appendix b - mobile bed model calibration report · will be appended to the project report as a...
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Appendix B
Mobile-bed model Calibration Report
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Missouri River Bed Degradation Study Mobile Bed Model Calibration Report
March 2017
Introduction
Bed Degradation on the lower Missouri River (RM 0 to RM 500) is a significant problem that has already caused considerable and costly damages to federal, state, and local infrastructure. Continued bed degradation has the potential to severely impact navigation structures, levees and floodwalls, bridges, water supply intakes, and a host of other features. The severity of these consequences prompted the 2009 Missouri River Bed Degradation Reconnaissance Study which recommended the Missouri River Bed Degradation Feasibility Study.
This document serves as an initial orientation to development of the mobile-bed model for the Missouri River Bed Degradation Feasibility Study. It is intended to aid in the technical review of the model and will be appended to the project report as a technical appendix. The model creation and calibration followed the basic principles outlined in the HEC-6 Calibration Guide (HEC 1982) and EM 1110-2-4000, with some adaptation. This document summarizes river behavior and provides information on the model set up and calibration.
The purpose of the mobile-bed model is to predict future bed elevations with no intervention (future without project condition) and to screen and evaluate various alternatives to solving the problem (future with project conditions). This is a planning level model to assess the reach and river scale effects of proposed solutions. It is anticipated that final design of solutions may require additional calculations or modeling beyond the output of this mobile-bed model.
River Behavior
1.1 River History and Modifications
The Missouri River in its current form is a highly regulated, highly stabilized river that drains approximately 529,350 square miles (USACE 2006). Major tributaries include the Yellowstone River, the Platte River, and the Kansas River, each of which drains more than 60,000 square miles. Prior to channel modification, the Missouri River was a wide, braided channel which occupied approximately 300,000 acres downstream of Sioux City, IA. Through the construction of a series of river training structures (dikes and revetments), the river was transformed into a single-thread channel with projected surface area of 112,000 acres (USACE 1981) downstream of Sioux City, IA. The current river is significantly narrower than the original, pre-modified river.
The system of river training structures is called the Bank Stabilization and Navigation Project (BSNP). Structures that run parallel to the river are called revetments, while those that protrude into the river are commonly called dikes. The dikes are generally several hundred feet to over a half mile long, but many of the dikes have most of their length buried in accreted land so that only a small portion of each dike is
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actually exposed to flow. Most dike structures downstream of Rulo, Nebraska are extended by a low sill which protrudes further into the channel. In common usage, the entire structure, both dike and sill, is referred to as a dike. Figure 1 illustrates a dike structure with a low sill with typical dimensions in reference to the CRP (Construction Reference Plane). The CRP is a sloping datum mirroring the water surface profile exceeded 75% of the time during navigation season, and is used to set structure heights to overtop at consistent frequencies based on design criteria from December 1973.
Figure 1. BSNP Dike and Sill with Typical Dimensions, not to scale
A detailed history of BSNP structure design standards, modifications, and current condition will be included in the Missouri River Bed Degradation Feasibility Study report. A brief history from the Missouri River Bed Degradation Reconnaissance Study report (USACE 2009) is provided below:
“The Missouri River Bank Stabilization and Navigation Project (BSNP) was first authorized by the Rivers and Harbors Act of 1912 and subsequent authorizations in 1925, 1927, and 1945. The existing BSNP spans 732.3 miles of the Missouri River, from Sioux City, Iowa, to the mouth, located near St. Louis, Missouri. The existing BSNP maintains a channel that is 9 feet deep and 300 feet wide. Features of the BSNP consist mainly of rock revetments and dikes that restrict lateral movement of the river channel and maintain a self-scouring navigation channel. The BSNP was built over a period of 50 years, with the final features being constructed in the early 1980s. Adjustments are made occasionally to these features to maintain the navigation channel at the authorized depth. The BSNP is a federally operated and maintained project.”
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In conjunction with the BSNP, a series of six mainstem dams were constructed. These dams store a significant volume of water, reducing downstream flooding and supplying water to support navigation on the lower Missouri River eight months out of the year. The authorized purposes for the Missouri River Mainstem Reservoir System as outlined in the Section 9 of the 1944 Flood Control Act include: flood control, navigation, irrigation, hydropower, water supply, water quality control, recreation, and fish and wildlife (USACE 2006).
The channel stabilization accomplished through the BSNP has allowed the construction of miles of federally operated and maintained levees and floodwalls and additional privately owned levees generally located on both banks of the Missouri River downstream of Omaha, Nebraska. Portions of these levees, particularly in the more urbanized areas, as well as smaller privately owned agricultural levees, are located immediately adjacent to the river bank. At many locations, these small, privately-owned levees contain flows with a 5 to 10-year return interval at top width only slightly larger than the channel. Larger floods exceeding a 50-year return period are generally only contained by the federally constructed levees and only a few private levee systems. Due to the varying levels of protection of these levees, channel widths for major floods vary considerably from location to location (see Figure 2.)
Figure 2 graphically depicts the level of confinement imposed on the river corridor by levees vs. the natural floodplain width. The widths shown in Figure 2 were developed using existing models that include the lower 500 miles of river, not the degradation study model which (as explained later) runs from St. Joseph, MO to Waverly, MO (155 miles). The “Valley Width” line in Figure 2 indicates the floodplain width for the 1% AEP profile if there were no levees and is provided as a reasonable approximation for the valley width. Figure 2 is not used in the degradation modeling, but is provided for context to differentiate geologic constrictions from levee-induced constrictions. The FWOP and all degradation alternatives include the levees at the actual locations.
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Figure 2. Valley Width and River Top Width at Different Flood Levels
There are no man-made grade controls on the lower Missouri River downstream of Gavin’s Point Dam which is located at RM 811. Riprap placed at bridge piers does not armor the entire bed and has not stabilized the river. There are no known natural grade controls in the active channel, though this has not been the subject of a thorough investigation. There are some natural bedrock outcroppings on the river banks (Laustrup et al. 2007). The stability of the river near Waverly may be due to natural rock outcropping at that location, but may be caused by other factors. Borings at bridge locations indicate 40 to 100 ft of sand to bedrock in the Kansas City Reach (MoDOT 2008).
2.2 Commercial Dredging
The bed of the Missouri River is dredged (mined) downstream of Rulo, Nebraska as a source of sand and gravel. Commercial dredging on the Missouri River has taken place for many years to varying amounts. Most of the extraction takes places from the bed of the Missouri River in the Kansas City metro area, with additional operations in St. Joseph, Waverly, Jefferson City, and St. Charles. Figure 3 shows the extracted quantities for the Missouri River in Kansas City (RM 350 to 400) from 1974 to 2014. As seen, the total dredging take increased sharply in the early 90s. This sharp increase was a
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result of regulatory restrictions on dredging of the nearby Kansas River and increased local demand for construction materials. The high level of dredging in 2002 includes USACE dredging for the construction of the L-385 unit of the Federal Missouri River Levee System.
