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MAXIMUM PEAK FLOWS FOR SELECTED RETURN PERIODS

FOR WATERSHEDS WEST OF THE CONTINENTAL DIVIDE IN IDAHO AND MONTANA

Nedavia Bethlahmy

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USDA Forest Service Research Paper INT-113 INTERMOUNTAIN FOREST AND RANGE EXPERIMENT STATION Ogden, Utah 84401

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USDA Forest Service Research Paper INT-113 December 1971

MAXIMUM PEAK FLOWS FOR

SELECTED RETURN PERIODS

FOR WATERSHEDS WEST OF THE CONTINENTAL DIVIDE IN IDAHO AND MONTANA

Nedavia Bethlahmy

INTERMOUNTAIN FOREST AND RANGE EXPERIMENT STATION Forest Service U.S. Department of Agriculture Ogden, Utah 84401 Robert W. Harris, Director

THE AUTHOR

NEDAVIA BETHLAHMY is Principal Forest Hydrologist for the Streamflow Regulation research work unit of the Intermountain Forest and Range Experiment Station in Moscow, Idaho. He began his career with the Forest Service in California in 1940, and since that time has worked and conducted experiments in watershed man- agement research in the Northeastern, Southwestern, Pacific North- west and Intermountain Regions. During the years 1966-1968, he was assigned to the Food and Agriculture Organization of the United Nations to help the Republic of China solve the watershed manage- ment problems of Taiwan. He is a Graduate Forester from Penn State, and holds M.F. and Ph.D. degrees from Yale and Cornell Universities.

CONTENTS

NLR OD UC AION Gmconicu omicl | cicureptciivei enleli oti inewel oie toil il eine EXAMPLES FOR FIELD APPLICATION ........... DISCUSSION oo GoeGo oboe oo oo Sb OOOO oOo bo

Tai CATHONS Weiss)! "=! 6) ce) eo re SOo00 00 GD OOo On REFERENCES......... ‘ . 6. OO Goo 6 0O1e AN PIV ASPDIDC IU o.d Oo O16 0 0 dig 06 GN Io oe kel isiiie’) olen ehte 0

APPENDIX TI .

ABSTRACT

The long-term average water yield of a watershed appears to be a good index to the magnitude of its expected peak flow. On the basis of this relation, tables are presented showing expected peak flows that are applicable to watersheds in Idaho and Mon- tana west of the Continental Divide. Tabulated peak flows are for four different return periods: mean annual; 5; 10; and 20 years. Three examples are given to illustrate the tables’ field application.

What is the 20-year flood potential of this watershed?

INTRODUCTION

Foresters and other land managers have long considered water an important product of forest lands. This product yields great benefits when its flow is orderly, timely, and is confined within the banks of a stream. On the other hand, water appearing as a flood is a potentially destructive force that land managers should consider when plan- ning future forest operations.

The effects of clearcutting operations on the hydrologic regime of a watershed are complex, and the magnitude of these effects is highly variable. Nevertheless, we do know that a clearcut watershed yields more water (Hibbert 1967), and that the pattern of runoff distribution is changed, including an increase in base flow and peak flow (Bethlahmy 1971). Thus, foresters and other land managers who contemplate clearcutting operations should consider the associated problem of future changes in the hydrologic regime.

Our research has shown that on a unit area basis the long-term average water yield of a watershed is a good index to the magnitude of its expected peak flow. The greater the average yield per unit area, the greater the expected peak flow for period of record. This relation is readily perceived from table 1 that shows data for 11 rivers in Idaho which have good or excellent streamflow records (U.S. Department of Interior 1964). Notice the regular decrease in values of both average annual flow and associated peak flow. Although peak flow per unit area is related to unit drainage yield, any discus- sion of peak flow should include the element of chance. A record of many years of data will probably include. greater peak flow values than a short record. Hence, a comparison of peak flows for different areas should be based not only on the watershed's average yields but also on the element of time; how long is the record, and how often can one expect a peak flow of a given magnitude? Such considerations are especially important to engineers and economists who are concerned with investments in structures having an economic life expectancy.

