PHABSIM Laboratory Exercises

Preface

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Appendices

Lab Exercises 1-6

Lab Exercises 7-12

Lab Downloads

Laboratory 1. Using the PHABSIM for Windows Interface

Introduction

The PHABSIM Windows interface considers all hydraulic and habitat simulation work planned for a study site to be one "project". All data entry, selection of simulation options, output option selection, and viewing of results takes place within the project. The purpose of Laboratory 1 is to familiarize the user with use of the interface to build a PHABSIM project data set.

Using the Menu System

The general steps to use the interface consist of creating a new project or opening an existing project; importing, entering, or changing data; entering or changing run options; running programs; viewing intermediate and final results; saving the project files; and capturing results in a format for creating reports. In the laboratory exercises, each of those steps is presented in the following format:

\Main Menu\Next Menu\Next Menu or Tab: followed by instructions.

For example, to enter cross section coordinate data for the second cross section, the user clicks on Edit, followed by clicking Cross Sections, followed by selecting the second cross section, followed by clicking the Coordinate Data tab, and then entering data in the spreadsheet-like interface. That sequence of operations is noted in the documentation as:

\Edit\Cross Sections\Number\Coordinate Data: Enter x, z, channel index, n (if known), VelSet1, VelSet2, ....

The actions are:

Move mouse to Edit item in the main menu, click.
Move mouse to Cross Sections tab, click.
Move mouse to the gray box showing number 2 in the left column, click.
Move mouse to Coordinate Data tab, click.
Enter data in the spreadsheet-like interface as described below.

Abbreviated notation, for example ..\Coordinate Data, is used in some places to abbreviate \Edit\Cross Sections\Number\Coordinate Data when moving within the same set of tabs or menus.

This notation convention is used through out the Laboratory exercises. If you find the notation is too terse or confusing, click on the first item that comes to mind and see what happens. Until the data entries or option selections are changed, you are merely viewing different portions of the interface so you can click on each successive item in this notation and follow where it leads.

To gain familiarity with the interface, we will begin by loading an existing project and navigating through the interface to get a feel of the process. First open the project:

Step 1. Open a Project

\File\Open Project: Navigate the Windows File Menu to \If310\Newlabs\Lab01 and double click on the file Lab1.phb

Step 2. Enter and Edit Cross Section Data

Data can be entered and viewed in the Edit area. Look at the cross section data in the Sampl1 project by:

\Edit\Cross Sections\Cross Section Data

Note that the data set contains four cross sections. For each cross section, the following information has been entered.

ID - The cross section identifier. In PHABSIM for Windows we always use the distance from the downstream cross section as the identifier. This allows a cumulative upstream distance to be calculated and displayed as the Y ordinate in the coordinate data tab.

Length - the cross section length or the distance from the downstream cross section. Length is used to calculate the y (cumulative distance) value. Cross sections are sorted by the cross section ID in ascending order.

Upstream WF - the weight assigned to this cross section. That is, the faction of distance upstream it represents.

L Bank WF - the left bank weight for a bend.

R Bank WF - the right bank weight for a bend. If these are equal, there is no bend.

SZF - stage of zero flow.

N - Manning's n value for the cross section.

Beta/D50 - beta exponent for use in the MANSQ program, if applicable, or median substrate particle size in mm.

Slope - energy slope at the cross section. Typically estimated as the water surface slope.

To edit or view individual cross sections use:

\Edit\Cross Sections\Coordinate Data

Under this tab, the cross section currently highlighted under Edit\Cross Sections\Cross Section Data will be displayed. Cross section ID is shown above the table and the number of points on the cross section is also displayed. To view the cross section profile, click the Graph button. You may drag the graph and Cross Section Data windows by their top bars so both can be viewed simultaneously. To view a different cross section, return to the Cross Section Data tab and click on a different cross section. The highlighted region will change. Return to the Coordinate Data tab and the graph will update.

The \Edit\Cross Sections\Calibration Data tab allows entry of data for left and right bank water surface elevations, the user-determined (or "given") water surface elevation, the "best estimate" discharge for the site, and the discharge measured at that cross section. As with the coordinate data, cross sections are selected in the Cross Section Data tab prior to viewing the Calibration Data tab for that cross section.

Entering and Editing Suitability Curves

Now that you have seen how to navigate around the cross section editing menu, take a look at the \Edit\Suitability Curves menu. You will find a similar set of menus and tabs there. Look at the data entry and display area for habitat suitability curves using:

\Edit\Suitability Curves

The\ Edit\Suitability Curves\File menu item allows you to create a new curve, import an existing curve file from another project, copy curve files, and save curve files. The \Edit\Suitability Curves\Curve menu item allows you to choose which curve in a suitability curve set is displayed in the data entry box. For example: by selecting ..\Curve\Select by ID you can view a list of all HSC curve sets currently entered into this project and select a particular curve for viewing. Individual curves for depth, velocity, channel index, or temperature are selected using the Curve Type buttons to the right. \Edit\Suitability Curves\Graph allows you to display a graph of the selected curve values displayed in the SI curve-editing box. These graphs can be scaled for a better view. See Chapter 1 for use of the mouse button graphing features in PHABSIM for Windows.

The \Edit\Suitability Curves\Curve\Display All Curves menu item displays the four HSC curves in one window.

Entering and Editing Simulation Discharges

This simple dialog allows you to start with a small number of simulated discharges to be used in calibrating the hydraulic models, then add additional discharges for final simulation runs. For calibration when comparing observed with simulated conditions, the calibration discharges have been entered as simulation discharges by default. They cannot be removed and will appear in all simulations you run. The calibration discharges are shown in gray and any other discharges you enter will be shown with a white background.

To add discharges to this list, either place the cursor on the next highest discharge and press the Insert key on the keyboard or, to add a discharge higher than the highest shown, place the cursor on the last discharge and press the down arrow. Either of these actions will provide a new row with a discharge of 0. You simply type the desired discharge value in the highlighted cell.

Step 3. Running the Models

The \Models menu is where you set-up and run the various models. Here hydraulic simulation is divided into water surface and velocity simulation and habitat simulation includes the Habtae, Habtam, and Habef models. Also included here is a combined Avdepth\Avperm model. Each model contains a Run button that is clicked after all of the model input parameters are selected.

Further instructions in running the models are contained in the remainder of the laboratory exercises.

Step 4. Close and Save the Project

To prepare for the next laboratory exercises, please close this project using:

\File\Close Project

If you had made any changes to your project, they would be saved now. The system will prompt you to save your project if changes have been made. In general it is a good idea to frequently use:

\File\Save Project

You may wish to save the project periodically to ensure you can recover from a mistake or a computer glitch.

Step 5. Manipulating PHABSIM for Windows Graphics

PHABSIM for Windows uses a third-party graphics package that allows the graphs displayed by clicking the various graphics buttons described in the labs and manual to be scaled, translated, zoomed and, in some cases, rotated. The following examples illustrate each of those functions.

Scaling (Figures L1-1 and L1-2):

• Press Ctrl and hold down both mouse buttons
  
• Move mouse down to increase the chart's size
  
• Move mouse up to decrease the chart's size

  

  Figure L1-1. Original image.
  

  

  Figure L1-2. Scaled view.

  Translation (Figure L1-3)

• Press Shift and hold down both mouse buttons
  
• Move mouse to shift the chart

  Zooming

  Axis Zoom

• Press Shift and hold down the left mouse button
  
• Move mouse to select the area to Zoom into (a box will be drawn around the area) then release the button

  Axis zoom is illustrated in Figures L1-4 and L1-5.

  Graphics Zoom does not retain axes, otherwise, same as Axis Zoom

• Press Ctrl and hold down the left mouse button
  
• Move mouse to select the area to Zoom into and release button

  

  Figure L1-3. Translated image.

  
  Rotation (3-D charts only, Figures L-6 and L-7)

• Hold down both mouse buttons
  
• Move mouse left and right to change the rotation angle
  
• Move mouse up and down to change the inclination angle

  Return to Default Position (Fig. L1-8)

• Press "r"
  
• All interactive scaling, translation, and zooming is removed

  

  Figure L1-4. Selecting a region to enlarge. Hold Shift and Left Mouse button, drag box to desired area.

  

  Figure L1-5. Zoomed view appears when mouse button is released.

  

  Figure L1-6. Default position of 3-D chart.
  

  

  Figure L1-7. Rotated 3-D chart.

  

  Figure L1-8. Press "r" o keyboard to return to original view.

  A Strategy for Using PHABSIM for Windows

  PHABSIM for Windows was designed to be used in combination with other Windows features to allow a large degree of flexibility in the PHABSIM analysis. The following suggestions constitute a strategy for using Windows to the maximum advantage while doing a PHABSIM analysis.

  Monitor Adjustments

  We have found it is most convenient to adjust your monitor to display the maximum number of pixels that can comfortably viewed. Current generation 17- inch monitors can reliably display 1024 x 768 pixels with font sizes in the range of normal printed text. If you can comfortably use 1280 x 1024 pixels you will find additional utility in being able to position various windows on the desktop for convenient use. The minimum resolution monitor that can be used with PHABSIM for Windows is 800 x 600 pixels. You may find that a 19-inch monitor operating at 1280 by 1024 pixels facilitates the analysis by allowing multiple windows to be open simultaneously.

  Location of the Working Directory

  PHABSIM for Windows places the sample files in C:\My Documents\Phabsim\Sample1 and ..\Sample2. This location was chosen solely because most computers using Microsoft Windows will have a My Documents directory on the C: drive. You may place your working directory for any project in the desired location at project creation. This may be accomplished by creating the directory using the Browse feature in the \File\Open Project dialog or by creating the directory prior to running PHABSIM for Windows using Windows Explorer. Place the working directory in a location that is relevant to your project and easy to remember.

  The PHABSIM Window

  The main program window need not be maintained at its full size. The primary purpose of the main window is to provide the top-level menu items in the menu bar. Thus, after a project is opened, the main PHABSIM window may be sized so only the menu bar or the text in the project description is displayed. This opens up space on the desktop without losing any of the main menu functionality. Drag the lower right corner of the window to resize it.

  Displaying Graphs

  Many of the plots of input data or model results display values that are either entered or displayed using various interactive tables in the PHABSIM for Windows interface. It is often convenient to drag the graph window to the lower right of the screen and drag the data entry or program option window to the upper right so at least portions of the data table may be viewed at the same time as the graph. Graph windows may be resized by dragging their corners.

  The Desktop

  We have found that it is very convenient to place icons on the desktop for PHABSIM, Projview (a PHABSIM file translation utility), Notepad, and Wordpad (also called Write). It is also convenient to have an icon for your spreadsheet program to provide ease of starting the spreadsheet by simply double clicking the icon.

  A convenient way to capture PHABSIM for Windows graphics (other than printing them) for use in other documents is to use the Print Screen feature of Windows and paste the graphic into Microsoft Paint. Thus, placing an icon for Paint on the desktop may also be convenient.

  PHABSIM for Windows produces numerous files that can provide ancillary information during the course of the analysis. It is convenient to have Windows Explorer running while using PHABSIM so those files may be accessed by simple drag and drop actions from Windows Explorer to the other programs noted here that are placed on the desktop.

  Auxiliary Programs

  Spreadsheet Program

  Though PHABSIM for Windows contains numerous automatically generated plots that can be used to display both input data and the results produced by the various models within the program, the plotting package can only display results from the current analysis. Thus, when the user wishes to compare results of different analyses, it is necessary to export those results to a different medium using cut and paste operations. We have found it very convenient to create spreadsheets for this purpose. Later lab exercises use spreadsheets to calculate differences between model results based on different model options and to display those different results graphically. When spreadsheets are used in conjunction with PHABSIM for Windows, the spreadsheet files should be saved with the PHABSIM files and should become part of the analysis record.

  Notepad

  While applying PHABSIM to a study site, numerous decisions are made regarding program options, data issues, and alternative approaches to describing habitat for the site. It is very difficult to recall each decision after the study is done. Thus, we suggest that the user create a Notepad file with a name like "Projectlog.txt" and keep a diary of the progress of the analysis including any problems encountered, the program options selected, and especially why they were selected, and any other pertinent information that will allow later defense of the study. For example, such a log file would be a good place to keep track of calibration error statistics and notes as to why a particular calibration was deemed satisfactory.

  Windows Explorer and Wordpad

  In addition to the results tables provided in the PHABSIM for Windows interface, the program produces numbered projectname.ZOUTxx files that contain computational details and other numerical results from running the models. Viewing these files facilitates some portions of the analysis. It is convenient to be able to "drag and drop" the numbered ZOUTxx files from Windows Explorer to Notepad for viewing. Some of the files will be too large for Notepad, but Wordpad will be able to display them. Further, Wordpad provides more formatting control, when portions of the ZOUT files are to be inserted in reports, than Notepad.

  Use Strategy

  When doing a PHABSIM analysis, the strategy we have found most convenient is to open and minimize the following programs and files:

• Notepad, open the log file
  
• Spreadsheet, open data comparison or error tracking file(s)
  
• Windows Explorer, move to the working directory so you can drag and drop conveniently

  The minimized programs will show as buttons on the task bar at the bottom of the screen. Click on the appropriate button to access them. Remember to save your log, PHABSIM and spreadsheet files often during the course of the analysis. Such a strategy will prevent data loss due to the occasional inevitable mistake.
  

  TOP OF PAGE

  Laboratory 2. Building a PHABSIM Project

  Objective

  The objective of this laboratory is to cover the use of PHABSIM for Windows to create a PHABSIM project file. PHABSIM for Windows will be used to create an example project file and the project will be reviewed for errors.

  Data Files Used: Data.xls

  Introduction

  In typical PHABSIM applications, the user will likely have a number of cross sections where the hydraulic characteristics of the river channel have been measured at one or more discharges. In this laboratory, we have provided data collected at four cross sections from the Fryingpan River, where water surface elevations and velocities have been measured at three calibration discharges. All the hydraulic data necessary to create a complete PHABSIM project file have been summarized in tabular form by cross section and provided in Tables L1-1 to L1-4 at the end of this lab. Information about reach lengths, Stage of Zero Flow (SZF), upstream weighting factors, reach length, slope, best estimate of the discharge, and measured discharge at each calibration flow is located at the top of each tabular summary. The remaining data in the table lists the x?distance, bed elevation, channel index, and observed velocities at each of the calibration flows.