Figure 3. Extracted Dredging Quantities for the Missouri River in Kansas City (RM 350 to 400)
2.3 Water Surface Degradation and Reach Screening
Bed of the Missouri River on the Missouri River has caused a corresponding though not necessarily equivalent drop in the water surface elevations for low discharges. Figures 4, 5, 6, and 7 demonstrate that the stage of low discharges has been dropping at St. Joseph, Kansas City, Boonville, and Hermann gages, respectively (USACE 2012).
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Figure 4. Missouri River Stage Trends- Missouri River at St. Joseph, MO
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Figure 5. Missouri River Stage Trends- Missouri River at Kansas City, MO
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Figure 6. Missouri River Stage Trends- Missouri River at Boonville, MO
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Figure 7. Missouri River Stage Trends- Missouri River at Hermann, MO
While this study encompasses the entire lower 500 miles of the Missouri—from Rulo, Nebraska to the confluence with the Mississippi near St Louis, Missouri— the rates of bed degradation and potential consequences of bed degradation vary considerably over the 500 miles. In some stretches of the river, degradation is insignificant, while in other areas, degradation has already threatened infrastructure and necessitated expensive repairs.
In order to better focus resources for analysis and plan formulation, a reach screening procedure was employed which used existing, readily accessible data to determine the locations where systemic degradation was the most severe. Degradation for reach screening purposes was approximated by changes in low water surface profiles. On the lower Missouri River, water surface elevations at dozens of locations were measured on an annual or biannual basis for decades, which provided a way to track degradation trends over time for the full lower 500 miles. These low water profiles were measured when flows fell within a tight range, and then were adjusted to a consistent discharge based on rating curves at nearby gages to allow valid comparison (USACE 2010). Selected water surface profiles from 1974 to 2009 are provided in Figure 8 which depicts any changes from the 1974 profile.
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Figure 8. Departures from 1974 Low Water Surface Profile
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As seen in Figure 8, relatively little degradation occurred from 1974 to 1990, but significant degradation occurred following 1990. The worst degradation occurred in Kansas City. For use in the reach screening procedure, the degradation of the water surface was assessed from 1990 to 2009. The 1990 – 2009 timeframe was chosen because it was recent enough to represent the response of the river to the current constraints on the river—BSNP structures, reservoir management, dredging rates, etc.—but still included nearly 20 years, long enough for degradational trends to substantially exceed yearly fluctuations. In addition, the time period included a range of high and low flow years and the effects of the major 1993 flood. At the time of this reach screening, the 2011 flood (discussed later) had not yet occurred. The change in elevation over each river mile was assessed as the elevation of the 2009 water surface minus the elevation of the 1990 water surface. A rolling 5-mile average was applied.
The mean elevation change for the 5-mile reaches is -1.61 ft. The standard deviation is 1.32 ft. Five-mile reaches with degradation worse than the mean minus two standard deviations were assigned a Critical degradation rating. Reaches with degradation between one and two standard deviations from the mean were assigned a Severe rating. Reaches that exhibit degradation between the mean and one standard deviation received a Significant rating. Reaches that exhibit degradation between zero and the mean received a Slight rating. Reaches with a zero or positive elevation change received a No Degradation rating. This led to the degradation classifications listed in Table 1. Reaches with Critical, Severe, or Significant ratings are shown in Figure 9.
Table 1. Degradation Classification Based on Water Surface Elevation Changes
Elevation Change 1990 to 2009 (ft)
Degradation Rating
Change < -4.24 Critical -4.24 < Change < -2.93 Severe -2.93 < Change < -1.61 Significant
-1.61 < Change < 0 Slight Change ≥ 0 No Degradation
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Figure 9. Differences in Low Water Profile 1990 to 2009 Adjusted to 2005 CRP
The Critical and Severe degradation reaches are centered on Kansas City. Accordingly, intensive modeling efforts and further analyses were focused on Kansas City and adjacent stretches of river, which indicated an analysis area of RM 457 to 329. For modeling purposes, the area of analysis was extended downstream to RM 293.42 (Waverly, MO) in order to end at a USGS gaging station and extended upstream to RM 458.18 to include all of the St. Joseph urban area. Since this original screening, additional data has shown an upstream migration of the most critical degradation by about 30 miles, which is still within the modeled reach (USACE 2015).
2.4 Cumulative Mass of Bed Change
Longitudinal cumulative mass change curves were created for the river miles included in the modeling reach. Volumes were computed from bathymetric survey data for the river bed in 1994, 2009, and 2014, merged with sidewall and overbank data from 1999. From 1994 to 2009 the river experienced a range of flows with daily flow values at the Kansas City gage ranging from 17,400 cfs in December of 2000 to 275,000 cfs (slightly smaller than a 20-year flow) in May of 2007. This time period was also marked by intensive dredging in Kansas City. Approximately, 53 million tons were extracted in the modeling reach from August 1, 1994 to September 30, 2009.
During the spring and summer of 2011, the Missouri River experienced a significant, prolonged high-water event. Record flood durations occurred during the 2011 Flood at most locations along the Missouri River, especially upstream of Kansas City, Missouri (USACE 2013). In Kansas City, the flow
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remained above 142,000 cfs (a 2-year flow) for over 100 days, which was approximately 40 days longer than the record flood of 1993. This event was also unique in that a majority of the flow volume passed through the upstream reservoirs, as opposed to local tributary inputs typical of many recent large floods including 1993. For example, from June 24 to July 29, 2011 Gavins Point Dam released 160,000 cfs, which comprised of 57 to 68% of the peak discharge in the Missouri River between St. Joseph and Waverly, Missouri (USACE 2013). Reservoir releases contain less sediment that tributary inflows, making this flood event abnormally sediment-poor and thus unrepresentative for long-term simulations.
Figure 10 shows the longitudinal cumulative mass change from 1994 to 2009 and from 1994 to 2011 for the active channel of the Missouri River. (These curves were computed using averaged cross sectional area change times the distance between cross sections.) As seen, from 1994 to 2009, the bed degraded significantly in Kansas City upstream of the Kansas River confluence (RM 367.57). Downstream of RM 367.57, the bed was much more stable. From 2009 to 2013, the river exhibited tremendous bed degradation, particularly upstream of Kansas City. The change in slope in Kansas City seen in both curves coincides with BSNP design criteria for a wider channel and the entrance of the Kansas River. The relatively stable reach seen downstream of RM 340 coincides with significantly lower levels of dredging and with dramatic increases in floodplain width for large floods, as discussed earlier.
Figure 10. Longitudinal Cumulative Mass Change in Model Reach
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2.5 Principal Causes of Degradation
While numerous factors have influenced the current condition of the river, the data suggests that the recent degradation experienced after 1990 in the St. Joseph to Waverly reach is predominantly a factor of the river’s response to flooding, high levels of commercial dredging (USACE 2011), and an overall decreasing sediment load.
Historically, during major flood events the Missouri River could capture new sediment primarily through meander erosion from a wide, accessible flood plain. Now, BSNP river training structures constrain the river to a considerably narrower width along a fixed alignment, which both induces high velocities and limits access to bank and floodplain sediments. Two additional factors added to the degradational nature of the flood of 2011. First, the flood of 2011 was dominated by prolonged, high-flow releases of clear water from the mainstem reservoirs with relatively little contribution from the downstream watershed. This resulted in significantly lower sediment concentrations than normal for similar flows. The flood of 2011also included multiple levee breeches, which resulted in significant sand deposition on the floodplain (Alexander, et. al 2013). While flooding is a natural phenomenon that occurs with or without a federal project in place, a portion of the current river’s degradational response to flooding is likely a function of the BSNP and adjacent levees.