Table 1.--Relation of peak flow to average annual flow for some Idaho rivers with good or excellent stream records

Average : : : : annual : Peak : Elevation :; Length : Watershed River : flow : flow! : of gage : of record : area “Chipfo@ollle “CoipoSolilh VRAGE Years Sq.mt. Cub 4.24 36.86 55520 Pil 19.4 Boundary 1.98 SSO a0, 34 97 Mission eval! 22.96 2,800 6 23 Clearwater (Kamiah) 1.68 oa! 1,162 54 4,850 Moyie (Eastport) ey25 18.60 2,620 $5 570 Yaak 1.20 15.80 1,850 8 766 Moyie (Eileen) 1.16 14.57 2,124 39 755 Big Lost River (Wild Horse) . 86 Hail gala! 6,820 20 114 Robie 550) ORS 2 4,960 14 15.8 Thomas Fork 44 7.69 6,280 15 PIS

Bannock . 36 Sow 5,240 16 5.75

1Peak flow for period of record. Cubic feet per second per square mile. 3Above mean sea level.

Peak flows which can be expected in Idaho and Montana, in watersheds west of the Continental Divide, are listed in tables 2 and 3 for four different return periods. The selected return periods are: 2.33 years (usually termed the mean annual return period) ; 5; 10; and 20 years. In these tables, peak flow is a function of average water yield and an expected return period, and is expressed in units of cubic feet per second per square mile (c.f.s.m.). In table 2, average water yield (the independent variable) increases by selected increments in inches, and in table 3 by selected increments in c.f.s.m. These tables were constructed in accordance with the methods described in Appendix 1, and are based on sources of data listed in Appendix 2.

Table 2.--Maximum peak flows (¢c.f.s.m.) for selected return pertods for watersheds west of the Continental Divide tn Idaho and Montana

Average annual : Return period (years) yield g DSSS : 5.0 : 10 : 20 Inches = ----+------------- C.f.S.m---------- - - - - = 5.0 2.6105 3.2904 4.1589 52,959 6.0 2.9845 3.7810 4.7295 5.9284 750 3.3984 4.3267 SS 57 6.6899 8.0 3.8526 4.9282 6.0433 7.5180 9.0 4.3465 5.5856 6.7854 8.4111 10.0 4.8791 6.2975 7.5818 9.3661 11.0 5.4484 7.0619 8.4294 10.3791 12.0 6.0520 7.8755 9.3240 11.4450 SIO) 6.6866 8.7343 10.2609 12.5578 14.0 7.3487 9.6336 TS 234'5 13.7109 15.0 8.0341 10.5679 12.2388 14.8972 16.0 8.3787 11.5314 13.2676 16.1092 17.0 9.4580 12.5180 14.3145 17.3395 18.0 10.1875 13.5216 15.3730 18.5808 19.0 10.9229 14.5361 16.4370 19.8258 20.0 11.6600 15.5554 17.5005 21.0677 21.0 12.3948 16.5741 18.5581 22.3004 22.0 13.1236 17.5867 19.6047 23.5181 23.0 13.8431 18.5885 20.6356 24.7157 24.0 14.5503 19.5751 21.6467 25.8885 25.0 15.2426 20.5426 22.6346 27.0356 26.0 15.9176 21.4877 23.5963 28.1450 27.0 16.5736 22.4075 24.5291 29.2226 28.0 17.2089 23.2997 25.4313 30.2636 29.0 17.8224 24.1624 26.3011 31.2663 30.0 18.4131 24.9941 ZT OUSTS 32.2294 31.0 18.9804 25.7938 27.9398 33.1524 32.0 19.5239 26.5609 28.7075 34.0348 33.0 20.0434 27.2948 29.4406 34.8767 34.0 20.5390 27.9956 30.1391 35.6784 35.0 21.0108 28.6634 30.8036 36.4404 36.0 21.4592 29.2985 31.4345 3751635 37.0 21.8846 29.9016 32.0326 37.8485 38.0 22.2876 30.4734 32.5988 38.4967 39.0 22.6689 31.0146 33.1341 39.1092 40.0 23.0291 31.5263 33.6394 39.6871 41.0 23.3690 32.0094 34.1159 40.2318 42.0 23.6893 32.4649 34.5648 40.7447 43.0 23.9910 32.8941 34.9873 41.2272 44.0 24.2747 33.2979 35.3845 41.6807 45.0 24.5413 33.6776 SST SIS 42.1065 46.0 24.7917 34.0343 SOmlO77 42.5061 47.0 25.0266 34.3690 36.4361 42.8807 48.0 25.2469 34.6830 36.7440 AS R254 49.0 25.4532 34.9774 S17 A0S235 43.5605 50.0 25.6465 35.2530 37.3022 43.8681

