Chapter 2. Hydraulic Modeling in PHABSIM

This chapter introduces the basic concepts of hydraulic simulation in PHABSIM followed by a detailed explanation of the specific calibration and simulation options for each hydraulic model within PHABSIM. Calibration and simulation of water surface elevations are treated first followed by calibration and simulation of velocities. Specific steps in use of the software for each stage of hydraulic simulation are presented. The chapter concludes with a general discussion of how to evaluate hydraulic modeling results.

Laboratories

The associated laboratories for this material are contained in Laboratory Exercises 3-7. They introduce the three principal water surface modeling options within PHABSIM, as well as the general approaches to velocity simulations. Laboratory 3 introduces the stage-discharge modeling of water surface elevations using STGQ, Laboratory 4 covers the use of the MANSQ model for this purpose, while Laboratory 5 introduces the use of the step-backwater model (WSP). Finally, Laboratory 6 covers the use of the VELSIM model for velocity simulations.

Introduction

Flow in an open channel is a three-dimensional process. It includes response to change in the channel shape, secondary currents, and it varies continuously across and along the axis of the stream. Models of varying complexity capture the overall streamflow process to different degrees. In PHABSIM, the Water Surface Profile model (WSP) uses the step-backwater method to obtain a one-dimensional representation of flow. The STGQ and MANSQ models use empirical means to obtain similar transect-based representations of flow. The hydraulic models in PHABSIM operate with assumptions of a fixed bed profile and a sloped water surface that is level across each cross section. There are many empirical relations used to simplify flow representations so they can be represented on transects, rather than continuously. Thus, flow representations within PHABSIM are discretized as cells located across transects. The influence of the assumptions and one-dimensional form of PHABSIM models will become more apparent as the reader progresses through this chapter.

Hydraulic modeling within PHABSIM characterizes the physical attributes within the stream (i.e., depth, velocity, and channel index) over a desired range of discharges. This characterization could be accomplished by direct empirical measurements taken at small increments of discharge covering the range of discharges of interest for a habitat study. However, time, safety and funding constraints typically prevent this empirical approach. Fortunately, it is possible to sample the stream's hydraulic properties at a few target discharges and then rely on these data to calibrate one or more hydraulic model(s) and use the model(s) to predict the stream hydraulic attributes over the full range of discharges of interest in the study. The success or failure of this effort is dependent on the quantity and quality of the field data, the complexity of the physical nature of the stream, and ultimately the ability of the hydraulic models to reflect the physical processes in the stream.

The material in this chapter represents concepts and application strategies of elements contained in the hydraulic simulation portion of the information flow within the PHABSIM system as indicated by the area labeled hydraulic simulation in Figure 1-2. The chapter concludes with a section on evaluating hydraulic model results.

Terms and Definitions for Open-channel Flow

Prior to presentation of these specific modeling approaches within PHABSIM, a brief introduction to the vocabulary and physical setting of open channel flows is necessary. A more technical and detailed treatment of the hydraulics of open channel flow can be found in any number of general texts on hydraulics such as Henderson (1966). Those readers who are interested in a more rigorous treatment of hydraulics should consult that or similar works.

The following terms and their definitions are important since they constitute the vocabulary of hydraulic analysis terminology within PHABSIM related to the analysis of open-channel flow and in particular to the use of hydraulic modeling options for the specific models within PHABSIM. The relationships between these terms and physical properties within a river channel or cross section(s) are illustrated in accompanying figures where possible. Figure 2-1 provides an idealized representation of a stream reach showing the location of several cross sections (transects), a hydraulic control, and a lateral view of a typical cross section profile.

Figure 2-1. Schematic of a PHABSIM representative reach and a typical transect.

Figure 2-2 provides a representation of a cross section view of a cross section (or transect) which relates the following hydraulic field data measurements to their equivalent terms as used by the various hydraulic (and habitat) models.

Figure 2-2. Schematic view of a Cross Section showing hydraulic measurement and modeling terms.

Figure 2-3 shows an idealized representation of a cross section which defines the relationship between the following terms and definitions.

Figure 2-4 illustrates the relationship between important hydraulic parameters and definitions applied between adjacent cross sections. These items define the principal factors and terms used by the WSP model to compute water surface elevations.

The following terms are provided for completeness. They are treated in more detail in the specific sections on hydraulic models which follow. Additional terms and definitions related to hydraulic modeling can be found in Appendix 1.

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Equations Used For The Description and Analysis of Open-Channel Flow

Several fundamental equations and relationships are important to understand, since they constitute the computational basis for the various hydraulic models used within PHABSIM. A fundamental tenant of open channel flow is that continuity and mass balance of discharge must be maintained between adjacent cross sections for proper application of the hydraulic models. In addition, the overall energy balance due to friction losses between two adjacent cross sections must also be maintained. This is addressed in the hydraulic models within PHABSIM through the application of Manning's equation, which describes open channel flow in terms of measured cross section properties and relationships between the discharge, water surface elevation, velocity, and resistance to flow and the Bernoulli equation which evaluates longitudinal energy dissipation.

Continuity and Mass Balance

The water surface elevation in a stream defines the cross-sectional area of flow if the bed geometry is known. If mean cross section (channel) velocity is also known, discharge can be calculated using the equation of continuity (see Figure 2-3):

In practical applications, if no inflows or outflows occur within the study site and the water surface elevations do not change during the period of field data collection, the estimated or user-computed discharge for individual cross sections should yield estimates of the discharge that are alike for similar habitat types. Hydraulic data collection for a PHABSIM study is usually undertaken in habitat types important to fish and, therefore, some channel types that are not ideal for estimating discharge will be sampled. It is not uncommon that riffle habitats have discharges that are 10-20% higher than the discharge estimated in runs, which are more ideal in terms of estimating the "true" discharge. Conversely, discharge estimates in pools can typically be 10-20% lower than runs. When selecting the best estimate of discharge, users are encouraged to consider cross section conditions as a major determinant of the user-supplied "best estimate" discharge. For example, an average of the discharge measurements obtained from three run cross sections in a study site may be superior to an average of the flow measured at all cross sections.

Manning's Equation

One of the most widely applied equations used to describe flow in open channels is referred to as Manning's equation (p. 96 in Henderson, 1966). The equation represents an alternative formulation of Equation 2-1 in which site specific channel characteristics are incorporated in order to describe the resistance of flow within the channel given the roughness of bed material, energy slope, and channel geometry. For U.S. Conventional units Manning's equation is:

This equation, in several different formulations, is used within PHABSIM in the MANSQ and WSP models for the simulation of water surface elevations and in the VELSIM program for the simulation of velocities.

Energy Balance and the Bernoulli Equation

In Manning's equation, the slope required as input is the slope of the energy grade line. This slope is defined as the difference in total energy at two (or more) channel sections, divided by the distance between them (refer to Figure 2-4). The total energy at a channel section is found with the open-channel form of the Bernoulli equation:

For practical purposes, Figure 2-4 shows that the term z + d equals the water surface elevation (WSL) for a given cross section, therefore, the slope of the energy grade line can be determined by:

If the assumption is made that flow in the channel is uniform, then bed slope, hydraulic slope, and energy slope are considered equal, S_o = S_h = S_e. Therefore, this equation represents the Energy Balance between two adjacent cross sections of the stream. The Bernoulli equation in conjunction with mass balance of the discharge and Manning's equation form the computational core to the WSP program as described later in this chapter.

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Applied Modeling of Water Surface Elevations in PHABSIM

Determining the relationship between the water surface (stage) and the discharge is the first step in the hydraulic calibration and simulation phases of PHABSIM (Figure 1-2). The stage is used to derive depth distributions for each cross section by subtraction of bed elevations across the channel from the stage. It is also used to identify the location of the free surface to establish boundaries (i.e., wetted cell locations) for some of the equations that describe velocity distributions. If stage and bed elevation are known, depth may be determined at any location on the cross section. Stage varies with discharge, so it is important to derive a reliable relationship between stage and discharge for the study site or hydraulic simulation results will be in error.

There are three approaches for predicting stage-discharge relationships in PHABSIM. The approaches described in this section include: (1) linear regression techniques based on multiple measurements from the field (the STGQ model); (2) use of Manning's equation (the MANSQ model); and (3) calculation of water surface profiles using standard step-backwater computations (the WSP model).

In the PHABSIM for Windows interface, all three models are accessed under the /Models/WSL menu. To provide maximum flexibility in modeling water surface elevations, the interface allows the user to select different models for different discharges at individual transects. Thus, it is possible to mix modeling approaches (including supplying water surface elevations from an outside source) for individual transects in a project and across the full range of discharges. The selected WSL calculation method is entered in the table displayed in the /Models/WSL/Method tab. Other tabs provide for selection of options within each model and are discussed below and in the laboratories.

Modeling the Stage-Discharge Relationship by Regression

One method of obtaining a relationship between stage and discharge is to measure the discharge at several stages and develop an empirical regression equation relating stage to discharge. In practice, typically three (FORT recommends three [3] or more) measurements of the stage and discharge are obtained at each cross section over as wide a flow range as practical or as necessary to meet the study objectives.

In a large number of channels, stage-discharge data of this nature has been found to be adequately approximated by the following equation:

Note that we have included the SZF in Equation 2-5 since the stage-discharge relationship at a channel cross section is a function of the SZF at that specific location, as discussed below under the STGQ model. The SZF is used within the STGQ model and one option in MANSQ. It should be included whenever using alternative stage-discharge regressions. Equation 2-5 can be transformed to a linear relationship between stage and discharge by taking the log of the equation which yields:

A simple linear regression can then be performed between the log of the discharge and the log of the water surface elevation (minus stage of zero flow) to determine the constants. The resulting regression equation is then used to predict stage over a desired range of discharges. An example of a measured stage-discharge relationship with the resulting regression equation derived from these data is given in Figure 2?6.