The initial design of Missouri River did not anticipate or allow for the tremendous quantities of commercial sand and gravel extraction seen in recent years. From 1994 to 2014, approximately 61 million tons of bed material was mined from the bed of the Missouri River from St. Joseph, MO to Waverly, MO, with the majority mined in the Kansas City metro area. Bathymetric surveys indicate approximately 38 million tons of bed degradation in the active channel (from the tip of the sill to the opposite bank or revetment) over the same time period, suggesting that commercial sand and gravel extraction prevented what would otherwise have been a bed recovery trend following the 1993 flood.
The historic flood of 1993 brought about a downward shift in the flow-sediment relationship at the St. Joseph gage, as seen in Figure 11. The exact cause of this phenomenon is not known, but may be due to the deposition of bed material on the floodplains leading to less in-channel sediments available for transport (Horowitz 2006). The flow-load relationship decreased again during the 2011 flood which can be explained by the tremendous volumes of clear water which came from the upstream reservoirs while the watershed downstream of the reservoirs was in drought. It appears that for low flows, the post-2011 sediment levels have again dropped, but for moderate flows, the flow-load relationship has returned to pre-2011 levels.
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Figure 11. Decreasing total suspended sediment load at the St. Joseph, MO gage. A similar trend is evident at the Kansas City gage.
Model
3.1 Model Introduction
A HEC-RAS 5.0 sediment model was developed to predict future degradation if no remedies are undertaken (future without project) and to screen and evaluate potential solutions (future with project). The model starts at RM 448.89, less than a mile upstream from the St. Joseph, MO USGS gaging station (RM 448.2). The model ends at RM 293.421, near the Waverly, MO USGS gaging station (RM 293.4). The downstream boundary is a historically stable location on the river. The model extents were chosen to encompass the “critical degradation,” “severe degradation” and adjacent “significant degradation” reaches determined during the reach screening process. The model contains 287 cross-sections which span approximately 155 river miles of the Missouri River. There are 6 to 12 cross-sections per river bend. The spacing ranges from 422 ft to 10,666 ft, with 90% of the cross section spacing from 898 ft to 4,594 ft. While there are no fixed criteria for sediment modeling, Figures 27 to 42 evidence that this this spacing is adequate for reproducing channel hydraulics and long-term degradation trends. This spacing allows testing of reach-scale effects, e.g. the effect on bed change of lowering all dikes over several miles and the reach-averaged effects of commercial dredging once the local dredge hole has begun to spread out.
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3.2 Model Schematic
Figure 11 provides a schematic of the model network with river miles, major tributaries, channel cross-sections, and USGS gages located. Figure 12 depicts the confluence of the Kansas River with the Missouri River, which demonstrates the preponderance of levees, floodwalls, dikes, and bridges. Due to the length of the river modeled, a detailed mapping of all pertinent features including bridges, levees, floodwalls, and river training structures for the full 155 river miles is not provided here. The reader is advised to review the Missouri River Hydrographic Survey Mapbook (USACE 2004).
Figure 11. Model Schematic
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Figure 12. Missouri River near Kansas River Confluence
3.3 Initial Conditions
Initial channel conditions consist of cross-sections, roughness values, and lateral extent, depth, and gradation of the bed. These initial conditions are described in the following paragraphs.
Cross-Sections The starting geometry was synthesized using bed bathymetry from the 1994 hydrographic survey data (USACE 1994) and bank and overbank data from 1998/1999, as used in the 2007 floodway model (USACE 2007). 1994 bed cross-sections were chosen to match the locations of the floodway model. The cross-sections utilize the Missouri River 1960 river mile nomenclature. However, reach lengths are based on the actual channel distance between cross-sections along the sailing line, which varies slightly from using a difference in river miles to compute lengths. The starting year of 1994 was chosen due to data availability; a full hydrographic survey was conducted in 1994 which documented bed elevations as well as dike and revetment geometry. Not all cross-sections present in the 2007 floodway model were retained in the degradation model. Cross-sections with unrealistically small or large cross-sectional areas, cross-sections that were too tightly spaced and bridge cross-sections were removed to achieve model stability.
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Dike, sill, and revetment structures were entered into the cross-sections as station/elevation points. Initial structure lengths to include in the cross-sections were computed by connecting the structure tips in GIS (see Figure 13). These initial lengths were corrected to account for available flow area between dike structures using a methodology similar to that used on the Missouri River by Teal and Remus (2001). This process is documented in the attached Memorandum: Reduction in Dike Lengths to Account for Expansion and Contraction.
Figure 13. Unadjusted Dike Length Calculation in GIS
Structures extending from the channel bank to the Rectified Channel Line were assigned the criteria for a dike (+2 CRP). Structures from the rectified channel line and further into the channel were assigned the design criteria for a sill (-2 CRP). The 1982 CRP, which was the official CRP in use in 1994, was used to set the structure elevations. L-head revetment heights were read individually from the 1994 Missouri River Hydrographic Survey Mapbook (USACE 1994).
While HEC-RAS can simulate flooding and conveyance in overbank areas, the sedimentation algorithms in the overbanks are unrealistically simplistic. Cross-sections were truncated at the first high levee that was unlikely to overtop. As this is a quasi-unsteady, not truly unsteady flow model, levee breaches were
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not modeled. Smaller levees were included as levee features or as ineffective flow areas. The levees were placed (or channel truncated) to maintain an accurate distance between the river bank and the levee, as measured in GIS from the National Levee Database shapefile. The simplified treatment of levees inherent to a quasi-unsteady flow model limits the ability of this model to predict flood heights or floodplain deposition during extreme (levee overtopping) events.
Tributaries Two major tributaries enter the Missouri River in the model reach: the Platte River (RM 391.29) and the Kansas River (RM 367.57). These rivers contribute water, sand and gravel to the Missouri River, though not nearly as much as the inputs from the Missouri River at the upstream end of the model. From Oct 1, 1962 to Sep 30, 2012, the Platte and Kansas Rivers contributed 3% and 14%, respectively, of Missouri River flow at the Kansas City gage. During the principle calibration period (Aug 1, 1994 to Sep 30, 2009), 91% of all incoming bed material comes from the upstream boundary of the model, 7% from the Kansas River, and 2% from the Platte.
These tributaries were included as flow and sediment boundary conditions instead of modeled reaches. Including these tributaries as boundary conditions disregards that a degrading main channel would cause degradation on these tributaries, which could increase their sediment yield to the Missouri River over time. However, as their sediment contribution is already relatively small, the difference between the boundary condition approach and a modeled approach was not deemed significant enough to justify the considerable additional time and expense of modeling these tributaries. For the larger Kansas River, a significant stone and sheet pile weir, owned and operated by the public water utility WaterOne, is located approximately 14 miles from the confluence. This weir structure combined with significant Kansas River commercial dredging further restricts this potential source of additional bed sediment.