Table 3.--Maximun peak flows (c.f.s.m.) for selected return pertods for watersheds west of the Continental Divide in Idaho and Montana

Average annual 3 Return period (years) yield : BEES : 5.0 : 10 : 20

a SSP 8 = = Cafes. — ==) =) = 2) | O82 1.8989 2.3648 3.0639 3.8924 OS 2.2982 2.8829 3.6801 4.6489 0.4 2.7664 3.4946 4.3972 5.5242 OSS 3.3070 4.2059 5.2192 6.5222 0.6 3.9216 5.0199 6.1472 7.6432 Os 4.6092 5.9363 7.1786 8.8830 0.8 5.3663 6.9514 8.3073 10.2335 0.9 6.1871 8.0581 9.5239 11.6827 1.0 7.0638 9.2462 10.8160 3), 215i LF 7.9868 10.5032 12.1695 14.8154 eZ, 8.9455 11.8146 13.5689 16.4635 1S 9.9289 13.1654 14.9980 18.1414 1.4 10.9259 14.5402 16.4414 19.8309 eS 11.9261 15.9241 17.8839 21.5148 1.6 12.9196 17.3031 19.3120 23.1778 The7/ 13.8976 18.6645 20.7135 24.8062 1.8 14.8526 19.9974 22.0783 26.3886 139 15.7782 21.2924 23.3978 27,5955 230 16.6694 22.5419 24.6652 29.3798 Ze WeES222 23.7401 25.8756 30.7759 Bez 18.3339 24.8825 27.0254 32.1004 DiS 19.1026 25.9662 28.1124 33.3509 D4 19.8273 26.9894 29.1358 34.5267 255 20.5079 27.9516 30.0954 35.6282 216 21.1447 28.8530 30.9921 36.6565 2, 21.7386 29.6946 31.8274 37.6136 258 22.2908 30.4779 32.6033 38.5018 2.9 22.8030 31.2051 5525222 39.3244 3.0 23.2768 31.8783 33.9867 40.0841 Sal 23.7143 32.5004 34.5997 40.7846 32 24.1173 33.0739 35.1642 41.4292 Sa5 24.4881 33.6018 35.6830 42.0215 3.4 24.8286 34.0868 36.1592 42.5649 S55) 25.1407 34.5317 36.5957 43.0626 3.6 25.4267 34.9395 36.9952 43.5182 Shih 25.6882 555126 37.3605 43.9346 3.8 25.9273 35.6537 37.6942 44,3148 359 26.1454 35.9652 37.9987 44.6617 4.0 26.3445 36.2494 38.2765 44.9781 4.1 26.5259 36.5086 38.5295 45.2662 4.2 26.6911 36.7446 38.7599 45.5285 4.3 26.8415 36.9595 38.9696 45.7672 4.4 26.9784 Sy US SZ 39.1604 45.9842 4.5 27.1028 37.3330 39.3338 46.1816 4.6 27-«2159 37.4947 39.4913 46.3608 4.7 27.3186 37.6416 39.6344 46.5236

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EXAMPLES FOR FIELD APPLICATION

Three examples are given to show how the tables can be used for field application. EXAMPLE 1

Problem: A road will be built across the outlet of a 1.5-sq.-mi. drainage having an expected annual water yield of 40 inches. What is the maximum rate of flow the culvert should accommodate:

(a) if designed for a 20-year flood? (b) if designed for a 50-year flood?

