Peak Streamflow on Selected Streams in Arkansas, 

December 2015

By Brian K. Breaker

Printed on recycled paper

Heavy rainfall during December 2015 resulted in flooding 

across parts of Arkansas; rainfall amounts were as high as 12 

inches over a period from December 27, 2015, to December 29, 

2015 (fig. 1). Although precipitation accumulations were highest 

in northwestern Arkansas, significant flooding occurred in other 

parts of the State. Flood damage occurred in several counties 

as water levels rose in streams, and disaster declarations were 

declared in 32 of the 75 counties in Arkansas. 

Given the severity of the December 2015 flooding, the U.S. 

Geological Survey (USGS), in cooperation with the Federal 

Emergency Management Agency (FEMA), conducted a study 

to document the meteorological and hydrological conditions 

prior to and during the flood; compiled flood-peak gage heights, 

streamflows, and flood probabilities at USGS streamflow-gaging 

stations; and estimated streamflows and flood probabilities at 

selected ungaged locations. 

This report provides hydrologic information pertaining 

to the severity of floods that occurred in Arkansas in 2015 

and recalculated flood-frequency statistics for 33 USGS 

streamflow-gaging stations in Arkansas that incorporate peaks 

from the December 2015 flood (table 1). In addition to streams 

with streamflow-gaging stations, nine ungaged locations in 

northwestern Arkansas were selected for indirect discharge 

measurement computations in order to calculate the peak flow 

and to estimate the annual exceedance probability (or recurrence 

interval) of the peak flow (table 1). For comparison, floodfrequency statistics were calculated for a previous event that 

occurred at streamflow-gaging station Red River at Index, Ark. 

(07337000). Methods used to obtain peak flows are briefly 

discussed. All data to support this study can be obtained from 

the USGS National Water Information System (U.S. Geological 

Survey, 2016). Flood probability statistics and associated 

inundation areas and peak water-surface elevations are used 

for infrastructure design, community planning, and for the 

protection of life and property. 

Estimating Peak Streamflows

Peak streamflow was calculated for 33 USGS streamflowgaging stations using the discharge-rating curve method 

(Rantz and others, 1982). Discharge-rating curves represent 

the graphical relation between measured streamflow and gage 

height. Streamflow can be calculated by the use of extrapolation 

between direct measurements, often beyond the highest 

streamflow measurement, when it cannot be measured at a site; 

however, excessive extrapolation—greater than two times the 

highest measured streamflow—can result in large errors in the 

estimation of peaks (Rantz and other, 1982). 

Field measurements of peak gage heights and streamflow at 

the selected stations during the December 2015 flood were used 

to verify the accuracy of recorded water-surface elevations and 

to supplement the high-flow data used to create discharge-rating 

curves for each site. Independent verifications of peak gage 

heights were obtained with auxiliary devices such as crest-stage 

gages and by identifying and surveying high-water marks. 

At locations where USGS streamflow-gaging stations did not 

exist, peak streamflows were determined by a variety of indirect 

methods including the USGS Slope Area Computation (SAC) 

program (Fulford, 1994; Bradley, 2012) and width contractions 

(Matthai, 1967). 

Probabilities of Peak Streamflows

The probability that a peak streamflow (annual exceedance 

probability) will occur at a given location in a given year is 

determined from annual peak streamflow data. The USGS 

streamflow-gaging stations with the longest period of streamflow 

record are considered the most reliable for estimating annual 

exceedance probabilities (AEP). An AEP of 0.02 means that 

there is a 2-percent chance that a specific peak streamflow may 

occur at a given location in a given year. Recurrence intervals 

are determined from the AEP for a given location by dividing 

one by the AEP; therefore, an AEP of 0.02 is equivalent to a 

50-year flood. 