Roughness Channel roughness was assigned as Manning ‘n’ values in four horizontally-varied regions: the active channel, the channel with sill influence, the channel with dike influence, and the floodplain. These regions are delineated in Figure 14. The active channel n values vary between 0.0207 and 0.0307. Sill, dike, and floodplain ‘n’ values were set to 0.03, 0.033, and 0.1, respectively.
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Figure 14. Active Channel and Inter-dike Regions
The two bed roughness predictors available in HEC-RAS (Brownlie and Limerinos) were evaluated and found to yield roughness that was too high at low flows and too low at high flows. Furthermore, it was found that a flow-based n-value adjustment listed in Table 2 could provide excellent agreement with observed stages at the Kansas City gage.
Measured water surfaces at the Kansas City gage indicate that roughness generally increases with flow, except for at the highest discharges. At very high flows, the roughness for the active bed decreases as the bed transitions from dunes to plane bed. This was physically verified using multi-beam bathymetric surveys. As expected, the dunes present during normal flows (67,000 cfs on May 27, 2010) had transitioned to a plane bed at the higher flows (196,000 cfs) seen during the 2011 flood (Figure 15). Roughness during the 2011 flood was markedly lower than for similar flows in 2007. This suggests that the sustained high flows unique to the 2011 flood may have created low roughness conditions that are likewise atypical of most Missouri River floods. Adjusting n-values at high flows to match the smooth bed during the 2011 flood under-predicted water surfaces during the more typical flood of 2007.
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Accordingly, the flow-roughness change factors, presented in Table 2, were calibrated to best match the 1994 to 2009 time period rather than calibrating to a single event.
Figure 15. Flatter bed-forms during 2011 flood flows at approximately RM 367
Table 2. Flow-Roughness Change Factors
US RM 448.89 399.53 350.50 DS RM 400.15 351.15 293.421 Q (cfs) Roughness Factors
0 1 1 1 55000 1 1 1 130000 1 1.17 1 260000 0.85 1 0.85
Bed Sediment Extent The moveable bed limits were set at the line connecting the tips of the training structures (see Figure 13) for cross sections from RM 448.89 to 307.6. During calibration, the moveable bed limits were adjusted inward over the final 13.3 miles (by 120 ft from RM 306.81 to 299.62 and by 160 ft from 299.12 to 293.421). Moving the moveable bed extents inward over the final 13.3 miles was required for the model to match prototype behavior. The depth of the erodible bed was set to 40 ft, which is beyond the limits of degradation expected to occur over the next 50 years. A river-wide sub-surface investigation has not been performed to accurately locate bedrock in the active channel, but specific borings near bridges indicate 40 to 100 ft of sand in Kansas City.
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Bed Sediment Gradation Bed sediments were sampled at 5-mile increments in 1994 over the entire model reach. Figure 16 illustrates that there are three overall zones with similar sediment characteristics. The first zone extends from the model start to the confluence of the Platte River. The second extends from the Platte River to the edge of Kansas City. The third extends from the downstream edge of Kansas City to the downstream end of the model. Average bed gradations for these three reaches were computed and used to smooth individual samples, as described below.
Figure 16. Regions of Bed Gradations
The model includes 31 separate bed gradations, computed as a weighted average of 95% of the individual gradation and 5% of a reach-average gradation. For gradations that fall in Zone 1 and 3, the 5% reach-average is the average gradation from that zone. Gradations that fall in Zone 2 are averaged with a river-wide average rather than the average of Zone 2. The rational is that degradation has likely coarsened the surface gradation in Zone 2, but the underlying reservoir of bed sediment is most likely similar to the rest of the river. This slight smoothing improves modeling results. All the gradations correspond to 1994, the starting year of the calibration. Bed gradation data in subsequent years were examined for temporal trends, but no trend was evident. Rather, the gradations tended to coarsen one year, then fine the next. This lack of apparent trend is most likely attributable to the limited number of samples available over time, inconsistent sampling locations in the cross-section, inconsistent sampling with respect to bedform morphology, and bed surface gradation changes due to current and antecedent flows. The final model gradations are provided in Table 3. Table 3 uses standard HEC-RAS sediment classes, i.e. the final letter designates sediment type as sand (S) or gravel (G) and the first letters designates very fine (VF), fine (F), medium (M), coarse (C), or very coarse (VC).
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Table 3. Final Model Gradations, Percent Finer
RM
Class d
(mm) 290 295 300 305 310 315 320 325 330 340 345 350 355 360 365 370 VFS 0.125 0.82 1.34 0.86 0.96 1.28 1.58 0.60 1.57 0.32 1.63 0.38 2.52 1.13 1.89 1.03 0.63 FS 0.25 24.07 31.52 29.59 19.63 48.56 16.56 12.81 21.97 7.41 38.64 5.39 32.36 40.48 57.09 15.18 25.81 MS 0.5 78.22 95.31 73.79 73.69 96.82 67.31 67.25 86.45 34.26 94.78 36.14 58.39 81.76 95.99 51.73 91.37 CS 1 95.81 98.39 88.38 96.43 98.95 89.55 93.17 99.16 71.96 99.30 77.75 73.21 86.29 98.14 74.30 99.26
VCS 2 99.40 98.82 95.01 99.13 99.39 95.89 97.92 99.78 90.20 99.74 91.17 87.23 87.24 98.74 86.04 99.74 VFG 4 99.90 99.30 98.19 99.81 99.73 98.11 99.76 99.94 95.83 99.91 96.93 98.05 90.51 99.35 93.94 99.84 FG 8 99.99 99.85 99.46 99.97 99.94 99.61 99.97 99.99 98.28 99.98 98.55 99.74 96.22 99.65 98.02 99.95 MG 16 100 100 100 100 100 100 100 100 99.65 100 99.68 100 99.29 99.92 99.63 100 CG 32 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
RM
Class d
(mm) 375 380 385 390 395 400 405 410 415 420 425 430 435 440 450 VFS 0.125 1.01 0.80 1.01 0.82 0.97 1.74 1.06 1.50 2.20 1.20 1.49 1.20 1.23 1.64 1.89
FS 0.25 51.70 16.62 14.13 22.02 36.35 62.79 40.05 48.11 58.66 20.08 45.76 44.18 27.32 39.17 51.64 MS 0.5 97.67 62.79 69.17 87.91 91.86 98.67 93.03 98.98 98.96 79.21 98.31 97.54 88.95 95.40 99.15 CS 1 99.40 80.22 89.39 96.22 98.91 99.80 97.81 99.82 99.82 94.38 99.80 99.79 99.16 99.57 99.83
VCS 2 99.74 89.36 95.34 97.14 99.73 99.96 99.06 99.96 99.96 98.40 99.89 99.96 99.76 99.87 99.96 VFG 4 99.91 95.25 97.43 97.49 99.95 100 99.63 100 100 99.69 99.97 100 99.95 99.97 100 FG 8 99.98 98.32 99.16 98.60 100 100 100 100 100 100 100 100 100 100 100 MG 16 100 99.67 99.85 99.71 100 100 100 100 100 100 100 100 100 100 100 CG 32 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
23
3.4 Boundary Conditions
Boundary conditions include flow, water temperature, downstream water surface elevation, incoming sediment load and gradation, and dredging amounts, locations, and timing. These boundary conditions are described in the following paragraphs.