  The laboratory illustrates use of \Edit\Cross sections to enter the data for the four cross sections. Two complete PHABSIM project data files containing these calibration data have already been created (SAMPLE1.PRJ and SAMPLE2.PRJ) as example data files. SAMPLE1.PRJ contains data entry only, while SAMPLE2.PRJ has been run through the habitat simulation stage. Both projects are included on the PHABSIM distribution disks. Proceed through the steps in order. If you run out of time to enter all the data described below, you can use SAMPLE1 to navigate the various menus and view diagnostic plots. A separate set of worked laboratory exercise project files is provided for each lab. The location of those files will vary depending on the computer system used for class instruction.

  Step 1. Create a New Data Set

  Now that you understand the basic PHABSIM for Windows navigation process from Lab 01, you are ready to open a new project and enter data.

  For ease of reference these instructions will use the Project name MYLAB02.

  \File\Open Project: Enter a project name in the Project folder name box. Then type a description of the project in the Project Description box. (The description is limited to 256 characters.) Next use the Browse button to navigate the Windows file tree to where you want the new folder to be stored. PHABSIM for Windows will create a directory and a set of files with the project name. For this lab, enter the new project name (i.e., MYLAB02) in the file name box, enter an appropriate description in the project description box, then click Browse and navigate to \IF310\Laboratories, and click OK. (See Figures L2-1, L2-1, and L2-3.)

  

  Figure L2-1. Opening a new project.

  

  Figure L2-2. Assigning a folder location.
  

  

  Figure L2-3. Entering project name and description.

  An example of a project description might be:

  "Fryingpan River 3 miles downstream from Reudi Reservoir. High flow data collected May 10, 1999, mid flow data collected July 10, 1999, and low flow data collected Aug. 23, 1999. By name, name, and name."

  You can revise the project description from the Edit menu using \Edit\Project Data. This allows adding short notes on the status of the analysis as the process progresses.

  Step 2. Enter Project Hydraulic Data for Lab02

  To build a project's data set, click the \Edit menu item. You are presented with choices of Cross Sections, Suitability Curves, and Discharges. You can enter and change data for each of these categories by selecting the corresponding menu item. However, you must begin with Edit\Cross Sections\Cross Section Data and enter the cross section data for at least one transect (cross section) prior to entering calibration data or coordinate data as shown in Figure L2-4. The Edit\Cross Sections dialog contains three tabs for Cross Section Data, Calibration Data, and Coordinate Data. The Cross Section Data tab is displayed by default.

  

  Figure L2-4. Preparing to enter cross section data.

  To create a new cross section, in the ..\Cross Section Data tab, use the down arrow. A row of cells appears with a cross section ID number of "-1.00". For each cross section, enter the id for the cross section by typing the cross section ID from Table L2-1 over the -1.00 entry. Move the highlight cursor to the right with the right arrow and enter the reach length. Continue moving to the right and enter the upstream weighting factor, the bend weights for the Left Bank and Right Bank, the stage of zero flow (SZF), Manning's n value (if known), Beta coefficient for MANSQ (if known), and the energy slope. Values for Manning's n and beta can be left unchanged for now. You would enter those values when using the WSP or MANSQ models later in the analysis. Your data for the first transect should now contain the following values.

  ID	-	0.0
  Length	-	0.0
  Upstream WT	-	0.0
  Left Wt	-	1.0
  Right Wt	-	1.0
  SZF	-	90.60
  N	-	0.0
  Beta	-	0.0
  Slope	-	0.0040

  Complete the cross section data table as shown in Figure L2-5. Scroll right to include beta and slope values.
  

  

  Figure L2-5. Entering cross section data.

  Next, click on the cross section ID 0.00 line and proceed to the Calibration Data tab (Fig. L2-6). Enter data for either left and right bank water surface elevations, or a single "user" selected water surface elevation, the user-determined or "given" discharge for the study site, and the measured discharge for the current transect. Enter these items for each calibration discharge (matching each VEL set) for this study. Return to ..\Cross Section tab to change to the next cross section ID.

  Note that the best estimate discharge must be a unique value (duplicates are not allowed). After you enter calibration data and exit the calibration data tab, the table sorts in ascending order on the Best Estimate Q values.

  

  Figure L2-6. Entering calibration data.

  Coordinate Data tab. Here you will find a difference from historical PHABSIM data entry in that there are values for X, Y, and Z. The inclusion of three dimensions is in anticipation of the ability to import GIS or spatially referenced data in the future. For now, enter the total distance upstream from the first transect as Y. Thus, X represents distance across the transect from the head pin, Y represents the distance upstream from the first transect (also referred to as Stationing), and Z represents the vertical distance above the datum selected for the study site. The program calculates Y values and those cells have a gray background.

  From the data in sheet xsec01 enter the x-distance in column X, the distance upstream from the first transect in column Y, and the elevation in column Z. Channel index and individual Manning's n values for each cell are entered in the columns labeled CI and N. Calibration velocity sets are entered in the Vel @discharge columns. Enter the coordinate and velocity data from Table L2-1. The coordinate data entry process is shown in Figure L2-7. When you have finished, proceed to the ..\Cross Section Data tab, select the next cross section and repeat the Calibration Data and Coordinate Data entry steps.
  

  

  Figure L2-7. Coordinate data entry.

  These steps would normally be repeated for all transects in the study. At that point, you have entered the basic hydraulic data for the study site. In this lab, we will also learn how to input coordinate data from a spreadsheet using Windows copy and paste functions for the third and fourth cross sections in this project.

  Entering Coordinate Data by Copy and Paste from a Spreadsheet

  PHABSIM for Windows allows entry of certain parts of the project data using Windows copy and paste operations. The third party data entry software has some quirks that must be accommodated to enable the copy and paste features. The next steps demonstrate how to paste coordinate data from a spreadsheet into PHABSIM for Windows.

  Move to the ..\Calibration Data tab for cross section 135. Enter (type) the calibration data contained in Table L2-1. Now move to the ..\Coordinate Data tab for cross section 135.

  Start your spreadsheet software and open the spreadsheet named Mylab02.xls. Move to the worksheet labeled XSEC135. There you will find a block of cells containing the X, Y, Z, channel index, Manning's n, and calibration velocity data for this cross section. Using the row index at the left, determine the number of rows of data in the transect. Highlight this block of cells and execute the Windows Copy command to copy those values into the Windows clipboard.

  Return to PHABSIM for Windows using a mouse click in that window.

  Using the Insert or Down Arrow key, insert the number of rows of data (not row numbers) found in the Coordinate Data tab worksheet. (If you insert too many rows, right click and select Remove Row as many times as needed. Then, using the left mouse button, Drag the cursor from the lower left (last X, last vel) corner of the worksheet to the upper left, being sure to include the calibration velocity set columns. That entire area should now be highlighted. Next, Right Click and select Fill from the pop-up menu. The entire area will be filled with 0.00. Finally, move to the upper left corner of the coordinate data entry area again. Right Click, and select Paste from the pop-up menu. The highlighted coordinate data area will be filled with the data from the spreadsheet. This process is shown in Figures L2-8 through L2-10.

  

  Figure L2-8. Opening and blocking coordinate data tab rows.

  Due to the nature of the data entry grid software, calibration velocity cells that were blank in the spreadsheet now have zeros. Delete those zeros using the Delete key so the data set follows the convention that a blank velocity means the cell was dry and a velocity of 0.0 means the cell had standing water. Compare the PHABSIM for Windows data entry sheet with Mylab02.xls to ensure all of the required velocity cells are changed to blank. Column Y may change during this cut and paste operation, but it will revert to the calculated value the next time you open this tab.
  

  

  Figure L2-9. Filling the coordinate data table with zeros.

  

  Figure L2-10. Pasting coordinate data from a spreadsheet.

  Repeat these operations (Calibration and Coordinate Data) for cross section 201.

  Step 3. Enter Suitability Data for Lab02

  Click \Edit\Suitability Curves and you are presented with a dialog box where habitat suitability of use curve (HSC) data can be entered for all species of interest for the study. Begin by using ..\Suitability Curves\Edit\Add Curve and entering the curve ID number and the species and life stage descriptions from the HSC sheet in the Mylab02 spreadsheet in the boxes provided. Note that curve ID numbers should be five or more digits to capture species and life stage coding. Then click OK. A table for entry of the Velocity curve information is displayed by default.

  The same Insert key convention to create a new line used with coordinate data entry applies. You may also copy and paste HSC curves into PHABSIM for Windows using the conventions described for coordinate data above. You must type the species, life stage, and HSC number, but the coordinate data can be entered using copy/paste operations.

  Enter the HSC data for velocity by copy and paste or by typing.

  To switch to the Depth, Channel Index, or Temperature HSC curves, click the appropriate button in the Curve Type box at the upper right and enter the HSC data by paste or typing as above.

  Repeat this process beginning with ..\Add Curve for all HSC curve sets in the HSC sheet.

  Enter Simulation Discharges for Lab01

  This step may be performed now or after the hydraulic models have been calibrated. To avoid excessive output during the calibration process, the user would typically select to run the full range of simulation discharges toward the end of the hydraulic model calibration process. Those selections will be made in the WSL and Velsim windows in later lab exercises. We will enter a small number of additional discharges here to illustrate the process.

  Select \Edit\Discharges to display the Simulation Discharges window. The user-defined calibration best estimated discharges (75.2, 139.0, and 250.0 cfs) are shaded in gray. They are automatically entered in the Discharge column. Note that they are marked "cal" in the Type column. Click on the first of these discharges and press the Insert key. A new cell with a value of 0.00 will appear. Enter a value of 15.0. Repeat this process with Insert (before the calibration discharges) or the Down arrow (after one or more calibration discharges) to enter the values of 60.0, 625.0, and 1250.0. Click the Close button to end discharge data entry.

  You have now finished the basic data entry process. Save your project using \File\Save Project.

  One more key data entry step remains, that of entering Suitability-of-use criteria (SI curves). This topic will be covered in Laboratory 7.

  Step 4. Evaluate Diagnostic Plots

  The quality of any modeling exercise begins with correct data entry. PHABSIM for Windows contains several means of viewing plots of the entered data for quality control. A longitudinal plot of the observed water surface elevations can be obtained using \Reports\Graphs\Longitudinal Profile and checking the Observed WSL box. Selecting \Edit\Cross Sections\Coordinate Data and clicking the graph button can view cross section geometry plots. The cross section profile is displayed for the cross section currently selected in \Edit\Cross Sections\Cross Section Data. To view different cross sections, return to the ..\Cross Section Data tab and select the desired cross section, then return to the ..\Coordinate Data tab. Combined plots of velocities, water surface elevations and bed geometry can be obtained using \Reports\Graphs\Bed Profile with WSL\Velocities and checking the Observed WSL and Observed Velocity boxes. You may wish to toggle on or off various calibration discharges for clarity.

  Step 5. Quality Assurance

  As noted earlier, a longitudinal plot of the observed water surface elevations can be obtained using \Reports\Graphs\Longitudinal Profile and checking the Observed WSL box. Cross section geometry plots can be obtained by selecting \Reports\Graphs\Bed Profile with WSL\Velocities and checking the Observed WSL and Observed Velocity boxes.

  First, look at the longitudinal profile using \Reports\Graphs\Longitudinal Profile, and then the cross section profiles for each transect using \Reports\Graphs\Bed Profile with WSL\Velocities. In the cross section profile plots, select the cross section and discharge to be viewed in the tables to the left of the plot and click Refresh. Examining the longitudinal profile of the water surface elevations and thalweg depths in conjunction with the cross section profiles for these data should indicate cross section 0.0 is a riffle (or channel control) and that cross section 201 is in a pool. This is shown by the increased depths at cross section 201 (see longitudinal profile) as well as the more parabolic shape of the cross section profile at station 201.

  Note in Table L2-1, the velocity values at verticals from 1.0 to 4.0 and vertical 44 have been left blank, since these verticals were out of the water at each of the calibration discharges.

  In general it is a good idea to examine the longitudinal and cross section plots and note any areas that appear unusual. Are there any characteristics of this data set that merit further attention? Hint: look at the three velocity profiles for cross section 201. Look carefully at the shape of the velocity profiles and at the stream margins. Do you see anything that does not make sense? Are the longitudinal water surface profiles (look at longitudinal plot) consistent? If there are any questions, you can refer to the original field notes, consult with the crew members or look for other means (assistance of a hydraulic engineer or hydrologist, for example) to resolve inconsistencies.

  Table L2-1. Data for cross section 0.0.
  
