APPENDIX B

Hydraulic Analysis in the Grand Forks Vicinity

The results of an hydraulic modeling analysis of the Red River of the North in the area of Grand Forks, North Dakota, and East Grand Forks, Minnesota are presented in this appendix. Some hydraulic conditions were not accounted for in the NWS forecast. The purpose of the analysis was to determine the effects of the hydraulic conditions of the record flood of 1997 on the gage at Grand Forks.

Hydrographs Used in Hydraulic Analysis

On the evening of April 16, 1997, the NWS issued a forecast for a crest stage of 50.0-50.5 feet at the East Grand Forks, Minnesota, gage (mi 297.65). (See Appendix A for details.) The peak stage was expected to occur April 20-22. A discharge of ~110,000 cfs was expected to coincide with the forecast peak stage. The observed peak stage at East Grand Forks occurred on April 22 and had a value of 54.35 feet. A peak discharge of 137,000 cfs (adjusted from an original USGS estimate of 151,000 cfs) occurred on April 18. Figure B-1 shows the stage hydrograph observed by the USGS and the peak stage forecast which underestimated the peak stage by ~3.8 feet.

Figure B-2 shows the discharge hydrograph observed by the USGS as well as the discharge hydrograph simulated by the NWS on April 24, 1997. (This analysis used the April 24 hydrograph, but the simulated hydrograph by the NWS changed minimally between April 16 and April 24.) Although the peak observed discharge (which occurred before the peak stage) was not captured in the NWS simulation (Figure B-2), the discharge (114,000 cfs) which did occur during the peak stage was close to the simulated value.

Extent of Study Area

Figure B-3 shows the extent of the Red River of the North Basin considered in this analysis. The analysis was done in two parts.

The first part of the study relates to the peak stage at the East Grand Forks gage. The particular reach of the Red River of the North studied in the first part of the analysis is 26.8 miles long. It begins immediately downstream of the confluence of the Red Lake River with the Red River of the North (mi 298.0) which is just upstream of Grand Forks and extends downstream to Oslo, Minnesota, (mi 271.2) as shown in Figure B-4. There are four bridges in the study reach within two miles of the Grand Forks gage (mi 297.65). During the 1997 flood, the natural earthen levees on both sides of the river were temporarily raised with sandbags for the first two miles of the study reach. These bridges and levees may have caused an increase in the flood crest. In addition to the bridges and levees, the Red River of the North has a very mild slope (~0.5 ft/mi in the Grand Forks area and ~0.2 ft/mi for the greater portion of the reach extending downstream of the Grand Forks area). Such extremely mild gradients may have caused the river to experience backwater effects. Although the Red River of the North during high flows is fairly wide (~5 miles at the end of the study reach), in the Grand Forks area, the channel is naturally constricted, measuring only 600 feet wide at some locations even during peak flood flows. This also may have caused backwater effects.

River of the North 19.2 miles above its confluence with the Red Lake River which "blew out" and allowed water to leave the Red River of the North prematurely and flow through the Bygland Coulee (a 12-mile drainage channel) into the Red Lake River 1.9 miles above its confluence with the Red River of the North (Figure B-5). This coulee flow was speculated by some to have increased the peak flow at East Grand Forks. A sensitivity analysis was done to determine the effect of the coulee outbreak on the peak discharge at East Grand Forks.

Model Calibration Results

The effects of the above hydraulic conditions (except for the coulee outbreak) on the Red River of the North in the Grand Forks area were analyzed using the NWS FLDWAV model which is a one-dimensional, dynamic routing model that utilizes the complete St. Venant equations of unsteady flow. FLDWAV simultaneously solved for the water level (h) and the discharge (Q) at 52 selected cross-sections located along the study reach (from immediately below the Red Lake River-Red River of the North confluence to Oslo, Minnesota) for each time interval during the specified simulation time period. FLDWAV utilized the following information in the simulation: an upstream boundary condition of known (measured) discharge time series; a downstream boundary condition of measured stage time series; cross-section properties; hydraulic roughness coefficients which vary with Q; and information describing the hydraulic effects of each of the four bridges. For this analysis, FLDWAV used calibrated hydraulic roughness coefficients.