Flows Daily flow values from Aug 1, 1994 – 29 July 2014, computed from three Missouri River and two tributary USGS gaging stations, were used as the flow inputs to the model.
Daily flow values were compiled for the following USGS gage stations: Missouri River at St. Joseph, MO (06818000); Missouri River at Kansas City, MO (06893000); Missouri River at Waverly, MO (06895500); Platte River at Sharps Station, MO (06821190); Kansas River at Desoto, KS (06892350).
For the degradation model, the upstream boundary was set to the daily flow reported by USGS for the Missouri River at St. Joseph, Missouri. Flows from the Platte and Kansas Rivers were added as lateral flow series. Table 4 lists the flow boundary conditions used in the degradation model. A uniform lateral flow series between St. Joseph and Kansas City incorporates all additional differences in observed flow, including infiltration/exfiltration, overland flow, and minor tributary inputs. These uniform lateral flows do not bring in or remove sediment.
Tributaries that enter the Missouri River between Kansas City and Waverly are insignificant, causing an increase in drainage area of only 0.4%. Also, because the tributaries are spatially distributed, it was found that a single uniform lateral flow series produced a similar flow profile as including each tributary as a separate lateral flow series and spreading the difference out as a uniform lateral flow. The single, simpler modeling option was chosen. Table 4 summarizes the flow boundary conditions used in the model.
Table 4. Flow Boundary Conditions for Degradation Model
Boundary Type Location Source Flow Series St. Joseph USGS Gage: Missouri River at St. Joseph, MO Lateral Flow Series Platte River confluence USGS Gage: Platte River at Sharps Station, MO
Lateral Flow Series Kansas River confluence USGS Gage: Kansas River at Desoto, KS
Uniform Lateral Flow St. Joseph to Kansas City (Kansas City Gage Flow – St. Joseph Flow) - Platte
River Input - Kansas River Input Uniform Lateral Flow Kansas City to Waverly Waverly Gage Flow - Kansas City Gage Flow
24
Water Temperature The HEC-RAS sediment model requires a water temperature for each day of the simulation to calculate fall velocity. Since 2007, USGS has regularly collected water temperature at three stream gages in the degradation modeling reach (St. Joseph, Kansas City, and Waverly). HEC-RAS allows a single temperature for the entire model for a given day (i.e. the temperature of the water is the same throughout the entire river). Temperature measurements at the Kansas City gage were applied to the entire modeling reach. Figure 17 shows the available daily temperature measurements at the Kansas City gage from Oct 10, 2007 to Oct 26, 2010.
Figure 17. Water Temperature at Missouri River at Kansas City Gage, Oct 10, 2007 – Oct 26, 2010
As seen in Figure 17, temperature values follow a cyclical pattern. Year-to-year variations are much less significant than the underlying seasonal shift. The temperatures during the years 2007-2010 were super-imposed to produce a smoothed typical year, shown in Figure 18. The daily temperature values given by this typical year were used as input to the HEC-RAS sediment model for calibration and future prediction.
Downstream Water Surface Boundary Condition The water surface elevation at the USGS Gage at Waverly, MO was used as the downstream water surface boundary condition. The downstream boundary cross-section was set as a pass-through node, meaning bed elevations were not allowed to change at that location.
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Figure 18. Averaged daily water temperature and best-fit trend line
Sediment Load The incoming sediment load and gradation was computed and entered into the model as a DSS time series for each grain class. The sediment load for a given grain class was computed as the total suspended sediment load multiplied by the percent of the suspended load corresponding to the grain class plus the total bed load multiplied by the percent of the bed load corresponding to that grain class.
Only sands and gravels were included in the model. Finer sediments are wash load in this system; they are not found in appreciably quantities on the bed and do not play a significant role in the physical degradation processes. Wash load causes a numerical artifact in HEC-RAS 5.0.1 and so was not included.
USGS Water Quality data was used to develop the flow/load relationship and gradational breakdown of the suspended load. Overall, the suspended sediment load fines considerably with increasing discharge. The original estimated loads and gradations were adjusted slightly (less CS and more FS) during calibration (still well within the data scatter) to reproduce the degradation profile. Figure 19 demonstrates the average, calibrated relationships compared to USGS measurements. (Note that the USGS report many suspended sediment samples that had no coarse sand, which could not be plotted in log space on Figure 19.)
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Figure 19. Model vs. measured suspended sand by grain class
The loads daily suspended sand loads developed for this model sum to a long-term value in agreement with available USGS published values. USGS (2010) estimates annual suspended sand loads at Missouri River gages through Water Year (WY) 2005. The estimated sand load for WY 1995 – WY 2005 is 105,120,000 tons with an upper 95% confidence limit (available for some but not all years) of 1.11 to 1.23 times the estimated load. The suspended sand load included in the model for WY 1995 – WY 2005 = 117,221,000 tons, which is within 12% of the USGS calculated load and within the average 95% confidence interval. Due to variability in the incoming load, the model sediment load for a given year could be higher or lower than the USGS estimate for any given year (see Figure 20).
As a check on the reasonableness of the gradational breakdown of the suspended sand load, the size gradation used in the model was compared against an analysis performed by David Heimann of USGS (Heimann 2014). Heimann produced the following as a reasonable gradational breakdown of the suspended sand load at St. Joseph for 1994 to 2009 using standard USGS methods. As seen in Figure 20 and Table 5, the loads and gradations used in the model are in reasonable agreement with other estimates.
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Figure 20. Annual suspended sand load at St. Joseph, MO
Table 5. Sand Gradation Estimate
Size % of Sand Load Heimann (2014) Model
VFS 19% 18% FS 62% 63% MS 17% 17% CS 1.8% 1.7%
During the 2011 flood, the tremendous volumes of relatively clear water released from the dams and relatively small contribution from the tributaries due to drought conditions resulted in a markedly different suspended sediment relationship (see Figure 11). As annual sand loads have not been published for 2011, the suspended loads and bed material load during the 2011 event was based on USGS measurements and the gradation of suspended sand was adjusted as a calibration parameter.
The bedload portion of the sediment load was computed from a bedload rating curve for the Missouri River just upstream of the confluence of the Kansas River. This bedload rating curve
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was computed by using successive multi-beam bathymetric surveys (Abraham et al. 2011) with the time correction suggested in Shelley et al. (2013). This rating curve is provided in Figure 21. This rating curve location does not coincide with upstream end of the model where the suspended sediment measurements were taken. However, as the location of this rating curve and the upstream end of the model share common design criteria for channel width and dike configuration, it was considered an appropriate estimate for bedload in the absence of site-specific measurements.
Figure 21. Missouri River Bedload Rating Curve at Kansas City (Above Kansas River Confluence)
The gradation of the incoming total sediment load is a function of the relative contributions from bed load and suspended load, which varies by flow and by whether the 1994 – 2010 or 2011 flow-load curve is used for the suspended sediment contribution.