  Cross Section	0					
  SZF	90.6					
  Upstream Weight	Left Wt	0.5	Right Wt	0.5		
  Reach Length	Left Dist	0.0	Right Dist	0.0		
  Slope	0.004		
  Manning's n	0.03					
  Beta	0.2
  
  Calibration Data						
  	LeftWSL   RightWSL  WSL   BestEstQ  Xsec Q		
  		0.0		0.0		91.9    75.2    55.2		
  		0.0		0.0		92.18	139		124		
  		0.0		0.0		92.67	250		240		
  
  	  
  X     Y    Z      Ci  N  VelSet1 VelSet2 VelSet3	  
  2   	0	94.8	6	0			
  4   	0	94	    6	0			
  6   	0	93	    6	0			
  8   	0	92.7	6	0			
  10	0	91.9	6	0	0.00	0.00	0.90
  12	0	91.3	6	0	0.10	1.30	1.50
  14	0	91	    6	0	0.50	1.50	2.40
  16	0	91.1	6	0	0.50	1.70	1.80
  18	0	91	    6	0	0.2	    1.40	2.00
  20	0	91.1	6	0	0.00	0.30	1.00
  22	0	91.3	5	0	0.00	0.30	0.80
  24	0	91.7	5	0	0.00	0.30	0.50
  26	0	92	    6	0	0.00	0.50	1.30
  28	0	91.8	6	0	0.00	0.90	0.60
  30	0	91.8	6	0	0.00	1.30	1.80
  32	0	92.1	6	0	0.00	1.00	1.20
  34	0	91.8	6	0	0.50	1.80	2.30
  36	0	91.5	6	0	0.60	1.60	2.20
  38	0	91.5	6	0	0.60	1.60	2.60
  40	0	91.5	6	0	0.90	1.30	2.00
  42	0	91.5	6	0	0.60	1.40	2.40
  44	0	91.5	6	0	1.10	1.10	2.00
  46	0	91.3	6	0	0.60	1.40	2.80
  48	0	91.4	6	0	0.60	1.80	2.40
  50	0	91.2	6	0	1.00	2.30	2.60
  52	0	91.3	6	0	1.20	2.50	2.90
  54	0	91.4	6	0	1.60	2.40	3.20
  56	0	91.4	6	0	1.50	2.60	2.80
  58	0	91.2	6	0	1.70	2.60	3.10
  60	0	91.2	6	0	1.90	1.80	3.40
  62	0	91.1	6	0	1.90	2.60	3.20
  64	0	91	    6.3	0	1.60	2.30	3.10
  66	0	91	    6.3	0	1.70	2.40	2.90
  68	0	91	    6	0	1.50	2.90	3.20
  70	0	90.8	6	0	2.00	2.20	3.00
  72	0	90.7	6	0	1.50	2.50	3.00
  74	0	90.8	6	0	1.90	2.50	3.10
  76	0	90.6	6	0	2.00	2.60	3.00
  78	0	90.8	6	0	1.70	2.30	2.80
  80	0	90.9	6	0	1.50	2.00	2.00
  82	0	90.9	6	0	1.50	1.70	0.60
  83.5	0	92.64	6	0	1.00	1.70	1.10
  86	0	92.8	6	0	0.00	0.80	0.00
  88	0	94.8	6	0			
  
  	  

  Table L2-2. Data for cross section 60.0.
  
  Cross Section	60					
  SZF	90.6					
  Upstream Weight	Left Wt	0.5	Right Wt	0.5		
  Reach Length	Left Dist	60.0	Right Dist	60.0		
  Slope	0.0032		
  Manning's n	0.03					
  Beta	0.2					
  			
  Calibration Data						
  	  LeftWSL  RightWSL  WSL  BestEstQ  Xsec Q		
  		0.0		0.0		92.08   75.2    61.4		
  		0.0		0.0		92.42	139		129		
  		0.0		0.0		92.95	250		265	
  								  
  X     Y    Z      Ci  N  VelSet1 VelSet2 VelSet3	  
    6	60	94.6	4	0			
  12.3  60	92.9	4	0			
  14	60	92.5	4	0			0.00
  16	60	92.1	4	0	0.40	0.00	0.50
  18	60	91.8	4	0	0.80	0.60	1.00
  20	60	91.5	4	0	0.40	0.80	1.00
  22	60	91.5	4	0	0.30	0.70	0.90
  24	60	91.5	6	0	0.10	0.70	1.20
  26	60	91.8	6	0	0.90	0.70	1.80
  28	60	92	    6	0	0.00	1.50	1.80
  30	60	92.2	6	0	0.30	1.00	2.00
  32	60	92.1	6	0	0.00	0.90	1.80
  34	60	92	    6	0	0.70	0.50	1.60
  36	60	91.9	6	0	0.60	1.80	2.50
  38	60	91.6	6	0	0.80	1.80	2.30
  40	60	91.6	6	0	0.60	1.30	2.20
  42	60	91.6	6	0	0.80	1.20	2.40
  44	60	91.4	6	0	0.50	1.60	2.20
  46	60	91.4	6	0	1.20	1.80	2.40
  48	60	91.5	6	0	0.70	1.70	2.50
  50	60	91.6	6	0	1.30	1.70	2.70
  52	60	91.4	6	0	1.80	1.70	2.60
  54	60	91.4	6	0	1.60	2.20	3.10
  56	60	91.3	7	0	0.70	2.40	2.70
  58	60	91.1	6	0	1.90	2.00	3.10
  60	60	91	    6	0	1.60	2.10	2.80
  62	60	90.7	6	0	1.40	1.70	3.20
  64	60	90.8	6	0	1.90	2.40	2.90
  66	60	90.6	6	0	1.90	2.30	3.20
  68	60	90.7	6	0	1.90	2.50	3.10
  70	60	90.9	6	0	1.70	2.40	3.10
  72	60	90.8	6	0	1.70	2.30	3.00
  74	60	90.9	6	0	1.80	2.40	3.10
  76	60	91.1	6	0	1.80	2.50	2.60
  78	60	91.3	6	0	1.50	1.80	3.00
  80	60	91	    6	0	0.00	2.00	3.10
  82	60	91.2	6	0	0.00	1.90	2.60
  84	60	91.2	7	0	0.00	0.30	0.00
  86	60	91.1	7	0	1.50	0.00	0.00
  88	60	93	    7	0	1.00	0.15	2.00
  90	60	94.4	6	0			0.60
  	  

  Table L2-3. Data for cross section 135.0.
  
  Cross Section	135					
  SZF	90.6					
  Upstream Weight	Left Wt	0.5	Right Wt	0.5		
  Reach Length	Left Dist	75	Right Dist	75		
  Slope	0.023		
  Manning's n	0.03					
  Beta	0.2
  
  Calibration Data						
    Left WSL Right WSL  WSL   BestEstQ Xsec Q		
  	  0.0  	    0.0	    92.25   75.2   86.7		
  	  0.0	    0.0	    92.59	 139	137		
  	  0.0	    0.0	    92.97	 250	252
  	  
  X     Y    Z      Ci  N  VelSet1 VelSet2 VelSet3
   6	135	94.3	4	0			
  10	135	93	    4	0			
  12	135	92.8	2	0       			0.00
  14	135	92.5	3	0	        0.00	0.00
  16	135	92.4	3	0	0.40	0.00	0.00
  18	135	92.3	3	0	0.80	0.50	0.60
  20	135	92.1	6	0	0.40	0.70	0.00
  22	135	91.6	6	0	0.20	0.90	1.70
  24	135	91.5	6	0	0.60	1.30	1.30
  26	135	91.5	6	0	1.10	0.70	1.70
  28	135	91.1	6	0	1.30	1.60	2.60
  30	135	91	    6	0	0.90	1.70	1.80
  32	135	91.1	6	0	1.30	1.20	2.70
  34	135	90.8	6	0	1.70	1.40	2.60
  36	135	91.1	6	0	1.70	2.30	2.90
  38	135	90.8	6	0	1.60	1.30	3.20
  40	135	90.6	6	0	2.10	2.30	3.30
  42	135	90.5	6	0	1.80	3.00	3.00
  44	135	90.7	6	0	1.50	1.80	3.40
  46	135	90.7	6	0	1.90	2.20	3.30
  48	135	90.8	6	0	1.60	2.70	2.80
  50	135	90.7	6	0	2.00	2.30	3.00
  52	135	90.9	6	0	1.60	2.00	2.90
  54	135	91	    6	0	1.90	2.30	3.10
  56	135	90.9	6	0	1.60	2.00	2.50
  58	135	91.2	6	0	1.60	1.40	2.90
  60	135	91.3	6	0	1.60	2.00	2.70
  62	135	91.3	6	0	1.30	1.70	2.20
  64	135	91.4	6	0	1.30	1.50	2.20
  66	135	91.6	6	0	1.00	1.40	2.40
  68	135	91.6	6	0	1.10	0.80	2.00
  70	135	91.6	6	0	0.30	0.80	2.10
  72	135	91.6	6	0	0.00	0.60	0.90
  74	135	92.3	6	0	1.80	0.30	0.00
  	  
  	  

  Table L2-4. Data for cross section 201.0.
  
  Cross Section	201					
  SZF	90.6					
  Upstream Weight	Left Wt	0.5	Right Wt	0.5
  Reach Length	Left Dist	66	Right Dist	66		
  Slope	0.023		
  Manning's n	0.03				
  Beta	0.2					
  
  Calibration Data						
    LeftWSL   RightWSL  WSL   BestEstQ Xsec Q		
  	  0.0	    0.0 	92.36	75.2	80.4		
  	  0.0	    0.0	    92.74	139	    99		
  	  0.0	    0.0	    93.1	250	    249
  	
  X     Y    Z      Ci  N  VelSet1 VelSet2 VelSet3
  
   4	201	93.9	6	0			
   6	201	93.1	6	0			0.00
   8	201	92.8	6	0			0.00
  10	201	92	    6	0	0.00	0.00	0.70
  12	201	91.6	6	0	0.30	0.00	1.00
  14	201	91.5	6	0	0.40	0.30	1.20
  16	201	91.2	6	0	0.50	0.40	1.40
  18	201	91.2	6	0	0.50	0.50	2.20
  20	201	91	    6	0	0.60	0.60	2.50
  22	201	90.8	6	0	0.70	0.80	2.50
  24	201	90.5	6	0	0.80	0.90	2.80
  26	201	90.3	6	0	0.90	1.50	2.80
  28	201	90.2	6	0	1.10	1.50	2.90
  30	201	90.1	6	0	1.20	1.90	3.10
  32	201	89.9	6	0	1.50	2.30	3.40
  34	201	89.8	6	0	1.60	2.40	3.30
  36	201	89.9	6	0	1.90	1.80	3.30
  38	201	89.9	6	0	1.90	1.60	3.00
  40	201	90.3	6	0	1.50	1.00	2.70
  42	201	90.4	6	0	1.30	0.90	2.40
  44	201	90.7	6	0	1.80	0.70	2.00
  46	201	91.3	6	0	1.40	0.70	1.80
  48	201	91.6	6	0	1.10	0.40	1.80
  50	201	91.9	6	0	0.60	0.20	1.30
  52	201	92.3	6	0	0.40	0.00	1.40
  54	201	92.7	6	0	1.60	0.00	0.80
  56	201	92.7	6	0	1.60	0.00	0.80
  58	201	93	    6	0	1.30	1.70	0.00
  60	201	93.1	6	0	1.30	1.50	0.00
  61	201	93.1	6	0	1.00	1.40	0.00
  66	201	94.1	7	0	1.10	0.80	2.00
  68	201	96	    7	0	0.30	0.80	2.10
  

  TOP OF PAGE

  Laboratory 3. Water Surface Modeling Using A Stage-Discharge Approach

  Objective

  The objective of this laboratory is to demonstrate modeling water surface elevations based on a stage-discharge regression approach. The reader will be introduced to the use of the STGQ program within PHABSIM for this purpose. The general theory of stage-discharge modeling using a regression approach is covered in the manual in Chapter 3.

  Program Used: STGQ

  Project File Used: C:\My Documents\Phabsim\Laboratories\Lab3.phb

  Introduction

  The purpose of this laboratory is to introduce stage-discharge regression modeling in PHABSIM using the STGQ model. Recall from the lecture material that under most circumstances an investigator will obtain measured water surface elevations at a specific cross section at three or more flows, which is illustrated in Figure L3-1 for cross section 0.0 for the Fryingpan River (see Laboratory 1 or access \Models\WSL\STGQ Options\Stage Discharge Graph in the Lab3 project).

  

  Figure L3-1. A stage-discharge relationship.

  As discussed in Chapter 3, the relationship between stage (i.e. water surface elevation) and discharge can often be represented at a cross section in a channel by the following equation:

  (WSL - SZF) = a Qb

  (L3-1)

  where:	Q = discharge
  	WSL = stage or water surface elevation
  	SZF = stage of zero flow
  	a = constant derived from measured values of discharge and stage
  	b = coefficient derived from measured values of discharge and stage

  Note that the SZF is included in Equation L3-1 since the stage-discharge relationship at a channel cross section is a function of the SZF at that specific location as discussed in Chapter 3. The SZF is used within the STGQ program and should be included whenever using alternative stage-discharge regressions. Equation L3-1 can be transformed to a linear relationship between stage and discharge by taking the log₁₀ of the equation, which yields:

  log10 (WSL - SZF) = log10(a) + b * log10 (Q)

  (L3-2)

  Given at least three sets of measured stage-discharge data at a cross section, a simple linear regression can then be performed using Equation L3-2 to determine the constant and coefficient and the resulting regression equation can be used to predict stage over a desired range of discharges. The effectiveness of this modeling approach for the simulation of water surface elevations is not only a function of the observed data, but also the channel geometry and relative difference in the slopes of the regression lines between adjacent cross sections (see Chapter 3 of the manual).

  In regression-based modeling, the primary modeling choices involve the selection of the appropriate calibration discharges (i.e., best estimate of discharge versus cross section specific [or "local"] discharges), determination of an appropriate SZF, and selection of the calibration water surface elevations. In this laboratory, the best estimate of the discharge and average water surface elevations will be used in the regressions. The SZF has also been determined based on the thalweg bed elevations at each cross section following the procedure outlined in Chapter 3 of the Manual.

  Figure L3-2 contains the log of the water surface elevations (minus SZF) versus the log of the discharges (best estimate) for all four of the cross sections for the Fryingpan River. This figure is provided to assist in an understanding of the laboratory data and in the interpretation of the laboratory results.

  Now proceed through the laboratory steps in the given order.

  

  Figure L3-2. Stage-discharge relationship for four cross sections.

  Step 1. Selection and Setup of STGQ Water Surface Simulation Model

  The complete project data set for the Fryingpan River is supplied with the PHABSIM distribution disks and is named SAMPLE1.phb.

  Begin by starting PHABSIM and opening the SAMPLE1 project. Select \Models\WSL. The Water Surface Elevation Simulation window opens and the Output Options tab is displayed by default. In this window the user can select which of the discharges supplied earlier are to be used at the current stage of the simulation process. For example, while calibrating the hydraulic models, it is suggested to use only the calibration discharges. Thus, the check boxes in the Use column should be toggled so only the "cal" discharges are checked. When doing a final production run, all discharges would be checked. In this lab, we are running a small number of discharges, so leave this set at Use All.