Solutton:

(a) For an annual yield of 40 inches, table 2, col. 5, shows a peak flow of 39.69 c.f.s.m. Since the drainage area is 1.5 sq. mi., we can expect a 20-year flood of 59.53 Crees (5 9/.091X) 1h. Si)iz

(b) The tables do not show peak flows for return periods exceeding 20 years. Extrapolation is required, but this procedure is fraught with great uncertainty. In table 2, opposite an average 40-inch annual yield, we find the expected peak flows for the 10- and 20-year floods to be 33.64 and 39.69 c.f.s.m., respectively. Plot the paired values (year versus flow) on log-log paper, connect them with a straight line, and extend the line to the 50-year flood. The peak flow is 49.3 c.f.s.m. Inasmuch as the area is 1.5 sq. mi., the expected SO-year flood is 74 c.f.s. (49.3 X 1.5 = 74).

It must be understood that such extrapolation results in only approximate values.

EXAMPLE 2

Problem: A road crosses the outlet of a 40-acre watershed over a 12-inch corrugated metal culvert whose top is 1 foot below the road surface. Plans call for clearcutting the watershed that has an annual yield of 35 inches. After cutting we expect annual water yield to increase by 15 percent. Assuming a 20-year-design flood, will the presently located culvert accommodate the increased flow?

Solutton:

The expected annual flow is 40.25 inches (35 inches X 1.15). In table 2, col. 5, interpolating for peak values between 40 and 41 inches, we obtain an expected peak flow of 39.82 c.f.s.m. Since the area involved is 40 acres, the expected peak flow is 2.49

40 : A Co LS 19282 0x $40) Using culvert discharge tables (e.g., Hendrickson 1957), we find

that the presently installed culvert (use 1,0 percent slope and 0.025 roughness coeffi- cient) will accommodate only 2.4 c.f.s. Because there is a present capacity of only 2.4 c.f.s., and the expected need is for 2.49 c.f.s., it appears that the road will probably be damaged by overflowing unless a larger culvert is installed or the surface of the road is raised to allow for ponding.

EXAMPLE 3

Problem: The annual water yield from a 5.0-sq.-mi. drainage is 40 inches. Plans call for clearcutting a 40-acre subwatershed. What are the present and expected peak flows at the outlet of the main drainage for a 10-year flood if the annual water yield of the clearcut area is ex- pected to increase by 15 percent?

Solutton:

Under present conditions (before cutting) the expected 10-year flood for the en- tire drainage is 168.20 c.f.s. In table 2, col. 4, opposite 40 inches, read 33.64 c.f.s.m. and multiply by 5.0 sq. mi., and for the 40-acre subwatershed it is 2.10 c.f.s.

40

(33.64 X 640)

After cutting, the average yield from the clearcut 40-acre subwatershed will be 46.0 inches (40 X 1.15). In table 2, col. 4, we read a peak flow value of 36.11 c.f.s.m. Since the subwatershed is 40 acres, the peak flow is 2.26 c.f.s. 40

(36.11 X =). 640

On the clearcut area, the peak flow will increase by 0.16 c.f.s. (2.26 - 2.10).

Add this value to the precutting peak flow for the entire drainage:

168320 F410 216) = 1G 8) SOC. t.S:.

It is apparent that clearcutting the 40-acre subwatershed will not alter the peak flow of the main watershed in any significant way.

ag * he Pa oes - nip, fs. OO nl ot Mea llc te Stn 9 A raging mountain stream overflows a bridge.

