This chapter illustrates the Corps of Engineers's application of risk analysis by reviewing two Corps flood damage reduction projects: Beargrass Creek in Louisville, Kentucky, and the Red River of the North in East Grand Forks, Minnesota, and Grand Forks, North Dakota. The Beargrass Creek case study describes the entire procedure of risk-based engineering and economic analysis applied to a typical Corps flood damage reduction project. The Red River of the North case study focuses on the reliability of the levee system in Grand Forks, which suffered a devastating failure in April 1997 that resulted in more than $1 billion in flood damages and related emergency services.

The Corps of Engineers has used risk analysis methods in several flood damage reduction studies across the nation, any of which could have been chosen for detailed investigation. Given the limits of the committee's time and resources, the committee chose to focus upon the Beargrass Creek and Red River case studies for the following reasons: committee member proximity to Corps offices, a high level of interest in these two studies, and the availability of documentation from the Corps that adequately described their risk analysis applications.

Differences in approaches taken at Beargrass Creek and along the Red River of the North to reducing flood damages are reflected in these studies. At Beargrass Creek, the primary flood damage reduction measures were detention basins; at the Red River of the North, the primary measures were levees. The Corps uses rainfall-runoff models in nearly all of its flood damage reduction studies to simulate streamflows needed for flood-frequency analysis, and a rainfall-runoff model was employed in the Beargrass Creek study. In the Red River study, however, the goal

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5
Case Studies
This chapter illustrates the Corps of Engineers's application of risk analysis by reviewing two Corps flood damage reduction projects: Beargrass Creek in Louisville, Kentucky, and the Red River of the North in East Grand Forks, Minnesota, and Grand Forks, North Dakota. The Beargrass Creek case study describes the entire procedure of risk-based engineering and economic analysis applied to a typical Corps flood damage reduction project. The Red River of the North case study focuses on the reliability of the levee system in Grand Forks, which suffered a devastating failure in April 1997 that resulted in more than $1 billion in flood damages and related emergency services.
The Corps of Engineers has used risk analysis methods in several flood damage reduction studies across the nation, any of which could have been chosen for detailed investigation. Given the limits of the committee's time and resources, the committee chose to focus upon the Beargrass Creek and Red River case studies for the following reasons: committee member proximity to Corps offices, a high level of interest in these two studies, and the availability of documentation from the Corps that adequately described their risk analysis applications.
Differences in approaches taken at Beargrass Creek and along the Red River of the North to reducing flood damages are reflected in these studies. At Beargrass Creek, the primary flood damage reduction measures were detention basins; at the Red River of the North, the primary measures were levees. The Corps uses rainfall-runoff models in nearly all of its flood damage reduction studies to simulate streamflows needed for flood-frequency analysis, and a rainfall-runoff model was employed in the Beargrass Creek study. In the Red River study, however, the goal

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was to design a system that would, with a reasonable degree of reliability, contain a flood of the magnitude of 1997's devastating flood. The Corps focused on traditional flood–frequency analysis and manipulated the frequency curve at a gage location to derive frequency curves at other locations (vs. using a rainfall-runoff model to derive those curves).
BEARGRASS CREEK
In 1997 the Corps held a workshop (USACE, 1997b) at which experience accumulated since 1991 in risk analysis for flood damage reduction studies was reviewed. O'Leary (1997) described how the new procedures had been applied in the Corps's Louisville, Kentucky, district office. In particular, O'Leary described an application to a flood damage reduction project for Beargrass Creek, economic analyses for which were done both under the old procedures without risk and uncertainty analysis and under the new procedures that include those factors. Conclusions of the Beargrass Creek study are summarized in two volumes of project reports (USACE, 1997c,d). These documents, plus a site visit to the Louisville district by a member of this committee, form the basis of this discussion of the Beargrass Creek study. The Beargrass Creek data are distributed with the Corps's Hydrologic Engineering Center Flood Damage Assessment (HEC-FDA) computer program for risk analysis as an example data set. The Beargrass Creek study is also used for illustration in the HEC-FDA program manual and in the Corps 's Risk Training course manual. Although there are variations from study to study in the application of risk analysis, Beargrass Creek is a reasonably representative case with which to examine the methodology.
As shown Figure 5.1, Beargrass Creek flows through the city of Louisville, Kentucky, and into the Ohio River on its south bank. The Beargrass Creek basin has a drainage area of 61 square miles, which encompasses about half of Louisville. The basin currently (year 2000) has a population of about 200,000. This flood damage reduction study's focal point is the lower portion of the basin shown in Figure 5.1 —the South Fork of Beargrass Creek and Buechel Branch, a tributary of the South Fork.
Locally intense rainstorms (rather than regional storms) cause flooding in Beargrass Creek. A 2-year return period storm causes the creek to overflow its banks and produces some flood damage. Under existing conditions, the Corps estimates that a 10-year flood will impact

