Introduction

The U.S. Geological Survey (USGS), in cooperation with the Ohio Water Development Authority and the Ohio Environmental Protection Agency, completed a study to compute low-flow frequency, flow-duration, and harmonic mean flow statistics for long-term streamflow gages (defined as gages with at least 10 years of streamflow record) in Ohio and to develop methods for estimating those statistics at unregulated, ungaged stream locations in Ohio. Low-flow and flow-duration statistics are useful for many purposes. For example, the statistics are often used to help make regulatory decisions about the appropriateness of a stream to be used as either a public or private water source, or to determine the amount of certain waste compounds that can be safely discharged into streams (U.S. Environmental Protection Agency, 2024). Despite the usefulness of low-flow statistics, the flow data required to compute the statistics have been collected at relatively few streams in Ohio. Because of the limited number of streams for which such statistics can be computed directly, there is a need to develop methods to estimate the flow statistics for ungaged stream locations. Note that “streamflow” and “flow” are used interchangeably in this report.

Selection of Streamflow Gages

In the context of this study, streamflow gages (hereafter referred to as “gages”) for which instantaneous flows are computed over periods of time long enough to permit the calculation of daily means are referred to as continuous-record gages. The other type of gages used in this study, referred to as low-flow partial-record gages, are gages where instantaneous flow is measured periodically—during low flows—so that they can be mathematically related to concurrent daily mean flows at a continuous-record gage, referred to as an “index gage.”

The first task required for selecting gages included in this study was to identify continuous-record gages in Ohio and in bordering States that had at least 10 years of flow data recorded during the analytical period (water years 1975–2020; for more on how the analytical period was selected, see the section “Temporal Trends in Low Flow”) and to identify low-flow partial-record gages in Ohio that had sufficient data and a strong enough correlation with their index gage to develop reliable estimates of low-flow statistics. A total of 180 continuous-record gages (118 in Ohio and 62 in adjacent States) and 5 low-flow partial-record gages (all in Ohio) met the stated criteria (fig. 1, tables 1 and 2).

Table 1.    

Streamflow gages in Ohio and border states for which low-flow statistics were computed (VonIns and Koltun, 2024).

[USGS, U.S. Geological Survey; NAD 83, North American Datum of 1983; mi², square mile; SVI, Streamflow-variability index; log₁₀, logarithm base 10; ft³/s, cubic foot per second; tau, annual 7-day 10-year low-flow Kendall’s tau coefficient; p-value, 7-day 10-year Mann-Kendall probability value; OH, Ohio; partial, partial-record site; NA, not applicable; PA, Pennsylvania; continuous, continuous-record site; WV, West Virginia; KY, Kentucky; IN, Indiana; MI, Michigan]

Table 1.    Streamflow gages in Ohio and border states for which low-flow statistics were computed (VonIns and Koltun, 2024).

