“The default option [Force Water Surface Elevation] makes some simplifying assumptions for the hydraulics at a junction… This simplifying assumption requires user’s [sic] to place cross sections fairly close together around a junction, depending on the slope of the stream…” HEC-RAS User Manual (page 6-29)
The guidance states that the only solution to minimizing error is to minimize cross-section distance; however, this is not always an option and/or may result in instabilities. It confirms that regardless of the cross-section layout, error is introduced due to the limited ability to define the confluence topography in a traditional 1D Junction.
- Where a tributary confluence is located under a bridge, a non-geospatial junction must be located either upstream or downstream of the bridge (see Figure 2). This requires tightly spaced cross-sections, to provide the minimum of two sections between the junction and internal boundary and small junction lengths to ensure the tributary is balanced using a realistic water surface. This often results in a complex geometry, errors, and instabilities.
Figure 2 – Traditional HEC-RAS Junction Methodology with a Coupled 1D/2D Unsteady Model – Complex Junction with Tributary Outfall Under Bridge
- When modeling a culvert outfall at the downstream end of a tributary where it connects to the main reach, an artificial downstream cross-section needs to be created with station-elevation data based on the main reach to allow tributary flow to enter a junction (see Figure 3). This often results in a complex geometry, errors, and instabilities.
Figure 3 – Traditional HEC-RAS Junction Methodology with a Coupled 1D/2D Unsteady Model – Complex Junction with Culvert Outfall
In addition to the above numerical simplifications, the traditional approach creates practical challenges when developing regional interconnected urban flood models. Adding or removing tributaries (and thus creating or removing Junctions) requires a significant amount of effort. Reach names must be changed, flows re-assigned, lateral structures subdivided or merged, and cross-sections re-aligned or cut new. Watershed inflows must also be subdivided at junctions since a uniform lateral inflow cannot be applied across a junction, requiring subdivision of the watershed to document the percentage of flow applied to each inflow. This translates to significant effort and opportunity for errors to be induced. Addressing these practical challenges would significantly aid the development of a regional, integrated HEC-RAS 1D/2D unsteady model in flat, urbanized areas, such as Harris County, Texas.
Develop a Junction method for a coupled HEC-RAS 1D/2D unsteady model that addresses the above simplifications and shortcomings. Specifically, the method should:
- Allow users to add and remove 1D tributaries with minimal effort and avoiding the need to rename reaches and updated flow assignments across multiple plans.
- Provide a robust, stable solution over a range of small to large storm events.
- Provide a solution that is numerically accurate to the same degree as the traditional Junction method, while recognizing that the traditional method simplifies Junction hydraulics and introduces errors depending on confluence complexity and cross-section layout.
- Can be adapted to allow the upstream end of 1D reaches to connect seamlessly to bounding 2D Flow Areas. This is necessary when the 1D reach does not encompass the entire channel or when the upstream section of the channel receives overland runoff from a 2D Flow Area.
The proposed method summarized here is based on experience developing coupled 1D/2D models across Harris County (Houston, Texas), an extremely urban and flat network of reaches. The proposed method includes a 1D main reach coupled to a Storage Area representing a small portion of the tributary, as illustrated in Figures 4 to 6 on the following pages. The Storage Area represents the volume between the tributary’s downstream cross-section and the top of bank of the main reach. The Storage Area Stage-Storage curve is computed from the underlying terrain with the maximum elevation set above the maximum anticipated water surface elevation. The tributary is connected to the Storage Area and the Storage Area serves as the downstream boundary condition. The 2D Flow Area along the Storage Area is connected with Storage Area Connectors to allow overbank flow to pass from or through the Storage Area.
A Lateral Structure placed on the main reach will serve to convey flow to/from the tributary and main reach. A weir coefficient of 2 is recommended to limit the head loss across the weir along with setting the weir stability factor to 3. The weir stability factor is often set to 2 or 3 for coupled 1D/2D models to address stability issues with 1D/2D flow transfer. Weir coefficients sensitivity was tested between 0.5 and 5.0. A weir coefficient of 0.5 was found to induce more model instability as compared to a coefficient of 2.0. This was attributed to more potential for head differences and the minor volume in the storage area used as junctions. There was no discernible difference noted in results using a weir coefficient between 2.0 and 5.0. In most areas of Harris County, tributaries enter the main reach with approximately equal flowline elevations. By using a high weir coefficient, a balance in water surface elevation at the confluence is maintained. If substantial differences in flowlines exist and it is anticipated that unequal water surface elevations in the main reach and Storage Area would exist, a weir coefficient of 2.6 may be more appropriate.
Figure 4 – Proposed HEC-RAS Junction Methodology with a Coupled 1D/2D Unsteady Model – Simple Junction
Note: HEC-RAS does not compute flow across lateral structures between structure bounding cross-sections. The upstream bounding cross-section must be graphically aligned to allow the tributary station-elevation data to be between upstream cross-sections. Reach lengths and station-elevation data should not be changed.
