Defining the Model Domain 40

The upstream, downstream, and lateral study boundaries are required to define the limits of data collection. The model must begin far enough downstream to assure accurate results at the bridge, and far enough upstream to determine the impact of the bridge crossing on upstream water surface elevations. The lateral extent should ensure that the model includes the area of inundation for the greatest flood analyzed.

Underestimating the domain can cause the water surface calculations to be less

accurate than desired or require additional survey at a higher cost than the inclusion in the initial survey. Overestimation can result in greater survey, data processing, and analysis cost.

3.4.1.1 Upstream

At a minimum, the upstream boundary should be set far enough upstream of the bridge to encompass the point of maximum backwater caused by the bridge. If a point of concern where the water surface elevation must be known is further upstream, then the model must be extended to that point. An example would be upstream houses or buildings because the 100-year water surface elevation must be kept below their floor elevation. Check with permitting agencies, including cities and counties, as some have limits on the amount of backwater allowed at a given distance upstream.

Equation 3-1 can be used to determine how far upstream data collection and analysis needs to be performed.

Lu = 10000 * HD0.6 * HL0.5 / S (Eq. 3-1) where:

Lu = Upstream study length (along main channel) in feet for normal depth starting conditions

HD = Average reach hydraulic depth (1% chance flow area divided by cross section top width) in feet

S = Average reach slope in feet per mile

HL = Headloss ranging between 0.5 and 5.0 feet at the channel crossing structure for the 1% chance flow

The values of HD and HL may not be known precisely since the model has not yet been run to determine these values. They can be estimated from FEMA maps, USGS

Figure 3-3 Open Channel Depth Profiles

3.4.1.2 Downstream

Open channel hydraulics programs must have a starting water surface elevation

specified by the user at the downstream boundary of the model. The programs allow for one or more of the following methods of specifying the starting water surface elevation:

 Enter a water surface elevation at the downstream boundary.

 Enter a slope at the downstream boundary which is used to calculate the normal depth from Manning’s Equation.

 Assume critical depth at the downstream boundary.

The modeler must decide which method will be used, and the decision will affect the distance to the downstream boundary of the model.

For the storm frequency being modeled, if a point of known water surface elevation is within a reasonable distance downstream, the model should be extended to that point.

Refer to the section below on convergence for guidance on determining if the point is within a reasonable distance.

Gages are points with a known relationship between the discharge and the water surface elevation. Lakes and sea level can also be points of known elevation. Other locations where the water surface elevation can be calculated from the discharge can include weirs, dams, and culverts if these locations are not significantly influenced by their tailwater.

The normal depth assumption to determine the starting water surface elevation can be used when the downstream channel and overbank is nearly uniform, both in cross section and slope, for a long reach downstream. The length of uniform channel that will be adequate will vary with the slope and properties of the channel, and can be

estimated using Equation 3-2. This reach should not be subject to significant backwater from further downstream.

Equation 3-2 can be used to determine how far downstream data collection and analysis needs to be performed.

Ldn = 8000 * HD0.8 / S (Eq. 3-2) where:

Ldn = Downstream study length (along main channel) in feet for normal depth starting conditions

HD = Average reach hydraulic depth (1% chance flow area divided by cross section top width) in feet

S = Average reach slope in feet per mile

Some engineering judgment must be made by the drainage engineer when determining the variables HD, S, and HL. Guidelines are presented below:

a. Average reach hydraulic depth (HD) – If limited existing data is available, an estimate can be made using FEMA maps and Quadrangle Maps. Using the FEMA map, outline on the Quadrangle Map the boundary of the 1 percent chance flow. Select a representative location and plot a cross section using the Quadrangle Map. Plotting several cross sections may improve the estimate. The area (A), top width (TW), and thus the hydraulic depth (A / TW) for these cross sections are now determined. Average these hydraulic depths to determine an average reach hydraulic depth. Survey data or other existing geometric data that is more accurate than the Quadrangle Maps should be used if available.

b. Average reach slope (S) - Using the Quadrangle Maps, determine and average the slope of the main channel, left overbank, and right overbank.

c. Head loss (HL) - This term is also known as the "backwater”. Backwater is defined as the difference in the water surface elevation between the constricted

(bridge) flow condition and the unconstricted (no bridge) flow condition at a point of interest upstream of the structure crossing. The drainage engineer must make an educated guess at the anticipated head loss. For a new bridge, the allowable head loss would be a reasonable estimate. In most cases, a maximum head loss of one foot would be expected for Florida.

3.4.1.3 Lateral Extents

The model should extend laterally on both sides of the floodplain to an elevation that is above the highest water surface elevation that will be modeled. Often this water surface elevation will not be known until the model is complete. But data must be collected in order to complete the model. Therefore, the water surface elevation and lateral extent must be estimated for the data gathering effort. The elevation or the lateral extent can be estimated from FEMA maps and other historical studies of the site. In some cases, it may be appropriate to set up a preliminary model based on limited data to estimate the water surface elevations. Whichever method is used to estimate the lateral extent of the model, consider making a conservative estimate to avoid additional data gathering at a later time, especially survey data.