  In this window, you may also choose to overwrite the ZOUT (results output) files. If you chose not to overwrite ZOUT, successive runs of the models in PHABSIM append their results to ZOUT. This can result in a very large file, but may be necessary when working on a particularly difficult simulation. You may select Overwrite ZOUT Filefor this lab by clicking on the box or the Overwrite ZOUT File text so a check mark appears.

  Next, click on the STGQ Options tab. Examine the options (see Chapter 3) and make sure that you understand which options are being used. In particular, note the Discharge (IOC Option 5) has been set to "Best Est Q" for all calibration sets for all transects. This instructs STGQ to use the first "best-estimate" discharge in the stage-discharge regressions. Setting the items in the Discharge column to Xsec Q will use the discharge measured at that cross section in the stage-discharge regression. This is not necessarily equivalent to the best estimated discharge for the reach at that calibration flow, but may provide a better fit to the observed water surface elevation for individual cross sections under some conditions.

  Also note that the project has seven simulation flows ranging from 15.0 to 1250.0 cfs, which represent a range of discharges both lower and higher than the three calibration, flows of 75.2, 139.0, and 250.0 (see Laboratory 1). The higher and lower discharges allow an evaluation of model performance over a simulated range of discharges that is needed for the final habitat-discharge relation.

  Step 2. Obtain the Calibration Water Surface Elevation and Discharge Data

  Select \Edit\Cross Sections\Calibration Data to find the calibration data sets for the first cross section (i.e., cross section 0.0) and note the three calibration flows and their observed water surface elevations.
  
  The three calibration flows (best estimate of discharge as well as the actual measured discharge at this cross section for each calibration set) and the corresponding water surface elevations from the CAL lines are:

  Cross section 0.0	Best estimated Q	Measured Q	Water Surface Elevation
  CAL1	75.2	55.2	91.90
  CAL2	139.0	124.0	92.18
  CAL3	250.0	240.0	92.67

  Find and record the water surface elevations, discharges, and SZF for all cross sections in Table L3-1 by first clicking on the Cross Section Data tab, and on the next desired cross section, then the Calibration Data tab. Once you have recorded the data in Table L3-1, choose cancel and return to the Models\WSL\STGQ Options tab.

  Table L3-1. Calibration information for the Fryingpan River.
  Cross section	Best estimated Q	Measured Q	Water surface elevation
  0.0 (SZF = 90.6)	75.2	55.2	91.90
  	139.0	124.0	92.18
  	250.0	240.0	92.67
  60.0 (SZF = ____)	75.2
  	139.0
  	250.0
  135.0 (SZF = ____)	75.2
  	139.0
  	250.0
  201.0 (SZF = ____)	75.2
  	139.0
  	250.0

  In this example, the best estimate of the discharge was determined from an examination of the measured discharges at each cross section. In some applications, the best estimate of the discharge could have been derived from a gage within the reach or from the average of a selected number of the measured transects where conditions for obtaining good flow estimates was possible.

  Step 3. Examination of the Stage-Discharge Relationships

  The summary data in Table L3-1 was used to create a plot of the observed longitudinal water surface elevations versus discharge for the calibration data and a plot of the log of the discharge versus the log of the (WSL-SZF) (see Figures L3-1 and L3-2).

  

  Figure L3-3. Observed water surface profiles.

  First, it should be apparent from the plot of the longitudinal profile of the calibration data (Figure L3-3) that at the high calibration flow, a flattening of the water surface elevation is apparent at the middle two cross sections. This may be indicative of a backwater effect at this discharge. Although backwater effects can be pronounced more often at low flows due to riffle type habitats, channel constrictions can produce this effect at higher discharges. We do not know (since we did not collect this data) what is actually occurring.

  Examining the plot of the log-log relationship between WSL-SZF and discharge shows that the observed data for cross sections 60 and 135 have almost identical WSL values at the high calibration discharge (see Figure L3-2). This should indicate that using a regression approach (i.e., stage-discharge with STGQ may be problematic at high simulated discharges since the regression lines will likely >cross over= each other. This will be explored in more detail in this laboratory.

  Step 4. Running the Stage-Discharge Regression

  Running the STGQ model to perform stage-discharge regression modeling is basically an automated process once the appropriate data have been entered and model options have been selected.

  Select \Models\WSL\STGQ Options and ensure that the SZF box is checked for each cal set for each transect (the default). In rare instances removing the check mark can be used to set the SZF used in the calculations to zero. You will not encounter such a situation in this class. Click the Write Computational Details check box so the program produces a file called ZOUT containing the computational results. Once you have experience with PHABSIM, this file can be omitted during the calibration process. It is often a good idea to turn on this option when doing production runs in case an "at the time" record is needed for documenting or defending the study.

  Next click the Assign Cal Sets button. Select each transect using the dialog box in the upper left and ensure that there is a check for each cal set for each applicable discharge. Selecting All On means that the WSL for all discharges will be simulated using all cal sets in the regression model. Under various circumstances of data quality or channel configuration it may be desirable to use only a portion of the available cal sets for a given discharge at a particular cross section. Note: you may have more than three Cal sets, but only certain ones may apply to specific cross sections. That selection is made in the Assign Cal Sets table.

  In PHABSIM for Windows it is possible to use different water surface elevation models for different transects at different discharges. Therefore, you must specify which model is being used for each transect/discharge combination. Clicking the Method tab and selecting a method from the list on the right and clicking the appropriate position in the cross section discharge table accomplish this. For this laboratory exercise, click STGQ and then click Set All. This tells PHABSIM for Windows that the STGQ model will be applied to all combinations.

  Now you are ready to run the STGQ program. Simply click the Run button at the bottom right. When the model has finished running a "WSL Simulation Completed" message will be displayed. To view the results, click OK and then click the Results tab.

  In the Results tab window you will see a table of water surface elevations for each transect - discharge combination. Plots of the water surface elevation results can be viewed by clicking either the Cross Section or Longitudinal buttons at the bottom.

  Step 5. Evaluation of the Stage-Discharge Model Results

  At this point, we are interested in determining how well the regression approach is working as a model for use in simulations of water surface elevations. Figure L3-4 contains simulated water surface profiles derived from the stage-discharge relations for the four cross sections.
  

  

  Figure L3-4. Water surface profiles simulated with STGQ.

  Click the Longitudinal button to view a plot of the water surface profiles for each discharge as simulated by STGQ. Remove checks from the Thalweg and Observed WSL boxes to arrive at Figure L3-4. The top line in this graph (i.e., labeled SIM.(1250.0)) represents the predicted water surface elevation at a discharge of 1,250 cfs. The predicted water surface elevations at each cross section are derived from each cross section's regression equation based on the three sets of calibration data. At this discharge, water appears to be flowing downhill from right to left in this figure. Note that at 1,250 and 625 cfs, water is >flowing uphill= from cross section 135 to 60. These results are irrational from a physical standpoint and indicate that the regression models are not appropriate at higher discharges for this data set. In reviewing the simulation results for 1250.0 cfs, it should be apparent that the >water flowing uphill= between cross section 135 and 60 is >worse= than that observed at 625 cfs. This suggests that the further you extrapolate above the highest observed discharge (250 cfs) the more error in estimated water surface elevation you will have.

  
  At this point, we only know that somewhere between 250 and 625 cfs, the stage-discharge regression approach >breaks down=. If we wanted to better define where the model no longer works properly, we could add additional QARD flows to our data set, such as 275, 300, 325, etc., up to 625 and rerun the STGQ model. Examination of the output would show the specific flow range at which water begins to 'run uphill'.

  Based on our examination of the plotted longitudinal profiles and the previous examination of the observed calibration data we can more easily understand how these irrational results can be generated by the regression modeling approach.

  The STGQ program performs the regression analysis at each cross section independently. Although the r² for the regressions at each cross section are > 0.99, the difference in slope for each regression equation results in predicted water surface elevations which cross at simulated discharges just above the highest calibration flow. This should be expected given the observed relationships between discharge and water surface elevations shown in Figure L3-2, where the observed water surface elevations at cross sections 60.0 and 135.0 are very close and tend to >converge= over the range of observed discharges.

  The modeling results would indicate that the stage-discharge modeling approach may be valid at simulated discharges up to our highest measured data (i.e., 250 cfs) but that an alternative modeling approach for higher simulated flows will be needed. In Laboratory 4, the MANSQ model will be used, while Laboratory 5 will employ the WSP model to deal with this phenomena.
  

  Step 6. Explore STGQ Regression Modeling Options

  This section of the laboratory is optional and intended to be completed at your convenience.

  As indicated previously in the laboratory, the user can select which of the cal set discharges to use in the regression modeling with STGQ. In the previous laboratory steps, the stage-discharge regressions were conducted using the best estimate of the discharge by setting the Discharge (IOC 5) column to 'Best EST Q' for all cross sections and cal sets. This forced STGQ to use the best estimate of the discharge in the regression computations. In this step of the laboratory, we will set these values to "Xsec Q" so that the regressions are performed using the calculated discharges at each cross section at each calibration flow.

  If you are not in the \Models\WSL window, move there now. Click the STGQ Options tab and click on the first entry "Best EST Q". Next, click on the small wedge arrow to the right of the cell and then click "Xsec Q". Repeat this for all cal sets for all transects.
  
  To ensure the PHABSIM for Windows interface recognized the change, go to the Methods tab and then click STGQ and click any one of the transect - discharge cells to ensure the Apply button becomes active. Then click the Apply button and view results as before.

  What you should find is that the 'error' values in the regression equations have remained the same or increased and that regression modeling of these data with discharges measured at each cross section instead of a best estimate of discharge does not eliminate the irrational results of simulated water surface elevations at flows higher than our high flow calibration data set. Using the computed discharges for each cross section can, and often will, result in poorer linear relationships using Equation L3-2. This type of variability between cross sections using computed discharges is not atypical when field data has been collected in a variety of fisheries habitats which are poor in terms of obtaining a >best estimate= of the discharge for hydraulic modeling.

  As a final wrap-up to this laboratory, go to the STGQ tab and reset all of the discharges to Best EST Q. Then go to the Methods tab, ensure that STGQ is marked and click Select All. Click Run, go to results, and view the longitudinal plot. Zoom on the calibration discharges (hold Shift and drag a box with the mouse and release the mouse button) and print the plot for later reference.

  TOP OF PAGE

  Laboratory 4. Water Surface Modeling Using the MANSQ Model

  Objective

  The objective of this laboratory is to demonstrate the technique of modeling water surface elevations based on using Manning's equation (i.e., the MANSQ model). The general theory for the MANSQ program is covered in the manual within Chapter 2.

  Programs Used: MANSQ

  Project Files Used: Lab4.phb

  Introduction

  The MANSQ model can be used to simulate the stage?discharge relationship for individual cross sections. The model assumes that flow variations caused by changes in channel configuration are negligible (i.e., minimal backwater effects). The application of the MANSQ model in pools can be problematic since pools are generally created by backwater effects of a downstream hydraulic control. The MANSQ model assumes that each cross section is independent of all other cross sections during calibration and simulations. Therefore, the longitudinal profile of the simulated water surface elevations should always be checked to assess overall model performance.

  At a computational level, the MANSQ model uses Manning's equation in the form:

  (L4-1)

  which is simplified to:

  Q = KAR 2/3

  (L4-2)

  The value of K is determined from a single measured discharge-water surface elevation data set and the measured channel geometry at a cross section. The program then uses additional calibration data sets (i.e. discharges and water surface elevations) to solve one of the following two equations selected by the user:

  		(L4-3)
  		(L4-4)
  where:	subscript 'o' refers to calibration values
  	b is a coefficient supplied by the user for each cross section

  Calibration of the model is accomplished by selecting an initial calibration discharge to compute K_o, and then employing a trial and error procedure for selecting a value of b that minimizes the error between observed and predicted water surface elevations for the remaining calibration data sets. Typical values of b range from 0.0 to 0.6 in most channels and as noted in Chapter 2. The steps in this laboratory represent a suggested order for MANSQ analysis.

  Step 1. Obtain an Initial Estimate of b

  Begin by initially setting that the b value for each transect in \Edit\Cross Sections\Cross Section Data to 0.2. This is an arbitrary default value derived from taking the median value for a large number of study sites. Final b values will be determined by observing the results of simulating water surface elevations with MANSQ.

  In this step, the CALCF4 program will be used to obtain an initial estimate of b. Run the CALCF4 program by clicking \Models\CALCF4. The results will be automatically displayed to the screen. Scroll down the file and locate the conveyance factor (CFAC) regression equation for cross section 0.0. Alternatively, use the Notepad editor to search for "CFAC" in the current ZOUTx file.

  The exponent of the CFAC regression equation represents an excellent initial estimate for b and is -0.003 for cross section 0.0. Continue through the output listing to locate and record the CFAC regression exponents at the three remaining cross sections. Record these values in Table L4-1.

  Note that the CFAC regression exponent at cross section 0.0 is negative. Under most circumstances, the use of negative b values is not expected since this would imply that roughness would be increasing with discharge. In typical applications of MANSQ, a negative b would be rounded up to 0.0 for use in the model.

  Table L4-1. CFAC regression exponents for each cross section.
  Cross section	CFAC exponent
  0.0	-0.003
  60.0
  139.0
  201.0

  Once the remaining CFAC exponents have been entered in Table L4-1, exit Notepad if you have been using it to find the CFAC exponents and return to \Models\WSL\MANSQ in PHABSIM for Windows.

  The MANSQ program requires a calibration flow and water surface elevation at each cross section in addition to the initial estimate of b. These data are derived from the calibration data sets entered in \Edit\Cross Sections\Calibration Data for each cross section. For this laboratory, the high flow calibration data at each cross section will be used as our initial calibration flow for MANSQ.
  