The AEPs corresponding to peak streamflows during the 

December 2015 flood event that occurred in Arkansas for 33 

USGS streamflow-gaging stations and 9 ungaged locations 

were estimated to determine the relative recurrence intervals 

for the peak streamflows. Streamflows associated with selected 

AEPs (0.10, 0.04, and 0.01) were estimated using the expected 

moments algorithm (Cohn and others, 1997; Cohn and others, 

2001) in the USGS PeakFQ program (Veilleux and others, 

2014). The AEP estimated from the peak streamflow record for 

a given USGS streamflow-gaging station and the AEP estimated 

from regional regression equations developed using peak 

streamflow records from USGS streamflow-gaging stations are 

used to create weighted estimates of AEPs. Where weighted 

estimates of AEPs can be made from multiple computations of 

AEPs, uncertainty of the AEP estimate is reduced. At locations 

where no USGS streamflow-gaging station was present, AEPs 

were estimated using regional regression equations. The AEP 

estimates at 22 USGS streamflow-gaging stations were obtained 

by weighting at-site AEP estimates with regional regression 

equations from Wagner and others (2016). The AEP estimates for 

eight USGS streamflow-gaging stations affected by regulation, 

diversion, or urbanization included in this report were not 

U.S. Department of the Interior

U.S. Geological Survey

Open-File Report 2016–1198
35

34

20

40 38

14 39

16 42

17

18

19 15 37

41

32

1

2 3

4

5

6

7

8

9

10

11 12

13

22

21

23 24

Base from PRISM Climate Group, Oregon State University EXPLANATION

Scale 1:3,600,000

0 25 50 75 100 MILES

0 25 50 75 100 KILOMETERS

USGS streamflow-gaging station–

Where streamflow data were used to compute 

an annual exceedance probability 

Where a peak streamflow record occurred 

and streamflow data were used to compute an 

annual exceedance probability 

Where a top five peak of record streamflow 

occurred and streamflow data were used to 

compute an annual exceedance probability

Non-USGS location–Where a peak streamflow was 

computed by indirect methods and was used 

to compute an annual exceedance probability

33

30

36

32

Precipitation accumulation, in 

inches–December 27–30, 2015. 

Data from PRISM Climate Group

 0.6 to 2

 >2 to 4 

 >4 to 6 

 >6 to 8 

 >8 to 10 

>10 to 12

94° 93° 92° 91° 90°

36°

35°

34°

33°

36

25

26

29

30

31

28

27

33

TEXAS

MISSOURI

OKLAHOMA

ARKANSAS

LOUISIANA

MISSISSIPPI TENNESSEE

Figure 1. Location of U.S. Geological Survey streamflow-gaging stations and the total precipitation accumulation that occurred over the 

duration of the December 2015 flood event.
Table 1. Site information for U.S. Geological Survey streamflow-gaging stations measured during the December 2015 flood event.

[ft3/s, cubic feet per second; AR, Arkansas; >, greater than; <, less than; Hwy, highway; OK, Oklahoma; L&D, Lock and Dam; misc, miscellaneous is the ungaged 

location used in the study]

Site 

identification 

number

Station 

number

Station or stream name 

and location

Latitude, 

in decimal 

degrees

Longitude, 

in decimal 

degrees

Peak 

streamflow, 

in ft3

/s

Recurrence 

interval, 

in years

1 07048550 West Fork White River east of Fayetteville, AR 36.053889 -94.083056 33,100 >10

2 07048600 White River near Fayetteville, AR 36.073056 -94.081111 54,000 10

3 07049000 War Eagle Creek near Hindsville, AR 36.200000 -93.855000 43,100 >25

4 07050500 Kings River near Berryville, AR 36.427222 -93.620833 47,600 20

5 07055607 Crooked Creek at Kelly Crossing at Yellville, AR 36.230278 -92.709444 34,000 20

6 07056000 Buffalo River near St. Joe, AR 35.983056 -92.747222 109,000 20

7 07056515 Bear Creek near Silver Hill, AR 35.940000 -92.713333 20,600 >10

8 07056700 Buffalo River near Harriet, AR 36.067778 -92.577500 130,000 20

9 07060500* White River at Calico Rock, AR 36.116667 -92.143056 165,000 >25

10 07061000* White River at Batesville, AR 35.760278 -91.641111 168,000 >10

11 07069305** Spring River at Town Branch Bridge at Hardy, AR 36.313611 -91.482778 39,900 <10

12 07069500 Spring River at Imboden, AR 36.205556 -91.171667 55,700 <10

13 07072500 Black River at Black Rock, AR 36.102500 -91.097778 91,500 10

14 07188804*** McKisic Creek tributary at Hwy 71B at Bentonville, AR 36.413222 -94.219556 1,780 10