DISCUSSION

The three examples illustrate how the tables may be used, and the practical signifi- cance of the effects of clearcutting operations. We once again remind the reader that

the tabulated values are expressed in yield per unit area, and hence may be applied to watersheds of any size or at any elevation.

In illustrating the use of the tables, we used a potential water yield increase of 15 percent. Some readers may consider this figure as too conservative, because it is considerably smaller than figures reported in the literature. At Fraser, Colorado, for example, where 75 percent of the annual precipitation occurs as snow, a 40-percent commercial clearcut in strips yielded a first-year increase of 30 percent in annual streamflow (Goodell 1958). We used the figure 15 percent as an example, and not as a

universal recommendation. In using the tables, the reader should consider the special circumstances applying to his case.

The tables may also be used to solve problems relating to channel stability, bank cutting, and stream level. However, because the characteristics of stream channels vary considerably from one segment to another, it is apparent that a particular problem May not have a unique solution. Nevertheless, the land manager may sometimes be particularly concerned with certain segments of a stream channel because they appear vulnerable to changes in the hydrologic regime. In such cases, it may be worthwhile to make the assumptions needed to perform the calculations and to determine the magnitude of changes that can be expected.

Limitations

Flood peaks reflect the complex interaction of many variables, and many formulas have been devised to account for the effects of these variables. In most cases, how- ever, the land manager has only limited information about the magnitude of the important variables. For example, Rosa (1968) published water yield maps for Idaho, but maps of this sort are not available for even such basic variables as rainfall intensity or soils grouped according to their hydrologic properties.

The user of these tables is cautioned that the tabulated values are far from being definitive; they are only an approximation to give the land manager an idea of what may be expected. Mr. C. A. Thomas has observed! that the tabulated values may be too high for streams with a high base flow and are probably too low for streams with flashy run- off and low base flows.

The user should bear in mind that the tables will probably be applied to areas considerably smaller than those from which the tables were derived. Furthermore, flow data for the very small drainages cover only a brief span of time.

1Personal communication, on file at Intermountain Forest and Range Experiment Station, Forestry Sciences Laboratory, Moscow, Idaho.

REFERENCES

Bethlahmy, Nedavia 1971. Effects of forest clearfelling on the storm hydrograph--a reanalysis. Amer. Geophys. Union Trans. 52(4): 204.

Bodhaine, G. L., and D. M. Thomas 1964. Magnitude and frequency of floods in the United States. Part 12. Pacific Slope Basins in Washington and Upper Columbia River Basin. Geol. Surv. Water-Supply Pap. 1687.

Goodell, B. C. 1958. A preliminary report on the first year's effects of timber harvesting on water yields from a Colorado watershed. USDA Forest Serv., Rocky Mountain Forest Exp. Sta. Res. Pap. 36, 12 p.

Hendrickson, John G., Jr. 1957. Hydraulics of culverts. Chicago, I11.: Amer. Concrete Pipe Assoc.

Hibbert, Alden R. 1967. Forest treatment effects on water yield. P. 527-543, tm: William E. Sopper, and Howard Lull (eds.), Forest Hydrology. Pergamon Press.

Rosa, J. Marvin 1968. Water yield maps for Idaho. USDA Agr. Res. Serv. 41-141.

Thomas, C. A., H. C. Broom, and J. E. Cummans 1963. Magnitude and frequency of floods in the United States. Part 13. Snake River Basin. Geol. Surv. Water-Supply Pap. 1688.

U.S. Department of Interior 1964. Surface water records of Idaho. USDI Geol. Surv., 281 p.

APPENDIX |

The published tables are based on the finding that peak flow is a function of mean water yield. The equation is:

In (P/A) = atb [1.5708 - arc tan (sinh F/A)] (Gis)

in which P, A, and F are, respectively, peak flow (c.f.s.), area (square miles), and mean flow (c.f.s.). The constant 1.5708 is the angle 90° expressed in radians.