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FIGURE 5.1 The Beargrass Creek basin in Louisville, Kentucky. SOURCE: USACE (1997a) (Figure II-1).
about 300 buildings and cause about $7 million in flood damages, while a 100-year flood will impact about 750 buildings and cause about $45 million in flood damages (USACE, 1997c). The expected annual flood damage under existing conditions is approximately $3 million per year.
Flood Damage Reduction Measures
Beargrass Creek has several flood damage reduction structures, the most notable of which is a very large levee at its outlet on the Ohio River (Figure 5.2a). This levee was built following a disastrous flood on the Ohio in January 1937, and the levee crest is an elevation of 3 feet above the 1937 flood level on the Ohio River. During the 1937 flood it was reported that “at the Public Library, the flood waters reached a height such that a Statue of Lincoln appeared to be walking on water!” (USACE, 1997b, p. III-2). Near the mouth of Beargrass Creek, a set of

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gates can be closed to prevent water from the Ohio River from flowing back up into Louisville. In the event of such a flood, a massive pump station with a capacity of 7,800 cubic feet per second (cfs) is activated to discharge the flow of Beargrass Creek over the levee and into the Ohio River.
Between 1906 and 1943, a traditional channel improvement project was constructed on the lower reaches of the South Fork of Beargrass Creek. It consists of a concrete lined rectangular channel with vertical sides, with a small low-flow channel down the center (Figure 5.2b). The channel's flood conveyance capacity is perhaps twice that of the natural channel it replaced, but the concrete channel is a distinctive type of landscape feature that environmental concerns will no longer permit. Other structures have been added since then, including a dry bed reservoir completed in 1980, which functions as an in-stream detention basin during floods.
The proposed flood damage reduction measures for Beargrass Creek form an interesting contrast to traditional approaches. The emphasis of the proposed measures is on altering the natural channel as little as possible and detaining the floodwaters with detention basins. These basins are either located on the creek itself or more often in flood pool areas adjacent to the creek into which excessive waters can drain, be held for a few hours until the main flood has passed, and then gradually return to the creek. Figure 5.2c shows a grassed detention pond area with a concrete weir (in the center of the picture) adjacent to the creek. Figure 5.2d shows Beargrass Creek at this location (a discharge pipe from the pond is visible on the right side of the photograph). Water flows from the creek into the pond over the weir and discharges back into the creek through the pipe. The National Economic Development flood damage reduction alternative on Beargrass Creek called for a total of eight detention basins, one flood wall or levee, and one section of modified channel. Other alternatives such as flood-proofing, flood warning systems, and enlargement of bridge openings were considered but were not included in the final plan.
The evolution of flood damage reduction on Beargrass Creek represents an interesting mixture of the old and the new—massive levees and control structures on the Ohio River, traditional approaches (the concrete-lined channel) in the lower part of the basin, more modern instream and off-channel detention basins in the upstream areas, and local channel modifications and floodwalls. Maintenance and improvement of stormwater drainage facilities in Beargrass Creek are the responsibility of the Jefferson County Metropolitan Sewer District, which is the principal local partner working with the Corps to plan and develop flood damage reduction measures.

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(a) Levee on the Ohio River
(b) Concrete-lined channel

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(c) Detention pond
(d) Beargrass Creek at the detention pond
FIGURE 5.2 Images of Beargrass Creek at various locations: (a) the levee on the Ohio River, (b) a concrete-lined channel, (c) a detention pond, and (d) the Beargrass Creek at the detention pond.

