## Log File Output

- can be generated during computations
- information about progression of simulation
- can make a large, large file
- are you sure you want to open it?

- HEC-RAS Version 3.1

- Feb 2003

**Notes:**
The log file can easily get into the hundreds of megabytes.  If your simluation is crashing a long way into it, consider creating a restart file before things go unstable.  Then restart the simulation nearer the point where it crashes.

## Post Processor

- Can be run after the unsteady simulation is completed
- Provides profiles for the maximum stage and at regular intervals
- All regular graphics and tables can be used to view the post process results
- Graphics can “animate” the simulation

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## Profile Animation

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## Accuracy/Stability/SensitivityObjective

- For students to have a better understanding of model accuracy, stability, and sensitivity.
- To become familiar with the available parameters within HEC-RAS that will allow you to develop a stable and accurate model.
- To learn how to detect, find, and fix model stability problems.

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## Overview

- Model Accuracy
- Model Stability
- Factors Affecting Accuracy and Stability
- Cross section spacing
- Computational time step selection
- Practical delta t, hydrograph rise time / 20
- Common Stability Problems
- Detecting Stability Problems
- Model Sensitivity

- HEC-RAS Version 3.1

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## Model Accuracy

- Accuracy can be defined as the degree of closeness of the numerical solution to the true solution.
- Accuracy depends upon the following:
- Assumptions and limitations of the model (i.e. one dimensional model, subcritical flow only for unsteady flow)
- Accuracy of the geometric Data (cross sections, Manning’s n values, bridges, culverts, etc...)
- Accuracy of the flow data and boundary conditions
- Numerical Accuracy of the solution scheme

- HEC-RAS Version 3.1

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## Numerical Accuracy

- If we assume that the 1-dimensional unsteady flow equations are a true representation of flow moving through a river system, then only an analytical solution of these equations will yield an exact solution.
- Finite difference solutions are approximate.
- An exact solution of the equations is not feasible for complex river systems, so HEC-RAS uses a finite difference scheme.

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## Model Stability

- An unstable numerical model is one for which certain types of numerical errors grow to the extent at which the solution begins to oscillate, or the errors become so large that the computations can not continue.

- HEC-RAS Version 3.1

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## Slide 53

- HEC-RAS Version 3.1

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**Notes:**
In this rather extreme example – cross sections spaced at x = 5000 m in a prismatic trapezoidal channel with bed slope, So, of 0.001; bottom width of 20 m; top width of 60 m; Manning’s n is 0.033; and the overall length is 100,000 m. – the average conveyance method shows instabilities, particularly on the falling limb of the hydrograph.  This cross section is near the downstream end of the reach, but upstream of the influence of the downstream boundary condition.  The average friction slope method solution remains stable and accurate.  In most circumstances, however, this will not be an issue.

## Factors Affecting Model Stability and Numerical Accuracy

- Cross Section Spacing
- Computation time step
- Theta weighting factor
- Solution iterations
- Solution tolerances

- HEC-RAS Version 3.1

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## Calculation Options and Tolerances

- HEC-RAS Version 3.1

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**Notes:**
See Chapter 8 of the user’s manual for a detailed description of each of the variables contained within the computations options and tolerances window.

## Cross Section Spacing

- Cross sections should be placed at  representative locations to describe the changes in geometry.
- Additional cross sections should be added at locations where changes occur in discharge, slope, velocity, and roughness.
- Cross sections must also be added at levees, bridges, culverts, and other structures.

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## Cross Section Spacing - Slope

- Bed slope plays an important role in cross section spacing.
- Steeper slopes require more cross sections
- Streams flowing at high velocities may require cross sections on the order of 100 feet or less.
- Larger uniform rivers with flat slopes may only require cross sections on the order of 1000 ft or more.

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## Cross Section Spacing - How do you know if you have enough XS:

- Use the HEC-RAS cross section interpolation.
- Make a new plan and run the model.
- Compare the before and after.
- If no significant difference, then OK!

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## Theta Weighting Factor

- Theta is a weighting applied to the finite difference approximations when solving the unsteady flow equations.
- Theoretically Theta can vary from 0.5 to 1.0.  However a practical limit is from 0.6 to 1.0
- Theta of 1.0 provides the most stability.  Theta of 0.6 provides the most accuracy.
- The default in HEC-RAS is 1.0.  Once you have your model developed, reduce theta towards 0.6, as long as the model stays stable.

- HEC-RAS Version 3.1

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**Notes:**
Larger values of theta increase numerical diffusion, but, by how much?  Experience has shown that for short period waves that rapidly rise, theta of 1.0 can produce significant errors.  However, these errors can be reduced by using smaller time steps.

When choosing theta, one must balance accuracy and computational robustness.  Larger values of theta produce a solution that is more robust, less prone to blowing up.  Smaller values of theta, while more accurate, tend to cause oscillations in the solution, which are amplified if there are large numbers of internal boundary conditions.  

## Common Stability Problems

- Too large of a time step.
- Not enough cross sections
- Model goes to critical depth – RAS is limited to subcritcal flow for unsteady flow simulations
- Bad downstream boundary condition (i.e. rating curve or slope for normal depth)
- Bad cross section properties, commonly caused by: levee options, ineffective flow areas, Manning’s n values, etc..

- HEC-RAS Version 3.1

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## Common Stability Problems - Continued

- Cross section properties that do not go high enough, or are way to high (curves are spread to far apart).
- Bad bridge/culvert family of rating curves.
- Wide and flat lateral weirs/spillways – send to much flow over a given time step.
- Gated spillways that are opened or closed to fast.

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## Detecting Stability Problems

- How do you know you have a stability problem?
- Program completely blows up during run
- Program goes to maximum number of iterations for several time steps in a row.
- Program has oscillations in the computed stage and flow hydrographs

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## Detecting Stability Problems - Continued

- What do you do when this happens?
- Note the simulation time when the program either blew up or first started to oscillate.
- Turn on the “Detailed Output for Debugging” option and re-run the program.
- View the text file that contains the detailed log output of the computations.  Locate the simulation output at the simulation time when the solution first started to go bad.
- Find the river station locations that did not meet the solution tolerances.  Then check the data in this general area.

- HEC-RAS Version 3.1

- Feb 2003

## Turning on Detailed Output for Debugging

- HEC-RAS Version 3.1

- Feb 2003

## Viewing Detailed Log Output

- HEC-RAS Version 3.1

- Feb 2003

## Model Sensitivity

- Numerical sensitivity:
- Computation time step – try a smaller value to see if the output changes significantly.
- Theta – start at 1.0, after you have a working model then try to reduce it towards 0.6.
- Weir/Spillway stability factors – if you are using stability factors, try to reduce them to the lowest value you can get away with.
- Weir/Spillway exponential decay factors – in general I would leave them alone, they will not effect the sensitivity of the output much.

- HEC-RAS Version 3.1

- Feb 2003

## Model Sensitivity - Continued

- Physical Parameter Sensitivity:
- Manning’s n Values – What if the true n values were 10% higher or Lower?
- Cross Section Spacing – Test by interpolating
- Cross Section Storage – What if there is really more or less storage in the cross sections (I.e. ineffective flow areas, etc...)
- Weir/Spillway coefficients – For lateral weirs/spillways the coefficient selected can have a great impact on the results.
- Bridge/Culvert Parameters – normally only effect the locally computed stages, unless it is a flat area in which the bridge causes great backwater.

- HEC-RAS Version 3.1

- Feb 2003

## The End