Estimation of design discharge for an ungauged overflow-receiving watershed using one-dimensional hydrodynamic model

Figures & data

Figure 1 Map showing the location of the Hartsville Coulee watershed and the river reaches modelled in this study

Figure 2 The dimensions of Thompson Bridge

Figure 3 The overtopped RRN right bank section downstream of Thompson Bridge, superimposed by the predicted highest water surface occurred in 1997

Figure 4 The cross-sections at the US Geological Survey (USGS) flow gauging stations at (a) Halstad (USGS 05064500) and (b) Grand Forks (USGS 05082500). The labelled numbers are the calibrated Manning's n values

Figure 5 The cross-sections at the USGS flow gauging stations at (a) Drayton (USGS 05092000) and (b) Emerson (USGS 05102500). The labelled numbers are the calibrated Manning's n values

Figure 6 Schematic of the HEC-RAS model

Table 1 The tributary reaches modelled as branch in this study

State	Tributary^a	Reach below	Length (km)	Number of cross-sections	Predicted 1997 daily peak discharge at the outlet (m^3 s^−1)^b
Minnesota	Marsh River	Shelly	10.73	5	225
	Sandhill River	Climax	3.27	4	128
	RLR^c	Crookston	43.41	53	568
	Snake River	Alvarado	33.21	7	410
	Two Rivers	Lake Bronson	43.92	7	135
North Dakota	Goose River	Hillsboro	17.91	7	218
	Turtle River	Arvilla	67.86	14	64
	Forest River	Minto	31.87	8	84
	Park River	Grafton	27.14	8	209
	Drain20 NR	Glasston	22.68	4	21
	Pembina River	Walhalla	61.40	10	544
^aThe locations of the tributaries are shown in Figure 1.
^bThe peak discharges were predicted using the SWAT models (Kurz et al. 2007). The models can be used to generate flow hydrographs at the outlets of, and at any locations of interest within, the watersheds drained by the tributaries.
^cThe cross-sections were obtained from St Paul District USACE.

Figure 7 The predicted and observed daily streamflows and stages at Halstad

Figure 8 The predicted and observed daily streamflows and stages at Grand Forks

Figure 9 The predicted and observed daily streamflows and stages at Drayton

Figure 10 The predicted and observed daily streamflows and stages at Emerson

Table 2 Summary of the calibrated Manning's n values

Modelled branch of^a	Main channel n ch	Floodplain n fl
RRN	0.015–0.049	0.05–0.2
Marsh River	0.05	0.12
Sandhill River	0.05	0.12
RLR	0.035–0.05	0.05–0.12
Hartsville Coulee	0.012–0.039	0.036–0.07
Snake River	0.03–0.05	0.03–0.06
Two Rivers	0.05	0.12
Goose River	0.05	0.12
Turtle River	0.05	0.1
Forest River	0.05	0.08–0.15
Park River	0.05	0.12
Drain20 NR	0.05	0.05
^aThese modelled river reaches are shown in Figures 1 and 6.

Table 3 The model performance in predicting peaks and volumes

Station	Peak in 1997						Volume from 14 April to 10 May 1997
	Observed		Predicted		E rr ^a (%)	E rrj (PER)^a (%)	Observed (10^6 m^3)	Predicted (10^6 m^3)	D vj ^b (%)	D vj (PER)^b (%)
	Magnitude (m^3 s^−1)	Timing	Magnitude (m^3 s^−1)	Timing
Halstad^c	1979	April 19	1979	April 19	0.00	0.00	2865	2865	0.00	0.00
Grand Forks	3596	April 18	2900	April 22	23.26	12.90	4457	4171	6.42	3.79
Drayton	3511	April 24	3451	April 24	1.73	0.00	4789	5231	−9.23	−6.36
Emerson^d	4004	April 26	3978	April 27	3.29	3.23	5476	6207	−13.36	−10.65
^a E rrj is error function as defined by Eq. 3, while E rrj (PER) is modified error function as defined by Eq. 3′.
^b D vj is deviation of volume as defined by Eq. 4, while D vj (PER) is modified deviation of volume as defined by Eq. 4′.
^cAs the model upper boundary, the predicted and observed values at this station are identical.
^dThe observed flow hydrograph was provided by Mr A. Warkentin from Manitoba Water Stewardship, Canada. This corrected hydrograph considers the overflows that occurred in 1997 at the west bank of the RRN in the vicinity of Emerson. In contrast, the USGS data did not consider the overflows.

Figure 11 The predicted daily overflow hydrograph from the RRN into the Hartsville Coulee

Figure 12 The predicted maximum instantaneous flow profile along the Hartsville Coulee. The zero location is the mouth of the coulee

Kurz , B. A. 2007 . An evaluation of basinwide distributed storage in the Red River Basin: the Waffle concept , Bismarck, North Dakota : Final Report for the US Department of Agriculture Natural Resources Conservation Service .

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