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In some locations, development has been prohibited in the floodway; but in other places, buildings are located adjacent to the creek. The Corps's feasibility report includes the following comments: “Urbanization continues to alter the character of the watershed as open land is converted to residential, commercial and industrial uses. The quest for open area residential settings in the late 1960s and early 1970s caused a tremendous increase in urbanization of the entire basin. Several developers have utilized the aesthetic beauty of the streambanks as sites for residential as well as commercial developments. This has resulted in increased runoff throughout the drainage area as development has occasionally encroached on the floodplain and, less frequently, the floodway” (USACE, 1997b, p. II-2).
Damage Reaches
To conduct the flood damage assessment, the two main creeks— South Fork of Beargrass Creek and Buechel Branch—are divided into damage reaches. Flood damage and risk assessment results are summarized for each damage reach, and the expected annual damage for the project as a whole is found by summing the expected annual damages for each reach. As shown in Figure 5.3, the South Fork was divided into 15 damage reaches and the Buechel Branch into 5 reaches (a sixth damage reach on Buechel Branch is not shown in this figure). Approximately 12 miles of Beargrass Creek, and 2.2 miles of Buechel Branch are covered by the these damage reaches. The average length of a damage reach is thus 0.8 miles for the South Fork of the Beargrass Creek, and the average length for Buechel Branch is 0.4 miles. The shorter reaches on Buechel Branch are adjacent to similarly short, upstream reaches in Beargrass Creek where most flood damage occurs. Longer damage reaches are used downstream on Beargrass Creek where less damage occurs.
The highest expected annual flood damage is on Reach SF-9 on the upper portion of the South Fork of Beargrass Creek. Results from this damage reach are used for illustrative purposes at various points in this chapter.

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FIGURE 5.3 Damage reaches on the South Fork of Beargrass Creek and Buechel Branch. SOURCE: USACE (1997a) (Figure III-3).
Flood Hydrology
Most of the flood damage reduction measures being considered are detention basins, which diminish flood discharge by temporarily storing floodwater. It follows that the study's flood hydrology component has to be conducted using a time-varying rainfall–runoff model because this allows for the routing of storage water through detention basins. In this case, the HEC-1 rainfall–runoff model from the Corps's Hydrologic Engineering Center (HEC) was used to quantify the flood discharges. The Hydrologic Engineering Center has subsequently released a successor rainfall-runoff model to HEC-1, called HEC-HMS (Hydrologic Modeling System), which can also be used for this type of study (HEC, 1998b).
In each damage reach, and for each alternative plan considered, the risk analysis procedure for flood damage assessment requires a flood – frequency curve defining the annual maximum flood discharge at that location which is equaled or exceeded in any given year with a given probability. In this study all these flood–frequency curves were produced through rainfall–runoff modeling. In other words, a storm of a given

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return period was used as input to the HEC-1 model, the water was routed through the basin, and the magnitude of the discharge at the top end of each damage reach was determined (Corps hydrologists have assumed, based on experience in the basin, that storms of given return periods produce floods of the equivalent return period). By repeating this exercise for each of the annual storm frequencies to be considered, a flood–frequency curve was produced for each damage reach. There are eight standard annual exceedance probabilities normally used to define this frequency curve: p = 0.5, 0.2, 0.1, 0.04, 0.02, 0.01, 0.004, and 0.002, corresponding to return periods of 2, 5, 10, 25, 50, 100, 250, and 500 years, respectively. In this study, because even small floods cause damage, a 1-year return period event was included in the analysis and assigned an exceedance probability of 0.999.
Considering that there are 21 damage reaches in the study area and 8 annual frequencies to be considered, each alternative plan considered requires the development of 21 flood–frequency curves involving 168 discharge estimates. During project planning, as dozens of alternative components and plans were considered, the sheer magnitude of the tasks of hydrologic simulation and data assembly becomes apparent.
The hydrologic analysis is further complicated by the fact that the design of detention basins is not simply a cut-and-dried matter. A basin designed to capture a 100-year flood requires a high–capacity outlet structure. Such a basin will have little impact on smaller floods because the outlet structure is so large that smaller events pass through almost unimpeded. If smaller floods are to be captured, a more confined outlet structure is needed, which in turn increases the required storage volume for larger floods. This situation was resolved in the Beargrass Creek study by settling on a 10-year flood as the nominal design event for sizing flood ponds and outlet works. The structures designed in this manner were then subjected to the whole range of floods required for the economic analysis.
Rainfall–Runoff Model
The HEC-1 model was validated by using historical rainfall and runoff data for four floods (March 1964, April 1970, July 1973, February 1990). Modeling results were within 5 percent to 10 percent of observed flows at two U.S. Geological Survey (USGS) streamflow gaging stations: South Fork of Beargrass Creek at Trevallian Way and Middle Fork