The time period of the analysis was April 9-27, 1997. Stage measurements (Figure B-1) and discharge measurements (Figure B-2) were taken by the USGS throughout the flood period. Stage measurements were taken at the East Grand Forks gage (mi 297.65). A maximum stage of 54.35 feet was measured on April 22. Discharge measurements were taken at the Sorlie Bridge (mi 297.61) until April 18 when a flow of 137,000 cfs (adjusted from an original USGS estimate of 151,000 cfs) was measured within the levees. On April 19, levees were overtopped/breached; and subsequent discharge measurements were taken at the Kennedy Bridge (mi 296.96). For the first part of the analysis, the upstream boundary condition (mi 298.0) was a discharge hydrograph (Figure B-6) based on the USGS measurements at East Grand Forks/Kennedy Bridge; and the downstream boundary (mi 271.2) was a stage hydrograph at Oslo, Minnesota (Figure B-7). The 52 cross-sections which describe the study reach were obtained from the U.S. Army Corps of Engineers (USACE).

The model results were compared with the observed stage hydrograph at the East Grand Forks gage (Figure B-8). Although FLDWAV had difficulty modeling the stages at or near the peak flow (maximum stage error of 1.8 feet), the peak stage (54.0 feet) simulated by FLDWAV which occurred approximately 18 hours after the peak flow was very close to the observed value (54.35 feet). The simulated peak water surface profile plotted against several observed high water marks along the study reach between the upstream boundary (mi 298.0) and the previous Grand Forks gage location (mi 296.0) are shown in Figure B-9. The simulated peak stages were within ~0.3 feet of the observed values, except at the Sorlie Bridge where the simulated peak stage was within ~0.6 feet of the observed value. A comparison between the observed and simulated stage-discharge relationship (rating curve) at East Grand Forks was also made. As shown in Figure B-10, the simulated rating curve matched the measured rating curve fairly well, especially at the peak stage.

Flood Forecast Results

As stated previously, the NWS forecast on April 16, 1997, a peak stage of ~50.5 ft at the East Grand Forks gage (mi 297.65) with a discharge of 110,000 cfs to occur on April 20-22. The observed peak stage at East Grand Forks was 54.35 feet on April 22. The peak stage was under-forecast by ~3.8 feet. Two primary factors contributed to the error in the stage forecast: (1) the difference between the forecast discharge hydrograph and the actual discharge hydrograph and (2) the difference between the rating curve used to produce the forecast stage and the actual rating curve for the event. Since FLDWAV was able to adequately simulate the 1997 flood event with its many complexities (e.g., bridges, levees, backwater), the results of the simulation will be used to determine how the discharge hydrograph and the rating curve affected the peak stage at the East Grand Forks gage.

Effects of Discharge Hydrograph on Stages Produced by FLDWAV

The NWS uses hydrologic models to generate discharge hydrographs (headwater runoff) in headwater basins and storage routing techniques to route the discharge hydrographs downstream. The hydrologic models also generate discharge hydrographs (local runoff) in sub-basins located adjacent to the river through which the routed flow is passing. The combined local runoff and routed flow are later adjusted based on observed flow data. A rating curve is then used to convert the forecast discharges into stage values.

A comparison (Figure B-2) was made between the discharge hydrograph measured by the USGS and the hydrograph forecast by NWS at East Grand Forks (mi 297.65). The 1997 flood, as measured by the USGS, was a double-peak flow event; the first and larger peak occurred on April 18; and the second peak occurred on April 22. The NWS forecast hydrograph captured the second peak flow which was also when the peak stage (54.35 feet) occurred; however, it was not able to capture the first peak flow. This inability may have resulted from local inflow not being represented by the NWS hydrologic model; or it may have resulted from upstream hydrographs that, likewise, failed to include the first discharge peak; however, it is not within the scope of this analysis to determine the source of the error in discharge.