Sediment rating curves at two major tributaries—the Platte River and the Kansas River—were included in the model as flow-load boundary conditions. The flow-load curve for the Platte River was based on USGS water quality data for the Platte River at Sharps Station. A bed material load was developed by subtracting the percent fines recorded in USGS measurements (which increases with increasing flow) and adding 5% as an estimate for bed load. In the absence of measurements, the bed material load was assumed composed of predominantly fine and medium sand. Table 5 and Figure 22 provide the loads and gradations used in the model.
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Table 5. Platte River Bed Material Load Rating Curve
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(tons/day) 0 426 5337 8454 10305 VFS 0.15 0.14 0.12 0.11 0.10 FS 0.50 0.49 0.48 0.47 0.45 MS 0.28 0.29 0.29 0.29 0.29 CS 0.06 0.09 0.11 0.13 0.15
Figure 22. Platte River Bed Material Load
The sediment load and gradation for the Kansas River was based on USGS water quality data for the Kansas River at Desoto, Kansas. A power-function was fit through the flow-load data to generate a total suspended sediment load rating curve. USGS measurements of the grain size distribution were analyzed to partition the suspended load into grain size classes. Five percent of the total suspended load was added as an estimate for bed load. As shown in Figure 23, the resulting bed material rating curve (load > 0.0625 mm) closely matches the bed material rating curve developed by Simons, Li, and Associates (1984). Table 6 and Figure 23 provide the loads and gradations used in the model.
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Table 6. Kansas River Sediment Rating Curve and Gradation
Q (cfs) 1000 28000 50000 100000 Qs (tons/day) 28 11452 32530 113324
% in Class VFS 20 43 24 21 FS 32 23 31 31 MS 28 21 34 34 CS 20 13 12 14
Figure 23. USGS total suspended sediment load and Model and Simons Li and Associates (1984) bed material loads for the Kansas River
Dredging Commercial dredging on the Missouri River was a significant driver of bed degradation during the calibration period (USACE 2011). The resolution of dredging data varies over time. From
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1994 – 1996, the annual tons dredged were reported to USACE’s regulatory branch on a reach basis. Since 1997, daily tons dredged and river miles were reported.
Figure 24 shows estimated dredged quantities for river miles 292 to 449, which encompasses the degradation modeling reach. Figure 24 also includes dredging in 2002 for L385 (a Corps of Engineers levee project) and dredging in 1989 for a MODOT project.
Figure 24. Annual Dredging 1974 – 2011 for Degradation Modeling Reach
Dredging was included in the degradation model as monthly totals at each cross-section with the start date the first day of the month and the end date the last day of the month. For 1997 and later, the reported monthly tonnages of dredging were assigned to the appropriate cross-sections and to the appropriate month. For 1994 – 1996, sufficient temporal and spatial data were not available on the actual locations and dates of dredging. To compensate, reach-wide, annual tonnages from 1994 to 1996 were apportioned among cross-sections and months following the average spatial and temporal distribution of dredging from 1997 – 2009. This spatial distribution is provided in Figure 25. The temporal distribution is provided in Figure 26.
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Figure 25. Cumulative Dredging by River Mile as Percent of the Total Dredging 1997 – 2009
The impact of dredging was restricted to the actual dredging tonnage, i.e. one ton of material extracted lowers the bed by a volume equivalent to one ton. Potential dredging effects due to material sorting, re-discharge, and bed disturbance were not included. Dredging volumes or locations were not adjusted during calibration.
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Figure 26. Monthly Distribution of Dredging from St. Joseph, MO to Waverly, MO 1997 to 2009
2011 Flood Boundary Conditions The historic flood of 2011 necessitated two changes to the boundary conditions developed for the 1994 – 2009 time period. First, as shown in Figure 10, the sediment concentrations were dramatically lower during the 2011 flood than typical. For March – November, 2011, a distinct load and gradation were used instead of the long-term relationships given in Figure 19. Second, sustained high releases coinciding with levee breaks deposited a tremendous volume of sand on the floodplain. A USGS study found that sand deposition covered 5,876 acres of floodplain in the model reach, with a minimum depth suggested as 2 ft (Alexander et. al, 2013). This equates to 24.8 million tons of sediment lost to the floodplain. Bathymetric surveys indicate that 8.7 million tons of sediment could have derived from the channel boundary outside the moveable bed limits, which equates to a net floodplain sink of bed sediments of 16.1 million tons. As HEC-RAS is unable to realistically model floodplain deposition in a long-term simulation, floodplain deposition during the 2011 flood event was explicitly added as a negative lateral load. The load was distributed proportional to the areal extent of deposition, shown in Figure 27. These unique boundary conditions were deemed necessary for modeling a time period including and just following the 2011 flood, but do not represent the normal behavior of the river during most floods. Accurately modeling river behavior during the 2011 flood would also require a change to the n-values and moveable bed extents, both of which are not possible in a continuous HEC-RAS simulation. Consideration for the repeat of these unique conditions will be given in the risk and uncertainty analysis, but are not included in the baseline future projections.
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Figure 27. Acreage of Floodplain Sand Deposition from the 2011 flood. Data from Alexander et. al (2013).
3.5 Model Parameters
Model parameters include sediment transport formula, bed mixing algorithm, and computational time steps. These model parameters are described in the following paragraphs.
Sediment Transport Formula Multiple sediment transport formula were tested, including Laursen-Copeland, Meyer-Peter and Muller, Toffaleti, and Yang. Maximum depths in the Missouri River during the calibration period reach 56 ft and 10.6 fps, respectively, which are similar to the depths and velocities for data used to develop Laursen-Copeland (54 ft, 9.4 fps), Toffaleti (56.7 ft, 7.8 fps), and Yang (50 ft, 6.4 fps). The maximum velocity is slightly higher than the velocities used in the development of any of the available sediment transport formula. The Toffaleti (1968) sediment transport formula was selected to compute the sediment transport capacity due to its applicability and history of use on large, sand-bed rivers and because it yielded reasonable results. The Toffaleti fall velocity method was also used. HEC (2010) details the Toffaleti computational procedure.
Bed Mixing Algorithm Two bed mixing/armoring algorithms were tested: Exner 5 and Exner 7. Exner 5 yielded reasonable results for total bed degradation and was selected for use in the model. Exner 7 produced excessive degradation compared to the prototype.
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Computational Increment The computational increment was set based on the flow rate. It ranges from 24 hr when flow is less than 50,000 cfs to 30 min when flow exceeds 200,000 cfs. Bed exchange iterations per time step was set to 10, the HEC-RAS default. 3.6 Calibration/Verification
The principle calibration period runs from Aug 1, 1994 to Oct 1, 2009. This time period includes a range of high and low flows and is most representative for future prediction. A second time period from Oct 1, 2009 to July 29, 2014 was also used in calibration. However, because this time period includes the historic Missouri River Flood of 2011 which exhibited unique boundary conditions, this time period serves more as a verification of reasonableness than a second calibration point. The principal parameters which were varied to achieve calibration were the Manning ‘n’ values for the active channel, inter-sill region, and inter-dike region, the flow-based ‘n’ adjustment factors, the level of smoothing of the gradation data, the sediment loading from the Kansas River, and the moveable bed extents. As described in the previous paragraphs, these calibrated initial conditions and boundary conditions have physical basis in measured data.