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of Beargrass Creek at Old Cannons Lane, which have flow records beginning in 1940 and 1944, respectively, and continuing to the present. A total of 42 subbasins were used in the HEC-1 model, and runoff was computed using the U.S. Soil Conservation Service (renamed the Natural Resources Conservation Service in 1994) curve number loss rates and unit hydrographs. The Soil Conservation Service curve numbers were adjusted to allow the matching of observed and modeled flows for the historical events. A 6-hour design storm was used, which is about twice the time of concentration of the basin. The design storm duration chosen is longer than the time of concentration of the basin so that the flood hydrograph has time to rise and reach its peak outflow at the basin outlet while the storm is still continuing. If the design storm is shorter than the time of concentration, rainfall could have ceased in part of the basin before the outflow peaks at the basin outlet. The storm rainfall hydrograph was based on National Weather Service 1961 Technical Paper 40 (NWS, 1961) and on a Soil Conservation Service storm hydrograph, and a 5-minute time interval of computation was used for determining the design discharges.
There is a long flood record of 56 years of data (1940–1996) available in the study area (USGS gage on the South Fork of Beargrass Creek at Trevallian Way). A comparison was made of observed flood frequencies at this site with those simulated by HEC-1, with some adjustment of the older flood data to allow for later development. Traditional flood frequency analysis of observed flow data had little impact in the study. This may have been the case because there was only one gage available within the study area, or because the basin has changed so much over time that the flood record there does not represent homogeneous conditions. Furthermore, the alternatives mostly involve flood storage, which requires computation of the entire flood hydrograph, not just the peak discharge.
Uncertainty in Flood Discharge
Uncertainty in flood hydrology is represented by a range in the estimated flood–frequency curve at each damage reach. In the HEC-FDA program, there are two options for specifying this uncertainty: an analytical method based on the log-Pearson distribution and a more approximate graphical method. The log-Pearson distribution is a mathematical function used for flood–frequency analysis, the parameters of which are determined from the mean, standard deviation, and coefficient

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of skewness of the logarithms of the annual maximum discharge data. The graphical method is a flood frequency analysis performed directly on the annual maximum discharge data without fitting them with a mathematical function. In this case the graphical method was used with an equivalent record length of 56 years of data, the length of the flood record of the USGS gage station at Trevallian Way at the time of the study. Figure 5.4 shows the flood–frequency curve for damage reach SF-9 on the South Fork of Beargrass Creek, with corresponding confidence limits based on ± 2 standard deviations about the mean curve.
The confidence limits in this graph are symmetric about the mean when the logarithm to base 10 of the discharge is taken, rather than the discharge itself. This can be expressed mathematically as:
where Q is the discharge value at the confidence limit, logQ is the expected flood discharge, σlogQ is the standard deviation (shown in the rightmost column of Table 5.1), and K is the number of standard deviations above or below the mean that the confidence limit lies. Because these confidence limits are defined in the log space, it follows that they are not symmetric in the real flood discharge space. As Table 5.1 shows, the expected discharge for the 100-year flood (p = 0.01) is 4,310 cfs, the upper confidence limit is 6,176 cfs, and the lower limit is 3,008 cfs. The difference between the mean and the upper confidence limit is thus about 40 percent larger than the difference between the mean and the lower confidence limit. The confidence limits for graphical frequency analysis are computed using a method based on order statistics, as described in USACE (1997d). In this method, a given flood discharge estimate is considered a sample from a binomial distribution, whose parameters p and n are the nonexceedance probability of the flood and the equivalent record length of flood observations in the area, respectively. In this case, n = 56 years, since this is the record length of the Trevallian Way gage.
River Hydraulics
Water surface profiles for all events were determined using the HEC-2 river hydraulics program from the Corps's Hydrologic Engineering Center in Davis, California. Field-surveyed cross sections were obtained

