Two-Dimensional Model between 63rd Street and Blue Parkway

Two-Dimensional Model Summary

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 used to simulate steady state flood flows within a hydraulically complex portion of the Blue River reach. Two-dimensional modeling can simulate flow around bends, piers, buildings, and encroaching hydraulic structures; flow within expanding and contracting reaches; and backwater effects on inflowing tributaries. The model computes water velocity, flow direction, depth, and inundation extent within the flood plain and was used to construct flood inundation maps in the simulated reach. Model results can help design potential channel and flood-plain improvements throughout the simulated reach.

Description of Study Reach

The study reach, the hydraulically complex portion of the Blue River between 63rd Street and Blue Parkway, is approximately 2 river miles long and consists of a deeply incised channel, sharp meander bends, small tributary junctions, and frequent riffles exhibiting substantial gradient change (Figure 3—Simulated study reach of the Blue River between 63rd Street and Blue Parkway) The study reach is bordered on the west by the Union Pacific Railroad and on the east by Hardesty Avenue. A thick riparian corridor exists along the Blue River, the western part of the flood plain is predominantly impervious, and the eastern part of the flood plain consists of residential dwellings. Three small unamed tributaries exist along the Blue River at the lower, middle, and upper end of the study reach (Figure 3—Simulated study reach of the Blue River between 63rd Street and Blue Parkway). The tributaries have small drainage areas and were not considered in the analysis due to limited contributions of flow at the time of main stem flooding.

Model Development

The two-dimensional model uses the finite element method to solve differential equations representing conservation of mass and momentum. A graphical interface known as Surface Water Modeling System (SMS, Environmental Modeling Systems Incorporated - Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the U.S. Government) was used to construct and execute the two-dimensional model. The SMS allows interactive editing and display of finite element networks and provides tools specifically designed for FESWMS.

Two-dimensional model geometry is characterized by elements and nodes in a finite element network. The SMS software was used to convert 2-ft contour data and field-survey data into a finite-element network of triangular and quadrilateral elements. Field surveys were conducted using Global Positioning Systems technology and conventional surveying techniques. First-floor elevations of structures, route detail, and the Blue River channel bathymetry were surveyed.

The quality of the mesh was checked to ensure better numerical stability in the finite element network using a utility within SMS. Smooth contours, smooth boundaries, adequate size transition among elements, density of elements, and using small elements at the wet/dry boundary interface were employed. The deeply incised channel within the study reach required smaller thin elements along and near the top of the banks.

Elements were assigned material and hydraulic properties, such as Manning’s n roughness coefficients, base kinematic eddy viscosities, and element storativity depth (Figure 4—Land use coverage used in flow simulations in the study reach). Manning’s n roughness coefficients were established throughout the overbanks and within the channel banks. The n-value is interpolated linearly from the upper and lower n-values. Manning’s n-roughness coefficients for the calibrated model run are listed in the  following table.

Manning’s n roughness coefficients for the calibrated model run.
[ft, feet]

Land-use coverage	Lower depth			Upper depth
	Manning’s n	Depth (ft)		Manning’s n	Depth (ft)
Channel and bank
Blue River main channel	0.040	3.0		0.025	4.0
Thick brush and timber banks	.110	2.5		.080	5.0
Thick timber corridor with thick sprouts	.125	3.0		.092	6.0
Thick grasses and scattered sprouts	.055	1.7		.040	3.2
Flood plain
Industrial area with kept grasses	0.050	1.0		0.033	2.7
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
Residential area with kept grasses and trees	.038	1.5		.032	2.5
Commercial area with cars and machinery	.150	5.0		.040	7.0
Sand and gravel stockpile	.032	1.0		.030	2.5

 Piers for the existing Blue Parkway Bridge and the downstream adjacent lower Blue Parkway Bridge were incorporated into the mesh (Figure 5—Finite element mesh incorporating pier configuration for the current (2005) Blue Parkway Bridge and downstream Lower Blue Parkway Bridge for the model calibration flood of May 19, 2004). A separate model was used to simulate proposed deck widening of the Blue Parkway Bridge and removal of the lower Blue Parkway Bridge. Piers for the proposed Blue Parkway Bridge also were incorporated into the mesh (Figure 6—Modified finite element mesh based on pier configuration of the proposed Blue Parkway structure).

Model Calibration

Flow into the mesh and stage elevation where flow leaves the mesh are required model inputs. A flood on May 19, 2004 produced both bank-full and overbank flow conditions. Peak-flow measurements and high-water marks were acquired during this event. The total flow along the study reach and stage elevation at the downstream face of the lower Blue Parkway Bridge were used as boundary conditions. At the downstream end of the reach, the Blue Parkway Bridge over the Blue River and the Union Pacific Railroad is approximately 50 ft upstream from the lower Blue Parkway Bridge (Figure 3—Simulated study reach of the Blue River between 63rd Street and Blue Parkway). The main channel columns for the Blue Parkway Bridge and the main channel piers for the lower Blue Parkway Bridge were incorporated into the mesh (Figure 5—Finite element mesh incorporating pier configuration for the current (2005) Blue Parkway Bridge and downstream Lower Blue Parkway Bridge for the model calibration flood of May 19, 2004).