USGS station number	Station name	Site type	Decimal latitude (NAD 83)	Decimal longitude (NAD 83)	Drainage area (mi2)	Low-flow regulation status	Computed SVI [log10(ft3/s)]	Estimated SVI [log10(ft3/s)]	tau	p-value
03115385	Clear Fork near Rinard Mills, OH	Partial	39.60	−81.16	48.6	Unregulated	0.73	0.72	NA	NA
03129205	Black Fork Mohican River near Shelby, OH	Partial	40.92	−82.63	60.3	Unregulated	0.6	0.63	NA	NA
03144471	Little Wakatomika Creek near Trinway, OH	Partial	40.16	−82.03	61.3	Unregulated	0.53	0.53	NA	NA
03237121	Scioto Brush Creek near Rarden, OH	Partial	38.95	−83.30	0.210	Unregulated	0.83	0.69	NA	NA
03238423	North Fork White Oak Creek near Sardinia, OH	Partial	39.02	−83.87	53.4	Unregulated	0.82	0.82	NA	NA
03021350	French Creek near Wattsburg, PA	Continuous	42.02	−79.78	92.0	Unregulated	0.50	0.45	−0.06	0.57
03022540	Woodcock Creek at Blooming Valley, PA	Continuous	41.69	−80.05	31.1	Unregulated	0.44	0.44	−0.10	0.51
03049000	Buffalo Creek near Freeport, PA	Continuous	40.72	−79.70	137	Regulated	0.49	NA	−0.02	0.89
03049800	Little Pine Creek near Etna, PA	Continuous	40.52	−79.94	5.78	Unregulated	0.53	0.54	0.02	0.82
03050000	Tygart Valley River near Dailey, WV	Continuous	38.81	−79.88	185	Unregulated	0.60	0.58	0.03	0.84
03065000	Dry Fork at Hendricks, WV	Continuous	39.07	−79.62	349	Regulated	0.49	NA	−0.20	0.07
03065400	Blackwater River near Davis, WV	Continuous	39.14	−79.42	54.7	Regulated	0.46	NA	−0.03	0.88
03066000	Blackwater River at Davis, WV	Continuous	39.13	−79.47	85.9	Regulated	0.46	NA	−0.05	0.64
03068800	Shavers Fork below Bowden, WV	Continuous	38.91	−79.77	151	Regulated	0.42	NA	−0.26	0.05
03069000	Shavers Fork at Parsons, WV	Continuous	39.10	−79.68	213	Regulated	0.40	NA	−0.12	0.50
03069500	Cheat River near Parsons, WV	Continuous	39.12	−79.68	722	Regulated	0.46	NA	−0.09	0.39
03070000	Cheat River at Rowlesburg, WV	Continuous	39.35	−79.67	936	Regulated	0.47	NA	−0.26	0.11
03070500	Big Sandy Creek at Rockville, WV	Continuous	39.62	−79.70	200	Regulated	0.53	NA	−0.02	0.84
03092000	Kale Creek near Pricetown, OH	Continuous	41.14	−81.00	21.7	Unregulated	0.72	0.65	−0.40	0.02
03092090	West Branch Mahoning River near Ravenna, OH	Continuous	41.16	−81.20	21.8	Unregulated	0.49	0.52	−0.37	0.03
03093000	Eagle Creek at Phalanx Station, OH	Continuous	41.26	−80.95	97.7	Regulated	0.43	0.57	−0.11	0.27
03102500	Little Shenango River at Greenville, PA	Continuous	41.42	−80.38	104	Regulated	0.45	0.55	−0.11	0.29
03102950	Pymatuning Creek at Kinsman, OH	Continuous	41.44	−80.59	96.6	Unregulated	0.60	0.58	−0.19	0.28
03109500	Little Beaver Creek near East Liverpool, OH	Continuous	40.68	−80.54	496	Regulated	0.41	0.59	0.01	0.93
03110000	Yellow Creek near Hammondsville, OH	Continuous	40.54	−80.73	147	Regulated	0.50	0.60	−0.07	0.53
03111500	Short Creek near Dillonvale, OH	Continuous	40.19	−80.73	123	Regulated	0.34	0.54	−0.13	0.23
03111548	Wheeling Creek below Blaine, OH	Continuous	40.07	−80.81	97.6	Regulated	0.33	0.54	0.24	0.04
03113990	Captina Creek at State Route 148 at Armstrongs Mills, OH	Continuous	39.91	−80.94	127	Regulated	0.62	0.61	−0.03	0.89
03114000	Captina Creek at Armstrongs Mills, OH	Continuous	39.91	−80.92	134	Regulated	0.61	0.62	−0.17	0.20
03114500	Middle Island Creek at Little, WV	Continuous	39.48	−81.00	458	Unregulated	0.67	0.69	−0.03	0.86
03115400	Little Muskingum River at Bloomfield, OH	Continuous	39.56	−81.20	210	Unregulated	0.73	0.72	−0.18	0.18
03115973	Schocalog Run at Copley Junction, OH	Continuous	41.10	−81.60	3.7	Regulated	0.39	0.46	0.27	0.24
03116077	Chippewa Creek at Miller Road at Sterling, OH	Continuous	40.97	−81.85	50.4	Regulated	0.59	0.52	−0.24	0.17
03117500	Sandy Creek at Waynesburg, OH	Continuous	40.67	−81.26	253	Regulated	0.39	0.56	−0.07	0.52
03118000	Middle Branch Nimishillen Creek at Canton, OH	Continuous	40.84	−81.35	43.3	Regulated	0.40	0.54	−0.10	0.35
03121850	Huff Run at Mineral City, OH	Continuous	40.60	−81.36	12.2	Regulated	0.36	0.57	0.20	0.28
03136500	Kokosing River at Mount Vernon, OH	Continuous	40.41	−82.50	202	Regulated	0.42	0.52	0.01	0.94
03139000	Killbuck Creek at Killbuck, OH	Continuous	40.48	−81.99	463	Regulated	0.40	0.51	0.15	0.14
03140000	Mill Creek near Coshocton, OH	Continuous	40.36	−81.86	27.2	Unregulated	0.57	0.55	−0.03	0.79
03141870	Leatherwood Creek near Kipling, OH	Continuous	39.99	−81.50	68.5	Unregulated	0.65	0.62	0.19	0.26
03144000	Wakatomika Creek near Frazeysburg, OH	Continuous	40.12	−82.14	144	Unregulated	0.52	0.53	−0.12	0.24
03144816	South Fork Licking River at Kirkersville, OH	Continuous	39.96	−82.60	47.0	Unregulated	0.71	0.67	0.18	0.45
03145000	South Fork Licking River near Hebron, OH	Continuous	39.99	−82.47	134	Regulated	0.58	0.62	0.00	1.00
03145483	Raccoon Creek near Granville, OH	Continuous	40.07	−82.55	78.2	Unregulated	0.54	0.58	0.33	0.15
03146500	Licking River near Newark, OH	Continuous	40.06	−82.34	537	Regulated	0.45	0.54	0.07	0.51
03149500	Salt Creek near Chandlersville, OH	Continuous	39.91	−81.86	75.6	Unregulated	0.58	0.59	0.08	0.67
03155500	Hughes River at Cisco, WV	Continuous	39.12	−81.28	453	Unregulated	0.69	0.69	−0.10	0.58
03157000	Clear Creek near Rockbridge, OH	Continuous	39.59	−82.58	88.8	Regulated	0.37	0.54	−0.13	0.23
03157500	Hocking River at Enterprise, OH	Continuous	39.57	−82.47	458	Regulated	0.42	0.59	−0.10	0.32
03158200	Monday Creek at Doanville, OH	Continuous	39.44	−82.19	114	Regulated	0.55	0.66	0.03	0.90
03159000	Sunday Creek at Glouster, OH	Continuous	39.50	−82.09	104	Regulated	0.00	0.64	0.33	0.73
03159500	Hocking River at Athens, OH	Continuous	39.33	−82.09	942	Regulated	0.48	0.66	−0.05	0.62
03159540	Shade River near Chester, OH	Continuous	39.06	−81.88	155	Regulated	0.72	0.74	−0.11	0.28
03180500	Greenbrier River at Durbin, WV	Continuous	38.54	−79.83	133	Unregulated	0.53	0.53	−0.16	0.12
03182500	Greenbrier River at Buckeye, WV	Continuous	38.19	−80.13	540	Unregulated	0.54	0.53	−0.05	0.62
03186500	Williams River at Dyer, WV	Continuous	38.38	−80.48	128	Regulated	0.53	0.48	−0.12	0.27
03187500	Cranberry River near Richwood, WV	Continuous	38.30	−80.53	80.4	Regulated	0.53	0.45	−0.08	0.47
03198350	Clear Fork at Whitesville, WV	Continuous	37.97	−81.52	62.8	Unregulated	0.45	0.45	0.20	0.19