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TABLE 5.6 Instantaneous Annual Peak Discharges (cfs) and their Annual Exceedance Probabilities (%) — Existing Conditions
Instantaneous Annual Peak Discharges (cfs)
Annual Exceedance Probability in Percent
Red River of the North Below Red Lake River
Red River of the North Above Red Lake River
Red Lake River at the Mouth [based on difference]
0.2
169,000
128,000
41,000
0.47
136,900
102,000
34,900
0.5
134,000
100,000
34,000
1.0
110,000
81,700
28,300
2.0
89,000
64,900
24,100
5.0
63,900
45,500
18,400
10.0
47,300
32,900
14,400
20.0
32,600
21,900
10,700
50.0
15,500
9,590
5,910
80.0
7,150
3,970
3,180
90.0
4,700
2,450
2,250
95.0
3,290
1,620
1,670
99.0
1,660
726
934
and downstream of Red Lake River (see column 4 in Table 5.6). Statistics for the adopted relationship were approximated by synthetic methods presented in Bulletin 17B (for more details, see USACE (1998a)).
The Plan Comparison Letter Report developed in February 1998 for flood damage reduction studies for East Grand Forks, Minnesota, and Grand Forks, North Dakota, evaluated an alternative flood damage reduction plan that included a split-flow diversion channel along with permanent levees. The discharge–frequency relationships for the modified conditions, shown in Table 5.7, were developed as follows. The modified-condition discharge–frequency curve for the Red River upstream of Red Lake River was graphically developed based upon the operation of the diversion channel inlet. Red River flows are not diverted until floods start to exceed those having return periods of 5 years (20% annual exceedance probability). The channel is designed to continue to divert Red River flows at a rate that allows the design flood (0.47%) discharge of 102,000 cfs (upstream of the diversion) to be split such that 50,500 cfs is diverted and 51,500 cfs is passed through the cities. This operation is reflected in the modified discharge–frequency relationship shown in Table 5.7 for the Red River upstream of Red Lake River (columns 2 and

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TABLE 5.7 Instantaneous Annual Peak Discharges (cfs) and their Annual Exceedance Probabilities (%)—Condition with Diversion Channels
Instantaneous Annual Peak Discharges (cfs)
Red River of the North Above Red Lake River
Annual Exceedence Probability in Percent
Above Diversion
Below Diversion
Red Lake River at the Mouth
Red River of the North Below Red Lake River
0.2
128,000
55,000
41,000
96,000
0.47
102,000
51,500
34,900
86,400
0.5
100,000
51,000
34,000
85,000
1.0
81,700
47,500
28,300
75,800
2.0
64,900
43,000
24,100
67,100
5.0
45,500
36,500
18,400
54,900
10.0
32,900
30,000
14,400
44,400
20.0
21,900
21,900
10,700
32,600
50.0
9,590
9,590
5,910
15,500
3).Synthetic statistics (mean, standard deviation, and skewness) in accordance with methodology presented in Bulletin 17B were computed for the discharge-frequency relationships of the below-diversion flows.
The modified-condition discharge–frequency curve for the Red River downstream of Red Lake River was graphically computed based upon the operation of the diversion channel. The modified-condition Red River discharges upstream of Red River were added to the coincident flows on Red Lake River (column 4). The resulting discharges were plotted for graphical development of the modified-condition discharge– frequency relationship for the Red River downstream of Red Lake River and are summarized in Table 5.7 (column 5). Synthetic statistics for this discharge–frequency relationship were computed for use in the risk analysis.
Elevation–Discharge Relationships
The water surface elevations computed using the HEC-2 computer program are shown in Table 5.8 for three cross sections (7790, 7800, and 7922) corresponding to the previous USGS gage locations and for cross

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section 44, which corresponds to the current USGS gage location (see Figure 5.10 for the cross section locations). These computed water surface elevations (CWSE) were based on the expected discharge quantities from the coincidental frequency analysis performed in June 1994 for the Grand Forks Feasibility Study. These data were used to transfer observed elevations from previous USGS gage sites to the current site (cross section 44) at river mile 297.65, and they were used in determining the elevation –discharge uncertainty. The water surface profile analysis was performed using cross-sectional data obtained from field surveys. Data were also obtained from field surveys and from USGS topographic maps. The HEC-2 model was calibrated to the USGS stream gage data and to high-water marks for the 1969, 1975, 1978, 1979 and 1989 flood events throughout the study area. Note that these water surface elevations assume the existing East Grand Forks and Grand Forks emergency levees are effective. The levees were assumed effective because through extraordinary efforts, they have generally been effective for past floods with the exception of the 1997 flood.
Ratings at stream gage locations provide an opportunity to directly analyze elevation–discharge uncertainty. The measured data are used to derive the “best fit” elevation-discharge rating at the stream gage location, which generally represents the most reliable information available. In this study, the adopted rating curve for computing elevation uncertainty is based on the computed water surface elevations from the calibrated HEC-2 model shown in Table 5.8.
This adopted rating curve for cross section 44 at the current USGS gage is shown in Figure 5.12. Measurements at the gage location were used directly to assess the uncertainty of the elevation–discharge relationship. The normal distribution was used to describe the distribution of error from the “best-fit” elevation–discharge rating curve. The observed gage data (for the four cross sections presented in Table 5.8) were transferred to the current gage site at river mile 297.65 based on the gage location adjustments presented in Table 5.9, which were computed from the water surface elevations in Table 5.8. These adjustments were plotted against the corresponding discharge below the Red Lake River, and curves were developed to obtain adjustments for other discharges.
The deviations of the observed elevations from the fitted curve were used to estimate the uncertainty of the elevation–discharge rating curve shown in Figure 5.11. The deviations reflect the uncertainty in data values as a result of changes in flow regime, bed form, roughness/resistance to flow, and other factors inherent to flow in natural streams. Errors also