  Table L4-2. Calibration discharges and water surface elevations for the Fryingpan River from MANSQ using 250 cfs (Cal Set 3) as the calibration discharge.
  Calibration Q	Cross section 0	Cross section 60	Cross section 135	Cross section 201
  75.2	91.90	92.08	92.25	92.36
  139	92.18	92.42	92.59	92.74
  250	92.67	95.95	92.97	93.10

  NOTE: You may choose either the high, medium or low flow calibration data sets (or any combination for specific cross sections). However, selection of the calibration discharge should be considered of the flow ranges most critical to the study. Remember, MANSQ will 'return' the observed water surface elevation at the calibration flow and the 'error' between predicted and observed water surface elevations at the other calibration discharges will be a function of the field data and selection of appropriate b's. We will select b's to minimize the error between observed and predicted WSL at each transect.

  Step 2. Running the MANSQ Model and Evaluating Results

  Select the \Models\WSL\MANSQ tab and note the options available in the MANSQ program and review the options that have be set. For this laboratory exercise, the default options will suffice. However, advanced users may wish to consider the alternative ratios of flow conditions given in equations L4-3 and L4-4, and other MANSQ options.

  Next, click on the Methods tab and click MANSQ followed by Set All. This assigns MANSQ as the model to be applied to all cross sections at all discharges. Now click Run.

  Since we have chosen the high calibration flow (i.e., 250 cfs) MANSQ will always return the observed water surface elevations for this flow at each cross section. We need to evaluate the predicted water surface elevation at each cross section for the medium (139 cfs) and low (75.2) calibration flows.

  The Results tab contains a table of predicted water surface at each of the simulated discharges for each cross section. Click the Print button to obtain a copy of this table for later use. Click the Longitudinal button to view a plot of the longitudinal profile for all discharges. Click the check boxes for Observed WSL and Simulated WSL. Note the wild divergence of the WSLs at transects 135 and 201. The steep water surface elevation at high flows is unrealistic for a pool. In addition, the water surface elevation at the lowest discharges runs uphill. Our initial b values are not working too well.

  Compare the predicted water surface elevations at 139 cfs and 75.2 cfs for each cross section against the observed water surface elevations for these calibration flows. It is apparent that an initial estimate of b of 0.2 results in a prediction of the water surface elevations at cross sections 0 and 60 that are too low, while this same b results in a prediction of water surface elevations at cross sections 135 and 201 which are too high at the high discharges and too low at the low discharges.

  This means that b coefficients at all cross sections need to be adjusted in order to obtain better agreement between observed and predicted water surface elevations.

  Table L4-3. MANSQ calibration table.
  
  X-Sec 0		Obs-WSL		ß:0.20	ß:0.02	ß:	ß:	ß:	ß:	ß:0.00
  250 cfs		92.67		92.43
  139 cfs		92.18		92.15
  75.2 cfs		91.90		91.90
  
  X-Sec 0		Obs-WSL		ß:0.20	ß:0.02	ß:	ß:	ß:	ß:	ß:0.00
  250 cfs		92.95		92.68
  139 cfs		92.42		92.35
  75.2 cfs		92.08		92.08
  
  X-Sec 0		Obs-WSL		ß:0.20	ß:0.02	ß:	ß:	ß:	ß:	ß:0.32
  250 cfs		92.97		93.12
  139 cfs		92.59		92.66
  75.2 cfs		92.25		92.25
  
  X-Sec 0		Obs-WSL		ß:0.20	ß:0.02	ß:	ß:	ß:	ß:	ß:0.51
  250 cfs		93.1		93.68
  139 cfs		92.74		92.99
  75.2 cfs		92.36		91.36
  

  Step 3. Trial and Error Calibration of MANSQ by Adjusting b at Each Cross Section

  You have now obtained an initial solution of the water surface profile using MANSQ but some adjustment is needed. Return to \Edit\Cross Sections and change the b coefficient from 0.20 to 0.02. Make this same change to the b value at cross sections 60 to 201. Note that these new estimates of b have been entered in Table L4-3.

  Click OK to exit Edit\Cross Sections and save the file changes. Return to \Models\WSL\Methods, check that the MANSQ method is selected, and click Set All again. When the program has finished, click OK and Results as before.
  
  Compare the Results table displayed on the screen to the one you printed earlier. What happened to the predictions for the water surface elevations when we increased or decreased b at the cross sections?

  You should find that increasing b will result in predicted water surface elevations which increase for discharges above the calibration discharge, while decreasing b results in the predicted water surface elevations decreasing. The opposite will be true below the calibration discharge.

  Return to \Edit\Cross Sections and change the b values for each cross section to induce the needed change in WSL at each transect to match the calibration discharges. Record these values in Table L4-3. Remember to use a b value of 0.00 instead of negative values for any cross section. Save these changes and re-run the MANSQ program and record the new predictions for the water surface elevations at each cross section for the medium and low calibration flows in Table L4-3. How close are the predictions of water surface elevations?

  Based on these results, make adjustments to the b values as necessary. Your strategy should be to minimize the error between predicted and observed WSLs at both the 139 cfs and 75.2 cfs calibration flows for each cross section (you cannot get them both to be exact) by selecting the 'best' b for each cross section. Remember, MANSQ treats each cross section independently, so if you get a particular cross section to work, you no longer have to adjust the b value at the cross section while continuing your calibration efforts at other cross sections. You should make several trial runs during the lab in your quest for the best fit; however, due to class time limitations, the final calibration b values are provided in Table L4-3.

  Step 4. MANSQ Final Calibration Run and Hydraulic Diagnostics

  Up to this point we have focused on the calibration discharges and have not dealt with the WSL for the other discharges in the data set. The particular b values entered at the far right in Table L4-3 generally result in a maximum error between observed and predicted water surface elevations at the calibration flows, which range between 0.00 and 0.06 feet. This magnitude of difference is on par with the results obtained from the stage?discharge regression approach covered in Laboratory 3. However, we still need to check the effectiveness of the hydraulic simulations further by looking at the longitudinal profile of the water surface elevations at all simulated discharges.

  View the longitudinal plot in \Models\WSL\Results again. Expand to full screen using the Windows maximize button for the graph window. It is useful to print this graph and label it MANSQ final for later reference.

  The thalweg depths for each cross section are displayed as the bottom line with the x-axis indicating the distance between each cross section moving in an upstream direction. The top line in this graph represents the water surface elevation at a discharge of 1250 cfs. Using the key at the bottom of the plot, the other discharges can be identified by their line and symbol combinations. To aid in viewing simulated water surface profiles only, the Observed WSL check box can be left blank (click to remove check).

  The predicted water surface elevations at each cross section are derived from the MANSQ model based on the calibrated b's. At this discharge, water appears to be flowing downhill for some cross sections and uphill for others.

  Note that at the simulated discharge of 625 cfs, water is 'flowing uphill' between cross sections 3 and 2. Although excellent agreement can be obtained with MANSQ for the calibration data, the simulated water surface elevations at discharges greater than 250 cfs are irrational.
  
  At this point, we know that somewhere between 250 and 625 cfs, the MANSQ model 'breaks down' in a similar fashion to the results obtained using the IFG4 model in Laboratory 3. The reason behind the production of irrational results with MANSQ for this data is basically similar to the reasons discussed in Laboratory 3 using IFG4. In MANSQ, the b value represents the exponent in a power law relationship (see Equations L4-3 and L4-4) that approximately tracks the changes in Manning's n over a range of discharges. Therefore, b acts as the 'slope' factor for the relationship between water surface elevation and discharge. Since the measured water surface elevations at cross sections 60.and 135 are very similar at the high calibration flows (see Table L4-2), the 'best fit' relationship derived from matching the water surface elevations at the two lower calibration flows 'causes' the predicted water surface elevations to 'cross over' at simulated discharges above 250 cfs.

  At this point, an alternative modeling approach for the simulation of discharges greater than our high flow calibration (i.e., 250 cfs) should be considered. Given the nature of these data, modeling options within MANSQ are not likely to improve the simulation results (i.e., use of Equation L4-4 rather than Equation L4-3). Given the results already examined in Laboratory 3 using IFG4, the WSP model would be the next step and is examined in Laboratory 5.

  TOP OF PAGE

  Laboratory 5. Water Surface Modeling Using the WSP Model

  Objective

  The objective of this laboratory is to demonstrate the technique of modeling water surface elevations based on the step-back water method as implemented in the WSP model. We will cover the steps of finding an overall Manning's n value that is a "best fit" for the study site, adjusting n values to capture localized roughness differences at each transect, and specifying roughness modifiers to accommodate the change in n value as a function of discharge. The general theory for the WSP program is covered in the manual in Chapter 3.

  Programs Used: WSP

  Project File Used: Lab5.phb

  Introduction

  The WSP model is a water surface profile program that is used to predict how the longitudinal profile of the water surface elevation changes over a range of simulated discharges. The initial objective in the calibration of the model is to use a trial-and-error procedure to select Manning's n coefficients at each cross section, which will replicate the longitudinal profile of the water surface elevations at this single calibration flow. This requires that the bed geometry elevations and water surface elevations have been measured to a common benchmark or elevation datum (i.e., the cross sections are 'dependent' and connected). We first attempt to find a global value (or overall channel roughness value) for n that is applied at each cross section to produce a "least error fit" of the water surface elevation profile to the observed data for one discharge. We then vary Manning's n for each cross section (within reasonable limits) to achieve a reasonably close fit between observed and predicted water surface elevations. Finally, we use a trial-and-error procedure to select main channel and overbank roughness modifiers that produce the best fit between observed and predicted water surface profiles for all remaining calibration flows. The relationship between the calibrated roughness modifiers and discharge is then used to develop either a regression equation or a good linear approximation, from which we can estimate the appropriate roughness modifiers for all simulation discharges of interest.

  WSP requires a starting water surface elevation or energy slope as an initial condition. We have already found stage-discharge relationships using a regression approach (i.e., STGQ) and by calibrating MANSQ for the downstream cross section. To provide WSP with the needed initial condition, the user selects the combination of starting conditions based on using the water surface elevation derived from STGQ or MANSQ in the \Models\WSL\Methods tab by clicking on ..\WSP\STGQ supplies initial WSL or ..\WSP\MANSQ supplies initial WSL or ..\WSP\User supplies initial WSL. The two combined WSP\XX options take the starting water surface elevation from one of those models and supplies it to WSP. The WSP\User option allows the user to set this value manually. The ..\User supplies WSL (no model run) option allows users to import WSL values for the entire study area and discharge range from an outside source.
  
  In this laboratory, we will select the high flow calibration data as the starting point in the calibration of the WSP model. In particular, we are interested in determining if this modeling approach can overcome the problem with simulated water surface elevations at higher discharges encountered when using a stage-discharge regression (i.e., STGQ in Laboratory 3) or the MANSQ model (Laboratory 4). The laboratory also provides a discussion of the implications of using a different initial calibration flow and resulting impacts to simulated water surface elevations. The given steps represent a suggested order for WSP analysis.

  Step 1. Prepare Data and Select Options to Run the WSP Program

  We begin by setting the same initial Manning's n roughness value for all cross sections. Start PHABSIM for Windows and load Lab5.phb. Select \Models\WSL\WSP Options and note that a Manning's n value of 0.030 has been entered for all cross sections.

  WSP requires that the water surface elevations at the down stream cross section for each discharge are supplied to the model as boundary conditions. For discharges of 75.2, 139, and 250 cfs we know the actual observed water surface elevations at the down stream most cross section (i.e., cross section 0.0). However, the water surface elevations for the remaining four discharges are not known. To resolve this issue, we use STGQ or MANSQ to obtain water surface elevations for the downstream cross section. From Labs 2 and 3 we know that STGQ produces a slightly better fit between observed and simulated water surface elevations at cross section 0. Thus, we will use STGQ as the source of starting water surface elevations.

  Move to \Models\WSL\Methods and first select WSP (click the radio button) followed by Set All. This saves clicking on each element of the table separately. Now select the ..\WSP\STGQ radio button and click in the cross section 0.0 row for each discharge. (Be sure and scroll the table so all cross section 0.0 entries for all cross sections are filled with WSP-S. This sets all initial conditions to use the WSL from STGQ and applies WSP to all cross sections at all discharges.

  We have the measured water surface elevations for the three calibration discharges. Will they be different than those predicted by STGQ? To ensure the best precision in calibrating WSP, it is wise to use the known values as the initial conditions. For the three calibration discharges, select ..\WSP\User supplies initial WSL and click the cross section 0.0 entry for each discharge and enter the starting WSL from the data. You have already entered this data as part of the calibration data sets, but to allow for improved estimates of the starting WSL, you must enter it here also.

  In the \Models\WSL\WSP Options tab, there is a table for entering roughness modifiers (RMODs) for each discharge. The RMODs are used by WSP to adjust the Manning's n values derived in the initial calibration of the longitudinal water surface profiles to account for changes in roughness as a function of discharge. The default value for the RMODs is '1', so initially there is no variation in Manning's n with discharge. These values are modified by the user as needed to obtain a reasonable fit between observed and simulated water surface profiles.

  For this exercise, we will use the high discharge as our reference discharge. This is generally a good practice when using WSP as calibration residual errors tend to compress (get smaller) as one simulates downward using backwater type models. As trial values, set the roughness modifiers for 139 cfs and 75.2 cfs to 1.1 and 1.2, respectively. These are strictly trial values so you can start by leaving them at 1.0 if you wish.
  
  Step 2. Run the WSP Program and Determine the Initial Water Surface Elevation Predictions

  Click the Run button now to run the combined STGQ (at cross section 0.0) and WSP (at all cross sections) model. A message window will indicate when the WSL simulation is completed. Click OK to clear this window.

  Select the \Models\WSL\Results tab or \Reports and click on the longitudinal plot option. Select Observed and Simulated WSL followed by Refresh. Zoom on the three calibration discharges by holding down the Shift key, moving the mouse to the lower left corner of the region you wish to zoom, holding the left mouse button and dragging to the upper right corner of the zoom area. Then release the mouse button and the plot will zoom to that area. Note that \Models\WSL\Results contains a table of water surface elevation information for all cross sections and all discharges. In this case, it has seven entries in each row corresponding to the seven discharges we have directed the model to simulate. Note, for example, that the predicted water surface elevation associated with the 250 cfs calibration flow at cross section 201 is 92.936.