Early Hydraulic Calibrations The model bathymetry is from 1994. The calibration period starts in Aug 1, 1994. On Aug 16 and 17, 1994, the water surface was measured at multiple points along the river. These measured water surface elevations are subject to more errors than USGS gage measurements but are still useful to verify the hydraulic model. Figures 28, 29, and 30 illustrate the model agreement to the low water surface elevations collected on August 16 and 17, 1994. The average absolute difference between modeled and measured water surfaces for August 16 and 17 is 0.8 ft. This analysis is similar to a “fixed-discharge, fixed-bed” analysis for a low discharge because it occurs so soon after the model start.
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Figure 28. Model hydraulic comparison at low flow: River Miles 450 - 400
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Figure 29. Model hydraulic comparison at low flow: River Miles 400 - 350
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Figure 30. Model hydraulic comparison at low flow: River Miles 350 - 290
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A major high-flow event occurred within a year of the model start. Figures 31 and 32 compares model results to the water surface elevation at the USGS Missouri River gage at St. Joseph and Kansas City, respectively.
Figure 31. Water surface at the St. Joseph gage during first year of calibration period
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Figure 32. Water surface at Kansas City gage during first year of calibration period
Output shown in Figures 31 and 32 is from the mobile-bed model and therefore includes slight bed changes over the course of the first year. However, these changes are relatively small. For the first year of simulation the average absolute difference between measured and modeled water surfaces is 0.40 ft and 0.43 ft at St. Joseph and Kansas City, respectively. During this event at the Kansas City gage, input from the Kansas River and overbank storage issues causes rapid fluctuations near the peak which are not reflected well in this model due to the use of steady-state hydraulics. Notwithstanding this limitations, the model reproduces channel hydraulics well.
Hydraulic Calibration- Long Term Figure 33 plots the difference between the measured and modeled water surface at the St. Joseph and Kansas City gage as a function of discharge (1994 to 2014). At the highest flows at St. Joseph, the model predicts water surfaces very well. At the Kansas City gage, the model under predicts during some high flow events and over predicts during other high flow events. The scatter is due to hysteresis in channel roughness, the timing of flows (particularly Kansas River flows), i.e. model flows occur instantaneously, while actual flows take time to arrive at the Kansas City gage, and other unsteady effects. In long-term sediment modeling, these effects are less important (i.e. whether a high flow occurs on June 1 or June 2 makes little difference in a long-term simulation), provided the overall sediment volumes are adequate.
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Figure 33. Difference in Water Surface Elevations as a Function of Flow
The agreement of the model water surface elevation over the full primary calibration period (1994 to 2009) is a verification of the temporal fidelity of the model. As seen in Figures 34, 35, 36, and 37 the model reproduces water surface elevations at the St. Joseph and Kansas City gages well over the duration of the principle calibration period (1994 to 2009), with an average absolute error of 0.49 ft (St. Joseph) and 0.60 ft (Kansas City).
During the second calibration/verification period (2009 to 2014), the average absolute error is 0.52 ft (Saint Joseph) and 0.69 ft (Kansas City). As seen in Figure 38 and 39, the model reproduces water surface elevations very well.
Of special interest is how well the model reproduces the minimum water surface elevation for any given year. The mean residual in the annual minimum water surface elevations are 0.54 ft at the St. Joseph gage (model predicts slightly high) and 0.00 ft and the Kansas City gage. The standard errors of estimate for annual minimums are 0.81 ft and 0.39 ft, respectively.
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Figure 34. Model vs. Measured Water Surface at the St. Joseph Gage: 1994 - 2002
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Figure 35. Model vs. Measured Water Surface at the St. Joseph Gage: 2002 - 2009
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Figure 36. Model vs. Measured Water Surface at Kansas City Gage: 1994 – 2002
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Figure 37. Model vs. Measured Water Surface at Kansas City Gage: 2002 – 2009
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Figure 38. Model vs. Measured Water Surface at the St. Joseph Gage: 2009 - 2014
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Figure 39. Model vs. Measured Water Surface at Kansas City Gage: 2009 - 2014
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Hydraulic Calibration- Peak Stages at Intermediate Gages National Weather Service (NWS) stage-only gages on the Missouri River provide additional information to validate the hydraulic parameters of the model, particularly the flow-roughness factors. As seen in Figure 40, the model predicts higher annual peak stages at Atchison and Sibley, but not at nearby Leavenworth or Napoleon. During calibration, it was found that adjustments to decrease the Atchison and Sibley water surface predictions could not be accomplished without worsening the calibration of adjacent gages and of other calibration parameters. Most likely, differences between model and measured flow between flow gages accounts for the discrepancy. The model uses daily flows, is steady state, and includes flow differences among gages that can’t be accounted for by tributaries as uniform lateral inflows. In contrast, the flows that induce the peak stages at the NWS gages include attenuation, timing of tributary inputs, event-specific levee failures, and other unsteady factors which are not reflected in the model. As seen in Figure 40, no strong bias with flow is evident, indicating that the flow roughness adjustments used in the model are appropriate.
Figure 40. Comparison between National Weather Service and Model Annual Peak Elevations
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Velocity Calibration Channel velocities were measured during, soon after, and one year after the 2011 flood via ADCP. As seen in Figure 41, model velocities are in reasonable agreement with measured velocities. The measurements in July of 2012 purposefully included locations with the heaviest dike influence, which explains some of the higher velocities.
Figure 41. Velocity Comparison
Bed Elevation and Mass Calibration Figure 42 presents bed elevation change at each cross-section compared against measured change at that location. In Figure 42, the measured change is an interpolation from the two nearest measured locations. As seen, the model accurately reproduces degradation trends, though both measured data and model output exhibit significant variability and scatter.
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Figure 42. Model vs. Measured Bed Elevation Change 1994 to 2009
The nature of the active bedforms on the Missouri River causes individual cross sectional measurements to vary by several feet even without persistent geomorphic change. USACE (2015) finds that 75% of cross sections varied 0.25 ft to 3 ft from 2008 to 2009, but some temporarily rose or fell by as much as 11 ft in a single year. The standard deviation of the difference between model and measured bed change (1994 to 2009) is 2.0 ft. For comparison, the standard deviation of natural variability (computed using 2008 to 2009 or 2007 to 2008 surveys) is 1.3 ft.
With a sufficient number of cross sections, these random fluctuations average out, which makes volume or mass change over reaches more useful for comparing model to measured output than bed change at an individual cross section. Figure 43 plots the longitudinal cumulative mass change for both model and measured cross sections from 1994 to 2009. The measured mass change was computed using the area change of the active channel at the full set of 546 cross-section locations surveyed in both 1994 and 2009. As seen in Figure 43, the calibrated model closely approximates the magnitude and location of mass change from 1994 to 2009.
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Figure 43. Longitudinal Cumulative Mass Calibration: 1994 to 2009
Figures 44 and 45 present the bed change and longitudinal cumulative mass change from 2009 to 2014. Figure 44 presents the measured value for bed change at each model location interpolated from the nearest measured cross sections. The standard deviation between model and measured bed change is 1.4 ft, only slightly greater than the 1.3 ft of natural variability.
