Two-Dimensional Model between Hickman Mills Drive and 63rd Street

A depth–averaged flow model Flo2DH [part of the Federal Highway Administrations’s Finite Element Surface–Water Modeling System (FESWMS) designed for hydraulic structures and flood plains] was chosen to simulate steady–state flood flows within a hydraulically complex reach of the Blue River. Two–dimensional models simulate flow around bends, piers, buildings, and encroaching hydraulic structures; flow within expanding and contracting reaches; and backwater effects on inflowing tributaries. The two–dimensional model was used to construct maps of flood-inundation extent, water velocity and flow direction, and depth within the flood plain. These model outputs also can be useful in designing potential channel and flood–plain improvements throughout the simulated reach.

Description of Study Reach

The modeled reach of the Blue River between Hickman Mills Drive and 63rd Street (Figure 3—Simulated model reach of the Blue River between Hickman Mills Drive and 63rd Street) is approximately 5.6 river miles in length and consists of a deeply incised channel, sharp meander bends, small tributary junctions, and frequent riffles exhibiting substantial gradient change. The model reach is bordered on the east and west by flood-plain valley walls. The flood plain of the model reach is mostly timber and brush, kept grasses (mowed park land and golf courses), and thick grasses with small sprouts.  A thick riparian corridor exists along the Blue River.  Several small unnamed tributaries exist in the model reach. The tributaries have drainage areas between 1 and 2 square miles and were not considered to contribute to flood discharges because of limited contributions of flow at the time of main stem flooding.

Model Development

Two–dimensional modeling provides more hydraulic detail than conventional one–dimensional analysis. The FESWMS Flo2DH model simulates flow in two dimensions in the horizontal plane. This two–dimensional model simulates longitudinal and lateral variations in water–surface elevations and velocities and can accommodate geometric features, such as highway embankments, bridge structures, channel bends, berms, buildings, and other flow obstructions. A graphical user interface called the Surface–Water Modeling System was used to construct the two–dimensional finite–element mesh, facilitate assignment of roughness coefficients and other hydraulic and material parameters to the mesh elements, execute the model, and evaluate the model output.

Two–dimensional model geometry is characterized by elements and nodes in the form of a finite-element network or mesh. The SMS software was used to convert existing 2–ft topographic contour data and supplemental onsite field-survey data into a scatter data set that was optimally configured into a finite–element network or mesh consisting of triangular and quadrilateral elements.

The quality of the mesh was checked to ensure better numerical stability in the finite–element network. Smooth contours, smooth boundaries, adequate size transition among elements, density of elements, and the necessity of constructing smaller elements at the wet/dry boundary interface often were employed. The deeply incised channel within the study reach has steep banks that required smaller thin elements along the banks and additional element refinement near the top of the banks (Figure 4—Finite–element mesh of the Blue River between Hickman Mills Drive and 63rd Street).

The elements of the mesh were characterized by assigning material (Figure 5—Land-use coverage used in the model of the Blue River between Hickman Mills Drive and 63rd Street) and hydraulic properties to the elements, such as Manning’s roughness coefficient, and additional turbulence parameters such as base kinematic eddy viscosity and element storativity depth. A depth–dependent Manning’s roughness coefficient (n-value) method was used to account for changes in the roughness with increased depth of flow. Final coefficients for the calibrated model are listed in the following table.

Manning’s roughness coefficients (n-values) for the calibrated model of the Blue River between Hickman Mills Drive and 63rd Street.
[ft, feet]

Land-use coverage	Lower depth			Upper depth
	Manning’s n	Depth (ft)		Manning’s n	Depth (ft)
Channel and bank
Sand and gravel channel	0.040	3.0		0.025	4.0
Riprap-lined channel	.045	1.5		.030	8.0
Timber and brush	.110	2.5		.080	5.0
Thick timber corridor with thick sprouts	.125	3.0		.110	6.0
Thick grasses and scattered sprouts	.055	1.7		.045	3.2
Flood plain
Kept grasses	0.050	1.0		0.033	2.7
Kept grasses and interspersed trees	.055	1.5		.040	2.5
Railroad embankment with ballast and sprouts	.038	1.0		.032	2.0
Impervious area with asphalt, concrete, and gravel	.027	1.0		.025	2.0
Commercial area with junkyard, cars, and machinery	.150	5.0		.080	7.0

Piers for bridges in the model reach were incorporated into the: Position, orientation, and dimensions of each pier were taken from bridge plans to accurately position and size the piers (Figure 6—Finite-element mesh in the vicinity of U.S. 71 Highway showing piers incorporated into the mesh using disabled elements and the pier module).