In some channels however, where complex geometry may result in a significant change in cross section area over a wide range in discharge as illustrated in Figure 2-7, or where a backwater effect from a downstream hydraulic control may occur, the stage-discharge relationship may not be log-linear as illustrated in Figure 2-8. In these instances, the user should take care to review the stage-discharge relation developed by the models in PHABSIM to ensure that the most accurate evaluation of the stage-discharge relationship is achieved. If the STGQ model is allowed to proceed normally, a single regression line will be derived from all of the data in the log-log domain as shown in Figure 2-9. In these instances, the analyst may choose to partition the data into multiple, piece-wise linear data sets and develop corresponding regression equations for specific ranges of discharges which are to be simulated as illustrated in Figure 2-10. In PHABSIM for Windows this can be accomplished by creating separate copies of the project for each regression range or by running STGQ for pairs of calibration flows and reentering the data in the methods table as fixed water surface elevations. Such two point lines have zero degrees of freedom and should be used for extrapolation with caution.

In addition, stage values may be generated entirely outside of PHABSIM and entered in the /Models/WSL/Methods table in lieu of running any of the PHABSIM models. Stage values entered in the ../Methods table must be converted to normal domain; that is, one must exponentiate to remove the log conversion.

Figure 2-6. Example of a stage-discharge relationship based on three observed discharges.

Figure 2-7. Asymmetrical cross section showing water surface elevations for four discharges.

Figure 2-8. Log-log plot of stage-discharge for asymmetrical cross section above.

Figure 2-10. Multiple linear regression equations arranged to achieve a piecewise linear stage-discharge relation.

Alternatively, the user may also elect to fit a nonlinear equation to the observed data for the purposes of modeling the relationship between stage and discharge as illustrated in Figure 2-11. It is advisable to use four or more points to allow for at least one degree of freedom in the regression. Nonlinear fitting functions are available in various spreadsheet and statistical programs. The results may be inserted into PHABSIM as fixed WSL values in the methods table.

Regardless of whether the observed data is fit using a log-linear, piece-wise log-linear, or nonlinear regression approach, the extrapolation of the regression equation to lower and higher discharge ranges than what was measured should be examined critically for reasonableness as discussed below. Upper and lower limits of extrapolated discharges are, to some degree, a matter of professional judgement and the specific analytical needs of a particular study. In general, the further away from the observed conditions, the greater the potential error between the actual stage and the stage predicted by extrapolation. The reasonable range of extrapolation varies among study sites so caution in extrapolation is advised.

Figure 2-11. Nonlinear function fit to stage-discharge data in logarithmic domain.

When using the regression approach, one should recognize that the regression equation developed for a specific cross section is independent of all other cross sections within a study site. Therefore, care should be exercised that internal consistency is maintained in the longitudinal profiles of the water surface elevations between adjacent cross sections within a specific study reach. For example, the results presented in Figure 2-12 show that the independent analysis of several cross sections using a log-linear regression approach (i.e., STGQ) results in the analysis predicting "water flowing uphill" for several discharges. Although the individual R2 values of each regression were high (e.g., > 0.95), longitudinal profile plots provide a simple diagnostic of model results that indicate an alternative modeling approach is required if the study requires simulating a range of discharges where water appears to flow uphill. Errors in water surface prediction will affect both the predicted depth and velocity values for this transect. Diagnostic evaluation of water surface modeling is discussed later in this chapter.

Determining the Stage of Zero Flow

Since the STGQ, and MANSQ models make use of the stage of zero flow (SZF) for computational purposes (see Equation 2-5 above and the MANSQ discussion below), it is important to understand how to obtain the proper SZF. The SZF is important since it is used directly in regression analysis of the stage-discharge equations in STGQ and in one simulation option within MANSQ. An error in estimating the SZF can alter hydraulic simulation results. The easiest way to determine the SZF is to plot the thalweg elevations at each cross section moving in an upstream direction as shown in the example provided in Figure 2-13.

Figure 2-12. Independent stage-discharge analysis can result in a simulated adverse water surface profile.

As can be seen, the SZF at cross section T1 corresponds to the thalweg depth at this cross section and will control the surface of the stream when the water level drops to this point. At that level, flow will cease, hence the concept of the stage at which zero flow will occur. It should also be apparent that this same SZF should be used at cross sections T2 through T4 since the elevation of the SZF at T1 will control the water surface at these next two upstream cross sections. The individual thalweg depths should be used as the SZF at transects T5 and T6.

Stage-Discharge Analysis using Regression in PHABSIM - the STGQ Model

The STGQ hydraulic simulation model predicts water surface elevation as a function of discharge. Given stage-discharge data, STGQ will automatically conduct the log-linear regression on the calibration data sets and determine the water surface elevations for all flows contained on the /Edit/Discharges table. When using the stage-discharge relationship, each cross section is treated independently of all others in the data set. This approach has the advantage that habitat areas from several locations in the stream (habitat mapping strategy) can be analyzed simultaneously. The principle disadvantage is that not all cross sections are well-suited for stage-discharge regression and the phenomenon of simulated adverse water surface gradients (see Figure 2-12) can occur. The STGQ program simulates water surface elevations using the stage-discharge relationship information supplied in the /Edit/Cross Sections/Calibration Data tab in PHABSIM for Windows.

Running the STGQ Model

Once the STGQ model has been selected for a combination of cross sections and discharges in the /Models/WSL/Method table, the user selects options to be run for the study site in the /Models/WSL/STGQ Options tab. These selections are made by clicking on the model type, eg. STGQ and then clicking each of the transect/discharge boxes in the table to which that model is to be applied. The boxes will then contain the term "STGQ".

Remember to review the output file ZOUT for error messages and inconsistencies in the data. (It will be the latest sequentially numbered ZOUT file in the directory where the project resides.) Error messages in the form of notes or other statements that do not appear on the screen or cause the program to abort may be written to the ZOUT file. Output from the STGQ model is variable depending on the selected simulation options. Examination of STGQ output is covered in the laboratory exercises.

The user has the ability to select a variety of simulation and reporting options during the execution of the STGQ model. The associated laboratory exercises will address the use of the most commonly used options and, therefore, a detailed discussion of each option will not be presented here. Table 2-1 lists each of the options within STGQ and provides a concise description of the function for each option.

A Practical Guide to Modeling Stage-Discharge Relationships Using the Regression Approach

In most applications, the analyst will need to determine the "best estimate" of the discharge at a given calibration flow. Typically, the discharge calculated from observed velocity distributions may vary considerably between all measured cross sections. For example, it is not uncommon for the discharges computed within a single study reach in which the stage remains stable during field measurements to vary by as much as 25%. This is due to measurements being taken in pools, riffles, runs, etc. Generally, pools and riffles are poor areas for discharge estimation but are typically measured since they often represent critical habitat types necessary for evaluation as part of the instream flow investigations. Field crews should indicate during data collection which cross section(s) are best for estimation of the actual flow for a particular calibration set. The best discharge measuring sections are used to estimate the discharge for use in the regression analysis for all cross sections within the reach. The difference between the measured right and left bank water surface elevations can vary considerably with differences of 0.1 to 0.5 feet occurring in highly turbulent conditions. The analyst should select the average of the left and right bank, only the left or only the right, or other water surface elevation at each cross section in the regression equations based on the conditions reported in the field notes.

Table 2-1. Options in the STGQ program.
Option description	Action when set to indicated value
Write computational details (check box)	Prints the numerical details of the computed velocities and water surface elevations for each simulated discharge to ZOUT.
Assign Cal Set (Button)	Displays a table where the user assigns a CAL set to each discharge for each cross section.
Discharge (IOC 5) (click cell, click down arrow to change from Best Estimate of Q to Xsec (transect) Q)	Selects whether the best estimate of the discharge or the discharge measured at this transect is used in stage-discharge calculations. If no transect Q is supplied, defaults to best estimate.
WSL (Click cell, click down arrow to change to Left, Right, Average or User supplied WSL)	Selects which of the WSL values supplied in /Edit/Cross Sections/Calibration Data is used in WSL simulation.
SZF (check box for each transect)	Selects if the stage of zero flow is used in the WSL simulation. Default is yes (checked).
Output Options (applies to all WSL Simulation Models)
Use (check boxes for each discharge)	Selects which discharges are simulated in the current run. Default is all (all boxes checked).

The analyst also has the option of using the actual calculated discharges at each cross section in the regression equations rather than the best estimate for the reach. The analyst may also elect to vary the water surface elevations at a cross section within the range of measured differences between the left and right bank in attempts to get a better log-linear regression fit to the data. Using discharges other than the best estimated discharge or water surface elevations different than the average should be carefully considered; but, this choice does not imply errors in modeling as long as a rational basis for the use of alternative data is clearly articulated and justified in the study report.

In some instances, the flow rate will change during the course of field data collection at a study reach either within the day or between successive days for a variety or reasons. This is most often noted by changes in the stage readings of the water surface elevation during field data collection or during data processing where calculated discharges show a consistent increase or decrease between successive measurements. A typical approach with data sets having these characteristics is to derive best estimates of the discharge for groups of cross sections, which represent consistent field measurements under similar flow conditions.

For example, the first three cross sections measured during the first field day may have a best estimate of discharge equal to 100 cfs at the low calibration set while cross sections 4 through 7, collected the next day, may have a best estimate of the discharge of 120 cfs. Because the STGQ program treats each cross section as an independent data set, it has the ability to accommodate different discharges between cross sections for a given calibration set. In those instances in which the discharge changes during the collection of data at a single cross section, it is best to stop data collection until the flow stabilizes. However, if this is not an option, or this was determined in the office during review of data collection efforts, advanced modeling approaches beyond the scope of this chapter need to undertaken. In those instances, the analyst should contact an experienced hydraulic engineer for technical assistance.

In summary, the following step-wise procedure can be followed for conducting stage-discharge modeling using the regression approach to estimate water surface elevations in PHABSIM.

1. Decide whether to use the best estimate of the discharge for each calibration set for all cross sections and whether to use the average of the right and left bank water surface elevations measured at each calibration flow. Be sure to check if the discharge remained constant during field collection efforts or whether different best estimates of the discharge need to be provided for different groups of cross sections. Finally, determine the appropriate stage of zero flow (SZF) for each of the cross sections.