03201902	Raccoon Creek near Bolins Mills, OH	Continuous	39.23	−82.29	200	Unregulated	0.71	0.69	−0.16	0.39
03201980	Little Raccoon Creek near Ewington, OH	Continuous	39.01	−82.45	99.4	Regulated	0.51	0.71	0.28	0.09
03202000	Raccoon Creek at Adamsville, OH	Continuous	38.87	−82.36	585	Regulated	0.60	0.71	0.05	0.69
03205470	Symmes Creek at Aid, OH	Continuous	38.60	−82.50	302	Regulated	0.86	0.77	−0.06	0.73
03207965	Grapevine Creek near Phyllis, KY	Continuous	37.43	−82.35	6.20	Unregulated	0.46	0.46	0.45	0.00
03210000	Johns Creek near Meta, KY	Continuous	37.57	−82.46	56.3	Regulated	0.48	0.51	0.50	0.00
03213700	Tug Fork at Williamson, WV	Continuous	37.67	−82.28	936	Regulated	0.42	0.43	0.10	0.32
03217500	Scioto River at La Rue, OH	Continuous	40.57	−83.38	257	Regulated	0.62	0.92	0.27	0.32
03219590	Bokes Creek near Warrensburg, OH	Continuous	40.32	−83.17	83.1	Unregulated	1.82	1.09	0.36	0.11
03220000	Mill Creek near Bellepoint, OH	Continuous	40.25	−83.17	178	Regulated	0.63	1.01	0.33	0.00
03223000	Olentangy River at Claridon, OH	Continuous	40.58	−82.99	157	Regulated	0.62	0.86	−0.26	0.09
03223425	Whetstone Creek at Mount Gilead, OH	Continuous	40.55	−82.82	37.8	Regulated	0.63	0.72	0.24	0.11
03228300	Big Walnut Creek at Sunbury, OH	Continuous	40.24	−82.85	101	Regulated	0.98	0.82	0.18	0.17
03228750	Alum Creek near Kilbourne, OH	Continuous	40.36	−82.92	64.9	Unregulated	0.64	0.78	0.11	0.47
03229610	Scioto River near Commercial Point, OH	Continuous	39.77	−83.01	2270	Regulated	0.44	0.61	0.11	0.62
03229796	Walnut Creek at Ashville, OH	Continuous	39.71	−82.96	273	Regulated	0.45	0.60	0.14	0.51
03230310	Little Darby Creek at West Jefferson, OH	Continuous	39.95	−83.27	163	Regulated	0.59	0.72	0.13	0.40
03230450	Hellbranch Run near Harrisburg, OH	Continuous	39.85	−83.16	35.9	Regulated	1.34	0.69	0.23	0.11
03230500	Big Darby Creek at Darbyville, OH	Continuous	39.70	−83.11	534	Unregulated	0.53	0.57	−0.14	0.18
03230700	Scioto River at Circleville, OH	Continuous	39.60	−82.96	3220	Regulated	0.43	0.60	0.36	0.11
03230800	Deer Creek at Mount Sterling, OH	Continuous	39.72	−83.26	228	Regulated	0.53	0.59	0.10	0.45
03231500	Scioto River at Chillicothe, OH	Continuous	39.34	−82.97	3850	Regulated	0.42	0.61	0.05	0.63
03232000	Paint Creek near Greenfield, OH	Continuous	39.38	−83.38	249	Regulated	0.67	0.59	0.02	0.92
03234500	Scioto River at Higby, OH	Continuous	39.21	−82.86	5130	Regulated	0.42	0.65	0.02	0.84
03237020	Scioto River at Piketon, OH	Continuous	39.07	−83.02	5840	Regulated	0.42	0.65	0.19	0.29
03237255	Kinniconick Creek below Trace Creek at Tannery, KY	Continuous	38.55	−83.22	214	Regulated	0.88	0.99	0.02	1.00
03237280	Upper Twin Creek at McGaw, OH	Continuous	38.64	−83.22	12.2	Unregulated	1.00	0.95	−0.13	0.25
03237500	Ohio Brush Creek near West Union, OH	Continuous	38.80	−83.42	387	Unregulated	0.78	0.79	−0.06	0.54
03238500	White Oak Creek near Georgetown, OH	Continuous	38.86	−83.93	218	Regulated	0.88	0.97	−0.01	0.96
03240000	Little Miami River near Oldtown, OH	Continuous	39.75	−83.93	129	Unregulated	0.40	0.41	0.12	0.26
03241500	Massies Creek at Wilberforce, OH	Continuous	39.72	−83.88	63.4	Regulated	0.50	0.47	0.04	0.73
03244936	O’Bannon Creek near Loveland, OH	Continuous	39.26	−84.23	54.3	Regulated	0.59	0.71	0.59	0.00
03248500	Licking River near Salyersville, KY	Continuous	37.75	−83.08	140	Unregulated	0.57	0.58	−0.09	0.62
03250322	Rock Lick Creek at State Highway 158 near Sharkey, KY Station D	Continuous	38.25	−83.59	4.20	Unregulated	1.21	1.17	−0.17	0.74
03251200	North Fork Licking River near Mount Olivet, KY	Continuous	38.59	−84.02	226	Unregulated	1.00	1.01	0.11	0.43
03252300	Hinkston Creek near Carlisle, KY	Continuous	38.25	−84.06	154	Unregulated	0.75	0.74	0.16	0.24
03255500	Mill Creek at Reading, OH	Continuous	39.22	−84.45	72.9	Regulated	0.46	0.89	0.37	0.05
03260700	Bokengehalas Creek near De Graff, OH	Continuous	40.35	−83.89	36.3	Regulated	0.36	0.46	0.03	0.89
03260706	Bokengehalas Creek at De Graff, OH	Continuous	40.31	−83.91	40.3	Regulated	0.36	0.44	0.08	0.63
03262000	Loramie Creek at Lockington, OH	Continuous	40.21	−84.24	257	Unregulated	0.64	0.62	0.13	0.23
03264000	Greenville Creek near Bradford, OH	Continuous	40.10	−84.43	194	Regulated	0.44	0.58	0.06	0.61
03265000	Stillwater River at Pleasant Hill, OH	Continuous	40.06	−84.36	505	Regulated	0.50	0.58	0.03	0.77
03266000	Stillwater River at Englewood, OH	Continuous	39.87	−84.29	651	Regulated	0.51	0.56	0.04	0.70
03266560	Mad River at West Liberty, OH	Continuous	40.25	−83.75	36.6	Regulated	0.24	0.42	0.34	0.02
03267000	Mad River near Urbana, OH	Continuous	40.11	−83.80	163	Regulated	0.23	0.33	0.22	0.04
03267900	Mad River at Saint Paris Pike at Eagle City, OH	Continuous	39.96	−83.83	310	Regulated	0.24	0.31	0.21	0.05
03269500	Mad River near Springfield, OH	Continuous	39.92	−83.87	481	Regulated	0.24	0.32	0.08	0.45
03270000	Mad River near Dayton, OH	Continuous	39.80	−84.09	636	Regulated	0.25	0.34	0.12	0.26
03271000	Wolf Creek at Dayton, OH	Continuous	39.77	−84.24	68.8	Regulated	0.42	0.53	0.33	0.02
03271300	Holes Creek near Kettering, OH	Continuous	39.65	−84.20	19.6	Regulated	0.47	0.51	0.32	0.13
03271500	Great Miami River at Miamisburg, OH	Continuous	39.64	−84.29	2720	Regulated	0.38	0.54	0.05	0.78
03271800	Twin Creek near Ingomar, OH	Continuous	39.71	−84.52	197	Regulated	0.58	0.60	−0.12	0.43
03272000	Twin Creek near Germantown, OH	Continuous	39.64	−84.40	276	Regulated	0.58	0.57	−0.03	0.78
03272100	Great Miami River at Middletown, OH	Continuous	39.52	−84.41	3138	Regulated	0.40	0.65	0.29	0.04
03272700	Sevenmile Creek at Camden, OH	Continuous	39.63	−84.64	69.0	Regulated	0.56	0.60	0.09	0.42
03274000	Great Miami River at Hamilton, OH	Continuous	39.39	−84.57	3640	Regulated	0.40	0.70	0.13	0.20
03274650	Whitewater River near Economy, IN	Continuous	40.00	−85.12	10.4	Unregulated	0.54	0.59	−0.05	0.64
03274750	Whitewater River near Hagerstown, IN	Continuous	39.87	−85.16	58.7	Regulated	0.34	0.48	−0.09	0.50
03275000	Whitewater River near Alpine, IN	Continuous	39.57	−85.16	522	Regulated	0.37	0.49	0.19	0.07
03275600	East Fork Whitewater River at Abington, IN	Continuous	39.73	−84.96	200	Regulated	0.41	0.51	0.04	0.67
03276700	South Hogan Creek near Dillsboro, IN	Continuous	39.03	−85.04	38.1	Unregulated	0.89	0.99	−0.25	0.17