  How do the simulated values compare with the observed values? Note from the plot that at all three calibration discharges the simulated water surface profile falls considerably below the observed profile. An adjustment to Manning's n is needed. The table in the \Models\WSL\Results tab can display the observed, simulated, and difference in water surface elevation at the calibration flows by clicking the Cal Comparison radio button. This is useful to display numerical values for the differences seen in the plot.

  Step 3. Calibrate WSP for the Longitudinal Water Surface Profile at 250 cfs

  For the calibration process it is useful to prepare a table such as Table L5-1 to record successive iterations of the Manning's n adjustment process. The first estimate of the water surface elevation at cross section 60 at 250 cfs recorded in Table L5-1 shows that the predicted WSL is low by 0.185 feet. The calibration strategy will be first to change the Manning's n values at all cross sections simultaneously to get the predicted water surface elevation at all cross sections for our chosen discharge of 250 cfs to fit through the observed values for all cross sections in a reasonable manner. Generally, we would like the simulated values to fit the observed values as closely as possible. We expect some values to be high and some to be low at this stage. Go back to \Models\WSL\WSP Options and raise the Manning's n to a new, higher value for all cross sections (.045 is suggested). Remember, raising n increases roughness will thus raise the simulated water surface profile.

  Return to Models\WSL\WSP Options and make sure the roughness modifier for a discharge of 250 cfs has a value of 1.0. Then click the Run button to run the model. Repeat this process of setting Manning's n, running the model, and viewing results until you have achieved a satisfactory fit between the simulated and observed water surface profile for the 250 cfs discharge.

  Figure L5-1 shows the plot resulting from raising Manning's n to 0.45 at all cross sections. Display this plot by clicking the Longitudinal button in the ..\WSL\Results tab.

  Table L5-1. WSP calibration table for Manning's n.
  X-sec 60	N: 0.030	N: 0.045	N:	N:	N:	N:	N:
  WSL = 92.95	92.74
  Xsec 135
  WSL = 92.97
  X-sec 20
  WSL = 93.10

  

  Figure L5-1. Water surface profiles resulting from Manning's n = 0.045.

  Increasing the Manning's n from 0.030 to 0.045 raised the water surface profile at all cross sections. Note that the elevation for 250 cfs at cross section 60 changed from 92.765 feet to 92.871 feet. Is this close enough? What about the 250 cfs WSL at the other transects? In this case they are higher than the observed values by 0.081 ft. for transect 135 and 0.066 ft. for transect 201. This would appear to satisfy the criteria of using a single n value to get the best fit through the data. However, we have a dilemma. Notice cross section 60 at 250 cfs. This is the only place where there is a pronounced rise in observed WSL above the values being predicted by WSP. Also notice that, at the other calibration flows, the predicted water surface profile lies above that of the calibration data. Examination of the cross section shapes, the thalweg profile, or relative transect location does not reveal a clear reason for the high observed value at cross section 60. The channel index codes in this study are based on bed material size. There are a few CI values of 7, but the predominant value is 6. The predominant value at cross section 0 is also 6. So, while the bed at cross section 60 may be slightly rougher than at cross section 0, there is no compelling reason to increase roughness above that at cross section 0.

  In this particular situation, we may suspect an error in measurement at the high discharge. Following this assumption, we adjust the n values such that the simulated 250 cfs water surface profile closely matches the observed values at the upstream two transects. To accomplish this, reduce the n values in Edit\Cross Sections and rerun WSP until good agreement is reached. As you make those adjustments, record n and WSL in Table L5-1. Agreement will occur near n = 0.041 at all cross sections.

  With global n = 0.041, the WSL is 0.109 ft. low at cross section 60, 0.032 ft. high at 135, and 0.005 ft. low at 201. The 0.109 ft. difference seems large. What kind of error may have occurred when the measurements were made? One possible scenario is that the water surface was recorded 0.1 ft. higher than reality. Let us use that assumption and determine which further local adjustments to n should be made to reach a WSL of 92.85 ft. instead of 92.95 ft.

  Local adjustments to n are best made in pairs stepping upstream. The Manning's n at the first cross section is changed concurrently with the value at cross section 60.0 since the predicted water surface at cross section 60 is dependent on the initial roughness at the down stream cross section as well as at cross section 60. Changing both Manning's n values also reduces the chance of obtaining unrealistic Manning's n values at upstream cross sections during the calibration process. To reach 92.85, we must raise n at the first two cross sections. Try a value of 0.042.

  Go to \Models\WSL\WSP Options and enter 0.042 for the first two transects. Then set the roughness modifiers to 1.0 for 250 cfs, 1.1 for 139 cfs, and 1.2 for 75.2 cfs, if you have not already done so, and click Run. Look at the table and longitudinal plot in ..\Results. Note that while the elevation for 250 cfs at cross section 60 has now reached 92.848, the elevations upstream have increased. To get those values back down to within 0.02 ft. of the observed values will require low n values for cross sections 60 and 135. It is possible to set the n value at cross section 0.0 high enough that even a low n value at cross section 60 will produce an elevation of 92.85. However, there is no evidence in this stream that radical changes in n are justified. Thus, the global value of 0.041 appears to be a reasonable best fit value that causes the simulated water surface profile at the selected discharge (250 cfs) to "bracket" the observed values.
  
  Set the n values back to 0.041 for all cross sections and rerun Now look at the water surface profile (longitudinal) plot. Note that the observed water surface profiles for the three calibration flows appear to arch up in the center and become flatter at cross section 201. This suggests that there is a legitimate increase in roughness between cross sections 135 and 201. Try modifying the n values for those cross sections to obtain a better overall fit for the 250 cfs water surface profile. Be sure to record both the Manning's n values and associated predictions of the water surface elevations in Table L5-1. An approximate rule of thumb is that no more than a 5% - 15% change in n values should occur between transects in an alluvial stream unless there is a topographic or geologic phenomenon to consider. For example, if large car-sized boulders densely filled a short section of stream, large changes in n would be anticipated. That does not appear to be the situation here.

  It is important to avoid varying n values merely for the purpose of obtaining an exact fit of the simulated to observed water surface profile. When n values vary substantially between transects, the reliability of extrapolating to higher or lower discharges may be affected. Generally, n represents the combined roughness of the bed particle size and bed form (dunes, for example) that resists the flow of water. Additional losses, such as expansion or contraction losses, are handled to varying degrees within the WSP model. In some circumstances, adjustments to n may be used to ensure such losses are fully represented.

  Step 4. Calibration of Roughness Modifiers for Remaining Calibration Data

  Now that Manning's n values have been selected to approximately reproduce the water surface profile at the high (250 cfs) calibration flow, the next calibration step involves using a trial-and-error procedure to select RMODs at the remaining calibration flows which most closely reproduce the longitudinal water surface profiles at those discharges. Since WSP treats each simulated discharge independently, calibration of the RMOD for the remaining two calibration flows can occur at the same time. The RMODs represent constants that change the magnitude of the Manning's n values at each cross section while simulating discharges. The RMOD for the calibration flow must therefore be 1.0 and the RMODs at other flows will be either higher or lower than 1.0 depending on whether these discharges are higher or lower than the initial calibration flow. Why?

  Recall from Chapter 2 in the manual that roughness or resistance to flow decreases with increasing discharge. Conversely, the roughness should increase as flows are reduced. Since the high calibration flow (i.e., 250 cfs) was used for the initial calibration of the WSP model, the calibrated Manning's n values alone will be too low to correctly predict the water surface elevations at the 139 cfs and 75.2 cfs calibration flows. Therefore, the RMODs at these remaining two calibration flows will need to be greater than 1.0. Think this through and reread Chapter 3 if it is still unclear why. This is why we assigned arbitrary RMODs of 1.1 and 1.2 to the 139 cfs and 75.2 cfs discharges earlier.

  Select \Models\WSL\WSP Options to display the RMOD table. Set the RMOD values for 139 cfs and 75.2 cfs to 1.1 and 1.2, respectively if they are not already so set. Then select ..\Results and display the longitudinal plot. Select both Observed and Simulated water surface elevations and Refresh to display them. It is convenient to drag the plot to the lower right of the screen so you can view both the PHABSIM window and plot window simultaneously. In the plot window, magnify (zoom) the area of water surface profiles for the calibration discharges. Now click the Run button to run the models. Click OK when the program has finished and click the Refresh button in the plot window. Where do the simulated water surface profiles for 75.2 and 139 cfs lie in relation to the observed profiles? Are they high or low? Return to the WSP Options tab.

  Figure L5-2 shows the predicted versus observed longitudinal water surface profiles at the three calibration flows based on our existing RMODs.

  

  Figure L5-2. Water surface profiles with RMODs of 1.0, 1.1, and 1.2.

  This figure illustrates several key factors in the calibration of WSP using RMODs. It should be apparent that the predicted longitudinal profiles for the calibration discharges at 139 cfs and 75.2 cfs 'mimic' the pattern of the water surface profile at the initial calibration flow of 250 cfs. This should be expected since the only effect that the roughness modifiers have in the simulation is to change the magnitude of the Manning's n values and therefore, the relative differences between the individual cross section Manning's n values are retained at the other simulated discharges.

  In Figure L5-2 (or by viewing \Models\WSL\Results\longitudinal) you can see that the simulated water surface profiles for 139 and 75.2 cfs are generally lower than the observed profiles for those discharges. Do not close the graph window, merely click on the PHABSIM window to move back to it. Remembering that increased roughness will raise a backwater curve, enter new values for the roughness modifiers for 139 and 75.2 cfs in the \Models\WSL\WSP Options RMOD table. Click Run to rerun the models, click OK when the simulation is done and click the Refresh button to see the results in the longitudinal profile graph. Continue changing the RMOD values until you achieve the best overall fit at the discharges of 139 and 75.2 cfs. You may record your iterations of this process in Table L5-2.

  It should also be noted that if either the 75.2 cfs or 139 cfs flow was selected as the initial calibration discharge, a close agreement between predicted and observed water surface elevations at the other flows would be achieved with the right RMOD. This would be expected given the similarity in the shape of the longitudinal water surface profiles at both of these discharges. However, neither of these lower calibration flows would be expected to achieve close agreement at all cross sections at the high calibration flow given the difference in the observed longitudinal profile at 250 cfs. This should reinforce the concept that you should carefully consider which initial calibration flow to select, or that you should use multiple calibration flows to see which is best. This determination should be made in light of both model performance and flow ranges of interest in the study.

  Staying within the 5%-15% guideline described earlier, try making final small changes to the n values for all cross sections and to the RMODs to best fit all three water surface profiles from cross section 0 to cross section 201. Observe the diff column in the Cal Comparison table and try to find a set of n values and RMODs that result in not more than a 0.02 ft. difference at all cross sections and discharges. This final step ensures that all observed water surface profile data has been used to achieve the final calibration of WSP over all calibration discharges and over all cross sections. Table L5-3 gives one possible final calibration of n values and RMODs. Other combinations of n and RMOD may give a similar range of WSL calibration errors.

  Table L5-2. WSP RMOD calibration table.
  
  Calibration Q = 75.2		X-Sec - 60.0		X-Sec - 135.0		X-Sec 201.0
  Target WSL					92.08				92.25				92.36
  RMOD: 1.20					92.20				92.23				92.30
  RMOD: 1.			
  RMOD:			
  RMOD:			
  RMOD: 1.28
  Calibration Q = 139.0       X-Sec - 60.0        X-Sec - 135.0       X-Sec 201.0
  Target WSL					92.42				92.59				92.74
  RMOD: 1.10	 				92.51				92.54				92.64
  RMOD: 1.			
  RMOD:			
  RMOD:			
  RMOD: 1.22		
  

  Table L5-3. A possible WSP calibration.
  
  Cross section		n value		Discharge		RMOD
  	0.0	 			0.038			75.2		1.28
  	60.0			0.038			139			1.23
  	135.0			0.043			250			1.00
  	201.0			0.043
  

  Laboratories 3 and 4 demonstrated that neither the stage-discharge or MANSQ models were able to simulate rational (water flowing downhill) profiles at the high discharge range. Let us assume that the current WSP model calibration results are the best that can be achieved and move to the next step in the calibration process.

  Step 5. Estimate the Roughness Modifiers for all Desired Simulation Discharges

  Assuming that our final calibration effort for RMODs listed in Table L5-2 represents the best compromise in matching the predicted and observed water surface profiles at the medium and low calibration discharges, the next step will involve trial-and-error approximation of a linear log-log relation between n and discharge or development of a regression between the log₁₀ of the discharges and log₁₀ of the RMOD values. The resulting regression equation or approximated relation will then be used to estimate the roughness modifiers for all remaining discharges to be simulated in WSP (i.e., 15.0, 30.1, 625.0, and 1250.0). The log regression is easily accomplished with a spreadsheet program.

  Figure L5-3 shows the log-log linear regression results for the relationship between discharge and roughness modifiers obtained using a spreadsheet program. The equation is:

  Log10RMOD = -0.2045*log10Discharge + 0.502

  (5-1)

  This regression equation was used to generate the estimated roughness modifiers listed in Table L5-4 for the remaining simulation flows to be used in the laboratory. Note that the log₁₀ of the discharge must be used in the equation and that the result is the log₁₀ of the roughness modifier. Therefore, the correct RMOD estimate is derived by exponentiating the result from the regression equation as the 'x' in 10^x.

  

  Figure L5-3. Log-log plot of RMOD and discharge.

  Table L5-4. Estimated RMOD values at simulation discharges.
  Simulation discharge	Estimated RMOD
  15.0	1.83
  30.1	1.58
  625.0	0.852
  1,250.0	0.739

  Enter these values in the RMOD table in the WSP Options tab and click the Run button. We now have a water surface profile for each discharge based on the WSP model. The resulting profiles can be viewed using ..\Results\longitudinal. If you have not already done so, include the remaining target discharges in the simulation by moving to ..\Output Options, placing a check in all check boxes, and re-running the simulation.