Equation (1) is based on data found in Thomas, Broom, and Cummans (1963) and Bodhaine and Thomas (1964). Only those rivers were analyzed whose records indicated no diversions, impoundments, or poor data. The equation was derived as follows: For each streamflow record, the annual peak flow data were arranged in a descending order of magnitude. If W represents the baa Ris of items in the series, and M. is the ordered position in the series (i.e. .V), then the probability of Gecumeence (Py) (or percent chance) for a peak ae ee to or smaller than that in ordered position M . is

(, - 0.5) 100 X ry

This probability was calculated for each ordered position, and defined the plotting position of the associated peak flow on log-normal paper. A smooth line was drawn through the plotted data, but was not extended beyond the range of the plotted data. We then read the adjusted peak flows for the selected recurrence periods: 2.33; 5; 10; and 20 years. (The recurrence period is 100 divided by the probability of occurrence; Ouse ae P, = 20, r., = 5.)

Data drawn from the smooth curves formed four new sets of data, one for each selected recurrence period. Each set of data was then analyzed to obtain the values of a and b in equation (1). We have listed below these values, as well as the correla- tion coefficient (Af) relating the dependent and independent variables.

Recurrence pertod a b R (Years) Zeros 3.3434 -1.9693 0.966 5 3.6653 -2.0440 -950 10 3.7141 -1.8908 .938 20 3.8733 -1.8324 902

Values for tables 1 and 2 were calculated for selected values of mean flow (F/A) using the equation P P atb[1.5708 - arc tan (sinh — )] (2) 7 wae A

where e is 2.71828, base for Naperian logarithms.

11

APPENDIX Il

Data for the following rivers were used to derive equation l.

River No. Length of (USGS) River name and location record : Area Years Sq.mt. IDAHO

12-3055 Boulder Creek near Leonia Sif 53 12-3065 Moyie River at Eastport 36 570 12-3075 Moyie River at Eileen 40 755 12-4110 Coeur d'Alene River near Prichard 14 335 12-4130 Coeur d'Alene River at Enaville 26 895 13-3170 Salmon River at White Bird 53 13,550 13-3375 South Fork Clearwater River at Elk City 21 261 13-3390 Clearwater River at Kamiah 55 4,850 13-3405 North Fork Clearwater River at Bungalow

Ranger Station NS 996 13-1200 Big Lost River at Wildhorse, near Chilly 21 114 13-1625 East Fork Jarbridge River near

Three Creek 16 89 13-1850 Boise River near Twin Springs 54 830 13-1965 Bannock Creek near Idaho City 17 56

WYOMING 13-115 Pacific Creek near Moran 21 160 13-320 Bear Creek near Irwin 12 UU 6 MONTANA

3505 Kootenai Creek near Stevensville 1 28. 3560 Skyland Creek near Essex 6 8. 3585 Middle Fork Flathead River near West

Glacier 18 1,128 3590 South Fork Flathead River at Spotted Bear 10 958 3595 Spotted Bear River near Hungry Horse 8 184 3600 Twin Creek near Hungry Horse 8 47 3610 Sullivan Creek near Hungry Horse 9 ilies 3615 Graves Creek near Hungry Horse 9 aif

09

Mean

elevation

Feet

4,980 4,870 4,710 4,120 3,610 6,720 5,150 5,010

4,930 8,540

7,600 6, 350 5,240

8,160 7,130

6,670 5,920

5,800 6,130 5,960 5,300 5,510 5,430

¥ U.S. GOVERNMENT PRINTING OFFICE: 1971—780-410/56 REGION NO. 8

12

Headquarters for the Intermountain Forest and Range Experiment Station are in Ogden, Utah. Field Research Work Units are maintained in:

Boise, Idaho

Bozeman, Montana (in cooperation with Montana State University)

Logan, Utah (in cooperation with Utah State University)

Missoula, Montana (in cooperation with University of Montana)

Moscow, Idaho (in cooperation with the University of Idaho)

Provo, Utah(in cooperation with Brigham Young University)