The peak stage of May 19, 2004, occurred at 6:30 p.m. at 63rd Street. The main stem peak stage at the lower Blue Parkway Bridge occurred at 7:00 p.m. Discharge measurements were made from a boat using hydroacoustic technology immediately upstream from the 63rd Street Bridge and  approximately 540 ft upstream from the mouth of Brush Creek (Figure 1—Study area, National Weather Service flood forecast locations, and channel improvement limit). Both measurements were made at the time of the peak stage. For the upstream and downstream locations, mean flow was computed. The average flow of 12,300 ft3/s was considered the upstream total flow boundary condition for a steady-state condition. A current-meter measurement was made at the upstream face of the lower Blue Parkway Bridge concurrent with the hydroacoustic measurement at the location above the mouth of Brush Creek. The measured flow from the current-meter measurement was 12,900 ft3/s.

Four distinct high-water marks indicating peak stage were identified for the May 19th flood. One mark, within a tributary approximately 1,700 ft upstream from the lower Blue Parkway Bridge, was unusually high and thought to represent a local peak prior to the Blue River peak of May 19, 2004 was not included in the calibration process. The measured area and velocity of the current-meter measurement were used as calibration values at the downstream boundary condition. Although the hydroacoustic measurement was made immediately upstream from the 63rd Street Bridge (upstream boundary location), a comparison of modeled velocity and measured area also was made at the upstream model boundary. Measured and simulated stage, cross-sectional area, and velocity are described in the following table. Generally, the measured stages were within 0.2 to 0.53 ft of the simulated stage.

Measured and simulated stage elevation, cross-sectional area, and velocity.
[ft, feet; ft², square feet; ft/s, feet per second; --, not determined/not applicable]

Location	Measured Stage Elevation (ft)	Simulated Stage Elevation (ft)	Measured Cross-sectional area (ft2)	Simulated Cross-sectional area (ft2)	Measured velocity (ft/s)	Simulated velocity (ft/s)
Lower Blue Parkway Bridge	748.59a	748.59a	1,883	1,797	6.85	6.87
Brighton Ave. toe of embankment	756.56	756.76	--	--	--	--
Byram’s Ford	760.32	760.85	--	--	--	--
63rd Street Bridge	762.39	762.80	4,230b	4,841b	2.88b	2.54b

^aStarting stage elevation boundary condition.
^bMeasurement made immediately upstream from 63rd Street Bridge. Simulated results obtained from downstream face of bridge.

Except for a flood-plain area in the middle of the study reach, the flood of May 19, 2004, was contained within the channel and overbanks. Velocities as high as 12 ft/s (feet per second) were simulated at the downstream end of the study reach due to increased slope (caused by the channelization immediately downstream), a narrow confined section of channel, and converging flow from the lower Blue Parkway Bridge (Figure 3—Simulated study reach of the Blue River between 63rd Street and Blue Parkway, Figure 7—Simulated velocity magnitude for the flood of May 19, 2004). The general stage elevation slope throughout the reach for the calibrated flood was approximately 0.0013 ft/ft (foot per foot) or about 7 ft/mi (feet per mile). Depths of 25 to 30 ft were simulated in the deeply incised channel (Figure 8—Simulated water depth for the flood of May 19, 2004). The stage elevation slope was greatest where substantial water velocity gradients occurred (Figure 9–Simulated stage elevation and high-water observations for the flood of May 19, 2004).

Development of Simulated Rating Using One-Dimensional Hydraulic Analysis

To produce flood inundation layers for the study reach, a range of boundary conditions was developed for high flows. This was accomplished using existing one-dimensional Hydraulic Engineering Centers River Analysis System (HEC-RAS) model results from the USACE on the lower Blue River main stem (denoted as the “lower Blue River HEC-RAS model”). Results were available from this model for a range of discharges on the improved channel from the mouth of the Blue River to a cross-section immediately upstream from the mouth of Brush Creek (Figure 1—Study area, National Weather Service flood forecast locations, and channel improvement limit). A new HEC-RAS model (denoted as the “constructed HEC-RAS model”) was constructed to extend the lower Blue River HEC-RAS model results from immediately upstream from the mouth of Brush Creek to the upstream face of the lower Blue Parkway Bridge. Cross-sections were derived from the available 2-ft contour data and cross-section data acquired from discharge measurements. Five cross-sections were used in the constructed HEC-RAS model (Figure 10—Cross sections used in the constructed HEC-RAS model). Input into the constructed HEC-RAS model consisted of stage elevation and discharge measurements made at the upstream side of the lower Blue Parkway Bridge (cross-section 4) and at the limit of channel improvement immediately upstream from the mouth of Brush Creek (cross-section 1) for the May 19, 2004, flood. The constructed HEC-RAS model was calibrated to the discharge measurements listed in the following table.