To determine the effect of the discharge hydrograph on the peak stage at East Grand Forks, the FLDWAV model was run with the NWS forecast hydrograph replacing the USGS-measured hydrograph as inflow to the model. As shown in Figure B-11, the peak stage (53.9 feet) produced by FLDWAV (using NWS forecast inflow) which occurred on April 22 was less than the observed stage (54.35 feet) by ~0.4 foot. When comparing the peak water surface profiles (Figure B-12), the profile generated using the NWS forecast inflow produced peak stages about 0.2 foot less than the peak stages in the profile generated using the USGS-measured inflow. Effects of the two discharge hydrographs on the relation between discharges and stages (rating curve) were also analyzed. The rating curve produced by FLDWAV using the NWS forecast inflow hydrograph was compared with the observed "looped" rating curve (Figure B-13). Although the rising limb of the FLDWAV-generated rating curve produced higher stages than were observed, the recession limb of the rating curve (including the peak) matched the observed rating curve very well.

Effects of Rating Curves on Stages Produced by FLDWAV

One of the critical tools used in river forecasting is an empirical (observed from previous floods) rating curve which describes the relationship between discharge (Q) and stage (h); this relationship is unique for a particular location along the river; and it may change with time due to changes in the river cross-section at the location of the rating curve; it is updated using measurements taken by the USGS. Although adequate for most rivers, such an empirical rating curve is single-valued (i.e., one-to-one relationship between h and Q) and may not reflect the hydraulic conditions in the river system (e.g., backwater due to very mild river bottom slopes (< 1 ft/mi - such backwater effects become more significant as the river slope approaches zero)). In such rivers, the water-surface elevation tends to be higher on the falling limb of the hydrograph than on the rising limb at the same discharge; this situation produces a "looped" rating curve. The band-width of the loop can range from a few inches to several feet depending on the hydraulic conditions ( i.e., primarily, the slope of the river profile and the rate of rise of the hydrograph). The magnitude of the loop increases as the slope decreases and as the rate of rise increases. The rating curve measured by the USGS at the East Grand Forks gage (Figure B-10) shows this looping effect; the band-width of the loop is 2.8 feet. The hydraulic effects which contribute to the loop will be discussed later. As stated previously, the rating curve generated by the FLDWAV model matched the measured rating curve fairly well especially at the peak stage (Figure B-10).

The USGS periodically issues a single-valued rating curve based on observed data. The NWS uses this empirical rating curve to forecast stages for real-time floods. When forecasting peak stages that go beyond the flood of record, the rating curve must be extended (extrapolated) to greater discharges and corresponding stages. Although the extrapolation technique may account for some of the hydraulic effects which are included in the empirical rating curve, hydraulic conditions may change as the flow increases and cause the rating curve to change in an unanticipated manner. During the 1997 flood event, the USGS Rating Curve No. 18 at East Grand Forks was used; however, it was extended along the same slope as the known curve using a logarithmic extrapolation technique. When compared with the FLDWAV- generated loop rating curve, Figure B-13 indicates that the extended rating curve is able to match the rising limb of the FLDWAV-generated rating curve; however, it cannot account for the looping effect. At the peak discharge (137,000 cfs) which occurs on the rising limb, the corresponding stage using the USGS-NWS extended rating curve is 51.9 feet which compares very closely to the observed stage (52.0 feet) at this flow (although FLDWAV produced a value of 53.3 feet). The peak stage occurs on the recession limb at 110,000 cfs for which the USGS-NWS extended rating curve produced a stage value of 50.5 feet compared to the observed stage of 54.35 feet. Prior to the 1997 flood event and in the course of performing an hydraulic design project, the USACE generated a single-valued rating curve (Figure B-13) which took into account some hydraulic effects (e.g., bridges). Although this USACE rating curve is unable to adequately represent the rising limb (e.g. it shows 57.0 feet at 137,000 cfs compared to the observed 52.0 feet), it represents the falling limb quite well especially at the peak stage (54.0 ft at 110,000 cfs).

Hydraulic Effects

The shape of the rating curve including the looping effect (mathematically, this is called hysteresis) was caused by hydraulic conditions including bridges, levees, and backwater due to the very mild slope downstream of Grand Forks. The effects of the bridges and levees are analyzed below.

