To use this feature, users must first enter an initial set of Manning's n values for all of the cross sections in the model. The initial set of Manning's n values should be a reasonable estimate of the main channel and overbank areas based on land use, Ariel photography, and knowledge of the river in general.

The second step in using the automated Manning's n value option is to break up the river system into logical calibration reaches in which a set of flow versus roughness values can be applied. Flow versus roughness factors can be applied to an entire river reach, or multiple flow versus roughness factor sets can be set up within a single river reach. However, each flow versus roughness factor calibration reach will need to be assigned an observed stage hydrograph in order for the automated procedure to perform a comparison of computed versus observed values. An example of how one could break up a river system for this purpose is shown in Figure 14-88.

Figure 14 88. Example Calibration Reach Layout.

As shown in Figure 14-88, each calibration reach must have an observed hydrograph location to compare against. It is not an absolute requirement that the observed hydrograph be at the very upstream end of each calibration reach, but it generally makes sense to do it that way, as Manning's n value changes that occur downstream will affect water surface elevation upstream. However, the observed hydrograph locations can be anywhere (even outside of that particular calibration reach), as long as the roughness changes that occur within the calibration reach will directly impact the computed water surface elevations at the observed hydrograph location.
The next step in performing the automated Manning's n value calibration is to set up a Flow Versus Roughness table for each calibration reach (Figure 14-89). The initial values entered, will be a placeholder for the automated routine to start from. In general, users should enter a range of flows that encompass the entire range of flows that will be experienced for the river system. However, the initial roughness factors can all be set to 1.0 (which means no change from the base Manning's n values). To get to the Flow Versus Roughness Factor Editor, the user can select it from the Geometric Data Editor under "Tools", then "Flow Roughness Factors". Flow versus roughness factors can also be set up as part of the Plan file by selecting the "Options" menu from the Unsteady Flow Analysis window, then selecting "Flow Roughness Factors". Shown below is the Flow versus roughness editor, with a starting set of factors of 1.0.

Figure 14 89. Flow versus Roughness Factor Editor.

The next required step to using the Automated Unsteady Flow Manning's n value calibration option is to enter observed stage hydrographs into the Unsteady Flow Data editor (Figure 14-90). Observed stage hydrographs must be assigned to each calibration reach in order to use this automated calibration feature. All observed stage data must be contained within an HEC DSS file and attached to specific cross section location from within the Unsteady Flow Data editor. To attach observed time series data to cross section locations, bring up the Unsteady Flow Data editor and select "Options", then "Observed (Measured) Data, then "Time Series in DSS". The following window will then appear:

Figure 14 90. Observed Time Series Data Editor

To learn more about how to assign observed time series data to cross section locations, review Chapter 7 of this manual, and the section on Unsteady Flow Data Options.
Once the user has set up flow versus roughness tables (With place holder factors of 1.0), and attached observed stage time series to cross sections, then the Automated Manning's n Value tool can be used. To use this feature select the "Options" menus from the Unsteady Flow Analysis window, then select "Automated Roughness Calibration". The following window will appear:

Figure 14 91. Automated Manning's n Value Editor for Unsteady Flow Analyses.

A shown in Figure 14-91, the Automated Manning's n Value calibration editor has three areas for data entry. These areas are labeled: Calibration Parameters; Calibration Regions; and Forcing Internal Observed Flows and Stages.

Calibration Parameters

The top area, called "Calibration Parameters" is required to use this tool. This is where the main information is entered to control the optimization feature. The following information is entered in this part of the editor:

Error Evaluation Method. There are two options for the error evaluation method: Average Error (default) and Squared Error. The error is computed separately for each flow band (ranges of flow rates) within the hydrograph. The Average Error is computed by taking the sum of the difference between the computed and observed water surface elevations (for all points within the optimization time window), and then dividing by the number of points. The Average Error equation is as follows:

Average \ Error = \frac{1}{n} \sum_{1}^{n}Comp.WS - Obs.WS

The squared error method is computed by taking the sum of the computed minus the observed water surface elevations, squaring that value, dividing by the number of points, then taking the square root. The sign of the error (positive or negative) is kept track of separately in order to decide if the n values should be increased or decreased. The use of the Squared Error method will put more weight on the points that have larger differences. The Squared Error equation is as follows:

Squared \ Error = \sqrt{\frac{1}{n} \sum_{1}^{n} \left(Comp.WS - Obs.WS \right)^2}

Optimization Method. There are two optimization methods available within the HEC-RAS Unsteady Flow Roughness Calibration methodology: Global (this is the default); and Sequential.
The Global method optimizes all calibration reaches simultaneously. Manning's n values are modified for all of the calibration reaches by adjusting the flow versus roughness values for each flow band. A full unsteady flow simulation is performed for the entire model for each iteration. The optimization process continues until either the convergence criteria is met or the maximum number of iterations is reached. This method is the preferred method. This is due to the fact that downstream stage changes will affect upstream stages, and upstream flow routing is affected by changes in roughness. So a simultaneous optimization of all reaches will often produce better results for the Manning's n values.