15 07194800 Illinois River at Savoy, AR 36.103056 -94.344444 30,200 10

16 07194880 Osage Creek near Cave Springs, AR 36.281466 -94.227984 5,850 10

17 07195000** Osage Creek near Elm Springs, AR 36.221944 -94.288333 23,900 25

18 07195400** Illinois River at Hwy 16 near 

Siloam Springs AR

36.144722 -94.494722 74,900 25

19 07195430** Illinois River south of Siloam Springs, AR 36.108611 -94.533333 94,400 50

20 07195855** Flint Creek near West Siloam Springs, OK 36.216111 -94.605278 7,020 10

21 07247000** Poteau River at Cauthron, AR 34.918889 -94.299444 26,100 25

22 07249800 Lee Creek at Short, OK 35.565833 -94.531944 37,600 <10

23 07249985 Lee Creek near Short, OK 35.517222 -94.464167 64,300 >10

24 07250085* Lee Creek at Lee Creek Reservoir near Van Buren, AR 35.484444 -94.392778 72,400 <25

25 07250550* AR River at James W. Trimble L&D near Van Buren, AR 35.348889 -94.298333 369,000 <100

26 07251500* Frog Bayou at Rudy, AR 35.525833 -94.271389 31,100 <25

27 07257500 Illinois Bayou near Scottsville, AR 35.466389 -93.041111 64,300 >25

28 07258000* Arkansas River at Dardanelle, AR 35.226111 -93.149444 421,000 <100

29 07260000 Dutch Creek at Waltreak, AR 34.986944 -93.613056 21,200 50

30 07260500** Petit Jean River at Danville, AR 35.058611 -93.395556 21,400 10

31 07261500** Fourche LaFave River near Gravelly, AR 34.872500 -93.657222 148,000 >100

32 07337000* Red River at Index, AR 33.551944 -94.041111 256,000 >100

32 07337000* Red River at Index, AR 33.551944 -94.041111 128,000 10

33 07340000** Little River near Horatio, AR 33.919444 -94.386667 68,600 >100

34 misc1*** Railroad Hollow Creek south of Gravette, AR 36.392206 -94.475949 500 <10

35 misc2*** Walnut Creek south of Gravette, AR 36.401821 -94.449604 1,200 25

36 misc3*** Muddy Fork south of Prairie Grove, AR 35.953373 -94.318459 700 10

37 misc4*** Clear Creek at Wheeler, AR 36.120098 -94.262847 9,700 >25

38 misc5*** Spanker Creek near Bella Vista, AR 36.430413 -94.206729 2,400 <25

39 misc6*** Brush Creek near Bentonville, AR 36.398099 -94.147009 1,800 >10

40 misc7*** Little Sugar Creek at Bella Vista, AR 36.425131 -94.215902 13,000 >100

41 misc8*** Brush Creek at Springdale, AR 36.186155 -94.197540 1,300 <10

42 misc9*** Turtle Creek at Rogers, AR 36.340292 -94.157765 600 <10

 *Known to be affected by regulation and not weighted with regional regression equations.

 **Known to be affected by regulation or urbanization and weighted with regional regression equations.

***Annual exceedance probability estimates computed from regional regression equations from Southard (2010).
weighted with regional regression equations. The AEP estimates 

for nine ungaged, urbanized locations, which have greater than 

a 1-percent impervious surface in their respective watersheds, 

were obtained using regional regression equations from Southard 

(2010).

Two USGS streamflow-gaging stations experienced record 

peak streamflows and 23 stations experienced top five peak 

streamflows (table 2) during the December 2015 flood event in 

Arkansas. Ranks for peak streamflows are based on water year, 

defined as October 1 of the previous year through September 30 

of a given year. The AEPs ranged from less than 1 to 30 percent 

for peak streamflows analyzed in this study. The Red River 

at Index, Ark. (07337000), experienced a peak streamflow of 

256,000 cubic feet per second (ft3/s) in June 2015 and a peak 

streamflow of 128,000 ft3/s in December 2015, corresponding to 

AEPs of 3 and 9 percent, respectively.
Table 2. Station number and information related to calculation of annual exceedance probability for the December 2015 flood event.