2. Plot the log of the discharge versus the log of the WSL-SZF (/Models/WSL/STGQ options/Stage Discharge Graph) and examine the relationship for linearity or piece-wise linearity before proceeding. If the relationship at a cross section is not log-linear, consider an alternative modeling approach such as MANSQ or WSP or proceed with a nonlinear analysis of the data (outside of PHABSIM for Windows) to predict the water surface elevations.

3. Ensure that all measured calibration data sets use the appropriate discharge and water surface elevations at each cross section and each calibration flow. Check that all such data are in the project file (See /Edit/Cross Sections/Calibration Data). When using a piece-wise linear approach, assign the Cal sets for a single "piece" and remove check marks from the rest to select the range of discharges you wish to simulate (/Models/WSL/Output options).

4. Run the STGQ model (Click Run under the ../WSL/Method tab) and examine the longitudinal profiles (Longitudinal profile plot in the ../Results tab) of the water surface elevations for all spatially linked cross sections to determine the quality of the model results.

5. If the longitudinal profiles look reasonable for all simulated discharges, proceed to the velocity calibration and simulation step of PHABSIM. If not, examine alternative WSL modeling approaches using MANSQ and/or WSP.

Review the output file ZOUTnn for error messages and inconsistencies in your data. Error messages in the form of notes or other statements that do not appear on the screen or cause the program to abort may be written to the output file. Output from the STGQ model includes a listing of the calibration data used in the stage-discharge regression, and the regression equation with diagnostic statistics for each cross section.

Modeling the Stage-Discharge Relationship Using Manning's Equation - The MANSQ Model

The MANSQ model can be used to determine the stage-discharge relationship for individual cross sections. The uniform flow assumption allows use of measured hydraulic slope instead of energy slope, since, by definition, they are equal if flow is uniform. In addition, this approach assumes that flow variations caused by changes in channel configuration are negligible (i.e., minimal backwater effects). Generally, the more uniform the channel, the more reliable the results using this approach, thus it is more reliable in run sections. The application of the MANSQ model in pools can sometimes be problematic since pools are generally created by backwater effects of a downstream hydraulic control. As was the case in using the STGQ model, the MANSQ model also assumes that each cross section is independent of all other cross sections during calibration and simulations. Therefore, as indicated for the STGQ program, the longitudinal profile of the simulated water surface elevations should always be checked to ensure water is flowing down hill between spatially linked cross sections in a study reach.

The MANSQ model uses Manning's equation in the form:

and simplifies it to:

The value of K is determined from one set of measured discharge and water surface elevation pairs and 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 three equations selected by the user:

Selection of the ratio of discharges, the ratio of the hydraulic radius, or the empirical relation between hydraulic radii and median particle size is a choice made by the investigator. There is no strong evidence to suggest the discharge ratio is generally superior to the hydraulic radius ratio. Functionally, given multiple sets of discharge-water surface elevation data at a cross section, the user employs a trial and error procedure for selecting a value of b that minimizes the error between observed and predicted water surface elevations at the calibration discharges, regardless of which equation formulation is used. Due to the ease of switching between the first two options, a trial-and-error approach may be used.

The third approach requires a sediment study to determine the median bed material size. This option cannot be used unless such a study has been conducted. When selecting the third option, the D50 value is entered in place of b (in the /Models/WSL/MANSQ Options tab). In all cases, the investigator should be able to justify the final calibrations by demonstrating minimum error between predicted and observed WSL at the calibration discharges.

The MANSQ b coefficients will typically be different for each cross section within a study reach. The range of the differences will depend on the variation in complexity of the channel at different cross sections. The range of b in typical applications is approximately 0.0 to 0.6; b cannot be less than 0. If calibrated b values fall outside this range, the results should be examined carefully, but such results do not necessarily imply that the data has errors or that hydraulic calibration is faulty. The investigator should examine the errors between predicted and observed water surface elevations in light of variations in cross section geometry and the observed ranges in discharge and water surface elevations. An average of several data sets evaluated at FORT yielded a b value of 0.22 for gravel bed channels. This may be a good starting estimate of b in the calibration process.

As previously noted, MANSQ treats each cross section independently. Therefore, once all cross sections have been suitably calibrated and the full range of desired discharges have been simulated, the longitudinal profiles of the water surface elevations should be checked for internal consistency (i.e., water flows downhill).

Running the MANSQ Model

Once the MANSQ model has been selected for a combination of cross sections and discharges in the /Models/WSL/Method table, the user selects options to be run for the study site in the /Models/WSL/MANSQ Options tab. You may find that by selecting only the desired calibration flows in the table in the /Models/WSL/Output Options tab during the calibration phase, calibration of the model is somewhat easier due to reduced amounts of output to evaluate. However, the user should ensure that after successful calibration of the model all flows of interest have been selected in ../Output Options prior to performing the final WSL production run.

Remember to review the output file (latest ZOUTnn file) for error messages and inconsistencies in the data. Error messages in the form of notes or other statements may be written to the output file that did not appear on the screen or cause the program to abort. Examination of MANSQ output is deferred to the Laboratory exercises.

The user has the ability to select a variety of computational and reporting levels for the MANSQ program. The associated laboratory exercises will treat the use of the most commonly used options and therefore a detailed discussion of each option will not be presented here. Table 2-2 lists each of the options within MANSQ and provides a concise description of the function for each option.

A Practical Guide to Calibrating MANSQ

The calibration of the MANSQ program involves a trial-and-error procedure to pick a b value that minimizes the error between predicted and observed water surface elevations at each transect. This can be summarized in the following steps:

1. Run /Models/Water Transport Parameters (CALCF4) by selecting that menu item. Use Notepad or Wordpad to view the table.calcf4 file and search for the text string 'WTP' at each cross section. This is the conveyance factor. Locate the regression equation between discharge and the channel conveyance factor or water transport parameter (WTP) term for each cross section. The exponent (B) in the WTP regression equation is an excellent initial estimate for the b coefficient for each transect in the MANSQ program. Alternatively, just make a guess (i.e., 0.22) and proceed.

2. Select MANSQ options in the /Models/WSL/MANSQ Options tab. Then take care to select which calibration flow you intend to use as the initial calibration flow since this will represent a "fixed" calibration set for the program. The calibration sets are numbered in order of ascending discharge magnitude. Then select only the CAL set flows shown in ..WSL/Output options, that is remove the checks from all but the calibration flows. Enter your best estimate for b at each cross section either derived from the WTP regression exponent term or your initial guess. Click Run.

3. Go to the ..WSL/Method tab and select MANSQ for all transects.). Set the b coefficient at each transect (in the ../MANSQ Options tab, change beta values in the table). Run the MANSQ program (../Method tab, click the run button). Compare the predicted versus observed WSL at each transect for all the calibration flows by moving to the ../Results tab and noting WSL values in the table compared to observed values. The Longitudinal graph button in the ../Results tab allows comparison of the observed and predicted WSL profile. Note that at the selected calibration flow the program will always return the given water surface elevation since this is an initial condition for determination of the K value at that discharge (see equations above). Change the b coefficient at each transect (../MANSQ tab, change beta values in the table) and repeat this process until the error between predicted and observed water surface elevations is minimized at all calibration flows. Remember each cross section is treated independently, so once one is calibrated, you can ignore it during the remaining calibrations of the other cross sections.

4. Once an adequate calibration is achieved, add all the flows of interest by checking the boxes in ../Output Options and make the production run using MANSQ.

5. Check the predicted longitudinal profiles of the water surface elevations to ensure water flows downhill at all discharges.

As discussed in modeling water surface elevations with STGQ, the analyst can use the MANSQ program when discharges change between data collection efforts and/or cross sections. The calibration flows at each cross section or groups of cross sections are simply those used in the calibration process. Users may select different calibration flows for each cross section in the table in the ../MANSQ Options tab. Similarly, the analyst can elect to use the computed discharge at each cross section rather than the best estimate of the discharge for the reach. Again, as long as a rational justification can be put forward and defended, these choices are a matter of professional judgement.

The reader is also encouraged to revisit the discussion in the section titled "A Practical Guide to Modeling Stage-Discharge Relationships Using Regression Approaches" provided above since many of the same situations will be encountered when applying the MANSQ model.

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Modeling The Stage-Discharge Relationship Using A Step-backwater Approach - WSP

General Theory of the WSP Model

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. Specific hydraulic relationships between the physical channel and discharge must be met to evaluate these changes in reference to a particular stream reach being modeled. These relationships are defined using concepts of mass balance (continuity) and energy balance. Several basic assumptions apply. These include assuming steady flow conditions existing during the period of field measurements and assuming boundary conditions remain basically rigid (i.e. the channel geometry does not change substantially over the range of measured data sets).

The following example illustrates the step-backwater computational process and introduces the relevant equations. In the example, two cross sections will be described which were illustrated in Figure 2-13. When more than two cross sections are involved, the process is repeated stepwise upstream; hence, the term step-backwater. The flow balance is calculated using the continuity equation:

	Q₂= Q₁ + DQ	(2-12)
where:	Q_1,2 = flow at each cross section as specified by the user
	D Q = specified change in flow (usually zero) between sections

The velocity is then calculated using the following equation:

The energy balance is then calculated using:

The total energy of the stream at a given cross-section is derived from the Bernoulli equation Chow (1959).

The Bernoulli equation written in terms of two adjacent cross sections in the stream is therefore (see Figure 2-4):

This equation accounts for the net effects of energy loss between two adjacent locations within the stream reach. Effects due to changes in bed elevation changes, depth, and velocity are accounted for by losses accumulated between cross sections and are accounted for within the WSP program.