Effect of Bridges on Stages at the East Grand Forks Gage

Bridges usually cause the flow in a river to be constricted since the cross-section at the bridge is usually narrower than the cross-sections of the natural channel; bridge piers further constrict the section. Channel constrictions cause some amount of backwater effect. Bridge decks may also affect the channel flow. As long as the water flows beneath the bottom of the bridge deck, the flow is less restricted (influenced only by the bridge piers and the width of the cross-section where the bridge is located); however, once the water impinges on the bridge deck, the flow is subjected to greater friction leading to a greater head loss which requires a higher water-surface elevation immediately upstream of the bridge to pass the given discharge. Road embankments crossing the flood plain and connected to the bridge also constrict the flow which overtops the banks of the cross-section. If the water level reaches the top of the road embankment, water can also flow over the road embankment as weir-type flow.

To determine the effects of the bridge components, the FLDWAV model was run with the following scenarios: 1) all four bridges were removed from the system; 2) all of the bridges were added without the bridge decks or embankments to determine the effect of the bridge constrictions; 3) the embankments were added and weir flow was allowed over the road embankments; and 4) the bridge decks were added to create additional head losses for the highest water level conditions. It can be seen in Table B-1 that the dominant component is the bridge constriction which resulted in 0.66 foot increase at the peak elevation. Allowing flow over the embankments caused the peak elevation to be reduced by 0.19 foot. The bridge decks further increase the peak elevation 0.31 foot. It was found that the overall effect of the four bridges on the East Grand Forks gage resulted in an increase in the water-surface elevation of 0.78 foot. Figure B-14 shows the rating curve at the East Grand Forks gage for the four scenarios along with the USGS-NWS extended rating curve used in the NWS forecast. It can be seen that the single-valued rating curve tends to behave like the "no bridges" scenario.

Table B-1. Effect of Bridge Components on the East Grand Forks Gage (mi 297.65).

An analysis was also done to determine the individual effect of each bridge. The FLDWAV model was run four times to reflect the elimination of each individual bridge. Table B-2 shows that the most critical bridges in the system were the Sorlie Bridge (mi 297.61) with an increase in head of 0.44 foot and the Foot Bridge (mi 297.55) with an increase in head of 0.25 foot. The Burlington R.R. Bridge (mi 297.75) and Kennedy Bridge (296.96) had minimal effect on the peak stage at the East Grand Forks gage. The peak stage profile of each scenario is shown in Figure B-15.

Table B-2. Effect of Each Individual Bridge on the East Grand Forks Gage (mi 297.65).

Effect of Levee Overtopping on Stages at East Grand Forks Gage

Levees, located along the banks of a river, tend to produce higher water levels than if the river were not leveed. In the study reach, the levees extend from mi 298.0 (the upstream end of the study reach) to mi 296.55 (approximately one mile downstream of the East Grand Forks gage). To determine the effect of the levees on the Red River of the North in the study reach, two simulations using FLDWAV were made. In the first simulation, the levees were allowed to overtop at the estimated levee top elevations including the temporary addition of sandbags (831.6 feet above mean sea level (msl)). In the second simulation, the levees were extended sufficiently upward such that no overtopping would occur. The second simulation, when compared to the first, provides the means to understand the effect of the levee overtopping. As shown in Figure B-16, the levees had minimal effect on the peak stage at the East Grand Forks gage. Overtopping of the levees caused a reduction in stage of 0.04 foot at the East Grand Forks gage. This indicates that the overbank storage volume behind the levees had minimal effect on the peak stage in this flood.

Effect of Coulee Outbreak on Peak Discharge at East Grand Forks Gage

There was an outbreak of flow from the Red River of the North at mi 317.18 ( ~19.2 miles above its confluence with the Red Lake River) into two coulees: the Bygland Coulee which is 12 miles long and connects into the Red Lake River 1.9 miles above the Red River of the North-Red Lake River confluence; and a secondary coulee which is 7.4 miles long and connects back into the Red River of the North 11.5 miles above the Red River of the North-Red Lake River confluence. The peak flow on the Red River of the North at Halstad, Minnesota, (mi 375.2) was 80,000 cfs; and the peak flow on the Red Lake River at Crookston, Minnesota, (mi 52.2) was 30,000 cfs. After the flood, estimated peak flows (based on the slope-area method) were computed as 16,000 cfs in the Bygland Coulee and 11,000 cfs in the secondary coulee. The peak flow determined by the USGS at the East Grand Forks gage (mi 297.65, 0.35 miles below the Red River of the North-Red Lake River confluence) was 137,000 cfs. The outbreak of flow from the Red River of the North into the coulees was thought by some to have produced additional flow (27,000 cfs) at the gage. As stated previously, the NWS forecast a peak flow at the gage of 110,000 cfs which is the sum of the inflows from the Red River of the North (80,000 cfs) and the Red Lake River (30,000 cfs).