[AEP, annual exceedance probability; ft3/s, cubic feet per second; NA, not applicable; misc, miscellaneous is the ungaged location used in the study]

Station 

number

Flood data AEP for observed 2015 flood

Rank

Number of 

annual peaks 

in analysis

Date of peak 

streamflow

Peak stage, 

in feet

Peak 

streamflow, 

in ft3

/s

66.7 percent confidence interval

Estimate, 

in percent

Lower, 

in percent 

Upper, 

in percent

07048550 5 24 12/28/2015 24.61 33,100 9 9 29

07048600 6 53 12/28/2015 30.39 54,000 11 6 15

07049000 3 58 12/28/2015 26.73 43,100 4 2 8

07050500 8 79 12/28/2015 33.18 47,600 8 6 13

07055607 4 32 12/28/2015 25.85 34,000 8 6 18

07056000 6 78 12/28/2015 45.58 109,000 6 4 11

07056515 3 17 12/28/2015 13.74 20,600 10 8 26

07056700 4 60 12/28/2015 48.49 130,000 5 3 10

07060500* 3 65 12/29/2015 34.20 165,000 3 2 7

07061000* 3 45 12/29/2015 24.13 168,000 8 3 10

07069305 6 15 12/28/2015 15.60 39,900 30 25 52

07069500 16 81 12/28/2015 24.84 55,700 20 15 24

07072500 11 112 12/29/2015 27.15 91,500 10 7 12

07188804*** NA NA 12/28/2015 NA 1,780 NA NA NA

07194800 5 24 12/27/2015 19.65 30,200 11 11 29

07194880 1 17 12/27/2015 12.55 5,850 10 1 11

07195000** 2 51 12/28/2015 16.84 23,900 5 1 6

07195400** 2 17 12/28/2015 25.00 74,900 4 4 19

07195430** 2 21 12/28/2015 26.95 94,400 3 3 15

07195855* 3 30 12/28/2015 14.07 7,020 10 4 15

07247000** 2 49 12/28/2015 22.83 26,100 4 1 7

07249800 5 17 12/28/2015 22.36 37,600 20 17 40

07249985 8 75 12/28/2015 24.79 64,300 7 7 14

07250085* 3 24 12/28/2015 26.99 72,400 8 5 19

07250550* 3 53 12/30/2015 400.23 369,000 3 2 9

07251500* 6 68 12/28/2015 17.43 31,100 7 5 12

07257500 5 70 12/28/2015 23.20 64,300 4 4 10

07258000* 2 53 12/30/2015 40.83 421,000 3 1 6

07260000 4 71 12/28/2015 20.21 21,200 3 3 8

07260500* 7 69 12/28/2015 29.15 21,400 10 6 14

072615000 3 78 12/28/2015 31.64 148,000 1 1 6

07337000* 2 73 6/4/2015 34.41 256,000 1 1 4

07337000* 7 73 12/31/2015 23.50 128,000 9 6 13

07340000* 1 48 12/30/2015 34.21 68,600 1 0 4

misc1*** NA NA 12/27–12/28/2015 NA 500 NA NA NA

misc2*** NA NA 12/27–12/28/2015 NA 1,200 NA NA NA

misc3*** NA NA 12/27–12/28/2015 NA 700 NA NA NA

misc4*** NA NA 12/27–12/28/2015 NA 9,700 NA NA NA

misc5*** NA NA 12/27–12/28/2015 NA 2,400 NA NA NA

misc6*** NA NA 12/27–12/28/2015 NA 1,800 NA NA NA

misc7*** NA NA 12/27–12/28/2015 NA 13,000 NA NA NA

misc8*** NA NA 12/27–12/28/2015 NA 1,300 NA NA NA

misc9*** NA NA 12/27–12/28/2015 NA 600 NA NA NA
Table 2. Station number and information related to calculation of annual exceedance probability for the December 2015 flood event.—Continued

[AEP, annual exceedance probability; ft3/s, cubic feet per second; NA, not applicable; misc, miscellaneous is the ungaged location used in the study]

Station 

number

Expected peak streamflows for selected AEP with 95 percent confidence intervals, in ft3

/s

10 percent AEP, 10-year recurrence 4 percent AEP, 25-year recurrence 1 percent AEP, 100-year recurrence