An additional equation is used to relate energy and flow values so that the computational procedure can cross check between the flow and energy balances. Using the user-supplied data for discharge (Q) and roughness (Manning's n), and the calculated values for area (A) and hydraulic radius (R) from the measured data at each cross section, Manning's equation is used to define the energy slope S_ei at each location by:

Manning's equation is empirical, and the roughness coefficient "n" is used to quantitatively express the degree of resistance to flow in the channel. The value of Manning's "n" is an indication of the roughness of the sides, bottom, and other irregularities of the channel profile. The value is used to indicate the net effect of all factors which resist the movement of water moving downstream through the channel. Typical values of Manning's roughness coefficient n in a natural river channel are given in Table 2-3 (derived from Henderson [1966]).

In the most general sense, the roughness or resistance to flow within a channel decreases with increasing discharge as illustrated in Figure 2-14. As can be seen the magnitude of Manning's n estimated for use in the model will be a function of the calibration discharge and will typically vary with simulated discharges according the general relationship shown in Figure 2-14.

This discharge-dependent change in roughness is accounted for in the WSP model by allowing the user to empirically determine this functional relationship and thus vary the Manning's n with discharge within the model as described below. Under practical working conditions, Manning's n values may fall outside reported handbook ranges. This parameter in the model is attempting to integrate all kinds of resistance to flow that include "errors" in approximations such as fixed expansion and contraction coefficients, etc. Also, many of the cited handbook values are more indicative of high flow conditions. In addition, the presence of aquatic vegetation, for example, will result in much higher Manning's values than would be obtained at the same cross section in the absence of vegetation. The overriding principal in the application of the WSP model and, in particular, deriving Manning's n values is whether or not the model adequately predicts the observed water surface elevations.

Computational Process of the Step-Backwater Approach to Water Surface Modeling

The basic step-backwater approach to compute water surface profiles proceeds as follows:

1. Starting at the farthest downstream cross section, a water surface elevation (WSL₁) is taken from user-supplied values or calculated from the user-supplied energy slope using Manning's equation.

2. The energy slope for cross section 1 (S_e1) may be calculated from Manning's equation if water surface elevations are supplied or may be used directly if energy slopes are supplied. (Values of A, R, and V are determined from channel geometry, WSL, and flow.)

3. The water surface elevation at the next cross section (WSL₂) is estimated by projecting S_e1 upstream over the distance (L) between the two cross sections.

4. The energy slope at cross section 2 (S_e2) is calculated using Manning's equations and an average slope for the section is determined from:

5. Flow and energy balances at the two cross sections are performed using:

Other losses associated with effects such as expansion and eddy losses are calculated within the program.

6. The water surface elevation at the second cross section is calculated by removing the velocity head from the total energy head yielding:

7. The WSL² values from steps 3 and 6 are compared and a numerical technique is used to adjust the estimated WSL² values.

8. Steps 3 through 8 are repeated until there is close agreement between estimated and calculated water surface elevations.

9. The entire process is repeated for cross sections 2 and 3, 3 and 4, and so on until all cross section are processed.

Users should note that the computed water surface elevations may not agree with those measured in the field even though internal agreement may be obtained within the WSP model. In this situation, the value of Manning's n is changed by the user and the program is rerun until the energy-balanced water surface elevations calibrate with observed water surface elevations at the single calibration flow. After this initial calibration is achieved, the additional calibration data sets are used to empirically derive the relationship between roughness and discharge illustrated in Figure 2-15 for use in the model as described in the following sections.

The user has the ability to select a variety of computational and reporting levels during the execution of the WSP program. The associated laboratory exercises will treat the use of the most commonly used options in WSP and therefore, a detailed discussion of each option will not be presented here. Table 2-4 lists the options within WSP and provides a concise description of the function for each option. Although various hydraulic options were provided in the original WSP program, most of them have a limited applicability to PHABSIM studies. Thus, the options available in PHABSIM for Windows are limited to those relevant to habitat studies. For a detailed explanation of these options, the reader should consult a "Guide to the Application of the Water Surface Profile Computer Program" (U.S. Bureau of Reclamation, 1968).

A Conceptual Overview of WSP Calibration

Calibrating the Longitudinal Water Surface Profile

We begin by recalling that WSP assumes the cross sections are connected and contiguous within a study site. Then, from an applied perspective, the first calibration step in WSP involves the estimation of an appropriate Manning's n value for the entire study site (that is, the same n is supplied for each cross section) which minimizes the error between observed and predicted water surface elevations at the selected discharge. In other words, the user selects a Manning's n value for all cross sections which allows the WSP model to approximate the observed longitudinal profile of the water surface elevation at all cross sections at this initial (or base) calibration discharge. Normally an increase in the roughness coefficients increases the predicted water surface elevation and a decrease in Manning's n usually reduces the predicted water surface elevation. The first phase of calibration consists of setting n for all cross sections, running WSP, evaluating the results, and adjusting n until suitable agreement between observed and simulated water surface elevation is achieved.

Note that the water surface elevation (or slope) at the downstream-most cross section is a given input to the model and as such, is not part of the actual calibration of WSP for the first cross section. If the user has not measured the starting water surface elevations for all flows of interest and for which the WSP program will be used, then either the STGQ or MANSQ model (or other suitable approach) must be used to generate the starting water surface elevations at the down stream cross section.

One can provide an initial estimate of the Manning's n value using handbook values based on the observed channel configuration and substrate characteristics (e.g., see Table 2-3, or [Chow, 1959]), however, the following technique provides a means of adjusting Manning's n that empirically reflects the dynamics of the resistance to flow based on field measurements.

Begin by using the observed WSL and an initial estimate (obtained from handbooks or by professional judgement) for the Manning's n value for the study site (a global value for all cross sections) and run the WSP model. Examine the output and record the average value of the computed slope obtained over the entire study site (see Equations 2-16 and 2-17, above).

Treating the initial estimate of Manning's n and computed slope from WSP as "trial" values, along with the actual average measured slope for the study obtained from field measurements, the following equation will yield an adjusted estimate of Manning's n for the study site.

This value can be substituted for the initial trial Manning's n value for all cross sections. The WSP model can then be re-run to evaluate the overall fit of the simulated water surface profile. The user should not expect that the n selected will result in a "perfect" match of all observed WSL's at all cross sections. When an apparent best fit has been obtained, proceed to "Calibration of WSP to Additional Longitudinal Profiles", below.

Calibration of WSP to Additional Longitudinal Profiles using Roughness Modifiers (RMODs)

In this calibration step, the relationship between discharge and roughness observed in open channels illustrated in Figure 2-15 is derived empirically. Since the roughness varies as a function of discharge, some means must be used to take into account the changes in roughness with discharge. Therefore, the Manning's n values obtained in the first step of the calibration must be modified appropriately in order to reproduce the observed longitudinal water surface profile at other calibration discharges. The objective is to select roughness modifiers so the new roughness (i.e., computed Manning's n values used during program execution) minimizes the error between observed and predicted longitudinal profiles of the water surface elevations at the remaining calibration flows.

To accomplish this step of the calibration, the remaining calibration discharges and starting water surface elevations (or slopes) at the downstream-most cross section are provided to WSP using the table in the /Models/WSL/Method tab. The user then uses a trial and error procedure to select appropriate roughness modifiers for each new calibration flow which minimize the error between predicted and observed water surface elevations for all cross sections at each of the new calibration flows. Note that the RMOD value for the initial (or base) calibration discharge used during the first step for calibration of Manning's n is 1.0 and should remain so for all simulations. The "base" condition represents our starting point for adjusting n as a function of discharge so it should be multiplied by 1.0 to preserve the starting point. Once the appropriate roughness modifiers associated with the other calibration discharges have been obtained, experience has shown that the roughness modifiers vary approximately with discharge as shown in Figure 2-15, which can be represented by a power law equation:

The coefficient and exponent can be empirically determined from a linear regression between the logarithm of the RMODs and the logarithms of their associated calibration discharges. This regression equation is then used to derive the appropriate RMODs at all flows of interest to be simulated with the WSP model and entered along with the starting water surface elevations (or slopes) at the downstream cross section. A linear regression for RMOD values can easily be performed in a spreadsheet and is not included in PHABSIM for Windows.

The user should not expect that the RMODs will result in a "perfect" match of all observed WSLs at all cross sections for the remaining calibration discharges. The final selection of a particular RMOD value for a given calibration flow will be based on an attempt to minimize the error between predicted and observed WSLs between all cross sections at a particular calibration flow. Often, for example, one will accept a larger error at some cross sections to preserve a better fit over the entire study site and range of observed discharges. This will require the analyst to exercise some degree of judgement which must have a rational basis in light of the conditions at the study site and the needs of the particular study.

PHABSIM for Windows provides effective graphical tools for n calibration. Viewing longitudinal profile graphs in the /Models/WSL/Results tab can give a quick visual comparison of calculated and observed water surface values at each transect. Adjustments to n and RMOD values can be made and the WSP model rerun rather quickly, so a trial-and-error procedure for n and RMOD calibration is both feasible and timely.

Adjusting n Values for Individual Transects

It is tempting to adjust n values to obtain an exact match between measured and simulated water surface elevations at your selected "base" calibration discharge. While visually appealing, such a practice can: (a) maximize the impact of any measurement errors, and (b) result in a poor fit to measured water surface profiles at other measured discharges. If there is a poor fit at the other measured discharges, the analyst cannot be confident about the quality of the simulated water surface profiles obtained using widely varying Manning's n values. In short, if n must vary over a wide range to obtain an exact match to the measured water surface profile at the calibration discharge, something is very wrong. Such a practice is strongly discouraged.

Instead, using different n values among cross sections at a study site should be based on some assessment of changes in the physical conditions among the cross sections. Such changes typically include variation in the bed material (where n represents bed particle roughness, e.g., friction) or in the channel configuration or bed form (where n also incorporates form roughness).