  The log-log linear RMOD versus discharge relationship can be visually approximated by trial-and-error by plotting that relationship in PHABSIM for Windows. In the WSP Options tab, click the Roughness Modifier Graph button and the log-log radio button. Prior to setting RMOD values for the simulation discharges, the graph will look something like Figure L5-4.

  

  Figure L5-4. Roughness modifier graph.

  This plot shows the initial RMODS of 1.0 (log₁₀ of 1 is 0.0) for all simulation discharges and log₁₀ of 1.2, 1.1, and 1.0 for 75.2 cfs, 139 cfs, and 250 cfs respectively. By displaying this plot and the RMOD table in the ..\WSP Options tab simultaneously, the user can quickly build a linear RMOD vs. discharge relationship visually. While not as precise as the regression approach, this is often an adequate approximation for estimating RMOD values.

  Step 6. Evaluate the Hydraulic Simulations

  In order to check the effectiveness of the hydraulic simulations, we examine the longitudinal profile and calibration error of the water surface elevations for all our simulated data. In particular, the performance of WSP at the high-simulated discharges is of interest, since neither STGQ nor MANSQ were able to produce rational results above our high calibration flow of 250 cfs.

  Zoom in on the water surface profiles for 625 cfs and 1250 cfs in ..\Results\Longitudinal. Compared to the STGQ and MANSQ results these profiles show water running downhill at the high discharges. The WSP model produces rational results for the high-simulated flows. This would suggest that the WSP model could be used for simulations above the highest calibration flow (i.e., above 250 cfs).
  
  Now zoom in on the water surface profiles for 15 cfs and 30 cfs. Do these results also look rational? It does appear that a weak pool is produced by backwater from cross sections 0.0 and 60. Neither of those sections shows clear evidence of being a strong control. More likely, control is the result of the overall resistance of the channel between those two sections. This condition is often referred to as channel control and helps explain the observed and simulated water surface profiles seen here.

  You may compare the water surface profiles developed using WSP and STGQ by starting another copy of PHABSIM and loading the lab03 SAMPLE data set. Longitudinal plots for both data sets can be displayed on the screen at once by sizing windows appropriately. Do not try to load two copies of the same project.

  Based on these results, the WSP simulated water surface elevations will be used for the subsequent steps in the laboratory exercises.

  A final note: We ignored the water surface elevation at cross section 60 for 250 cfs and assumed it was a measurement error. What if it was not a measurement error? What would need to be done differently in this WSP calibration to achieve the "best" simulation? Specifically, could we stay within the 5%-15% change in 'n' guideline? Could the maximum water surface simulation error be held to + 0.02 ft.? How would the RMODs change?

  To explore these questions you can make a copy of the project at the present stage using \File\Save As and re-calibrate assuming that the cross section 60 value is correct.

  TOP OF PAGE

  Laboratory 6. Velocity Modeling - VELSIM

  Objectives

  The objectives of this laboratory are to explore various methods for velocity modeling within PHABSIM using the VELSIM program and to introduce the basic techniques for evaluation of the effectiveness of velocity simulations.

  Programs Used: VELSIM, WSP

  Data Files Used: Lab6.phb

  Introduction

  In this laboratory, different empirical approaches to simulating velocities are examined. Recall from Chapter 2 of the manual, that VELSIM can use specific velocity calibration sets for specific ranges of discharges, and a conveyance area-based velocity distribution can be developed when no calibration velocities are available. The 'best' approach can only be determined by evaluating a combination of available data, model performance, and objectives of the particular study.

  This laboratory explores several different velocity set combinations and simulation control options within VELSIM to help the user understand the effects and consequences of selecting a particular velocity calibration data set and modeling option(s) within VELSIM. The laboratory is also intended to demonstrate the implications of selecting a particular water surface elevation model and subsequent effects during the simulation of velocities in VELSIM. The overall objective of velocity calibration and simulation is to pick the best combination of calibration velocity(s) and simulation options to represent the velocity profiles at each cross section over the range of simulated flows. The steps in this lab provide a good sequence for velocity simulation.

  Step 1. Evaluate Observed Velocity Profiles

  Prior to beginning the modeling efforts, examine the observed velocity profiles at each cross section for all three calibration flows provided in Figures L6-1 through L6-4. The velocity profiles between different cross section geometries are highly variable as would be expected. Also note, however, that the velocity patterns at specific cross sections are 'generally' similar at all three calibration flows, but differences in the location of high versus low velocities and changes in the transverse patterns of velocities between the different calibration flows are also evident.

  

  Figure L6-1. Observed velocity distribution for cross section 0.0.

  

  Figure L6-2. Observed velocity distribution for cross section 60.0.
  

  

  Figure L6-3. Observed velocity distribution for cross section 135.0.

  

  Figure L6-4. Observed velocity distribution for cross section 201.0.

  Step 2. Assign Velocity Calibration Sets for Simulation of Velocities

  Go to \Models\Velocity Simulation\Velocity Calibration Set Assignments and assign velocity sets as shown in Table L6-1.

  Table L6-1. Initial velocity set assignments.
  Transect			Discharges
  15	30		75.2	139	250	625	1,250
  0	1		1	1	1	1	1	1
  60	1		1	1	1	1	1	1
  135	1		1	1	1	1	1	1
  201	1		1	1	1	1	1	1

  Assigning velocity set 1 to all cross sections and discharges tells the program to use the low calibration discharge velocity distribution as the template for simulating discharges across the entire flow range of the study. Later we will reset some or all of these values and compare the different velocity simulation results to obtain a final set of assigned calibration sets to use for each transect and discharge combination in this table.

  We can now simulate velocities for all discharges at all cross sections using the low flow calibration set as the velocity distribution template. Remember that water surface elevations (WSLs) were previously established using the WSP program.

  Step 3. Velocity Simulations Based on Different Velocity Calibration Data Sets

  Begin by simulating velocities using the low discharge calibration set as the velocity distribution template. To do this, click the Run button. When the VELSIM program has completed its execution. A small message box will announce velocity simulation is finished. Click OK.

  Now click the Results tab and the Cross section button at its bottom to display cross sectional plots. Click on 75.2 in the discharges table to display results for 75.2 cfs for cross section 0. Click the check boxes such that a check shows in all four boxes for Observed WSL, Simulated WSL, Observed Velocities, and Simulated Velocities. Now click the Refresh button. The graph should look like Figure L6-10. To view it better, use the Windows maximize button in the upper right corner of the graph window. You can now visually compare the observed and simulated velocities at a discharge of 75.2 cfs for cross section 0 based on using the 75.2 cfs calibration set as the velocity distribution template. Click on cross section 60 in the box at the top left of the window and then the Refresh button. The graph changes to display the WSL and velocity data and simulation results for cross section 60 at 75.2 cfs. In the classroom situation, it would take too long for each student to make printed copies of all of the plots of observed and to simulate velocities based on different templates, so the results of using calibration set 1, calibration set 2, and calibration set 3 for all cross sections at all discharges are given in Figures L6-10 through L6-45 at the end of this laboratory.

  A cursory examination of these figures shows that the best fit occurs when the simulated discharge is equal to the calibration set discharge. So it seems reasonable to use Cal Set 1 for discharges less than or equal to 75.2 cfs, Cal Set 2 for 139 cfs, and Cal Set 3 for discharges greater than or equal to 250 cfs. Try assigning calibration sets in that order and run the model again. Figures L6-5 to L6-8 contain the VAF relationships for the four velocity template runs. These results will be compared in the next section.

  

  Figure L6-5. Velocity adjustment factor for calibration flow of 75.2 cfs.

  

  Figure L6-6. Velocity adjustment factor for calibration flow of 139 cfs.

  

  Figure L6-7. Velocity adjustment factor for calibration flow of 250 cfs.

  

  Figure L6-8. Velocity adjustment factor for mixed calibration flow sets.

  Step 4. Examine the VAF Relationships and Velocity Profiles

  We will first examine the VAF relationships for each of the four simulations. Remember, velocity predictions at a simulated discharge are a function of the Manning's n derived from the calibration velocities at a single calibration flow. Also recall that VELSIM uses the VAF to maintain mass balance between simulated and computed discharges. Since roughness decreases with increasing discharge, VAF's below the calibration flow should generally be less than 1.0 and greater than 1.0 for flows above the velocity calibration flows. The degree to which the VAF departs from 1.0 at the velocity calibration flow is a function of the difference between the calculated discharge and the 'best estimate of the discharge' as well as the difference between predicted and observed water surface elevations (see Chapter 2 in the manual).

  In Figure L6-5 (where the 75.2 cfs calibration set was used to simulate all discharges), all the VAF relationships except at cross section 0 follow the expected pattern. The relationship at cross section 0 'suggests' that roughness is decreasing with as the discharge decreases below 139 cfs, which is counter to expected results. The remaining cross sections appear to behave 'normally'.

  The VAF relationships for all four simulations are shown in Figures L6-5 to L6-8. We can learn several things by comparing these figures.

  First, it should be apparent that the use of a single velocity calibration set results in VAF relationships, which are more 'typical' of expected results for all but cross section 0. Use of a mix of all three velocity sets produces an irregularity between 75.2 and 250 cfs for all but cross section 0. Though the VAF traces appear to have a break in slope at either 75.2 cfs or 139 cfs and drop to the value at 250 cfs, they do appear to be ascending with increased discharge within each range of simulation, e.g. 0.0 - 75.2 cfs and above 250 cfs. As only one discharge was simulated using the 139 cfs template, we do not know if this will hold true for the 139 cfs calibration set without running additional discharges. What do the other VAF plot suggest?

  Note the magnitude of the velocity adjustment factors using the four different approaches. These results show that the choice of a particular velocity calibration data set can impact both the magnitude and functional relationship of the VAF's. As might be expected, since the WSP modeled water surface elevations were used for these simulations, the VAF relationship for the high flow velocity set is 'best behaved' over all ranges of simulated discharges. The results at cross section 0 would suggest that either alternative velocity simulation options in VELSIM should be attempted, that an alternative water elevation modeling approach may be required, that a combination of the two may be warranted, or that the channel conditions warrant further study.

  Although an examination of the VAF relationships helps in the general diagnostics of the velocity simulations, an examination of the actual predicted velocities for each vertical for all cross sections at all simulated discharges must be undertaken to critically evaluate the simulation results. Actual velocity predictions should receive more emphasis than 'strict' adherence to an expected pattern of the VAF relationships in evaluation of the effectiveness of the velocity simulations.

  A careful examination of the results shown in Figures 10 - 45 should reveal several key points about this particular data set and VELSIM velocity simulations in general. First, the predicted velocities at a given calibration flow using that calibration flow velocity set do not exactly reproduce the observed velocities. The velocities measured at each cross section do not necessarily result in a computed discharge equal to the best estimate of the discharge or calibration discharge. Thus, the predicted velocities are adjusted by the computed VAF to maintain mass balance between the simulated flow and computed flow at the cross section (see Chapter 3 in the manual).

  The second thing to note is that at a given calibration flow, using that calibration flow velocity set results in some computational cells at the stream margin that have predicted velocities where none were observed. This is due to the discrepancy in the observed and predicted water surface elevations at each cross section and possible errors in the original data.

  It should also be apparent that the velocity pattern at the calibration flow used in the simulation is 'replicated' at all simulation flows. This can result in relatively large discrepancies between observed and simulated velocities when using for example a low velocity calibration set to simulate high flows or vice versa. This can often occur when the velocity profiles change dramatically between discharges due to channel geometry heterogeneity, especially due to unobserved conditions upstream of the transect.

  Collection of a single high flow velocity data set for use in modeling should be carefully evaluated based on complexity of the channel geometry at specific cross sections. If significant changes in velocity profiles are expected over different ranges of discharge of interest in a study, additional velocity data sets should be collected.

  The results also suggest that simulation of velocities higher than an observed calibration velocity data set can be problematic at some cross sections since VELSIM must 'guess' at a Manning's n value for computational cells where no observed velocities have been provided at the velocity calibration flow.

  The simulation results for cross section 201.0 also demonstrate the influence of water surface modeling on the predictions of velocities with VELSIM. Go to Results\Graphs\Longitudinal Profile and zoom in on the region encompassing the three calibration discharges. Note that at cross section 201.0 the WSP model is slightly under-predicting the water surface elevation at the 139.0 cfs and 75.2 cfs calibration flows. Now view Results\Graphs\Cross Section and select cross section 201, discharge 75.2 cfs, observed and simulated WSL and velocities. At 75.2 cfs VELSIM predicts slightly slower water at the cross section but one cell on the left bank shows a simulated velocity of 0.236 fps where the calibration velocity was 0.0. This provides enough conveyance to slightly lower the other velocities. At 139 cfs, however, the simulated velocities are significantly higher than the observed velocities. The simulated water surface elevation is 0.001 ft higher than the observed value, not a significant difference. Yet, the velocities are slightly higher. Why? Noting the calibration data, we find that the local discharge was 249 cfs, but the best estimate discharge is 250 cfs. Thus, a VAF slightly greater than 1.0 was needed to achieve mass balance resulting in a very slight increase in velocities in spite of the slightly higher WSL.

  In general, improving the water surface elevation predictions for any cross section at the calibration flows would bring the simulated cross sectional areas closer to the observed values. This would therefore reduce the VAF adjustments and result in a better match between observed and predicted velocities at the lower calibration flows. This can be seen the results at the 250 cfs calibration flow which identically match the calibration velocities over most of the cross section. Try simulating additional discharges that match the local discharges measured at cross sections 60 and 135. Do the simulated velocity results match the observed values better?