Figure 5 –Proposed HEC-RAS Junction Methodology with a Coupled 1D/2D Unsteady Model – Complex Junction with Tributary Outfall Under Bridge
Figure 6 –Proposed HEC-RAS Junction Methodology with a Coupled 1D/2D Unsteady Model – Complex Junction with Culvert Outfall
Similarly, connecting 1D reaches to 2D Flow Areas at the upstream end of the 1D reach can be performed using a Storage Area and Storage Area Connection (see Figure 7). The 2D Flow Area would connect to a Storage Area which would connect to the upstream node of the 1D reach. This connection may be made directly to the 2D Flow Area but use of a Storage Area connection has been found to provide increased model stability.
Figure 7 –Proposed HEC-RAS Junction Methodology with a Coupled 1D/2D Unsteady Model – Upstream Reach Connected to 2D Flow Area
Benefits of Proposed method:
The proposed method for a coupled 1D/2D model has the following benefits over the standard method:
- The main reach is simulated using the full momentum and continuity equations and the confluence volume is accounted for. This allows for greater flow continuity through confluences when compared to the standard method, which relies on the Standard Step Energy equation or forcing of water surfaces to match the Junction’s downstream cross-section.
- Flow transfer to/from 1D/2D across the “far bank” of the confluence is included. The standard method does not allow a 1D/2D connection between the bounding cross sections of a junction. This results in flow being trapped or prevented from entering the 2D Flow Area between junction-bounding cross-sections.
- The Lateral Weir and Storage Area combination provide a very stable solution. This is particularly helpful at complex confluences where tightly spaced cross-sections are required.
- For confluences with complex 2D flow patterns, the proposed method better represents flow paths and conveyance than the standard method (as shown later in this report).
- Tributaries can be added and removed without modifying the main reach. The main reach does not need to be broken into new downstream reaches when a tributary is added or combined when a tributary is removed. This reduces the significant time and potential for user error involved with adjusting all flow files and lateral structures each time a tributary is added or removed.
- Debugging individual reaches is simplified. Tributaries can be disconnected from the storage area, allowing the reach to be run and debugged independently. This provides the modeler the ability to quickly identify and address model issues.
- The modeler has the ability to set initial condition stages at each Storage Area, providing better control over tributary boundary conditions when needed.
- Uniform lateral flows can be assigned across junctions where appropriate without the need to ratio or subdivide watersheds.
- Future model expansions can be performed without greatly impacting model setup, this will aid in future impact analysis.
The HEC-RAS Hydraulic Reference Manual, when referring to conducting dam failure analyses with a flood wave routed through a main reach, appear to set a precedent for the proposed method. It suggests the following as alternative to modelling tributaries with reaches (see Figure 8):
“The next best option for accounting for tributary storage, is to model the tributary as a storage area, and connect the storage area to the main river with a lateral structure. The lateral structure can be a weir, in which the weir geometry is represented with a cross-section from the tributary.” HEC-RAS Hydraulic Reference Manual (Page 14-61)
Figure 8 – Example of using storage areas and lateral weirs to account for flow reversals up tributaries (copied from HEC-RAS Hydraulic Reference Manual, Figure 14-18, Page 14-62)
In the above, HEC states that the tributary experiences “low-velocity backwater” driven by volume and can be sufficiently represented using a storage area. The proposed method improves on this approach, since the storage area volume is minimal and limited to the confluence. The remainder of the tributary is modeled in 1D. Given that the majority of Harris County tributaries are governed by backwater at their confluence, it follows that the proposed method aligns with the USACE-HEC’s recommended methodology above.
The proposed storage area junction approach was tested and compared against the standard method. Hunting Bayou in Harris County, Texas was modeled in its entirety, with major tributaries represented in 1D and tributary confluences modeled using the standard and proposed methods. For the proposed method, tributary lateral structure weir coefficients were set to of 2. Figure 9 shows the difference in maximum WSE between the proposed and standard methods (i.e., proposed maximum WSE minus standard maximum WSE). Model results show the two methods are within 0.1-ft or less for the entire model extents. The results illustrate that the two methods perform equally in terms of both stage and flow.
Figure 9 – Maximum WSE Difference (Proposed minus Standard method)
Hydrograph flow comparisons were also performed at several locations along the H100-00-00 channel reach. The comparisons show no significant differences in the two model approaches through the entire run simulation. The comparison hydrographs are presented in Figures 10 and 11.
Figure 10 – Flow hydrographs at River Station 57340.2 downstream of H119-00-00
Figure 11 – Flow hydrographs at River Station 7685.5 near downstream boundary of Hunting Bayou