03280700	Cutshin Creek at Wooton, KY	Continuous	37.17	−83.31	61.3	Unregulated	0.60	0.60	0.26	0.01
03281040	Red Bird River near Big Creek, KY	Continuous	37.18	−83.59	155	Unregulated	0.68	0.68	0.12	0.41
03281100	Goose Creek at Manchester, KY	Continuous	37.15	−83.76	163	Unregulated	0.68	0.67	0.09	0.40
03281500	South Fork Kentucky River at Booneville, KY	Continuous	37.48	−83.68	722	Regulated	0.63	0.75	0.03	0.79
03282040	Sturgeon Creek at Cressmont, KY	Continuous	37.50	−83.81	77.3	Unregulated	0.78	0.75	0.02	0.90
03282500	Red River near Hazel Green, KY	Continuous	37.81	−83.46	65.8	Unregulated	0.75	0.75	−0.05	0.70
03285000	Dix River near Danville, KY	Continuous	37.64	−84.66	318	Regulated	0.78	0.83	−0.03	0.76
03291780	Indian Kentuck Creek near Canaan, IN	Continuous	38.88	−85.26	27.5	Unregulated	1.39	1.21	0.01	0.92
03299000	Rolling Fork near Lebanon, KY	Continuous	37.50	−85.32	239	Regulated	0.75	0.74	−0.24	0.35
03300400	Beech Fork at Maud, KY	Continuous	37.83	−85.30	436	Regulated	0.91	0.84	−0.04	0.71
03302050	Brier Creek at Pendelton Road near Louisville, KY	Continuous	38.05	−85.86	4.00	Regulated	1.23	0.69	0.06	0.76
03302110	Otter Creek at Otter Creek Park Near Rock Haven, KY	Continuous	37.92	−86.03	99.2	Regulated	0.46	0.63	0.24	0.30
03302680	West Fork Blue River at Salem, IN	Continuous	38.61	−86.09	19.0	Unregulated	0.74	0.71	−0.06	0.56
03327520	Pipe Creek near Bunker Hill, IN	Continuous	40.67	−86.10	159	Regulated	0.54	0.65	−0.07	0.59
03364500	Clifty Creek at Hartsville, IN	Continuous	39.27	−85.70	91.4	Unregulated	0.88	0.76	−0.05	0.66
03366200	Harberts Creek near Madison, IN	Continuous	38.78	−85.49	9.31	Regulated	1.25	1.23	−0.08	0.59
03366500	Muscatatuck River near Deputy, IN	Continuous	38.80	−85.67	293	Regulated	0.74	1.14	−0.09	0.41
03368000	Brush Creek near Nebraska, IN	Continuous	39.07	−85.49	11.4	Unregulated	1.32	1.23	−0.04	0.71
04096900	Nottawa Creek near Athens, MI	Continuous	42.06	−85.31	162.0	Regulated	0.23	0.17	0.21	0.18
04102776	Middle Branch Black River near South Haven, MI	Continuous	42.43	−86.21	83.00	Regulated	0.28	NA	0.07	0.75
04104945	Wanadoga Creek near Battle Creek, MI	Continuous	42.40	−85.13	48.30	Regulated	0.28	0.24	0.19	0.19
04105700	Augusta Creek near Augusta, MI	Continuous	42.35	−85.35	38.90	Regulated	0.14	0.17	−0.06	0.57
04117000	Quaker Brook near Nashville, MI	Continuous	42.57	−85.09	7.60	Regulated	0.23	0.31	0.10	0.55
04161580	Stony Creek near Romeo, MI	Continuous	42.80	−83.09	25.6	Unregulated	0.34	0.43	−0.02	0.89
04177000	Ottawa River at University of Toledo, Toledo, OH	Continuous	41.66	−83.61	154	Regulated	0.55	0.65	0.00	1.00
04177720	Fish Creek at Hamilton, IN	Continuous	41.53	−84.90	37.5	Regulated	0.51	0.52	−0.16	0.12
04178000	Saint Joseph River near Newville, IN	Continuous	41.39	−84.80	610	Regulated	0.49	0.57	0.00	1.00
04180000	Cedar Creek near Cedarville, IN	Continuous	41.22	−85.08	270	Regulated	0.44	0.61	0.04	0.72
04180988	Saint Marys River at Rockford, OH	Continuous	40.69	−84.65	295	Regulated	0.63	0.87	0.56	0.01
04182810	Spy Run Creek at Fort Wayne, IN	Continuous	41.11	−85.15	14.0	Regulated	0.41	0.75	−0.21	0.24
04184500	Bean Creek at Powers, OH	Continuous	41.66	−84.25	206	Unregulated	0.48	0.55	0.19	0.20
04185440	Unnamed tributary to Lost Creek near Farmer, OH	Continuous	41.36	−84.69	4.52	Regulated	0.82	0.68	0.11	0.42
04187100	Ottawa River at Lima, OH	Continuous	40.72	−84.13	129	Regulated	0.66	0.82	−0.07	0.69
04188337	Blanchard River below Mount Blanchard, OH	Continuous	40.92	−83.56	141	Unregulated	0.79	1.03	0.36	0.11
04188433	Lye Creek above Findlay, OH	Continuous	40.98	−83.59	18.8	Unregulated	1.65	1.11	0.16	0.56
04188496	Eagle Creek above Findlay, OH	Continuous	40.98	−83.65	51.0	Unregulated	0.95	1.08	0.53	0.02
04189131	Blanchard River at Gilboa, OH	Continuous	41.02	−83.92	503	Regulated	0.60	0.97	0.29	0.28
04189174	Riley Creek below Pandora, OH	Continuous	40.97	−83.98	70.3	Unregulated	0.64	0.89	−0.11	0.72
04189260	Blanchard River at Ottawa, OH	Continuous	41.02	−84.05	628	Regulated	0.61	0.92	0.07	0.86
04192500	Maumee River near Defiance, OH	Continuous	41.29	−84.28	5520	Regulated	0.56	0.72	−0.07	0.51
04193500	Maumee River at Waterville, OH	Continuous	41.50	−83.71	6310	Regulated	0.55	0.71	−0.01	0.93
04196000	Sandusky River near Bucyrus, OH	Continuous	40.80	−83.01	88.9	Regulated	0.57	0.89	0.09	0.50
04196500	Sandusky River near Upper Sandusky, OH	Continuous	40.85	−83.26	296	Regulated	0.60	0.94	−0.03	0.83
04197100	Honey Creek at Melmore, OH	Continuous	41.02	−83.11	149	Unregulated	0.74	0.92	0.21	0.05
04197137	Sandusky River at Tiffin, OH	Continuous	41.11	−83.18	966	Regulated	0.63	1.00	0.02	1.00
04198000	Sandusky River near Fremont, OH	Continuous	41.31	−83.16	1250	Regulated	0.61	1.04	0.10	0.34
04199000	Huron River at Milan, OH	Continuous	41.30	−82.61	370	Regulated	0.55	0.93	0.16	0.15
04199155	Old Woman Creek at Berlin Road near Huron, OH	Continuous	41.35	−82.51	21.8	Unregulated	1.32	1.01	0.13	0.35
04199500	Vermilion River near Vermilion, OH	Continuous	41.38	−82.32	262	Unregulated	0.64	0.79	−0.22	0.13
04200500	Black River at Elyria, OH	Continuous	41.38	−82.10	397	Regulated	0.63	0.78	−0.04	0.74
04201500	Rocky River near Berea, OH	Continuous	41.41	−81.88	267	Regulated	0.48	0.67	−0.06	0.57
04206043	Mud Brook at Cuyahoga Falls, OH	Continuous	41.15	−81.51	25.4	Regulated	0.45	0.43	1.00	1.00
04206212	North Fork at Bath Center, OH	Continuous	41.17	−81.63	5.72	Regulated	0.49	0.47	0.24	0.30
04206220	Yellow Creek at Botzum, OH	Continuous	41.16	−81.58	30.6	Regulated	0.38	0.46	−0.35	0.16
04208460	Mill Creek at Garfield Heights, OH	Continuous	41.42	−81.64	18.3	Regulated	0.35	0.51	0.20	0.26
04208502	Big Creek at Cleveland, OH	Continuous	41.45	−81.72	34.2	Regulated	0.40	0.57	−0.39	0.03
04212100	Grand River near Painesville, OH	Continuous	41.72	−81.23	684	Regulated	0.63	0.58	0.08	0.47
04213000	Conneaut Creek at Conneaut, OH	Continuous	41.93	−80.60	176	Unregulated	0.57	0.58	−0.02	0.82
412141081412100	West Creek at Pleasant Valley Road near Parma, OH	Continuous	41.36	−81.69	1.12	Regulated	0.62	0.52	−0.20	0.47
412325081415500	West Creek at Ridgewood Road at Parma, OH	Continuous	41.39	−81.70	0.23	Regulated	0.52	0.52	0.05	0.93