Model Calibration

The amount of flow into the mesh and a water–surface elevation where flow leaves the mesh are required model inputs. The two–dimensional model from phase one of the project was calibrated to a flood that occurred May 19, 2004, that produced both bank–full and partial overbank flow conditions at a discharge of 12,300 cubic feet per second (ft³/s). Peak–flow measurements and high–water marks were acquired during this event. A study which used a version of the two–dimensional model from phase one was calibrated to the May 19, 2004, flood, but also was calibrated to a flood that occurred May 15, 1990, which had a discharge of approximately 31,800 ft³/s, and for which flow occurred on the flood plain on both sides of the channel.

The peak stage of May 19, 2004, occurred at 6:30 p.m. at 63rd Street. A discharge measurement was made in a boat using hydroacoustic technology at a location immediately upstream from the 63rd Street bridge.  The narrow and sinuous channel, timbered corridor, considerable velocities, standing waves, and turbulence prevented adequate hydroacoustic measurements anywhere else in the study reach.  In phase one of the project, an average flow of 12,300 ft³/s was used for this flood, and this value was considered the upstream total flow boundary condition for a steady-state condition of the current (2008) two-dimensional model because there are no major inflow tributaries between U.S. 71 Highway and Blue Parkway.

Six high-water marks indicating peak stage were identified along the study reach for the flood of May 19, 2004. Because the ALERT gage at U.S. 71 Highway was not functioning during the flood, a peak stage at the gage was estimated from the existing flood forecast stage from the NWS, based on the peak stage at 63rd Street.  The cross-sectional area and average velocity from the discharge measurement made upstream from the 63rd Street bridge were used as calibration values near the downstream boundary.  Measured and simulated water-surface elevations are described in the following table.

Measured and simulated water-surface elevations for the calibration floods of May 15, 1990, and May 19, 2004.
[ft³/s, cubic feet per second; ft, feet;  --, not determined/not applicable]

Location	May 19, 2004, flood (12,300 ft3/s)				May 15, 1990, flood (31,800 ft3/s)
	Measured water-surface elevation (ft)	Simulated water-surface elevation (ft)	Simulated minus measured (ft)		Measured water-surface elevation (ft)	Simulated water-surface elevation (ft)	Simulated minus measured (ft)
63rd Street	762.4	762.3	-0.1		775.8	775.8	0
Lewis Road, north westa	764.2	764.0	-0.2		--	--	--
Lewis Road, north easta	763.8	764.0	0.2		--	--	--
Lewis Road, south westa	763.7	764.0	-0.3		--	--	--
Gregory Boulevard	769.3b	769.5	0.2		781.6	781.6	0
Blue River Road	771.4	771.4	0		--	--	--
Stage-only gage at U.S. 71 Highway	778.9c	778.3	-0.6		788.9c	788.8	-0.1

^aThese three measurements were all in the same area of Swope Park, except that the northeast mark was in an area of backwater away from the main channel.  Therefore, the “average” water-surface elevation created by these three marks (763.9 ft) was used as the comparison value for the calibration.
^bThe measured water-surface elevation for the flood of May 19, 2004, was obtained from a paint mark on the downstream side of one of the Gregory Boulevard bridge piers and was considered a “poor” mark.  The difference between the simulated and measured values likely is the result of drawdown effects from the pier.
^cThe estimated water-surface elevation was obtained from the forecast stage from the National Weather Service (Steve Predmore, written commun., 2007) based on the water-surface elevation at the 63rd Street gage for current (2007) conditions.

The water-surface elevation, cross-sectional area, and velocity from the measurement upstream from the 63rd Street bridge are shown with the simulated results in the following table.  Generally, the simulated water-surface elevations were within 0.2 ft of the measured water-surface elevations for the May 19, 2004, flood, with the exception of the southwest mark near Lewis Road and the estimated water-surface elevation at the ALERT gage at U.S. 71 Highway (Figure 7—Simulated water-surface elevation and high-water observations for the flood of May 19, 2004). Two similar floods on March 5, 2004, and June 4, 2005, which had water-surface elevations that bracketed water-surface elevations for the May 19, 2004, flood at the gage at 63rd Street (759.0 ft and 763.3 ft,—a difference of 4.3 ft), had nearly identical peak-stage readings at the gage at U.S. 71 Highway (782.9 ft and 782.8 ft). These stages were both about 4 ft higher than the forecast stage.  Therefore, the water-surface elevation at the gage at U.S. 71 Highway was not considered crucial to the calibration to the flood of May 19, 2004.