The Sequential method optimizes calibration reaches one at a time from upstream to downstream. This method requires more observed data, in that the user must have an observed stage hydrograph at the downstream end of each calibration reach to be used as a downstream boundary condition. This is in addition to the observed stage at the upstream end, which is used for comparing observed and computed stages (see Figure 14-92). A computed or an observed flow can be used at the upstream boundary condition for each reach. The optimization is performed in its entirety for a single upstream reach, then the 2nd and subsequent reaches are optimized separately, until all reaches are optimized. While this process does a good job at isolating each reach from any downstream influences/errors (this is due to using the observed stage hydrograph as a downstream boundary for each reach), the method takes much more compute time, and can end up with sets of flow versus roughness factors that do not work as well once they are used in a normal simulation mode, without forcing all the stages in the middle of the system.

Figure 14 92. Decomposition of Reaches for the Sequential Optimization Method

Maximum Number of Iterations. This field is used to set the maximum number of iterations that the optimization process will try in order to adjust the roughness factors to the optimal values. The default value is 10 iterations, however the user can enter anywhere from 1 to 100. For each optimization iteration, the model is run for the entire time window, before evaluating the model error and adjusting the roughness factors. So for example, if a single model run takes 5 minutes, then 10 iterations will take 50 minutes.

Maximum Change in Factor per iteration (Optional). This field is used to enter a maximum amount that any roughness factor can change from one iteration to the next. While this field is optional, it can be very useful in ensuring that the optimization method does not make too large of a change at any one location between iterations.

Error evaluation tolerance. This field is used to enter the tolerance that is used to compare against the computed error for each flow band. The optimization process will continue until either the maximum flow band error (Average error or squared error) is less than the user entered tolerance in this field, or the maximum number of iterations is reached. If computed water surface elevations are in feet, then this tolerance is in feet. If computed water surface elevations are in meters, then this tolerance is in meters.

Limits to flow roughness factors (Maximum Factor and Minimum Factor). These fields are used to enter maximum and minimum values for the flow roughness factors. In other words, during the optimization no flow factor will be allowed to go above the "Maximum Factor", and no roughness factor will be allowed to go below the "Minimum Factor".

Optional specified optimization time window. This area is used to enter a starting data and time, and an ending data and time for evaluating the computed versus observed data. This does not change the actual computation window. It only changes the time window in which computed versus observed flows will be compared for computing the model error and evaluating changes in roughness factors. This is very useful for windowing in around the main hydrograph, such that the error in computed versus observed data is only evaluated in the important region of the event, and not during times of insignificant results. Very often in unsteady flow modeling, the very beginning of the simulation can be off by quite a bit due to bad starting conditions. So not including this beginning model warm-up period can often produce better optimization results.

Calibration Regions

The second area, labeled "Calibration Regions" displays all of the locations in which flow versus roughness tables have been set up on a reach basis (see Figure 14-91). These are the regions (user define flow versus roughness reaches) in which the calibration option can be applied to. The user can turn on any one region, combinations of regions, or all of the regions, by checking the Calibrate column for that region. Additionally, this table is used to assign an observed gage location (Observed stage data) to a calibration region. Note: Assigning an observed stage hydrograph to each calibration region (calibration reach) is required in order to perform the optimization process.

Forcing Internal Observed Flows and Stages

The third area of the editor, labeled "Forced Internal Observed Flows" and "Forced Internal Observed Stages" is only used if the Sequential optimization method is being applied (Figure 14-91). If the "Sequential" Optimization method is turned on, then the user must turn on the options to "Force Internal Observed Stages" at the downstream end of every Calibration Region (calibration reach). See the example in Figure 14-92, that shows how a model would be broken into reaches when the "Sequential" optimization method is used. The table labeled "Forcing Internal Observed Flows" is an optional input. This is an optional method, and it requires observed flow time series in addition to the observed stage time series.

For more information on how to use the automated roughness calibration feature for unsteady flow modeling, please see example 24 in the HEC-RAS Applications Guide.