95 percent confidence interval 95 percent confidence interval 95 percent confidence interval

Estimate Lower Upper Estimate Lower Upper Estimate Lower Upper

07048550 30,540 19,130 51,940 43,700 26,000 83,100 64,400 35,600 14,400

07048600 58,600 44,800 82,300 81,700 59,300 128,000 124,000 81,700 229,000

07049000 30,800 24,600 40,800 41,100 31,600 59,500 58,700 41,500 98,200

07050500 41,800 33,700 53,800 57,600 44,600 80,500 85,600 60,600 139,000

07055607 28,900 18,800 50,800 43,200 26,600 85,900 72,100 40,600 166,000

07056000 92,000 74,100 119,000 124,000 96,300 173,000 178,000 126,000 283,000

07056515 20,200 14,300 34,700 25,900 17,300 51,600 35,300 21,600 85,700

07056700 105,000 82,500 135,000 144,000 110,000 199,000 210,000 148,000 331,000

07060500* 113,000 95,000 148,000 152,000 122,000 229,000 221,000 165,000 441,000

07061000* 156,000 124,000 223,000 208,000 159,000 364,000 301,000 212,000 769,000

07069305 61,000 35,100 128,000 86,300 47,200 208,000 130,000 64,800 372,000

07069500 72,000 56,400 97,000 103,000 78,100 152,000 157,000 106,000 276,000

07072500 95,000 81,100 115,000 131,000 108,000 171,000 203,000 154,000 302,000

07188804*** 2,350 1,630 3,380 3,000 2,110 4,280 4,320 2,860 6,500

07194800 32,200 20,300 58,200 46,800 28,400 93,900 72,500 40,700 170,000

07194880 5,880 4,100 9,690 8,090 5,440 14,900 12,000 7,540 25,900

07195000** 17,900 13,000 26,300 26,300 18,200 42,400 41,300 26,200 77,300

07195400** 48,200 31,500 78,700 72,000 45,800 134,000 115,000 67,800 259,000

07195430** 59,400 40,000 102,000 83,500 53,700 159,000 126,000 75,000 235,000

07195855* 7,700 4,870 15,100 12,100 7,350 30,600 20,100 9,910 72,300

07247000** 20,100 16,400 26,400 26,100 20,500 38,200 36,300 26,100 63,200

07249800 45,700 28,700 84,500 63,300 38,600 129,000 92,900 52,700 220,000

07249985 54,500 40,000 75,900 77,300 60,700 105,000 110,000 79,600 168,000

07250085* 65,440 48,000 105,300 86,500 48,000 170,000 119,000 75,600 303,000

07250550* 275,000 239,000 335,000 336,000 285,000 448,000 428,000 344,000 448,000

07251500* 27,800 23,700 33,300 34,550 29,240 44,290 43,460 34,730 63,600

07257500 44,900 35,500 60,000 61,400 46,300 89,600 93,000 67,100 155,000

07258000* 333,000 297,000 389,000 389,000 341,000 485,000 468,000 397,000 686,000

07260000 14,700 12,300 18,000 19,200 15,600 25,100 25,900 19,000 38,600

07260500* 22,800 19,000 29,300 30,700 24,700 43,800 43,700 32,600 74,800

072615000 66,300 52,700 87,500 90,400 68,900 130,000 137,000 96,200 226,000

07337000* 138,000 120,000 165,000 172,000 146,000 221,000 224,000 178,000 322,000

07337000* 138,000 120,000 381,000 172,000 146,000 221,000 224,000 178,000 322,000

07340000* 44,400 38,300 55,430 54,600 45,800 76,900 62,500 51,200 98,500

misc1*** 890 620 1,290 1,190 830 1,700 1,730 1,140 2,620

misc2*** 960 660 1,380 1,300 910 1,860 1,920 1,270 2,910

misc3*** 710 490 1,020 980 680 1,400 1,450 960 2,200

misc4*** 6,750 4,660 9,780 8,950 6,260 12,800 13,300 8,770 20,000

misc5*** 1,990 1,380 2,890 2,770 1,940 3,970 4,170 2,760 6,300

misc6*** 1,630 1,130 2,360 2,240 1,570 3,210 3,340 2,210 5,050

misc7*** 5,350 3,700 7,760 7,480 5,230 10,700 11,400 7,530 17,200

misc8*** 2,320 1,600 3,360 2,780 1,950 3,980 3,860 2,550 5,840

misc9*** 1,610 1,110 2,330 1,950 1,370 2,790 2,720 1,800 4,110

 *Known to be affected by regulation and not weighted with regional regression equations.