Because Manning's equation does not differentiate between the types of roughness described by n, the user must supply (and defend) the rationale for varying n among cross sections. The initial "global" n approach captures the overall resistance to flow of the channel within the study site. Then, local variations in n may be considered where there is some physical justification. For example, if there is an area with large numbers of colluvial boulders in the stream, the boulder field would be expected to have a higher-than-site-average flow resistance. Other areas would be likely to have resistance below the average. Similarly, changing from a rectangular cross section in a riffle to a parabolic cross section in a pool may justify small local adjustments to n by trial and error. In general, adjustment of n values for individual cross sections more than approximately ±10% ~15% of the global value for the study site needs to be justified by specific evidence about large changes in bed material or channel configuration. Whenever making local n adjustments keep two criteria in mind: (1) there must be some physical basis and (2) the adjustment is intended to obtain a better match between predicted and observed water surface profiles. If an adjustment made to obtain a better water surface elevation match is contrary to the apparent physical processes in the channel, it cannot be defended.

Note that the Manning's n value at a downstream cross section can have an "impact" on the magnitudes of the Manning's n values at the remaining cross sections. During the calibration procedure, care must be taken to avoid a see-saw effect in selected n values.

Determining Initial Water Surface Elevations for Calibrated WSP Models

The final required step for using the calibrated WSP model for WSL simulation is to define the starting water surface elevations at the downstream cross section for all unmeasured flows. The most common approaches are to use either a stage-discharge regression (STGQ model) or Manning's equation (MANSQ model). In both of these instances, the user can instruct the PHABSIM interface to extract the water surface elevations for a single cross section from the existing STGQ or MANSQ results by selecting the WSP/STGQ or WSP/MANSQ methods for the downstream-most cross section in the Models/WSL/Method tab. It is highly recommended that practitioners place the downstream-most cross section on a hydraulic control. This enables use of the STGQ or MANSQ model to establish starting WSL's for unmeasured discharges at the control cross section. Use of either STGQ, MANSQ, or another source of the initial conditions for backwater modeling, is the analyst's responsibility. The predictions of the water surface elevations produced by STGQ or MANSQ are transferred to the WSP model by the PHABSIM interface when the WSP/STGQ or WSP/MANSQ options are selected. If the water surface elevations for unmeasured discharges are obtained from an outside source, the user may enter those values using the WSP/User supplies initial WSL option in the Models/WSL/Method tab.

Regardless of the method used to supply initial WSP water surface elevations, the user must set appropriate RMOD values for all discharges prior to use of WSP for production runs. As stressed previously, the user should then check the overall quality of the hydraulic simulations by checking the longitudinal water surface profiles over the full range of simulated flows.

A Step-by-Step WSP Calibration Strategy

The WSP program is used most often in those instances where multiple stage-discharge measurements are available. The following approach is provided as a guideline to calibrate the WSP model.

1. Select WSP as the water surface profile simulation method in /Models/WSL/Method. Note the downstream cross section must have an entry of WSP/STGQ, WSP/MANSQ, or WSP/User supplies initial WSL and that the MANSQ or STGQ models must have been calibrated for the downstream cross section where WSP will be used. Supply an RMOD value for each discharge in the ../WSP Options tab. Initial RMOD values can all be 1.0.

2. Run the WSP program and examine the results and ZOUT files to find the computed slope for the downstream-most cross section and use Equation 2-22 or trial-and-error to estimate a revised Manning's n value for the study site. Edit the cross section data so the all cross sections have this Manning's n value. Note: an error message: "WSP Terminated with an Unknown Error" usually indicates you did not supply an RMOD value for each discharge.

3. Rerun the WSP model and note the agreement of predicted WSL with observed values at the base discharge. Based on the difference between predicted and observed WSL, adjust the global Manning's n value for all cross sections and rerun the WSP model. Continue to change the Manning's n value until the predicted and observed water surface elevations are as close as can be obtained with the global n applied to all cross sections. Some variation between the observed and predicted WSL values is likely to occur at some transects. But the overall error should have been minimized.

4. Adjust local (cross section by cross section) n values (within ±10% ~15%) to reduce the remaining error between the observed and predicted water surface profile. Make those adjustments with the physical processes in mind and avoid adjustments that cannot be physically justified, i.e., do not "curve fit". Evaluate if the agreement error is within the tolerance limits that meet your study objectives. Remember, the WSP model works in an upstream manner and therefore the predicted WSL at the second cross section will be the starting WSL for making the predictions of the WSL at the third cross section, and so on proceeding upstream. For example, a low predicted WSL at the second cross section will "start" the model lower than wanted while attempting to reach the WSL at the next cross section. This can result in supplying unusual Manning's n values at the next upstream cross section in order to get agreement at that cross section. The user should also note that in many instances, exact agreement is not always possible and WSLs at some cross sections may be high while at others they will be low. Again, some level of professional judgement, based on experience, will be necessary in order to determine how close predicted versus observed water surface elevations must be to be acceptable for individual cross sections or for all cross sections. Once suitable agreement between predicted and observed water surface profiles has been obtained for the base discharge, proceed to step 5.

5. Once the initial longitudinal water surface profile has been calibrated by selecting the appropriate Manning's n values at each cross section, broaden the evaluation to include the remaining calibration discharges and starting water surface elevations at the down stream cross section. Select the other calibration discharges in /Models/WSL/Output Options. Initially the roughness multipliers (RMODs) for these new calibration flows can be set to 1.0. Or, based on whether the other calibration flows are higher or lower than your initial calibration flow, you can set the RMODs to be greater or less than 1.0 based on the relationship shown in Figure 2-15. New calibration flows greater than your initial calibration flow will require a Manning's n lower than 1.0, while new calibration flows lower than the initial calibration flow will require a Manning's n greater than 1.0. The relative magnitudes of the RMOD estimates will be a function of how different the magnitude of the discharges are relative to your initial calibration flow.

6: Rerun the WSP model with the new roughness modifiers and compare the predicted and observed WSL at all cross sections at these new calibration flows. Adjust the RMODs at the new calibration flows until suitable agreement between predicted and observed water surface elevations are obtained. Each discharge is computed independently within WSP so once an RMOD is found which works for a specific calibration flow, that RMOD can be left unchanged while continuing your work at the remaining calibration flows. RMODs should be adjusted to obtain an overall minimum error between predicted and observed WSL for all calibration discharges.

7. Perform a linear regression between the logs of the RMODs and the logs of the discharge and use this equation to estimate the RMODs for all flows of interest for the study that you plan to use the WSP model to predict the water surface elevations.

8. Use the STGQ program or MANSQ program to supply initial WSL's to WSP at the most downstream transect for all other discharges to be simulated. That is, use WSP/STGQ or WSP/MANSQ at the WSP starting transect in the Models/WSL/Method tab. Remember a starting water surface elevation must be specified for all flows of interest at the first or downstream-most cross section when using the WSP model. If the STGQ or MANSQ models are used for WSP initial conditions, those models must be calibrated first before proceeding with WSP.

9. Add any additional desired discharges to the PHABSIM project using Edit/Discharges. RMODs determined from Step 7 must be associated with each of these flows (see the WSP Options tab) and the water surface elevation simulation must have those discharges specified in the Models/ WSL/ Output Options tab.

10. Check the quality of the hydraulic simulations by plotting the longitudinal profiles of the water surface elevations for all simulated discharges (use the ../Results/Longitudinal graph button). Zoom in on the calibration discharges for one last comparison of the predicted and observed water surface profiles and make any final adjustments to n or RMOD as needed. If the very highest discharges produce unusual water surface profiles, check for predicted water surface elevations higher than the highest measured bed elevations. The model becomes invalid if WSL's significantly greater than the highest bed elevation are predicted. If such high discharges must be simulated, more field data is needed to define the channel at those heights.

Some Practical Aspects of Calibrating and Use of the WSP Model

The quality of calibration that can be obtained for a stream section will vary with the hydraulic characteristics of the stream and the nuances of the field data. Steep, rough streams often exhibit large fluctuations in water velocities and water surface elevations and may be difficult to calibrate. Typically, achievable agreement between observed and simulated water surface elevations is ± 0.01~0.02 feet (±0.00305~0.0061m) for the profiles at each calibration discharge. However, the investigator must be aware that specific situations may require establishment of more lenient or stricter standards. For example, an investigator may relax this standard somewhat at the highest calibration flow profile in order to achieve a closer agreement at the middle and lowest calibration flow profiles since this lower range of discharges is most important in view of the particular instream flow project under consideration.

Although text book values of Manning's n can serve as a reference point, it should be noted that many of these values are most appropriate for higher discharges at or near bank full conditions and as illustrated in Figure 2-15, may, in fact, be too low under lower flow conditions. In other words, do not be surprised if the calibration Manning's n values do not match the ranges reported in the hydraulic handbook values. This should not be a source of concern as long as a physically based meaning can be attached to the values. Perhaps the most critical factor should be how well the model is able to reproduce the observed data. This of course assumes that any obvious data collection and entry errors have adequately discounted or corrected.

The WSP model will produce unreliable results if water surface elevations significantly higher than the highest cross section elevations are necessary to simulate the desired discharges. Always review the longitudinal profile for realism of the simulation. When very high discharges must be simulated as part of a PHABSIM study, it is imperative that at least bed elevations high on the bank and water surface elevations for a discharge in the vicinity of the desired high discharge be collected to ensure the PHABSIM models can run within reasonable bounds.

Transects should start and end at hydraulic controls if at all practical. Calibration problems are greatly exacerbated when starting and ending transects are not located at hydraulic controls. The effect of hydraulic controls in a WSP calibration are often profound. It is often possible to alter the water surface profile through an entire reach simply by modifying the roughness at the downstream control. One overriding principle of the WSP model is that the downstream-most transect must be on a control and all other controls in the reach should be defined by a transect. This means the downstream control associated with specific habitat features, such as a pool, should be included even if they are of no interest for representing the habitat feature of interest.