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TABLE 5.8 Computed Water Surface Elevations of the Red River of the North at Grand Forks, North Dakota (units in feet above sea level)
Floods
Cross Section Number
River Mile
Minimum Channel Bottom in Feet
20% (5-year)
10% (10-year)
4% (25-year)
2% (50-year)
1% (100-year)
0.2% (500-year)
7790
295.70
773.15
817.20
821.70
825.00
827.30
829.60
834.80
7800
296.00
774.2
817.39
821.87
825.19
827.52
829.83
835.01
7922
297.55
774.60
818.26
822.74
826.27
828.83
831.58
837.25
44a
297.65
772.40
818.39
822.91
826.67
829.18
831.84
837.59
a Current Location of USGS gage.

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FIGURE 5.12 Rating curve (water elevation vs. discharge)for the Red River at Grand Forks.

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TABLE 5.9 Adjustments Used in Transferring Observed Elevations from Previous USGS Gage Sites to Current Gage Site at RM 297.65 (XS 44)
Expected Probability Discharge (cfs)
Adjustment Factor (cfs)
Probability
Below Red Lake River
Above Red Lake River
XS 7790, RM 295.70
XS 7800, RM 296.00
XS 7922, RM 297.55
38%
20,000
12,500
1.28
1.06
0.12
27%
25,000
16,100
1.23
1.02
0.12
20%
30,600
20,300
1.19
1.00
0.13
10%
43,900
30,300
1.21
1.04
0.17
4%
63,500
45,800
1.67
1.48
0.40
2%
81,500
58,800
1.88
1.66
0.35
1%
101,000
73,500
2.24
2.02
0.26
result from field measurements or malfunctioning equipment. A minimum of 8–10 measurements is normally required for meaningful results. The measure used to define the elevation–discharge relationship uncertainty is the standard deviation:
Where X = observed elevation adjusted to current gage location (if 5.12 necessary), M = computed elevation from adopted rating curve, and N = number of measured discharge values (events).
The elevation uncertainty was computed for two different discharge ranges for this analysis. Based on the observed elevations plotted on the adopted rating curve, it appeared that there was greater uncertainty for discharges less than about 10% of annual exceedance probability event due to ice effects on flow. Therefore, the standard deviation was computed for discharges greater than between 22,000 cfs, which corresponds approximately to the zero damage elevation based on the adopted rating curve, and 44,000 cfs, which is slightly greater than the 10 percent annual exceedance probability. The standard deviation was also computed for discharges greater than 50,000 cfs. During the period of record, there were 25 events with a discharge between 22,000 and 44,000 cfs and 10 events with a discharge greater than 50,000 cfs. The standard deviation was 1.66 feet for discharges between 22,000 and 44,000 cfs and was 1.55

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feet for discharges greater than 50,000 cfs. In the risk and uncertainty simulations, the standard deviation was linearly interpolated between 1.66 and 1.55 feet for discharges between 44,000 and 50,000 cfs. (See USACE (1998b) for more details.)
In an earlier risk analysis that was performed for the Grand Forks Feasibility Study, a much lower standard deviation of 0.50 feet was used for discharges greater than 50,000 cfs. However, adding the 1997 flood to the analysis resulted in a standard deviation of 1.55 feet, which is similar to that computed for discharges less than 44,000 cfs. It should be noted that the discharge and elevation used in this analysis for the 1997 flood was the peak discharge of 136,900 cfs occurring on April 18, 1997 (see Table 5.4), and an elevation of 831.21 feet (Stage 52.21). The peak elevation of 833.35 feet (Stage 54.35) occurred on April 22, 1997 at a discharge of 114,000 cfs. The elevation of 831.21 feet was almost 5 feet below the rating curve at a discharge of 136,900 cfs; however, the peak elevation of 833.35 feet at a discharge of 114,000 cfs was essentially on the adopted rating curve. Both of these points are plotted on the rating curve in Figure 5.12. Lines representing ± 2 standard deviations for the normal distribution, which encompasses approximately 95 percent of all possible outcomes, are also shown on the rating curve. An illustration of the normal distribution at the 1 percent (100-year) event for the project levee condition is also shown in Figure 5.12.
Risk and Uncertainty Analysis Results
Four index locations were selected to evaluate project performance and project sizing. These locations are cross sections 57, 44 (current USGS gage), 27, and 15 (Figure 5.10). The four locations were selected based on economic requirements for project sizing (see USACE, 1998c). The elevation–discharge rating curves (based on HEC-2 analysis) for existing and project conditions at these locations can be found in the USACE (1998b). Each of these rating curves shows three conditions, where applicable: (1) existing conditions, (2) removal of the pedestrian bridge at cross sections 7920-7922 and with project levees (“levee only”); and (3) with removal of the pedestrian bridge, with project levees, and with the diversion channel (“diversion channel”). Existing conditions means that the existing emergency levees are assumed to be effective up to and including the 5 percent (20-year) event and are ineffective for larger floods. The 5 percent (20-year) event was selected based