Table 2.    

Partial-record streamflow gages in Ohio for which low-flow statistics were computed.

[Data from VonIns and Koltun (2024). USGS, U.S. Geological Survey; R², coefficient of determination of the ordinary least square regression that defined the relation between the gage and its index site; OH, Ohio]

Table 2.    Partial-record streamflow gages in Ohio for which low-flow statistics were computed.

USGS station number	Station name	USGS index station number	USGS index station name	R2
03115385	Clear Fork near Rinard Mills, OH	03115400	Little Muskingum River at Bloomfield, OH	0.76
03129205	Black Fork Mohican River near Shelby, OH	04197100	Honey Creek at Melmore, OH	0.77
03144471	Little Wakatomika Creek near Trinway, OH	03144000	Wakatomika Creek near Frazeysburg, OH	0.84
03237121	Scioto Brush Creek near Rarden, OH	03237500	Ohio Brush Creek near West Union, OH	0.81
03238423	North Fork White Oak Creek near Sardinia, OH	03237500	Ohio Brush Creek near West Union, OH	0.82

The second task was to check for upstream regulation, diversion, or other anthropogenic activity or features that could affect low flows. Gages that were substantially affected were not used to develop the regression equations. This review consisted of using the Geospatial Attributes of Gages for Evaluating Streamflow II dataset (Falcone, 2017), notes from USGS field personnel documented in the USGS National Water Information System (NWIS; USGS, 2022), satellite imagery from Google Earth (Google, 2022), the Ohio Dam Locator (Ohio Department of Natural Resources, 2023), and the National Inventory of Dams (U.S. Army Corps of Engineers, 2020) to look for indications that low flow at the streamflow gage was likely to be appreciably altered from its natural, unregulated state. Another review looked for the presence of karst drainage features in or near each gage’s drainage basin using maps and geospatial data on karst geology available through State agencies (Kentucky Geological Survey, 2023; West Virginia GIS Technical Center, 2024). Although karst drainage features are natural, their effect on low flows cannot be reliably accounted for by data that can be extracted from available geospatial datasets. Based on the results of the reviews, each gage was categorized as either “regulated” or “unregulated” (table 1), where unregulated is defined as low flows thought to be subject to no or minimal regulation and regulated is defined as low flows that are regulated by anthropogenic modifications (for example, withdrawals or diversions) or karst drainage features to the extent that these flows may differ appreciably from low flows in otherwise undeveloped settings without appreciable karst drainage.

Upstream features that resulted in a gage being categorized as regulated include urbanization, actively managed upstream dams, selected industry (such as mining), known diversions, wastewater treatment plant discharges, and water treatment plant intakes. Categorizing each gage was not a definitive process. Many streams at gaged locations in Ohio (especially those with large drainage basins) have some amount of upstream regulation or anthropogenic activity that could affect low flow, and it was frequently difficult to determine the magnitude of the effect. A total of 58 gages—53 continuous-record gages (27 in Ohio and 26 in adjacent States)—and 5 partial-record gages (all in Ohio)—were categorized as unregulated and therefore suitable for use in the low-flow regression analyses (table 1). Drainage areas of the gages that were deemed suitable for use in the low-flow regression analyses ranged from 0.21 to 540 square miles (mi²).

Methods for Computing Low-Flow Statistics

Selected low-flow statistics (frequently referred to as “design flows” in a regulatory context) have been chosen by agencies tasked with protecting the environment and the health of human and aquatic life to evaluate and regulate risks from contaminants that are transported in streams. Regulatory agencies use both hydrologically and biologically based design flows (U.S. Environmental Protection Agency, 2024). Hydrologically based design flows were computed by using the single lowest average N-day flow event (N being the number of days used to calculate the average) from each year of record, which were then examined by using extreme-value statistical methods. Biologically based design flow methods empirically examine all flows, but additional weight is placed on low-flow events within a period of record (even if several low-flow events occur in 1 year) to emphasize the actual frequency of low-flow periods when contaminants discharged from point sources are poorly diluted in streams (U.S. Environmental Protection Agency, 2024).

Throughout this document, annual and seasonal low-flow frequency statistics are designated by using the following convention: (averaging period in days)Q(recurrence interval in years). For example, the annual minimum 7-day flow with a 10-year recurrence interval is designated as 7Q10. Some of the analyses were based on yields, which are determined by dividing the statistic (for example 7Q10) by the drainage area at the gage, in square miles. Low-flow yield statistics are designated by appending an “m” to the flow statistic designation (for example, the 7Q10 yield is designated as 7Q10m). Flow-duration statistics are designated by prepending a “D” to the percent duration value. For example, the 80-percent duration value is designated as D80.

Temporal Trends in Low Flow

Mann-Kendall tests (Mann, 1945) were used to evaluate temporal trends in the annual minimum N-day flows and to test for stationarity, which is a requirement for the frequency analysis. The Mann-Kendall test statistic, tau, is a rank correlation coefficient between the annual minimum N-day low flow and time. It provides information on the strength of monotonic (unidirectional) temporal trend in the time series, with a Kendall’s tau of 0 indicating no trend, a tau of 1 indicating a perfect monotonically upward trend, and a tau of −1 indicating a perfect monotonically downward trend.