Measured and simulated water-surface elevation, cross-sectional area, and area-weighted average velocity at the discharge measurement location upstream of the 63rd Street Bridge for the calibration flood of May 19, 2004.
[ft, feet; ft², square feet; ft/s, feet per second]

Parameter	Measured	Simulated	Percentage difference
Water-surface elevation (ft)	762.4	762.3	0.01
Cross-sectional area (ft2)	4,230	4,072	3.74
Average velocity (ft/s)	2.88	3.02	4.86

Two historical high-water marks indicating peak stage were identified along the study reach for the flood of May 15, 1990, and an historical peak stage was recorded for the ALERT gage at U.S. 71 Highway.  Although the conditions of the Blue River channel and flood plain between 75th Terrace and 63rd Street Figure 3—Simulated model reach of the Blue River between Hickman Mills Drive and 63rd Street) currently (2008) are essentially the same as existed in 1990, substantial changes have occurred in land use and channel conditions in the vicinity of U.S. 71 Highway and downstream.  Therefore, the historical peak stage at the ALERT gage at U.S. 71 Highway (788.0 ft) was not used, and a value again was estimated from the existing flood forecast rating from the NWS, based on the peak stage at 63rd Street.  The simulated water-surface elevations (Figure 8—Simulated water-surface elevation and high-water observations for the flood of May 15, 1990) were within 0.1 ft of the measured or estimated water-surface elevations.

The flood of May 19, 2004, primarily was contained within the channel and adjacent overbanks (Figure 7—Simulated water-surface elevation and high-water observations for the flood of May 19, 2004). Depth-averaged velocities as high as 6.5 feet per second (ft/s) were simulated in the channel in the vicinity of U.S. Highway 71, and velocities as high as 6.0 ft/s were simulated under the Gregory Boulevard Bridge and at several locations between Gregory Boulevard and 63rd Street (Figure 9—Simulated velocity magnitude for the flood of May 19, 2004). Velocities in the channel between U.S. 71 Highway and Gregory Boulevard generally were lower than in the downstream channel, where velocities as high as 5.3 ft/s occurred at a few locations of local flow constriction (Figure 9—Simulated velocity magnitude for the flood of May 19, 2004). The general water-surface elevation slope throughout the reach for the May 19, 2004, flood was approximately 0.00059 feet per foot (ft/ft) or about 3.1 feet per mile (ft/mi). Water depths of 23 to 28 ft were simulated in the deeply incised channel, with a few local scour holes as deep as 33 ft (Figure 10—Simulated water depth for the flood of May 19, 2004).  On the flood plain, water depths ranging from 10 to 15 ft were simulated in the overbank areas immediately adjacent to the channel.  Localized terraces with simulated water depths of 5 ft or less exist on the inside of several of the meander bends (Figure 10—Simulated water depth for the flood of May 19, 2004).

The flood of May 15, 1990, was not contained to the channel or adjacent overbanks, but was more widespread throughout the flood plain (Figure 8—Simulated water-surface elevation and high-water observations for the flood of May 15, 1990).  Depth-averaged velocities as high as 7.5 ft/s were simulated in the channel upstream from U.S. Highway 71, and velocities as high as 6.5 ft/s were simulated under the Gregory Boulevard Bridge and between Gregory Boulevard and 63rd Street in an area of local flow constriction (Figure 11—Simulated  velocity magnitude for the flood of May 15, 1990). As with the 2004 flood, velocities in the channel between U.S. 71 Highway and Gregory Boulevard generally were lower than in the downstream channel; however, velocities as high as 6.3 ft/s were simulated at a few locations of local flow constriction (Figure 11—Simulated  velocity magnitude for the flood of May 15, 1990).  Unlike the 2004 flood, however, velocities in the meander bends upstream and downstream of Gregory Boulevard were substantially lower as flow increased across the narrow flood plain between the upstream and downstream sides of each bend. The general water-surface elevation slope throughout the reach for the May 15, 1990, flood was approximately 0.00047 ft/ft, or about 2.5 ft/mi. The water-surface elevation had the greatest changes where substantial water-velocity gradients occurred (Figure 8—Simulated water-surface elevation and high-water observations for the flood of May 15, 1990). Water depths of 36 to 46 ft were simulated in the deeply incised channel (Figure 12—Simulated water depth for the flood of May 15, 1990). On the flood plain, water depths ranging from 15 to 25 ft were simulated in much of the overbank areas immediately adjacent to the channel (Figure 12—Simulated water depth for the flood of May 15, 1990).  Localized terraces with simulated water depths of 10 ft or less existed on the inside of several of the meander bends in the model reach (Figure 12—Simulated water depth for the flood of May 15, 1990).

Simulated Velocity Magnitude and Direction

Discharge values associated with water-surface elevation at the 63rd Street Bridge at 2-ft increments from 763.8 through 787.8 ft were selected and input into the two-dimensional model and are listed in the following table.  Each discharge and water-surface elevation pair was simulated in the two-dimensional model, using the “spindown” process.  The process was initiated with the first boundary conditions of a discharge of 92,000 ft³/s and water-surface elevation at 787.8 ft.  Once the model attained acceptable convergence, the next water-surface elevation and discharge were simulated.  Thirteen water-surface elevations (2-ft increments from 763.8 to 787.8 ft) are depicted with flow-trace animations for the model reach.