Flow partitioning is a necessity when the channel around one side of an island is longer than the other side. When the length of one channel exceeds the length of the other by a factor of approximately 1.5 or more, or the channel configurations differ significantly, flow partitioning should be considered. In essence, flow partitioning involves breaking up the total discharge of the stream into component discharges for each channel. The WSP program is calibrated for each channel at the component discharge as if it were a separate stream (see below). At the calibration discharge(s), this is a relatively easy procedure because field notes should contain all the information needed to break out component discharges. The problem arises when alternative stream flows are modeled. At discharges other than the calibration discharge(s), the proportion of the total flow carried by either channel changes as a function of total discharge. The process of flow partitioning often is very difficult. It is advisable to consult an experienced hydraulic engineer before attempting this type of analysis. Basically, the problem is to determine the component discharges at a range of unobserved flows so that a rating table can be built. This is done by first calibrating the component channels as measured; then for some unobserved total discharge, component flows for each side channel are split out by estimation and run individually through the model.

Calibration of the WSP model can be difficult when flow splits into two or more channels. In general, the water surface elevation models in PHABSIM are not designed to work in split channels. A few streams may have small enough differences between channels on either side of an island to follow one of the transect placement or data adjustment approaches described below. However, in most cases, those approaches will introduce considerable error. FORT recommends users partition the flow empirically through each of the channels and treat each channel as if it were a separate stream to be calibrated and simulated separately. This means that discharge measurements for the full channel and each side channel must be made for at least the calibration discharges. A regression of side channel discharge against full channel discharge (or other means to build a rating table) can then be used to determine the flow split for the unmeasured discharges to be simulated in the study.

When partitioning the flow, care must be taken to ensure that the water surface elevations simulated at the top of each separate channel are the same (or within an acceptable tolerance) for all discharges. This allows an island to be represented by four backwater models: main channel downstream of the island, left side channel, right side channel, and main channel upstream of the island. A backwater simulation can be run for the main channel downstream of the island to produce the starting water surface elevation for both side channels for all discharges of interest. Then the two side channels are simulated with Manning's n calibrated to produce the same water surface elevation at the top of the island. And finally, the main channel upstream of the island is simulated using the initial water surface elevations derived for all flows from the simulation of the two side channels. In PHABSIM for Windows, this will require four projects covering the four separate portions of the channel and ensuring that the transects at the partitions are duplicated in the appropriate data sets. Though tedious, this is the only way to assure that the flow conditions around the island are modeled accurately over a wide range of discharges.

When there are small differences between the two channels around an island and the study site is represented with a single backwater model, two generic types of problems are presented by divided flow. The first, and most common, is unequal water surface elevations on both sides of a flow division. The most common cause of this problem is crossing an island with one straight transect when a dogleg transect should have been used (see Figure 2-15). By their very nature, islands rarely have the same bed and water surface elevation at equidistant points along the bank. Ideally, the transect should cross the island with a dogleg in order to obtain an equal water surface profile on both sides of the island. In braided channels, this is the rule rather than the exception. The two elevations may be averaged if the discrepancy between two water surface elevations is small compared to the difference in elevations between transects for all calibration flows. What constitutes small in this instance is a matter of judgement. However, if the discrepancy between water surface elevations is large, bed elevations of the smaller channel may be raised or lowered a distance equal to the difference in water surface elevations. All of these manipulations of the data may introduce their own noise in the analysis. Again, splitting the study site into four backwater models is preferred.

The energy loss between the two channels must be the same for water surface elevations to equalize at the head of the island. The two component flows giving the same energy loss for both channels (which should equal the total flow in the channel) are the proper component flows. If finding flow rates and energy losses that satisfy these conditions seems extremely tedious and difficult, it is! Alternatively, such ratings can be built empirically by collecting both water surface elevation and discharge data at several flows over the range of discharge of interest to the study. Hence, if you have split flow, plan on making many more water surface and discharge measurements in both the main channel and side channels.

Running the WSP Model

WSP must have starting conditions supplied at the downstream-most transect to which it will be applied. In the /Models/WSL/Method table select either WSP/MANSQ, WSP/STGQ, or WSP/Supplied for the downstream starting condition at each starting transect for each discharge. Then fill with WSP upstream (fill down in the table) over the extent of the river to which WSP is to be applied. Make these selections by clicking on the model, e.g., WSP/STGQ and then clicking each of the transect/discharge boxes in the table to which that model is to be applied. An example of a completed WSL method table is shown in Figure 2-16.

Figure 2-16. Water surface elevation method table showing entries for WSP analysis.

Next, in the ../WSP Options tab, enter a Manning's n for each transect in the table on the left. Roughness modifiers, which are entered in the right hand table, will be discussed later. While in this tab, select the desired options using the check boxes and click Apply. Note, all combinations of WSL simulation models are run at once by clicking the Run tab in ../Method. As with STGQ and MANSQ, after the models have run, compare simulated with observed water surface elevations using the tables and graphs in ../Results. In general, for cross sections where WSP is applied, Manning's n should be increased when the predicted WSL is low and decreased when predicted WSL is high. The WSL at the downstream transect is not changed by the WSP model. The laboratory exercises will provide you with experience with the WSP calibration process

Several key hydraulic parameters related to the computational procedure within WSP are output to ZOUTnn. Although not all of these variables are in the output for each cross section, they are usually located somewhere in the output from a WSP run. Their definitions are provided below and have been illustrated in Figure 2-4.

HF1 = Head loss computed at downstream section.
HF2 = Head loss computed at upstream section.
HSF = Slope (Se) of energy grade line at section.
HV1 = Velocity head (v12/2g) computed for downstream section.
HV2 = Velocity head (v22/2g) computed for the upstream section.
Total Head = Total head loss (hf) between sections.

Remember to review the output file for error messages and inconsistencies in the data. Error messages in the form of notes or other statements may be written to the output file and not appear on the screen or cause the program to abort. Output from the WSP model is both extensive and variable depending on the particular run options that the user selects. Examination of WSP output is deferred to the laboratory exercises.

TOP OF PAGE

Modeling Of Velocities In PHABSIM

The second major step of hydraulic modeling within PHABSIM involves simulating velocity profiles at each cross section within the river. Transect based open channel flow models face a serious limitation in simulating velocity distributions across the channel. Both step-backwater and stage-discharge type models were developed and have been verified only for whole channel calculations. Thus, lacking a theoretical method of distributing velocities, PHABSIM relies on empirical means to approach this problem.

PHABSIM models velocities for individual cross sections and as such treats the cross sections independently regardless of the model employed to generate the WSLs. In most cases, only limited resources are available to do field work in any particular instream flow study; hence, a limited number of velocity profile readings are used to estimate the velocity distribution at flows for which velocities were not measured. Within PHABSIM, the VELSIM model is used for all velocity predictions. Those velocity values are subsequently used in the habitat modeling portion of PHABSIM. Figure 2-17 illustrates the relationship between a measured velocity at a cross section vertical and a computational cell as viewed by the VELSIM model.

Note that both the STGQ and VELSIM programs define a computational cell as the region one?half way between two sets of adjacent verticals (see Figure 2-17). A vertical is a measurement point specified as the X (distance from the head stake) coordinate values (see Chapter 1). All references to the computational cell are then made to the vertical. Note that this definition of a cross?sectional cell is different from that used by the habitat models. These differences are discussed in more detail under the appropriate habitat models in Chapter 5.

In PHABSIM, each computational cell in a cross section is treated separately, with its own depth, substrate, and average velocity. In the VELSIM program, there is a one-to-one correspondence between mean column velocities and the X coordinate of the vertical at which the velocity was observed or simulated. Velocities can only be provided at X coordinate values in /Edit/Cross Sections/Coordinate Data. PHABSIM for Windows does not limit the number of subdivisions (or cells) used to define the velocity distribution across a cross section. Obviously, the more computational cells per cross section, the more detailed the description of the velocity distribution. The VELSIM program defines a cell as the region half way between two sets of adjacent verticals as illustrated in Figure 2-17.

Calibration and Simulation of Velocities

In the following discussions, approaches to estimating the velocity distribution at a cross-section are described. The first section describes use of Manning's equation where no velocity measurements are made to calibrate the equation. The second section discusses the use of Manning's equation with measured velocities at one flow while the third section describes procedures using more than one set of measured velocities.

VELSIM with No Measured Velocities

The VELSIM program can be used to simulate velocities at a cross section although no velocities were measured. This is accomplished by rearranging Manning's equation to solve for "n" in terms of the measured discharge and individual cell attributes and substituting the depth of flow for the hydraulic radius:

The net effect of this approach is that the magnitude of the velocity predicted at any vertical across the cross section is directly related to the depth of flow, and, therefore, the relative magnitudes of the velocity distributions will mimic the channel geometry as illustrated in Figure 2-18. Note that in VELSIM, if a user specifies a Manning's n value at a particular vertical, the VELSIM program will use that Manning's n to compute velocities when employing Manning's equation. The user should always check this type of simulation for realism. Experience has shown that under some circumstances, this approach yields satisfactory results, while in other circumstances it is not acceptable. Viewing plots, such as shown in Figure 2-18 in /Models/Velocity/Results, allows visual detection of unusual velocity distribution patterns. Note that the velocity profile in Figure 2-18 is proportional to depth.

FORT suggests that this approach be limited to those cases where field conditions or equipment failures prevented collection of at least one velocity data set and limits of time (deadlines) or resources prevent collecting at least one velocity profile at a later time. The judgement is left up to the investigator and the particular objectives of the model application.

VELSIM with a Single Velocity Data Set

If one set of velocities is used to calibrate the VELSIM program, a different approach is taken based on an initial solution of Manning's equation to obtain an estimated Manning's n at each vertical along a cross section. This approach treats the observed velocity profile as a template for describing velocities for other discharges. Since slope, water surface, and observed velocity are given as part of the calibration data, Manning's equation can be solved for ni at each vertical:

Note in this equation, that depth DI at the vertical has been substituted for the hydraulic radius and is computed from the difference between specified water surface elevation and bed elevation at each vertical. The measured velocity (vi) at each vertical is obtained from the input data. If a slope has not been provided (i.e., specified in /Edit/Cross Section Data) a default slope of 0.0025 will be used. The specific slope used is not critical to the calculation of velocities using this approach as illustrated below. Having obtained individual Manning's n values at each vertical, individual cell velocities can be computed at any alternative discharge by solving Manning's equation for velocity and using the initial Manning's n value derived from the calibration velocity set:

As noted above, if a user specifies a Manning's n value at a particular vertical, the VELSIM program will use that Manning's n in the computation of velocities when employing Manning's equation even though an initial calibration velocity had been provided. Figure 2-19 provides an example of a single observed velocity calibration set with the associated predicted velocities at the calibration flow. Since the best estimate of the discharge is typically used in the simulation of water surface elevations and the VELSIM maintains mass balance for the discharge, the simulated velocities at the calibration flow will not exactly "match" the observed velocities.