At the inception of this study, it was planned that all available period-of-record flow data would be used to compute the low-flow statistics; however, initial screening for temporal trends using the period-of-record annual minimum 7-day flows indicated an upward trend for many of the candidate gages in Ohio and many of those were statistically significant (all tests of statistical significance discussed in this report are based on an alpha of 0.05). In addition, time-series plots showed what appeared to be an abrupt increase (hereafter referred to as a “step change”) in the annual minimum 7-day flows at many of the gages, occurring between the late 1960s and early 1970s. Change-point detection tests (Pettitt, 1979) were subsequently used to test for the presence of step changes in the flow statistic and to identify the year when each step change occurred. The Pettitt tests indicated that many of the time series that had shown statistically significant trends had step changes occurring between the late 1960s and 1975. As an example, figure 2 shows the step change that occurred at USGS gage Mill Creek near Coshocton, Ohio (03140000), in 1972 (p=9.75×10⁻⁵). A subsequent literature search revealed that McCabe and Wolock (2002) had also identified noticeable increases in annual minimum and median daily flow in eastern U.S. streams for the period 1941–1999, and they stated that the changes in flow appeared to occur as a step change around 1970, rather than as a gradual trend. They attributed the changes to a hydroclimatic regime shift. Because of these findings, the USGS, in consultation with cooperating agencies, decided to restrict our analyses to data collected after the 1974 water year. That was done to produce a more stationary time series and to yield flow statistics that better reflect low-flow characteristics of more recent decades.

After data were restricted to the post-1974 period (water years 1975–2020, hereafter referred to as the “analytical period”), Kendall’s tau values were again computed for annual minimum 1-, 7-, and 30-day flows. The computed tau values were approximately evenly mixed between positive and negative. Table 1 shows tau and p-value results (for the null hypothesis that tau is zero) for the annual minimum 7-day low flows. The 1- and 30-day low-flow tests had similar results: the same gages that had significant trends in the 7-day low-flow test had significant trends in the 1- and 30-day low-flow test results (not shown). In total, Mann-Kendall tests on data from gages ultimately classified as “unregulated” indicated that six gages (five in Ohio and one in Kentucky) had tau values that were significantly different from zero; two had negative trends and the others were positive (table 1).

Determination and Selection of Explanatory Variables

In order to develop regression equations for estimating low-flow statistics at ungaged stream locations, factors (hereafter referred to as “explanatory variables”) must be identified that can be used to mathematically explain all or part of the observed variation in the statistics. Explanatory variables in low-flow studies are typically measures of physical characteristics that vary in a systematic fashion with the low-flow statistics. Potential explanatory variables investigated in this study were selected in part because of their theoretical relation to low flows and in part because they can be or have been computed by using a geographic information system (GIS). The requirement that explanatory variables be determinable with a GIS comes from the desire to automate their determination within the StreamStats application.

Determining values of explanatory variables can be a time-consuming and expensive process. Some potential explanatory variables were determined from geospatial datasets that spanned the study area; however, others were determined from geospatial datasets with more limited geographic scope. Consequently, some potential explanatory variables were determined for all gages and others for just a subset of gages. For potential explanatory variables that were determined for a subset of the gages, it was necessary to ascertain whether the low-flow statistics of interest varied in a systematic fashion with those explanatory variables. As it turned out, none of the potential explanatory variables that were determined for only a subset of the gages showed sufficient potential as explanatory variables to warrant what would have been the next step: expanding the geographic scope of the geospatial dataset so that the explanatory variable could be determined for all the gages whose data were used to develop regression equations.

Approximately 260 potential explanatory variables were tested for this study (app. 3). Five primary sources of information were used to compute them: (1) the existing StreamStats application (https://streamstats.usgs.gov/ss/), (2) the USGS Hydro-Network Linked Data Index (NLDI; see https://labs.waterdata.usgs.gov/docs/nldi/about-nldi/index.html), (3) previously published geospatial datasets (for example, digital elevation models, watershed boundaries, and streamlines), (4) point data compiled for this study, and (5) grids of hydrogeologic information created for this study from standardized water-well drillers’ records.

The NLDI is a system that indexes previously published geospatial datasets to the National Hydrography Dataset Version 2 (https://nhdplus.com/NHDPlus/) catchments. The NLDI has a search service that permits retrieval of indexed information for points of interest through several retrieval mechanisms. A wide variety of local and catchment-level characteristics were retrieved from the NLDI for the gage locations (see app. 3). Among other categories, the NLDI data include information on (1) agricultural management and land conservation practices, (2) climate and water balance model characteristics, (3) climate characteristics, (4) geologic characteristics, (5) hydrology and hydrologic modifications, (6) landscape/landcover characteristics, (7) population and infrastructure, (8) ecoregions and physiography, (9) soil and topographic characteristics, and (10) water use. Not all the characteristics retrieved from NLDI had strong theoretical relations to the selected low-flow statistics, but they were readily available, so they were tested anyway. More information on the characteristics that can be retrieved from the NLDI can be found in Wieczorek and others (2018).

Grids of hydrogeologic characteristics were created for this study by using the methods described in Martin and others (2016) and Bayless and others (2017). Those methods used data from standardized water-well drillers’ records obtained from State-maintained databases to estimate the hydrogeologic characteristics. The grids of hydrogeologic characteristics created for this study have a 10- x 10-meter cell size and included

Potential explanatory variables computed from the hydrogeologic grids included catchment-area mean values and mean values for buffered areas extending 500 and 1,000 ft adjacent to streamlines upstream from the gages. Martin and others (2016) used the average horizontal hydraulic conductivity of the first 70 ft of unconsolidated deposits as an explanatory variable in regression equations that they developed for estimating 1Q10, 7Q10, and 30Q10 in Indiana. They used the average transmissivity of the full thickness of unconsolidated deposits within 1,000 ft of the stream channel as one of the explanatory variables in logistic-regression equations that they developed for estimating the annual probability of zero flow for those same statistics. For this study, the average horizontal hydraulic conductivity of first 30 ft of unconsolidated deposits was computed, rather than the 70 ft used in the Indiana study, because large areas of Ohio have unconsolidated deposit thicknesses considerably less than 70 ft.

A streamflow-variability index (SVI) was used as an explanatory variable in the most recent USGS publication that included equations for estimating low-flow statistics in Ohio (Koltun and Kula, 2013). SVI is a measure of the variability in streamflow at a gage resulting from variation in precipitation as it is mitigated by the physical characteristics of the basin. Typically, unregulated streams with relatively small SVIs have proportionally more flow contributed from groundwater discharge (or surface storage or both) than streams with larger SVIs (Lane and Lei, 1950). SVI is computed with the following equation:

A variety of methods were used to select explanatory variables included in the regression equations for estimating the low-flow statistics. The first (and potentially most informative) method was to create scatterplots of the low-flow statistics in relation to the potential explanatory variable. In general, if a potential explanatory variable is useful for estimating low-flow statistics, its scatterplot should show indication of a systematic relation between the variable and the statistic. If there is a random scatter of points in the plot, it is unlikely that the potential explanatory variable will be useful for estimation. Other methods, including bidirectional stepwise regression and forward stepwise regression, also were used to evaluate potential explanatory variables. Stepwise regressions can help in choosing good candidate explanatory variables when two or more explanatory variables are correlated.