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on comparison of water surface profiles with effective and probable failure point (PFP) levee elevations provided by the Geotechnical Design Section analysis (see USACE, 1998b, paragraph A.2.11 and Appendix B of this report). The pedestrian bridge was removed based on input from the cities of East Grand Forks and Grand Forks. The rating curves for the diversion channel alternative were based on limited information. The Red River to the North would start to divert into the diversion channel at the 20 percent (5-year) flood; therefore, up to this point the rating curve for existing conditions with levees was used.
An additional location was also selected to evaluate the performance of the levee only and diversion channel with 1 percent (100-year) levee alternatives. This location is at cross section 7700 at the downstream end of the project levees (see Figure 5.10). Cross section 7700 was selected based on hydraulic analysis as the least critical location—the location where the levees in combination with the diversion channel would first overtop from downstream backwater (see USACE, 1998b).
Project Reliability
The project reliability results are summarized in Table 5.10, Table 5.11 through Table 5.12. Table 5.9 contains the results for the levees-only alternatives. Table 5.11 contains the results for the diversion channel in combination with 1 percent (100-year) levees. Note that in Table 5.10, three different alternative top-of-levee heights are evaluated, whereas in Table 5.11, it is always the same alternative—diversion channel with 1 percent levees— but for the three different events. The top-of-levee elevations were computed based on a water surface elevation profile to ensure initial overtopping would occur at the least-critical location (here, cross section 7700). The downstream top-of-levee elevations were selected with the intent of having 90 percent probability of containing the specified flood and were based on previous risk analysis for the Grand Forks Feasibility Study preliminarily updated to include the 1997 flood. The 2 percent (50-year), 1 percent (100-year), and 0.47 percent (210-year/1997 flood) top-of-levee profiles are 3.2, 3.4, and 2.7 feet above their respective water surface profiles at the downstream end (Table 5.10).
As seen in Table 5.10, the intent of having 90 percent probability of containing the specified flood is generally realized. The 2 percent levees have a 92 percent probability of containing the 2 percent flood. The 1 percent levees have a 90 percent probability of containing the 1 percent

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flood. The 0.47 percent levees have an 87 percent probability of containing the 0.47 percent flood.
TABLE 5.10 Reliability at Top of Levee for Three Top-of-Levee Heights
2 % (50-year) Leveea
1% (100-year) Leveeb
0.47% (210-year) Leveec
Gage Location
Top of Levee (ft.)
Reliability (%)
Top of Levee (ft.)
Reliability (%)
Top of Levee (ft.)
Reliability (%)
XS 7700d
830.2
92.5
832.7
90.7
834.8
87.7
XS 57
832.0
92.0
834.2
90.5
836.2
86.4
XS 44
833.2
93.2
835.6
91.3
837.5
86.3
XS 27
834.3
92.1
836.9
89.5
839.0
86.5
XS 15
835.2
92.7
837.7
90.0
839.7
85.5
aTop of levee for the 2% levee is computed water surface elevation plus 3.2 feet.
bTop of levee for the 1% levee is computed water surface elevation plus 3.4 feet.
cTop of levee for 0.47% levee is computed water surface elevation plus 2.7 feet.
dDownstream end of project.
TABLE 5.11 Project Reliability at Top of Levee for Diversion Channel with 1 Percent (100-Year) Levees for Three Different Events
Gage Location
Top of Levee (ft)
Reliability 2% (50-year) Event
1% (100-year) Event
0.47% (210-year) Event
XS 7700a
832.7b
99.9
99.6
98.9
XS 57
834.2
100.0
99.6
99.2
XS 44
835.6
99.9
99.6
99.4
XS 27
836.9
99.6
99.5
99.1
XS 15
837.7
99.7
99.6
99.2
aDownstream end of project.
bTop of levee is computed water surface elevation plus 3.4 feet.
Reliability results for the diversion channel with 1 percent levees are summarized in Table 5.11. Note again that the levees constructed in combination with the diversion are the same as for the 1 percent flood without the diversion channel and are the same for all three floods analyzed. As seen in the table, there is a 99 percent or greater probability of containing the flood for all three floods considered when the project includes the diversion channel.
As previously noted, the most critical location for project performance is at cross section 7700 at the downstream end of the project. Table 5.12