During simulation, if VELSIM simulates a water surface elevation at a cell for which no velocities were available for estimation of Manning's n or a Manning's n value was not supplied, the program will search for an adjacent cell to obtain an estimated or user-specified n value for use in the computation of velocities at that vertical. The user has several options for setting Manning's n in VELSIM either through a calibration velocity template or by estimation. These options are discussed in more detail at the end of this section.

VELSIM with Multiple Velocity Data

Although the investigator may have measured multiple velocity sets for use in the study, FORT recommends that the multiple velocity calibration data sets be treated as independent data sets for modeling purposes. The recommended strategy uses the highest observed velocity data set to simulate at all flows higher than the highest measured flow, the lowest observed velocity set to simulate flows lower than the lowest measured flow, and user judgement for which discharge ranges between observed velocity sets to assign each calibration velocity set. For example entirely different velocity distributions between a high flow velocity data set and a medium or low flow velocity calibration set may be found when channel geometry is very different at the associated stages. In this instance, the use of a single calibration data set over all ranges of discharges would not accurately reflect the observed velocity profiles at alternate discharges. One strategy would be to "switch" among different calibration data sets at the break in the channel geometry. The investigator would only need to determine the elevation at which this break in channel shape occurs and then determine the appropriate flow from the water surface modeling. It should also be apparent that this exercise is somewhat idealistic in that only a single cross section is shown. In practice, the user would need to consider all cross sections within the modeled reach and will therefore likely need to find a single "compromise discharge" where velocity calibration sets are changed in the model.

Following the strategy recommended above will result in dissimilar velocity profiles for discharges immediately above and below the break between assigned flow ranges. In some channels, this effect can be pronounced. Lacking additional velocity profile measurements, the exact transition between the calibration set velocity profiles is unknown.

An alternate scheme is provided in PHABSIM for Windows to handle this situation. That is to replace the velocity values in the ranges between observed calibration flows with a smooth transition based on the assumption that a log-log linear transition takes place. After VELSIM has been run with calibration sets assigned to each discharge of interest, the Velocity Regression tab is accessed. When clicked, the Run Velocity Regression button causes velocity values for each cell in the ranges between calibration discharges to be predicted using a two point regression. These values replace the values produced by running VELSIM. Note: this approach affects only the velocities in the discharge ranges between calibration discharges.

VELSIM Computational Procedures and Mass Balance

In order to more fully understand the remaining computational aspects of velocity simulation within the VELSIM program, the following section describes the governing equations and process by which the VELSIM program maintains a mass balance between the requested simulation discharge and computed discharges, given its implicit computation of individual cell velocities.

The area of the cell is computed by the following equation:

The "trial" discharge computed for a requested simulated discharge at the transect is then determined by using the velocity predictions for each computational cell derived from the velocity simulation method selected. These values are used to calculate cell discharges which are summed for all cells across the transect:

This apparent or trial discharge is not necessarily the same as the discharge requested in the simulation. Reference to Figure 2-15 shows the relationship between discharge and roughness and should indicate that a particular Manning's n value derived from a velocity calibration set at a single discharge will not be the "correct" Manning's n value at higher or lower discharges. This is the same basic concept that led to the use of RMODs in the calibration of the WSP program. An index of the difference between the requested simulation discharge and computed discharge derived from the velocity simulations is called the Velocity Adjustment Factor (VAF) and is computed by the following equation:

This ratio is then used to adjust individual cell velocities, v_I, which also adjusts the computational cell discharges. This adjustment proceeds until the calculated discharge for the cross section equals the requested or simulated discharge. The adjustment of the individual simulated discharges is accomplished with the VAF by adjusting the individual computational cell velocities by the following equation:

The use of the VAF in the VELSIM program represents an empirical approach to approximate the role of the RMODs in the WSP program. The relationship shown in Figure 2-15 indicates that at simulated flows lower than the velocity calibration flows, the Manning's n value derived from the velocity calibration flow will be too low. Since the roughness (i.e., Manning's n) values used to estimate the velocities are too low, the estimated velocities at each vertical will be too high (see Manning's equation). This results in a computed trial discharge for the cross section that is greater than the requested simulation discharge and the resulting VAF would be less than 1.0 (see Equation 2-30). Conversely, at simulated discharges greater than the velocity calibration flow, the estimated Manning's n values will be high and the resulting individual computed cell velocities will be low. This results in a computed trial discharge that is less than the requested simulation discharge and the VAF will be greater than 1.0. This process suggests that in most cases the relationship between discharge and VAF should be approximately an inverse of the relationship shown in Figure 2-15 and resemble the example illustrated in Figure 2-20. Although this general pattern is typical of most cross sections, there are occasions where the VAF versus discharge relationship will not and should not follow this generalized pattern such as when lateral bank vegetation increases the composite roughness at intermediate discharges.

In Figure 2-20, there are two ranges of discharges for which the VAF plot ascends in what appears to be different patterns. The apparent break in the VAF plot at about 250 CMS is due to using different calibration sets to produce the velocity template used for velocity simulation. Within the range of discharges for which a particular set of calibration velocity measurements were used to develop the Manning's n template, an ascending VAF relationship indicates the expected outcome of velocity simulation. It should also be noted that the VAF at the calibration flow will not always be equal to 1.0. For example, during the modeling process, the user may have selected the best estimate of discharge for a group of cross sections where the measured variability in computed discharges may have been 15-20%. For any cross section that has a computed discharge based on a set of calibration velocities that is not exactly the same as the best estimate of the discharge, the VAF will deviate from 1.0. The magnitude of the deviation will depend on the magnitude of the deviation between the best estimate of the discharge and the discharge computed using the calibration velocity set.

It is also reasonable to expect that the VAF relationships for sections with similar cross section geometry will be similar in their functional relationships and the variation between VAF versus discharge relationships will be directly related to the degree of variability in the cross section geometry. As a final note on VAFs, there is no rational basis for judging the "validity" or quality of the hydraulic simulations based strictly on the magnitude of the range in computed VAF values. That is, there is no specific set of envelope values that the VAF should absolutely lie within. It is only an index of the relative change in discharge from the calibration discharge used at the calibration velocity versus the simulated discharge which follows the relationship between roughness and discharge shown in Figure 2-15. The shape of the VAF versus discharge plot is a better indicator of model performance than the VAF magnitude. When a monotonically increasing VAF relation is not obtained, it is not necessarily an indication of model failure. Rather, it simply is an indication that the model calibration and simulation steps should be reviewed. Some channels exhibit non-standard VAF plots even when the models are performing well.

Significance of Initial Slopes and Manning's n Values in VELSIM

Note that slope does not appear in the four equations above which describe the computation of velocity and mass balance in the VELSIM program. Also, the slope used in the initial calculation of Manning's n will not influence the final calculation of the velocity. The slope is important only in being able to compare individual Manning's n values at cross section verticals from one cross section to another or from one stream to another. The selection of Manning's n values to add to a data set to control velocity simulations is easier however, if a reasonable estimate of slope is used to calculate roughness from the calibration velocities. The Manning's n value at this point within the VELSIM program really represents a velocity distribution factor. The user should not be too surprised if individual cell Manning's n values do not fall within the expected ranges reported in hydraulic roughness tables for cross sections containing a particular substrate characteristic. Handbook values are estimated for whole channel conditions (often for high flow conditions as well) and not for a particular vertical within a cross section.

The role of Manning's n in VELSIM is important since it functions strictly as a velocity distribution factor and can have an impact on results of the habitat models. In general, since velocities are not measured at previously dry verticals, n values will have to be estimated by the program or supplied (i.e., estimated) by the user. However, the Manning's n values for velocity distribution are derived in one way or another. Whether they are calculated from observed velocities, estimated for the cell by the VELSIM program when no velocity data is supplied, or supplied by the user, that Manning's n values are used to calculate the cell velocity for all simulated discharges. This is primary importance when simulating higher flows because, when simulating down from a measured velocity calibration set, the program will have Manning's n values computed from known velocities at all verticals.

Simulation of higher discharges can, however, lead to problems at the edge of the stream where fringe cells may contain very small cross sectional areas at the calibration discharge. When Manning's ni values for dry cells are not supplied by the user, the program will search adjacent cells for a given or calculated ni or will assume a value of 0.06 if none are found. However, the VELSIM program will occasionally predict unrealistically high velocities on the stream margin (e.g., 20 feet/second!) due to the combination of Manning's n estimation and application of the VAF to achieve mass balance. Since these areas may be very important to certain life stages of aquatic species being studied, the user should carefully examine the velocity simulation results for these "artifacts" of the computational process during VELSIM calibration. Use the Cross Section plot button in Models/Velocity/Results to view simulated velocity profiles and the tabular velocity results to determine which cells need to have n values supplied to improve erroneous edge velocities. In these instances or where other factors may warrant, the value of ni for dry cells (or wet cells) should be supplied by the user in the /Edit/Cross Section/Coordinate Data tab. This is covered in more detail in Laboratory 6 on velocity calibration and simulation.

Much attention has been given to the debate on mean column versus nose velocities (also called focal point velocities) in PHABSIM applications for prediction of available habitat. The HABTAE model offers the user a variety of modeling choices for the computation of nose velocities either based on the distribution of bed material particle sizes, regression equations based on mean and nose velocity measurements, or by empirical relationships based on the 1/7 power law, to name a few. The application of these techniques however, is limited to those situations where nose velocity habitat suitability curves are available and sufficient field data has been collected to support use of these hydraulic modeling options. Additional descriptions of nose velocity calculations and options are included later in this manual under the HABTAE model program and will not be discussed further here.