Simulated rating depicting water-surface elevation at the 63rd Street Bridge and discharge as boundary conditions for developed flood inundation results in the two-dimensional model reach.
[ft, feet; ft³/s, cubic feet per second]

Simulated rating
Water-surface elevation(ft)	Discharge (ft3/s)
763.8	14,000
765.8	17,000
767.8	20,300
769.8	23,000
771.8	26,320
773.8	29,000
775.8	33,700
777.8	37,630
779.8	41,920
781.8	48,100
783.8	56,670
785.8	71,600
787.8	92,000

To illustrate the range of conditions, velocity magnitude and direction video clips of model results for the overall reach, lower reach, meanders, and upper reach for selected flows can be accessed by clicking on the following links. These files are located in Appendix 1 of the report.

Description of Appendix 1

Four sets of animations are contained in four directories in appendix 1. Each directory contains animations of a different part of the model reach. These include the lower reach, meanders, overall reach, and upper reach. Figure 1.1 shows the location of the lower reach, meanders, and upper reach. The overall reach includes the entire model reach.

File names of animations within each directory reflect the stage at the Kansas City, Missouri ALERT gage for each flood inundation stage. Flood inundation was determined for 2-foot stage intervals from 763.8 to 787.8 feet.

For example, the file 763.8.avi depicts the flow animation for flood inundation at 763.8 ft stage elevation at the Kansas City, Missouri ALERT gage at 63rd Street.

In each directory two files, 1990flood.avi and 2004flood.avi, depict the flow animations for floods from May 15, 1990 and May 14, 2004.

Each animation depicts velocity magnitude and direction by randomly distributing particles throughout the simulated flow field. Each particle has a fixed time until it decays and another particle is added. Particles travel in the direction of flow and particles distributed in areas of greater velocity magnitude have longer flow traces because they travel farther within the fixed time before they decay. Particles distributed in areas of lesser velocity magnitude have shorter flow traces because they do not travel far within the fixed time before they decay. As water transitions between areas of low and high velocity, the speed and length of the flow trace reflects these changes. Furthermore, contractions, expansions, and bends in the flow (i.e. through bridge openings, over road embankments, and around meander bends) are reflected by the flow traces in these areas.

Appendix 1

Figure 1.1. Locations of lower reach, meanders, and upper reach depicted in velocity magnitude and direction animations in Appendix 1  (PDF file approximate size 13M)

Appendix 1.2—Overall Reach — Video Files (.avi files approximate size 33M)

Overall Reach—Flow animations for floods from May 15 1990, and May 14, 2004
1990 Flood													2004 Flood
Overall Reach—Flow Animations at two-foot intervals
Feet	763.8		765.8		767.8		769.8		771.8		773.8		775.8		777.8		779.8		781.8		783.8		785.8		787.8

Appendix 1.3—Lower Reach — Video Files (.avi files approximate size 33M)

Lower Reach—Flow animations for floods from May 15 1990, and May 14, 2004
1990 Flood													2004 Flood
Lower Reach—Flow Animations at two-foot intervals
Feet	763.8		765.8		767.8		769.8		771.8		773.8		775.8		777.8		779.8		781.8		783.8		785.8		787.8

Appendix 1.4—Meanders — Video Files (.avi files approximate size 33M)

Meanders Reach—Flow animations for floods from May 15 1990, and May 14, 2004
1990 Flood													2004 Flood
Meanders Reach—Flow Animations at two-foot intervals
Feet	763.8		765.8		767.8		769.8		771.8		773.8		775.8		777.8		779.8		781.8		783.8		785.8		787.8

Appendix 1.5—Upper Reach — Video Files (.avi files approximate size 33M)

Upper Reach—Flow animations for floods from May 15 1990, and May 14, 2004
1990 Flood													2004 Flood
Upper Reach—Flow Animations at two-foot intervals
Feet	763.8		765.8		767.8		769.8		771.8		773.8		775.8		777.8		779.8		781.8		783.8		785.8		787.8

 

Appendix 2—Estimated Flood–Inundation Mapping for the Upper Blue River, Indian Creek, and Dyke Branch in Kansa City, Missouri, 2006—08 Plates (PDF Files approximate size 65M)

Plate 2.1 (763.8 feet)	Plate 2.2 (765.8 feet)	Plate 2.3 (767.8 feet)
Plate 2.4 (769.8 feet)	Plate 2.5 (771.8 feet)	Plate 2.6 (773.8 feet)
Plate 2.7 (775.8 feet)	Plate 2.8 (777.8 feet)	Plate 2.9 (779.8 feet)
Plate 2.10 (781.8 feet)	Plate 2.11 (783.8 feet)	Plate 2.12 (785.8 feet)
Plate 2.13 (787.8 feet)

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