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summarizes the results for all the alternatives considered and for numerous floods. The probability of the diversion channel in combination with 1 percent levees for the 0.2 percent event is listed in the table as greater than 95%. A more specific reliability was not cited for the 0.2 percent event for two reasons: (1) the discharge–frequency curve based on the approximate statistics starts to diverge from the graphical curve for extreme events and, (2) there was limited information available to develop the Red River to the North rating curves for the diversion alternative. These reasons are also why more extreme events were not analyzed.
TABLE 5.12 Conditional Exceedance Probability of Alternative for Various Events (based on analysis at downstream end of project—XS 7700)
Alternative
Event
2% (50-year) Levees
1% (100-year) Levees
0.47% (210-year) Levees
Diversion with 1% (100-year) Levees
4 % (25-year)
99.5
100.0
100.0
100.0
2% (50-year)
92.5
99.1
99.7
99.9
1% (100-year)
64.3
90.7
98.3
99.6
0.52% (192-year)
29.5
65.6
89.8
—a
0.5% (200-year)
28.2
64.4
88.7
—a
0.47% (210-year)
25.3
61.9
87.7
98.9
0.2% (500-year)
4.4
21.5
48.0
>95
0.1% (1,000-year)
0.7
6.0
20.7
—b
aEvent not analyzed.
bEvent not analyzed because (1) the discharge–frequency curve based on the approximate statistics starts to diverge from the graphical curve for extreme events and (2) there was limited information to develop the RRN rating curves for the diversion alternative.
Table 5.13 presents the simulated conditional exceedance probabilities from the economic project sizing analysis. The without-project condition is also included in this table for comparison purposes. The without-project condition is based on a zero damage elevation of 824.5 feet, assumes credit is given to the existing levees, and assumes all properties that were substantially damaged (50% or more damage) in the 1997 flood have been removed.
Based on the above analysis of alternative plans and further economic and environmental considerations, the recommended National

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TABLE 5.13 Residual Risk Comparison
Alternative
Annual Performance (Expected Annual Probability of Design Being Exceeded)
Without Project
0.0918
2% (50-Year) Levees
0.0086
1% (100-Year) Levees
0.0036
0.47% (210-Year) Levees
0.0010
Diversion with 1% (100-Year) Levees
0.0002
Economic Development (NED) plan consists of a permanent levee and floodwall system designed to reliably contain the 210-year flood event. This equates to an 87.7 percent reliability of containing the 210-year flood event (Table 5.12) and would reliably protect against a flood of the magnitude of the 1997 flood.
The recommended plan would remove protected areas from the regulatory floodplain, increase recreational opportunities, and enhance the biological diversity in the open space created. The recommended plan anticipates the need to acquire over 250 single-family residential structures, 95 apartment or condominium units, and 16 businesses along the current levee/floodwall alignment.
The total cost of the recommended multipurpose project is $350 million including recreation features and cultural resources mitigation costs. The federal share of the project would be $176 million and the nonfederal share would be $174 million. The benefit-to-cost ratio has been calculated as 1.07 for the basic flood reduction features of the project and as 1.90 for the separable recreation features (USACE, 1998b). The recommended project has an overall benefit-to-cost ratio of 1.10.
The cities of East Grand Forks, Minnesota, and Grand Forks, North Dakota, will serve as the project's nonfederal sponsors. Through legislation, the State of Minnesota has committed to provide financial support in the form of bonds and returned sales taxes to the city of East Grand Forks. In verbal and written comments from its governor, the State of North Dakota has committed to provide financial assistance to the city of Grand Forks.