  The final water surface elevation simulation using WSP allowed a very large difference (0.137 ft.) between the observed and predicted water surface elevation at cross section 60 for the 250 cfs discharge. This was based on the assumption that an error of at least 0.10 ft. had been made in the water surface measurement at that discharge. In spite of the large difference in water surface elevation, the simulated velocities are only slightly lower than the observed velocities. Two cells at the right of the channel, which have significant simulated velocities when the measured velocities were zero, explain the lower velocities. The overall close agreement in simulated and observed velocities further supports the assumption of a water surface elevation measurement error.

  No single velocity calibration set is guaranteed to work at all ranges of simulated discharges at all cross sections. The 3-calibration data set approach would appear to represent the best compromise at all cross sections for all flow ranges. Selection of an appropriate velocity set(s) should be carefully considered in light of model performance and study objectives. These results should reinforce the importance of accurate water surface elevation modeling prior to undertaking the velocity modeling in VELSIM. A critical examination of the velocity modeling can also be used to revise water surface modeling approaches (for example, what to do with cross section 60) based on the effectiveness of the velocity predictions at specific ranges of discharge of importance to a particular study.

  Step 5. Revise Water Surface Elevations at Discharges below 250 cfs Based on MANSQ

  The water surface elevation modeling conducted in Laboratories 3, 4, and 5 indicated that either the VELSIM or MANSQ model matched the observed water surface elevations at the medium and low calibration flows. In this step of the laboratory, the WSL data for each cross section will be updated to use the water surface elevation predictions derived from the MANSQ model for all simulation flows below 250 cfs. Table L6-2 lists the water surface elevations for each cross section that will be used for this part of the laboratory.

  Table L6-2. MANSQ derived water surface elevations for each cross section.
  Discharge	Cross Section
  	0.0	60.0	135.0	201.0
  15.0	91.37	91.46	91.68	91.67
  30.1	91.57	91.70	91.88	91.94
  75.2	91.90	92.08	92.25	92.36
  139.0	92.21	92.43	92.59	92.71

  Go to \Models\WSL\Method and set the starting combination for the WSP backwater at cross section 0.0 for discharges of 75.2 and 139 cfs to WSP-MANSQ and Run the selection.

  Now go to \Models\Velocity and click Run to rerun the velocity simulation using the new elevations derived from using MANSQ as the starting point in the WSP backwater calculation. Compare the VAF relationship in Figure L6-9 with Figure L6-8. Updating the WSLs at the lower discharge ranges (i.e., below 250 cfs) improves the VAF relationship at cross section 0.0 by reducing the variation above a VAF value of 1.0 even though it does not result in transforming the VAF curve into the desired shape.

  

  Figure L6-9. Velocity adjustment factors using MANSQ for low flow starting WSLs.

  Based on these simulation results, the user would likely conclude that if only one calibration set is to be used, the high velocity calibration data set could be used for all ranges of simulated discharges. Alternatively, the user could also use each velocity calibration data set over a specific range of simulated discharges such as the high velocity calibration set for all flows greater than 250 cfs and for flows down to a discharge of 139 cfs. The 139 cfs velocity calibration data set could then be used to model flow down to 75.2 cfs and then use the 75.2 cfs velocity calibration data set for all lower simulated discharges. The choice of modeling strategy is a matter of professional judgment based on the quality of the available data. The goal is to produce a simulated velocity distribution that is as near as possible to that which occurs in the stream. A carefully kept set of analysis notes explaining why a particular strategy was selected is strongly advised. PHABSIM for Windows maintains a History.project name text file that records the order of model runs. This file can be periodically copied to another file and annotated as a means of tracking the analysis.

  Step 6. Use of the NMAX Option in VELSIM to Control Velocity Simulations

  One of the ways to control velocity simulations in VELSIM is to restrict the magnitudes of the estimated Manning's n values. This can be accomplished by using the NMAX or NMIN options. Restriction of Manning's n values can often improve velocity simulations in computational cells at the margin of the stream where velocity calibration data does not exist (i.e., verticals in the channel above the highest velocity calibration data set). Since velocity simulations at the stream margins can be controlled, the velocity predictions at all other verticals are also affected due to the interaction of conveyance and the VAF's.

  Selection of a limit on Manning's n, whether a maximum or minimum, is a matter of professional judgment. One rational approach is to examine the calculated Manning's n values at computational cells along the margins of each cross section for each calibration flow and select a Manning's n which is an 'average' of these values. Alternative approaches include the estimation of a Manning's n value using handbook values (see Chapter 3 in the manual) based on substrate characteristics. It should be noted that use of an NMAX and/or an NMIN applies to all computational cells at all cross sections at all flows when running VELSIM. Therefore, in those instances where substrate characteristics vary dramatically between cross sections, separate VELSIM data files containing only selected cross sections may be necessary. In this laboratory, the NMAX constraint will be applied to the entire data set over all ranges of simulated discharges.

  Go to \Models\Velocity\Options and check the box labeled Limit Manning's n. Enter an NMAX value of 0.035 and click the Run button. Then view the VAF relation by clicking the ZVAFF tab and its Graph button.

  It is apparent the constraint of Manning's n values to a maximum of 0.035 has resulted in a reduction in the magnitudes of the VAF's at all cross sections. This would be expected since lowering the upper limit on estimated Manning's n should result in higher velocity predictions. This in turn should decrease the VAF that is derived from the ratio of simulated discharge over computed discharge. A comparison of predicted Manning's n and velocities at the first 25 computational cells at cross section 135 at 15 cfs clearly illustrates the effect of NMAX on velocity modeling (Table L6-3).
  

  Table L6-3. Comparison of Manning's n and velocity predictions at cross section 135.0 at 15.0 cfs.
  
  			NMAX = 0.035							No NAMX
  Cell	Manning's n		Velocity			Manning's n		Velocity
  	8		0.035		0.09				0.052			0.07
  	9		0.035		0.19				0.071			0.11
  	10		0.035		0.19				0.054			0.14
  	11		0.035		0.44				0.042			0.43
  	12		0.035		0.49				0.063			0.32
  	13		0.035		0.44				0.04			0.45
  	14		0.035		0.59				0.046			0.52
  	15		0.035		0.44				0.037			0.48
  	16		0.035		0.59				0.038			0.64
  	17		0.035		0.68				0.039			0.72
  	18		0.035		0.72				0.044			0.68
  	19		0.035		0.64				0.036			0.71
  	20		0.035		0.64				0.038			0.69
  	21		0.035		0.59				0.043			0.56
  	22		0.035		0.64				0.041			0.63
  	23		0.035		0.54				0.040			0.55
  	24		0.035		0.49				0.036			0.56
  	25		0.035		0.54				0.047			0.48
  		

  The overall pattern of velocities generated by limiting Manning's n needs to be considered before accepting the improved VAF relation as the best velocity simulation outcome that can be obtained for velocity simulation. Using \Models\Velocity\Results\Cross Section, look at the velocity patterns obtained for each cross section at the three calibration discharges. How well do they match? Do you think that limiting Manning's n has improved the overall velocity simulation across all transects over the full range of discharges?

  At this point in the analysis, users would need to determine from the context of their particular application which set of velocity simulation options and results is best over what target flow ranges in choosing the appropriate velocity modeling approach. In some applications it may be desirable to use simulation results that minimize the error between measured and observed velocities over the full range of simulations. In other situations, the investigator may choose to use each single velocity calibration set only over a specific range of discharges. This is often the case where velocity patterns vary dramatically across cross section geometries as discussed in Chapter 2 of the manual.

  Step 7. Specifying n values for Problem Areas

  Look through Figures L6-10 to L6-45 for those cases where simulated discharge is equal to the calibration discharge. Note that some edge conditions are not well simulated due to being dry at the observed discharge. Table L6-4 contains a summary of the diagnostic conditions revealed by those figures. Some data errors can be seen and some velocity simulation problems stand out.

  Table L6-4. Summary of data and simulation diagnostic conditions.
  
  	Sim Q     X-sec		Cal Q   Figure	
  	75.2		0		75.2	L6-10	Simulated velocity anomaly between 18 and 30, non-
  											zero observed velocity in dry area on right bank
  	75.2		60		75.2	L6-13	Zero observed velocities in deep area near right bank
  	75.2		135		75.2	L6-16	Zero observed velocity in wet cell near right bank
  	75.2		201		75.2	L6-19	Zero observed velocity in wet cell near left bank
  	139			0		139		L6-23	Non-zero observed velocity in dry area on right bank
  	139			60		139		L6-26	Zero observed velocity in wet cell near both banks
  	139			135		139		L6-29	Zero observed velocities in wet cells near left bank, n 
  											may be too low near left bank
  	139			201		139		L6-32	Zero observed velocity in wet cells near both banks, 
  											VAF scaling very clear
  	250			0		250		L6-36	Observed velocity values reversed at right bank?
  	250			60		250		L6-39	Zero observed velocities in deep area near right bank
  	250			135		250		L6-42	n appears low at edge on left bank (sim velocity > obs 
  											velocity), odd velocities at 18 and 20
  	250			201		250		L6-45	n appears low at edge on both banks (sim velocity > obs 
  											velocity)
  

  In \Edit\Cross Sections\Coordinate Data you can set Manning's n values for specific cells on each cross section. After examining how VELSIM handles edges (or other parts of the channel) automatically, you may wish to enter n values for specific cells and rerun the velocity simulation. Roughness values set for specific cells apply at all discharges so you must take care that a good n value for one condition does not perturb the results for other discharges. Try setting n values on the left bank of cross section 201 for 250 cfs, rerun the simulation, and see how velocity values are affected at all flows.

  The user is encouraged to try additional velocity simulation options within VELSIM (e.g., placing specific Manning's n values at specific verticals or using the NMIN option). Examine the effects on the velocity simulations in terms of both the VAF relationships and observed versus predicted velocity distributions at each cross section. Remember that water surface simulations for each cross section affect the velocity simulations. In some cases water surface errors can be the main contributing factors for discrepancies between observed and predicted velocities.

  

  Figure L6-10. Simulated and observed velocity profile for 75.2 cfs at Xsec 0, Cal Set 75.2.

  

  Figure L6-11. Simulated and observed velocity profile for 139 cfs at Xsec 0, Cal Set 75.2.
  

  

  Figure L6-12. Simulated and observed velocity profile for 250 cfs at Xsec 0, Cal Set 75.2.

  

  Figure L6-13. Simulated and observed velocity profile for 75.2 cfs at Xsec 60, Cal Set 75.2.

  

  Figure L6-14. Simulated and observed velocity profile for 139 cfs at Xsec 60, Cal Set 75.2.

  

  Figure L6-15. Simulated and observed velocity profile for 250 cfs at Xsec 60, Cal Set 75.2.

  

  Figure L6-16. Simulated and observed velocity profile for 75.2 cfs at Xsec 135, Cal Set 75.2.

  

  Figure L6-17. Simulated and observed velocity profile for 139 cfs at Xsec 135, Cal Set 75.2.
  

  

  Figure L6-18. Simulated and observed velocity profile for 250 cfs at Xsec 135, Cal Set 75.2.
  

  

  Figure L6-19. Simulated and observed velocity profile for 75.2 cfs at Xsec 201, Cal Set 75.2.
  

  

  Figure L6-20. Simulated and observed velocity profile for 139 cfs at Xsec 201, Cal Set 75.2.

  

  Figure L6-21. Simulated and observed velocity profile for 250 cfs at Xsec 201, Cal Set 75.2.
  

  

  Figure L6-22. Simulated and observed velocity profile for 75.2 cfs at Xsec 0, Cal Set 139.

  

  Figure L6-23. Simulated and observed velocity profile for 139 cfs at Xsec 0, Cal Set 139.
  

  

  Figure L6-24. Simulated and observed velocity profile for 250 cfs at Xsec 0, Cal Set 139.
  

  

  Figure L6-25. Simulated and observed velocity profile for 75.2 cfs at Xsec 60, Cal Set 139.
  

  

  Figure L6-26. Simulated and observed velocity profile for 139 cfs at Xsec 60, Cal Set 139.

  

  Figure L6-27. Simulated and observed velocity profile for 250 cfs at Xsec 60, Cal Set 139.
  

  

  Figure L6-28. Simulated and observed velocity profile for 75.2 cfs at Xsec 135, Cal Set 139.
  

  

  Figure L6-29. Simulated and observed velocity profile for 139 cfs at Xsec 135, Cal Set 139.

  

  Figure L6-30. Simulated and observed velocity profile for 250 cfs at Xsec 135, Cal Set 139.

  

  Figure L6-31. Simulated and observed velocity profile for 75.2 cfs at Xsec 201, Cal Set 139.

  

  Figure L6-32. Simulated and observed velocity profile for 139 cfs at Xsec 201, Cal Set 139.

  

  Figure L6-33. Simulated and observed velocity profile for 250 cfs at Xsec 201, Cal Set 139.

  

  Figure L6-34. Simulated and observed velocity profile for 75.2 cfs at Xsec 0, Cal Set 250.

  

  Figure L6-35. Simulated and observed velocity profile for 139 cfs at Xsec 0, Cal Set 250.
  

  

  Figure L6-36. Simulated and observed velocity profile for 250 cfs at Xsec 0, Cal Set 250.

  

  Figure L6-37. Simulated and observed velocity profile for 75.2 cfs at Xsec 60, Cal Set 250.

  

  Figure L6-38. Simulated and observed velocity profile for 139 cfs at Xsec 60, Cal Set 250.

  

  Figure L6-39. Simulated and observed velocity profile for 250 cfs at Xsec 60, Cal Set 250.

  

  Figure L6-40. Simulated and observed velocity profile for 75.2 cfs at Xsec 135, Cal Set 250.

  

  Figure L6-41. Simulated and observed velocity profile for 139 cfs at Xsec 135, Cal Set 250.

  

  Figure L6-42. Simulated and observed velocity profile for 250 cfs at Xsec 135, Cal Set 250.

  

  Figure L6-43. Simulated and observed velocity profile for 75.2 cfs at Xsec 201, Cal Set 250.

  

  Figure L6-44. Simulated and observed velocity profile for 139 cfs at Xsec 201, Cal Set 250.

  

  Figure L6-45. Simulated and observed velocity profile for 250 cfs at Xsec 201, Cal Set 250.

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