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Figure 44. Model vs. Measured Bed Elevation Change 2009 to 2014
Figure 45 computes mass change from 2009 to 2014, computed using area change of the active channel from the full set of 1,641 cross-sections surveyed in both 2009 and 2014. As seen, the model reasonably approximates the magnitude and location of mass change over this second time period. Importantly, it reflects the upstream migration of the degradation from Kansas City towards St. Joseph. Downstream of Kansas City, the model predicts sediment accumulation slightly upstream from where it actually occurred, and the cumulative model result diverges from the measured data for the active channel by 4 million tons. This is most easily explained by uncertainty in the volume of floodplain deposition during the 2011 flood event and other factors such as an unmeasured sources of sediment from river banks or tributary inputs in this reach. Notwithstanding, the model performs reasonably well.
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Figure 45. Longitudinal Cumulative Mass Calibration/Verification: 2009 to 2014
Figure 46 averages the difference between model and measured output over 5-mile reaches for both the 1994 to 2009 and 2009 to 2014 time period. The magnitude of residual error is similar to the natural variability over 5-mile reaches, as documented in USACE (2015). Sources of model error beyond natural variability are model approximations, such as steady state vs. unsteady state flow modeling, set moveable bed boundaries vs. dynamic boundaries, etc. and uncertainty in input data. The implications of these residual errors is that while the model can project trends and differences among alternatives, the actual bed elevation for an individual feature can be higher or lower than the predicted value. The Future Without Project/ Risk and Uncertainty Appendix includes the model error along with other sources of uncertainty to compute reasonable confidence intervals around future projections.
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Figure 46. Difference between model and measured bed elevations averaged over 5-mile reaches for two time periods. Differences are similar to the range of natural variability.
Sediment Load USGS (Heimann et al., 2010) provides an estimate for annual suspended sediment sand loads through water year 2005 at multiple gages on the Missouri River. The USGS estimate at St. Joseph was used to develop the sediment load at the upstream model boundary, as explained. The total sand load at the next downstream gage, the Kansas City gage, provides an additional validation of the sediment model. The model values include sand moving as bed load as well as in suspension, whereas the USGS estimates include only sand moving in suspension. On the Missouri River, the bed load contributes around 5% to the total bed material load. Accounting for bed load, the USGS estimate adjusts to 135.1 million tons, with 108.8 to 165.0 million for the 95% confidence intervals. The model estimate for the same years is 143.3 million tons, which is 6% higher than the USGS estimate and within the 95% confidence intervals. This is excellent agreement for a sediment model.
Robustness As a final measure of model suitability, a robustness test was performed. This test consisted of running 43 kcfs, which for the Missouri River is just above the full service navigation flow (41 kcfs), for a period of 30 years starting with the initial 1994 geometry and gradations. For this robustness test, no dredging, floodplain deposition, or tributary inputs were included. In this Missouri River robustness test, aggradation occurred in previously degraded areas. At the end of the 30-year period, the standard deviation of bed elevation change over the final 30 days was < 0.008 ft for 100% of the cross-sections (compared to only 3% of the cross sections for the first month), and the model was assumed to be reasonably robust.
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Conclusion This report described the mobile-bed model developed for modeling and predicting degradation in conjunction with the Missouri River Degradation Feasibility Study. It served as an orientation to the inputs, assumptions, and modeling choices that have occurred and aided in the technical review of the model. The model outputs for water surface, mass change, velocity, and sediment transport over the calibration period match the prototype using realistic initial conditions and boundary conditions and appropriate model parameters. The magnitude of floodplain deposition of sediments during sustained, major floods cannot be adequately predicted using this model, and will be addressed with uncertainty analysis. The model has been calibrated to the Missouri River and is deemed suitable use in planning-level studies and other assessments.
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References Abraham, D., Kuhnle, R., and Odgaard, A. J., (2011), “Validation of Bed Load Transport Measurements with Time-Sequenced Bathymetric Data.” J. Hydr. Engrg., ASCE, 137(7), 723-728. Alexander, J.S., Jacobson, R.B., and Rus, D.L., 2013, Sediment transport and deposition in the lower Missouri River during the 2011 flood: U.S. Geological Survey Professional Paper 1798–F, 27 p., http://dx.doi.org/10.3133/pp1798f.
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Heimann, D.C., Rasmussen, P.P., Cline, T.L., Pigue, L.M., and Wagner, H.R. (2010). Characteristics of sediment data and annual suspended-sediment loads and yields for selected lower Missouri River mainstem and tributary stations, 1976–2008: U.S. Geological Survey Data Series Report 530, 58 p.
Horowitz, A.J. (2006). “The effect of the ‘Great Flood of 1993’ on subsequent suspended sediment concentrations and fluxes in the Mississippi River Basin, USA.” Sediment Dynamics and the Hydrogeomorphology of Fluvial Systems. IAHS Publ. 306, 2006.
Julien, P.Y. (1994). Erosion and Sedimentation, Cambridge University Press, QE571.J85, ISBN 0-521-44237-0 Hardback in 1995, Paperback in 1998, 280p.
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Shelley, J., Abraham, D., and McAlpin, T. (2013). "Removing Systemic Bias in Bed-Load Transport Measurements in Large Sand-Bed Rivers." J. Hydraul. Eng., 0.1061/(ASCE)HY.1943-7900.0000760 (Mar. 22, 2013). http://ascelibrary.org/doi/abs/10.1061/(ASCE)HY.1943-7900.0000760
Simons, Li & Associates (1982). Engineering Analysis of Fluvial Systems. Fort Collins, CO.
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USACE (1981). Missouri River Bank Stabilization and Navigation Project Final Feasibility Report and Final EIS for the Fish and Wildlife Mitigation Plan. U.S. Army Corps of Engineers, Missouri River Division.
USACE (1994). Missouri River Hydrographic Survey: Rulo, Nebraska to the Mouth. U.S. Army Corps of Engineers, Kansas City District. Kansas City, MO.
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USACE (2007). Calibrating a HEC-RAS Model of the Missouri River for FEMA Floodway Development. http://www.nwd-c.usace.army.mil/PB/HHCOP/MO%20R%20FLOODWAY.pdf .
USACE (2009). Missouri River Bed Degradation Reconnaissance Study Section 905(b) (Water Resources Development Act of 1986) Analysis. U.S. Army Corps of Engineers, Kansas City District. Kansas City, MO.
USACE (2010). Memorandum for Record: Documentation of Missouri River Low Water Surface Profile Adjustment Procedure. U.S. Army Corps of Engineers, Kansas City District. Kansas City, MO.
USACE (2011). Missouri River Commercial Dredging Final Environmental Impact Statement. U.S. Army Corps of Engineers, Kansas City District. Kansas City, MO. Prepared by Cardno-Entrix, Seattle, WA.
USACE (2012). Missouri River Stage Trends Technical Report. U.S. Army Corps of Engineers, Missouri River Basin Water Management Division. Omaha, NE. http://www.nwd-mr.usace.army.mil/rcc/reports/pdfs/MRStageTrends2012.pdf