After review of the scatterplots and the stepwise regression results, SVI was chosen as the explanatory variable for the regression equations to predict harmonic mean flow; the annual 1Q10m, 7Q10m, 30Q10m, and 90Q10m; the May–November 1Q10m, 7Q10m, 30Q10m, and 90Q10m; and the September–November 1Q10m, 7Q10m, 30Q10m. SVI alone, however, was not satisfactory as the only explanatory variable for the 80-percent duration flow, the September–November 90Q10m, and the December–February 1Q10m, 7Q10m, 30Q10m, and 90Q10m. For those statistics, one of two scenarios was selected to explain the flows more fully: (1) SVI, the drainage area, and the decimal longitude or (2) just the drainage area and the decimal longitude, when SVI was not a statistically significant explanatory variable.

Estimating the Streamflow-Variability Index at Ungaged Sites

To enable computation of low-flow statistics at ungaged sites in Ohio, it was necessary to develop statewide datasets for each of the explanatory variables. Drainage area, decimal longitude, and SVI are already computed within StreamStats; however, new estimates of SVI were needed to reflect streamflow variability during this study’s analytical period. In past studies (Koltun and Whitehead 2002; Koltun and Kula 2013), a grid of SVI estimates was created by using inverse-distance-weighted (IDW) interpolation on at-site values of SVI. The IDW interpolation effectively assumed that SVI varied in a distance-weighted linear fashion among the gages where SVI was known. However, if SVI does not vary linearly in space, as assumed, the accuracy of the resulting SVI grid is dependent on the number and spatial density of known SVI points. With spatially dense datasets, the accuracy of the assumption of linear variation in space is likely to be less important because interpolations are made over relatively short distances. Because the number of gages included in the regression analyses in this study was appreciably smaller than in the previous studies (due to the decision to include only data after the 1974 water year), other methods for developing the SVI grid were explored that were less dependent on the assumptions inherent in the IDW method.

The decision was made to develop the SVI grid using empirical Bayesian kriging (EBK) regression prediction (Esri, 2022b). EBK regression prediction is a geostatistical interpolation method that uses an explanatory raster (grid) known to systematically covary with the values of the data being interpolated (Krivoruchko, 2012). EBK regression prediction models simultaneously estimate both a regression model for the mean value and a semivariogram/covariance model for the error term. By operating on both components at the same time, they can make more accurate predictions than either regression or kriging can achieve on their own.

The SVI grid was created by using the EBK regression prediction routine implemented in the Esri ArcGIS Pro (version 3.2) Geostatistical Analyst software (Esri, 2022a). After reviewing scatterplots of SVIs computed from the analytical-period flow record of the gages in table 1 designated as “unregulated” and the potential explanatory variables described in the section “Determination and Selection of Explanatory Variables,” a previously published grid of estimated mean annual natural groundwater recharge (Wolock, 2003) was chosen as the explanatory grid. The recharge grid was chosen because it had a moderately strong negative correlation (R = −0.59), which was stronger than the other variables considered.

Residuals calculated from the SVI values computed from streamflow observations at unregulated gages and the SVI values from the EBK regression predictions ranged from −0.25 to 0.73 with a mean of 0.02 and a standard deviation of 0.15. Despite fewer gages being used in the current study, these results are similar to those reported by Koltun and Kula (2013), which used an IDW approach. In the analysis by Koltun and Kula (2013), residuals were computed by using a leave-one-out cross-validation technique and ranged from −0.51 to 0.63 with a mean of 0.01 and standard deviation 0.16. The grid of estimated SVI developed for Ohio by using EBK regression prediction is shown in figure 3, and at-gage EBK regression estimates from the grid are shown in table 1.

Equations for Estimating Low-Flow Statistics

The relation between SVI and low-flow yields were not linear, so the options for developing low-flow yield equations were either to transform the model variables to fit a linear equation or to use a nonlinear or curvilinear equation. Log transformation and square root transformation were considered and rejected because of problems with zero-valued data or unwanted effects in the regression (Koltun and Kula, 2013). Because of these problems, and for consistency with previous studies, a cubic polynomial of SVI was used in the equations to predict the harmonic mean flow; annual yields; May–November 1Q10m, 7Q10m, 30Q10m, and 90Q10m; and the September–November 1Q10m, 7Q10m, 30Q10m. SVI alone was not a powerful enough predictor for September–November 90Q10m yield; the December–February 1Q10m, 7Q10m, 30Q10m, and 90Q10m yields; or the D80 flow, so a model with explanatory variables consisting of drainage area, decimal longitude, and, in most cases, SVI, was used to predict these statistics. In models that used drainage area as an explanatory variable, a square root transformation was applied to the low-flow yields and drainage area to improve linearity in the regression equations.

All linear regression equations were developed by using censored regression routines implemented in the censReg function of the USGS R package smwrQW (https://code.usgs.gov/water/analysis-tools/smwrQW). Zero values in the yield statistics were treated as left censored (meaning they were less than a specified value) because there is uncertainty in the measurement of the flow that makes it difficult in some cases to ascertain whether the flow (and associated yield) is truly zero. A censoring level of 0.00001 cubic feet per second per square mile ([ft³/s]/mi²) was used in the analyses when the yield statistics included zero-valued observations. Because weighted regression analyses were performed, the regressions were computed by the censReg function using maximum likelihood estimation, which accounts for the unequal sampling probability for each observation depending on whether the magnitude of the dependent variable is above or below the censoring level.

Observations used in the regressions were weighted as a function of the length of record of the associated gage. The weighted regression served to down-weight the importance of observations for gages with shorter records, which are more susceptible to time-sampling error. For continuous-record gages, the weight for a gage’s observations was computed by first computing a time fraction (the number of days with a computed daily mean flow in the gage record from 1975 through 2020 divided by the maximum number of days in that same period) and then dividing it by the average of time fractions for all gages included in the regression. For partial-record gages, the weight was estimated as the product of the weight computed for its index gage and the coefficient of determination (R²) from the MOVE.1 regression that defined the relation between the partial-record gage and its index site.

For polynomial models, first a regression model using orthogonalized (uncorrelated) polynomial terms was developed to assess the statistical significance of the explanatory variables. That was done because collinearity among the polynomial terms can inflate the variance in the coefficients, making it difficult to assess the statistical significance of the explanatory variables. The cubic polynomial matrix was orthogonalized by using the poly function in R (see https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/poly for more information). Once the statistical significance (or lack thereof) of the explanatory variables was established, a second regression model was developed by using the untransformed data to develop the equations presented in this report. Both models produce identical estimates and model metrics (such as pseudo R²); however, the magnitudes of the model parameter coefficients differ to account for the transformed explanatory variables.

Constraints were placed on equations if the equations could compute yields less than the censoring level (outside of the censReg function) or if the computed yields did not monotonically decrease with increasing SVI. In the first case, the constraint consisted of setting computed low-flow yields that were less than the censoring level to the censoring level. In the second case, the constraint consisted of setting the low-flow yield to the value at which the yield switched from decreasing to increasing with increasing SVI.