To determine the effect of the coulees on the flow at the East Grand Forks gage, the Red-coulee-Red Lake river system was modeled using FLDWAV. As shown in Figure B-5, the river system consists of the Red River of the North from the Thompson Road Bridge (mi 317.68 - 0.5 mile upstream of where the outbreak occurred) to just below the Red River of the North-Red Lake River confluence (mi 298.0), the Red Lake River from mi 16.2 to its confluence with the Red River of the North, the 12-mile reach of the Bygland Coulee, and the 7.4-mile reach of the secondary coulee. The inflow hydrographs on the Red River of the North at Halstad (about 58 miles above the upstream boundary) and on the Red Lake River at Crookston (about 34 miles above the upstream boundary) were used as upstream boundary conditions. The stage hydrograph generated by FLDWAV at the upstream end of the reach (mi 298.0) in the previous study was used as the downstream boundary condition in the current study. The outbreak on the Red River of the North was modeled as a weir with a maximum peak outflow of ~30,000 cfs (which was reasonably close to 27,000 cfs in question) being released from the Red River of the North and entering the Bygland Coulee near its upstream end (mi 12.00). A portion of the flow entering the Bygland Coulee was diverted into the secondary coulee. This diversion was modeled as a weir with a maximum peak outflow of ~10,000 cfs entering the secondary coulee near its upstream end (mi 7.40). Although FLDWAV generated peak discharges of 30,000 cfs within the Bygland Coulee and 10,000 cfs within the secondary coulee, the peak flow at the downstream end (mi 298.0) of the river system remained ~110,000 cfs. Thus, the 30,000 cfs peak flow that left the Red River of the North and proceeded down the two coulees resulted in a decrease of the Red River of the North flow from 80,000 cfs to 50,000 cfs. This 50,000 cfs then combined with the 30,000 cfs from the two coulees along with the 30,000 cfs in the Red Lake River to produce a total flow of 110,000 cfs below the confluence. Therefore, no additional flow resulted below the confluence due to the coulee effect.

To account for additional storage above the coulee which may have contributed to the flow after the outbreak, the upstream boundary on the Red River of the North was extended ~50 miles upstream of the Thompson Road Bridge. Although the peak flow into the Bygland Coulee increased due to the availability of water which had been in storage on the Red River of the North, the peak flow on the Red River of the North was attenuated as it moved through the 50-mile storage reach. Therefore, the peak flow below the Red River of the North-Red Lake River confluence did not increase beyond the inflow amounts.

In summary, the flows through the coulees do not appear to have increased the discharge below the confluence of the Red River of the North and the Red Lake River by either adding to the ability of the combined system to convey inflows in the Red River of the North downstream to the confluence or by draining waters stored in the Red River of the North. For the coulee flows to have had an impact, some source of water not included in the inflow hydrographs from Halstad, Minnesota, and Crookston, Minnesota, would be required.

Conclusion

Table B-3 lists a summary of the conditions that were not captured with the single-valued rating curve used by the NWS for the April 16 forecast of ~50.5 ft at 110,000 cfs at the East Grand Forks gage (mi 297.65) on the Red River of the North. The primary hydraulic condition contributing to the increase in stage between the observed crest (54.35 feet) and the crest produced by the single-value rating curve of 50.5 feet was a +2.0 foot backwater effect (hysteresis loop rating phenomenon) due to a rapidly rising hydrograph flowing through a river with a very mild slope and a backwater effect of +0.8 foot due to the four bridges wherein the primary contributor was the Sorlie Bridge (+0.4 foot). The effect of not including the first peak in the modeled discharge hydrograph also contributed to +0.4 foot to the error in the NWS forecast. The failure of the levees was found to have had a minimal effect of lowering the actual stage by 0.04 foot.

Table B-3. Contributing Factors to the Peak Stage Simulation Error at the East Grand Forks Gage (mi 297.65).