Measured and simulated conditions for the constructed HEC-RAS model.
[ft, feet; ft², square feet; ft/s, feet per second]

Hydraulic parameter	Cross-section 1			Cross-section 4
	Measured	Simulated		Measured	Simulated
Stage Elevation (ft)	747.4	747.4		749.16	749.16
Flow area (ft2)	2,901.8	2,909.5		1,883.00	1,888.40
Top width (ft)	238.2	238.4		146.00	145.30
Velocity (ft/s)	4.3	4.34		6.85	6.60

Eight flood frequency discharge values acquired from the Kansas City USACE were modeled. The simulated stage for each of the flood frequency discharge values was used to develop a stage-discharge rating at the face of the lower Blue Parkway Bridge to provide the boundary condition information needed to use the two-dimensional simulation to create flood inundation maps from the lower Blue Parkway Bridge to 63rd Street. Discharge values associated with stage at the lower Blue Parkway Bridge at 2-ft increments from 750 through 772 ft were selected from the rating curve and input into the two-dimensional model are listed in the following table.

Simulated rating depicting stage elevation at the lower Blue Parkway Bridge and discharge as boundary conditions for developed flood inundation maps in the study reach.
[ft, feet; ft³/s, cubic feet per second]

Simulated rating
Stage Elevation (ft)		Discharge (ft3/s)
750		13,930
752		16,740
754		20,110
756		23,210
758		26,650
760		29,970
762		33,700
764		37,630
766		41,920
768		48,100
770		56,670
772		71,690

To illustrate the range of conditions, velocity magnitude and direction profiles and video clips of model results for the upstream vicinity of the lower Blue Parkway Bridge, the middle of the study reach, and the downstream vicinity of 63rd Street for selected flows can be accessed by clicking on the links in the following table.

Upstream boundary condition equals 33,700 cubic feet per second. Downstream boundary condition equals 762.0 feet.
Figure A-1. Two-dimensional model results depicting velocity magnitude and direction in the upstream vicinity of Blue Parkway.	Upper Image(PDF File Size 866 KB)	Upper Video Clip (AVI File Size 8.21 MB)
Figure B-1. Two-dimensional model results depicting velocity magnitude and direction in the upstream vicinity of Blue Parkway.	Middle Image(PDF File Size 907 KB)	Middle Video Clip (AVI File Size 8.09 MB)
Figure C-1. Two-dimensional model results depicting velocity magnitude and direction in the upstream vicinity of Blue Parkway.	Lower Image (PDF File Size 899 KB)	Lower Video Clip (AVI File Size 8.42 MB)
Upstream boundary condition equals 41,920 cubic feet per second. Downstream boundary condition equals 766.0 feet
Figure A-1. Two-dimensional model results depicting velocity magnitude and direction in the upstream vicinity of Blue Parkway.	Upper Image(PDF File Size 900 KB)	Upper Video Clip (AVI File Size 8.12 MB)
Figure B-1. Two-dimensional model results depicting velocity magnitude and direction in the upstream vicinity of Blue Parkway.	Middle Image(PDF File Size 873 KB)	Middle Video Clip (AVI File Size 7.87 MB)
Figure C-1. Two-dimensional model results depicting velocity magnitude and direction in the upstream vicinity of Blue Parkway.	Lower Image (PDF File Size 888 KB)	Lower Video Clip (AVI File Size 832 MB)
Upstream boundary condition equals 71,690 cubic feet per second Downstream boundary condition equals 772.0 feet
Figure A-1. Two-dimensional model results depicting velocity magnitude and direction in the upstream vicinity of Blue Parkway.	Upper Image (PDF File Size 932 KB)	Upper Video Clip (AVI File Size 8.18 MB)
Figure B-1. Two-dimensional model results depicting velocity magnitude and direction in the upstream vicinity of Blue Parkway.	Middle Image (PDF File Size 933 KB)	Middle Video Clip (AVI File Size 7.94 MB)
Figure C-1. Two-dimensional model results depicting velocity magnitude and direction in the upstream vicinity of Blue Parkway.	Lower Image (PDF File Size 907 KB)	Lower Video Clip (AVI File Size 8.24 MB)

Simulated Flood Inundation Maps

The flood inundation model for the study reach incorporates design plans for the proposed Blue Parkway structure over the Blue River and Union Pacific Railroad. New pier alignment and pier dimensions were coded into the finite element mesh (Figure 6—Modified finite element mesh based on pier configuration of the proposed Blue Parkway structure) and another “spindown” process was initiated beginning with the first boundary conditions at a discharge of 71,690 ft3/s and stage elevation at 772 ft. Once the model attained acceptable convergence parameters, the next flood stage elevation was simulated. Acceptable convergence was achieved with an average change in unit flow rate of less than 0.1 ft2/s (square foot per second) and an average change in stage elevation less than 0.1 ft. Flood inundation information for the study reach was incorporated into the flood inundation maps for the lower Blue River and are accessible from the main web page of the Blue River Flood Inundation Mapping web site.

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