 **Known to be affected by regulation or urbanization and weighted with regional regression equations.

***Annual exceedance probability estimates computed from regional regression equations from Southard (2010).
Selected References

Bradley, D.N., 2012, Slope-area computation program graphical 

user interface 1.0—A preprocessing and postprocessing tool 

for estimating peak flood discharge using the slope-area 

method: U.S. Geological Survey Fact Sheet 2012–3112, 4 p.

Benson, M.A., and Dalrymple, Tate, 1967, General field and 

office procedures for indirect measurements: U.S. Geological 

Survey Techniques of Water-Resources Investigations, 

book 3, chap. Al, 30 p. [Also available at http://pubs.er.usgs.

gov/publication/twri03A1.]

Cohn, T.A., Lane, W.L., and Baier, W.G., 1997, An algorithm 

for computing moments-based flood quantile estimates when 

historical flood information is available: Water Resources 

Research, v. 33, no. 9, p. 2089–2096. 

Cohn, T.A., Lane, W.L., and Stedinger, J.R., 2001, Confidence 

intervals for expected moments algorithm flood quantile 

estimates: Water Resources Research, v. 37, no. 6, p. 1695–

1706.

Fulford, J.M., 1994, User’s guide to SAC, a computer program 

for computing discharge by the slope-area method: U.S. 

Geological Survey Open-File Report 94–360, 31 p.

Matthai, H.F., 1967, Measurement of peak discharge at width 

contractions by indirect methods: U.S. Geological Survey 

Techniques of Water-Resources Investigations, book 3, 

chap. A4, 44 p. [Also available at http://pubs.usgs.gov/twri/

twri3-a4/.]

PRISM Climate Group, 2016, PRISM climate data: Northwest 

Alliance for Computational Science and Engineering, 

accessed June 20, 2016, at http://prism.oregonstate.edu/.

Rantz, S.E., and others, 1982, Measurement and computation 

of streamflow—Volume 2. Computation of discharge: U.S. 

Geological Survey Water-Supply Paper 2175, v. 2, 631 p. 

[Also available at http://pubs.usgs.gov/wsp/wsp2175/html/

wsp2175_vol2_pdf.html.]

Southard, R.E., 2010, Estimating the magnitude and frequency 

of floods in urban basins in Missouri: U.S. Geological Survey 

Scientific Investigations Report 2010–5073, 27 p.

U.S. Geological Survey, 2016, National Water Information 

System—Web interface, accessed September 28, 2016, at 

http://dx.doi.org/10.5066/F7P55KJN.

Veilleux, A.G., Cohn, T.A., Flynn, K.M., Mason, R.R., Jr., and 

Hummel, P.R., 2014, Estimating magnitude and frequency 

of floods using the PeakFQ 7.0 program: U.S. Geological 

Survey Fact Sheet 2013–3108, 2 p. [Also available at 

http://pubs.usgs.gov/fs/2013/3108/.]

Wagner, D.M., Krieger, J.D., and Veilleux, A.G., 2016, Methods 

for estimating annual exceedance probability discharges 

for streams in Arkansas, based on data through water year 

2013: U.S. Geological Survey Scientific Investigations 

Report 2016–5081, 136 p.[Also available at http://dx.doi.

org/10.3133/sir20165081.]

For additional information about this report, contact:

Director, Lower Mississippi-Gulf Water Science Center

U.S. Geological Survey

401 Hardin Road

Little Rock, AR 72211

http://ar.water.usgs.gov

Suggested citation: 

Breaker, B.K., 2017, Peak streamflow on selected streams in Arkansas, 

December 2015: U.S. Geological Survey Open-File Report 2016–1198, 

7 p., https://doi.org/10.3133/ofr20161198. 

ISSN 2331-1258 (online)

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Lafayette Publishing Service Center

U.S. Department of the Interior

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Director

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