Control of VELSIM Calibration and Simulation Options

Much of the utility of the VELSIM program lies in the ability of the user to provide very specific control over all aspects of the computational procedures. The user should review available options for the VELSIM program listed in Table 2-6. This review often results in some confusion for the user to decide which combination(s) of options should be selected to achieve the desired results. This problem can be overcome by breaking up available options into several discrete conceptual parts that are provided below.

Velocity Adjustment Factor and Mass Balance

Use Velocity Adjustment Factor: {tc /l4 "Use Velocity Adjustment Factor}This option in essence will allow the user to ignore application of the VAF to achieve a mass balance within the VELSIM model. If this option is not checked, mass balance determined from application of the VAF will be ignored. In most cases, this box should be checked so mass balance will be enforced and the VAF applied.

Controlling Roughness: Several options are available to the user to control the way in which the VELSIM program will use roughness.

Calculate N for Wet Cells {tc /l4 "Calculate N for wet cells}: This option allows the user to control the way in which the VELSIM program will calculate roughness or how it uses the roughness if supplied (i.e., Manning's n).

Limit Manning's n {tc /l4 "Limit Manning's n}:This option allows the user to specify the maximum and/or minimum value of the roughness computed with the Manning's equation during the simulation of velocities. The maximum and/or minimum value is specified in the input cells provided in the /Models/Velocity/Options Window.

Variable roughness coefficient {tc /l4 "Variable Roughness Coefficient}: This option allows the user to adjust the roughness in a cell as a function of depth in a cell. This option can help reduce the negative impacts arising from too high a roughness at edges of the stream calculated at lower discharges that would be expected to become less rough as flow (i.e., depth) increases. NOTE: Leave the Velocity Adjustment Factor box blank or the results will be irrational when using this option.

The general equation for changing roughness as a function of depth is:

The estimation of "B" for use in variable roughness has received little discussion in the literature and only those with an advanced familiarity with hydraulic modeling should consider the use of this option.

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Evaluating Quality of the Hydraulic Modeling

In the preceding sections, the basic theory and steps to achieve the calibration and simulation of both water surface elevations and velocities were presented. This section address some of the more fundamental issues in evaluating the quality of the hydraulic modeling effort. Evaluation of water surface elevations is discussed first followed by a discussion of velocities.

Evaluation of Water Surface Modeling

Predicted Versus Observed Water Surface Elevations at the Calibration Flows

Perhaps the most fundamental diagnostic of the quality of hydraulic modeling of the water surface elevations is how close are the predicted and observed water surface elevations at the calibration flows. This leads to the question of how close is close enough? Unfortunately, no readily available answer can be dogmatically stated. In general, the user should attempt to match the observed and predicted water surface elevations with no error, but this represents a case not readily achieved in applied hydraulic modeling. The user will often be faced with trading accuracy at one set of measured calibration flows to achieve a better fit at over the full range of calibration flows. For example, the user may be able to replicate the observed water surface elevation longitudinal profile using WSP at the lowest calibration flow but no RMOD can be found to achieve an exact match for the high calibration water surface profile. An alternative re-calibration of the WSP model to the high flow may result in replication of the longitudinal profile, but again, no RMOD can be found which adequately replicates the low flow profile. In this instance, the user is likely to use the WSP model which is most accurate nearest to the flow range in which the instream flow questions are likely to be the most contested. As a general guideline, in most applications predicted versus observed water surface calibration errors which are on the order of 0.01-0.02 feet can be achieved. It is not uncommon; however, that a single or a few cross sections may deviate more (e.g., 0.03-0.05 feet or more) depending on the characteristics of the channel geometry, gradient, left versus right bank differences in water surface elevations (remember that only a single value is used for all models). Potentially, a hydraulic control may have been missed during field collection or a hydraulic control is migrating within the channel over the range of discharges collected. It is possible however, to evaluate the application or performance of each of the models and demonstrate that the "best" calibration/model combination achievable with the available data is actually used in the study. It may not be possible to overcome poor model performance with the collection of new or additional data. In such a situation, the degree of uncertainty must be clearly reported and kept in the forefront during the evaluation of study results.

Longitudinal Profiles of the Water Surface Elevations

A second measure of the quality of the modeling for water surface elevations is the examination of the longitudinal profiles of the water surface elevations over the entire range of simulated discharges. That is, where the cross sections are all measured to a common survey datum, the longitudinal WSL plots can be examined to determine whether or not water "flows uphill". Such a situation would indicate that the range of simulated discharges should be restricted for the application of that particular WSL model to flow ranges over which the results are consistent (i.e., water flows downhill). In many applications, one or more models (e.g., STGQ and MANSQ) may perform well within the range of the measured calibration discharges but only work well at some reduced range of extrapolated discharges. At these higher discharges of interest, the only WSP model may be adequate and the user can elect to WSP to simulate over all ranges of flows or for only the higher flows where the other models would not be appropriate.

Valid Ranges of Simulated Discharges

Some individuals have used the absolute range of simulated discharge, that is, how much higher than the highest calibration flow and how much lower than the lowest calibration flow, as a measure of the quality of the simulations. In earlier PHABSIM manuals, ranges of "acceptable" simulations have been reported as 0.4 to 2.5 times the measured discharges. Under some circumstances a range of 0.2 to 1.5 has also been reported. The user should note that, from a functional, algorithmic, or mathematical perspective, none of the models (i.e., STGQ, MANSQ, or WSP) are inherently restricted to any range of acceptable simulation limits from a hydraulic perspective. In some applications, very restrictive ranges are required due to channel configuration, model performance and adequacy of the available data, while in others, extremely wide ranges (i.e., 0.1 to 10) are justified by model performance. What constitutes a valid range of simulated discharges in the absence of poor model performance (i.e., "water flowing uphill", large calibration errors, etc.) is a matter of professional judgement. At present, no rigorous peer reviewed evaluation of WSL simulation limits using any of the hydraulic models for specific types of channels and site specific field conditions has been undertaken. The user is cautioned that a reasoned limit to the reliable range of simulations should be based on model performance given the available data rather than an arbitrary "rule of thumb".

Evaluation of Velocity Modeling

Perhaps one of the most difficult aspects of evaluating hydraulic simulations involves the evaluation of the velocities. When no calibration velocities are available, it is a matter of professional judgement as to the utility of the velocity distributions based on depth as long as the obvious "errors" such as high velocity artifacts at the stream margins have been corrected. Another potential indication of problems in the simulations would be extremely "odd" VAF relationships which have no rational basis in physical characteristics at a cross section.

In those instances in which a single velocity set has been used in the simulations, it is a matter of professional judgement as to the quality of the simulations, assuming that any erroneous velocity errors have been accounted for. However, if during a review of the channel characteristics for the cross sections it is determined that gross changes in channel geometry occur at some "threshold" water surface elevation (i.e., discharge), then the velocity simulations should be carefully examined to determine if the distribution across the change in channel geometry makes rational sense. This situation often arises where only a single velocity set was collected at a low flow or alternatively at only the high flow and a large "floodplain" type geometry exists. It is unlikely (but not impossible) that a standard application of the single calibration velocity set will reflect the velocity magnitudes and distributions across such a radical change in channel geometry. Modification of the velocity simulations using professional judgement is the only real option if the collection of an additional velocity calibration set(s) cannot be accomplished under the constraints of the project.

In those instances where multiple velocity sets have been collected, the user can easily check the validity of the velocity simulations by comparing the predicted velocities to one or more of the other calibration velocity sets. In the event that the predicted versus observed velocity profiles are not within an acceptable range, then one or more of the other calibration velocity sets should be used for the appropriate range of discharge. Channel geometry changes in this situation can often provide guidance to the analyst for the water surface elevation and hence discharge ranges, that a particular velocity calibration set might be most appropriate. Again, any VAF functional relationship which deviates from the "expected" relationship should have a physical justification based on site-specific characteristics.

Chapter 2. Hydraulic Modeling in PHABSIM

Objectives

Laboratories

Introduction

Terms and Definitions for Open-channel Flow

Cross Section:

Reach Length:

Backwater:

Hydraulic Control:

Backwater:

Hydraulic Control:

Water Surface Elevation (WSL):

Stage:

Depth:

Hydraulic Depth:

Thalweg Depth:

Width:

X-distance (X):

Bed Elevation (Z):

X,Y,Z-coordinate:

Cross Section Vertical:

Computational Cell (hydraulic programs):

Habitat Cell (habitat programs):

Cell Discharge (q):

Cell Area (a):

Cross-sectional Area (A):

Wetted Perimeter (P):

Hydraulic Radius (R):

Mean Channel Velocity (V):

Mean Column Velocity (vi):

Discharge (Q):

Hydraulic Slope (Sh):

Bottom Slope (So):

Energy Slope (Se):

Velocity Head:

Longitudinal Profile:

Velocity Adjustment Factor (VAF):

Conveyance Factor (CFAC):

Thalweg Slope:

Roughness (n):

Stage of Zero Flow (SZF):

Equations Used For The Description and Analysis of Open-Channel Flow

Continuity and Mass Balance

Manning's Equation

Energy Balance and the Bernoulli Equation

Applied Modeling of Water Surface Elevations in PHABSIM

Modeling the Stage-Discharge Relationship by Regression

Stage-Discharge Analysis using Regression in PHABSIM - the STGQ Model

A Practical Guide to Modeling Stage-Discharge Relationships Using the Regression Approach

Modeling the Stage-Discharge Relationship Using Manning's Equation - The MANSQ Model

Modeling The Stage-Discharge Relationship Using A Step-backwater Approach - WSP

General Theory of the WSP Model

A Conceptual Overview of WSP Calibration

Modeling Of Velocities In PHABSIM

Calibration and Simulation of Velocities

Control of VELSIM Calibration and Simulation Options

Evaluating Quality of the Hydraulic Modeling

Evaluation of Water Surface Modeling

Evaluation of Velocity Modeling