In the yield regressions that used the orthogonalized polynomial parameters, one of the SVI parameters (typically, SVI squared, but in one case SVI cubed) was not statistically significant in the 1-, 7-, and 90-day May–November equations and the 1- and 7-day equations for September–November. In each case, the statistically insignificant variable coefficient was small (always less than 0.04), making the equation result insensitive to that parameter relative to the other model parameters. Despite this, we chose to use a cubic polynomial model in each case to maintain consistency across the various equations that used a polynomial model form. Yield equations were plotted to confirm that the following three conditions were met: (1) yields monotonically decreased or were the same with increasing SVI, (2) yields did not decrease as the low-flow averaging period increased for the same seasonal period (for example, the annual [April–March] 1Q10m was less than or equal to the annual 7Q10m for a given SVI), and (3) annual low-flow yields were less than or equal to seasonal low-flow yields for the same frequency statistic (for example, the annual 7Q10m was less than or equal to the September–November 7Q10m for a given SVI). The first two conditions were met, but the third condition was not met in all cases. At SVI values greater than about 0.50, the May–November equations produced slightly lower yield estimates than the annual equations (the maximum difference was less than 0.00053 [ft³/s]/mi²). On further examination, we found that the annual and May–November 1Q10 and 7Q10 estimates for each gage in the calibration dataset were nearly equal (average absolute differences of 0.0186 and 0.0238 cubic foot per second [ft³/s], respectively) and the differences between the estimates were much smaller than the statistical uncertainty of the regression equations. Because of this and because the annual value must, by definition, be less than or equal to the seasonal values, we recommend (and intend to implement in StreamStats) that the April–March low-flow estimates be set to the lesser of the computed annual (April–March) and May–November low-flow estimates for a given averaging period. The final regression equations (table 3) have been formatted to provide estimates in units of cubic feet per second, which required that the yield equations be multiplied by the drainage areas. Fit statistics, including the root mean square error (RMSE) and the bounds for the interquartile range of residual errors (the range that contains 50 percent of the observations in the calibration dataset) are also reported in units of cubic feet per second. Censored estimates were set equal to the censoring level when computing the RMSE. As examples of the fit of the yield-based equations, figure 4 shows scatterplots of observed in relation to predicted 7Q10 and 30Q10 for the April–March season (table 3, eqs. 2 and 3), along with 1:1 lines.

Regression residuals were reviewed for spatial biases and homoscedasticity (nonconstant error variance). Residual plots sorted by region were reviewed to check for spatial biases, and standardized residuals were plotted against predicted yields and against explanatory variables to check for heteroscedasticity. The plots showed no obvious signs of spatial biases; however, some equations showed indications of potential heteroscedasticity. For example, there were more positive residuals than negative residuals with the 7Q10 equation when observed 7Q10 values exceeded about 3 ft³/s, indicating that the equations may tend to underestimate flows in that range more than would be expected if the errors were random. Because the calibration dataset was small (58 observations), it is uncertain whether the heteroscedasticity is real or a function of that particular sample set.

Summary

The U.S. Geological Survey, in cooperation with the Ohio Water Development Authority and the Ohio Environmental Protection Agency, completed a study to compute low-flow frequency, flow-duration, and harmonic mean flow statistics for long-term streamflow gages and to develop methods for estimating those statistics at unregulated, ungaged stream locations in Ohio. The study began by identifying continuous-record gages in Ohio and bordering States that had at least 10 years of flow data and low-flow partial-record gages in Ohio that had periodic instantaneous low-flow measurements that had strong mathematical relations to concurrent daily mean flows at a continuous-record gage. A total of 180 continuous-record gages and 5 low-flow partial-record gages met those criteria. For continuous-record gages, the following statistics were computed: annual and seasonal minimum 1-, 7-, 30-, and 90-day flows with 2-, 5-, 10-, 20-, and 50-year recurrence intervals; annual and seasonal 98-, 95-, 90-, 85-, 80-, 75-, 70-, 60-, 50-, 40-, 30-, 20-, and 10-percent duration flows, and the harmonic mean flow. For partial-record gages, a smaller set of statistics were estimated by using a Maintenance of Variance Extension, Type 1 regression developed from the low flows measured at the partial-record gages and the concurrent daily mean flows recorded at their index gages, generating annual and seasonal minimum 1-, 7-, 30-, and 90-day low flows with 2-, 10-, and 20-year recurrence intervals and annual and seasonal 98-, 95-, 90-, 85-, and 80-percent duration flows.

Initial screening for temporal trends in period-of-record time series of annual minimum 7-day flows computed for continuous-record gages indicated statistically significant upward trends for many of the candidate gages in Ohio. Change-point detection tests indicated that many of the time series that had shown statistically significant trends had step changes occurring after the late 1960s but before 1975. Because of these findings, the U.S. Geological Survey, in consultation with cooperating agencies, decided to restrict the analyses to data collected after the 1974 water year through the 2020 water year (referred to as the “analytical period”) to produce a more stationary time series and to compute flow statistics that better reflect low-flow characteristics of recent decades.

Gage drainage basins were inspected for upstream regulation, diversion, or other anthropogenic activity or features that could affect low flows. This was done to identify gages whose low flows are likely to be appreciably altered from a natural, unregulated state. Based on that review, each gage was categorized as either “regulated” or “unregulated.” A total of 53 continuous-record gages and 5 low-flow partial-record gages were categorized as unregulated, and their data were subsequently used in regression analyses to develop equations for estimating low-flow statistics.

Approximately 260 potential explanatory variables were tested for this study. With a few exceptions (for some statistics in the September–November, December–February seasons, and the 80-percent duration flows), a streamflow-variability index (SVI) was chosen as the sole explanatory variable for the regression equations to predict the harmonic mean and annual and seasonal low-flow yields. A model with explanatory variables consisting of drainage area, decimal longitude, and, in most cases, SVI, was used to predict those exceptions. The SVI values used in the regression analysis were obtained from a geospatial grid of SVI values developed for this study by means of empirical Bayesian kriging regression prediction.

Observations for continuous-record gages whose data were used in the regressions were weighted in the regression as a function of their length of record. Weights for partial-record gages were estimated based on the weights determined for their index gages. All linear regression equations for low-flow yields were developed by using censored regression, with a censoring level set to 0.00001 cubic foot per second per square mile. Numerical constraints were placed on equations if they could compute yields less than the censoring level or if the computed yields did not monotonically decrease with increasing SVI.

All regression equations in this report are presented in a form that permits computation of low-flow statistics in units of cubic feet per second. Logistic-regression equations were developed as a secondary check to estimate the probability that the N-day, 10-year low flow is greater than the censoring level (0.01 cubic foot per second). If the computed probability is less than 0.50, it is suggested that the flow be assumed to be less than 0.01 cubic foot per second.

The regression equations presented in this report were developed to be implemented in the Ohio StreamStats application. The equations are applicable to unregulated streams in Ohio. They are not applicable to streams with karst drainage features, diversion, regulation, or other conditions that can appreciably affect low flows. The range of SVI values used to develop the equations was 0.41 to 1.23 log₁₀ cubic feet per second, and the range of drainage areas was 0.21 to 540 square miles (table 1). The applicability of these equations to stream locations with SVIs or drainage areas outside of these ranges has not been determined.