GEOLOGICAL SURVEY CIRCULAR 98 

April 1951 

TRENDS IN CLIMATE AND IN 

PRECIPITATION-RUNOFF RELATION IN 

MISSOURI RIVER BASIN 

By 

Roy E. Oltman and Hubert J. Tracy 

Compiled as Part of Interior Department Program 

for Development of Missouri River Basin 
UNITED STATES DEPARTMENT OF THE INTERIOR 

Oscar L. Chapman, Secretary 

GEOLOGICAL SURVEY 

W·. E. Wrather, Director 

Washington, D. C.,. l952 

Free on applieation to the Geological Survey, Washington~. D: C. 
TRENDS IN CLIMATE AND IN PRECIPITATION-RUNOFF RELATION IN 

MISSOURI RIVER BASIN 

By Roy E. Oltman and Hubert J. Tracy 

CONTENTS 

Page 

Abstract 

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Temperature trends . . . . . . . . . . . . . . . . • . . • • . . • 17 

Introduction ...........................•.... 

Precipitation ....•..................••...... 

Trends in the precipitation-runoff relationship. 17 

Possible explanation of·trends . • • . . • • . . . . • • . . 20 

Variation of precipitation distribution within Map of limiting water loss . . . . . . . . . . . . • . . . . • 108 

the year •........................•...• Conclusions .......... : . . . . . • • . . • . • . . . . • . . . 111 

Areal variation of precipitation ........•... References Cited . . . . . . . . . • . . . . . • . . • • • . . . • • 113 

ILLUSTRATIONS 

Figure 1. Plots of 10-year centered moving average annual precipitation with computed trend lines for 

selected weather stations in Missouri .•...............•.......•.•.........••...........•. 

2. Plots of 10-year centered moving average annual precipitation with computed trend lines for 

selected weather stations in Kansas ...................•.......•...•... ~ ....•••..•••.••.•• 

· 3. Plots of 10 -year centered moving average annual precipitation with computed trend lines for 

selected weather stations in Nebraska •..•.........••........ , ....•. , •.. , ••...... , , ...••. 

4. Plots of 10-year centered moving average annual precipitation with computed trend lines for 

selected weather stations in Nebraska ..•.•...••................•.. · ..•..•....•••• ·~ •••.••• 

5. Plots of 10-year centered moving average annual precipitation with computed trend lines for 

selected weather stations in South Dakota , .....••...... , . : ...•• · .... , •...•.•••••..••••.••• 

6. Plots of 10-year centered moving average annual precipitation with computed trend lines for 

selected weather stations in Montana and North Dakota •...•..................••••.•..•..•• , 

7. Plots of 10-year centered moving average annual precipitation with computed trend lines for 

selected weather stations in Colorado and Wyoming,.,., •..•...... , ...••••.. , .. , •.•....•••.• 

8. Long-term trends in annual precipitation in the Missouri River Basin •.. , ...• , •••....••....••. 

9. Plot of 10-year centered moving average annual precipitation with computed trend lines for 

two periods at Milan, Italy .•......•.•.•... · ....•.••..•.•.•••••.•.•••......••...••••••••.. 

10. Average monthly distribution of annual precipitation by decades for selected weather stations •••• 

11. Roses showing correlation of annual precipitation at selected weather stations and surrounding 

stations •....•..•....•.••..••...••.....•••.... , .•••...••••..••...•.•..•....•••...•••.• 

12. Plots of 10-year centered moving average annual mean temperature with computed trend lines 

for selected weather stations •....•....•..•.•..•.•.••...•.•......•..........••••.•••.•.• 

13. Relationship of annual precipitation to mean annual temperature at selected weather stations •••• 

14. Relationship of effective annual precipitation to annual runoff of Osage River near Bagnell, Mo ••. 

15. Double mass curve of measured runoff plotted against computed runoff for Osage River near 

Bagnell, Mo. . . . . . . . . • . . . • . . . . . . . . . . . ............•.......•.•.••.••..•....•..•.•..••••• 

16. Relationship of effective annual precipitation to annual runoff of Beaverhead River at 

Barratts, Mont .............. : .....••...•.....•..........•.• · .............•••••.•••.•••• 

17. Double mass curve of measured runoff plotted against computed runoff for Beaverhead River 

at Barratts, Mont ••••.....•.•....•....•.......•...•.....•......•...•...••....•.....••.•. 

18. Relationship of effective annual precipitation to annual runoff of Missouri River at· Fort 

Benton, Mont ...••..........•......•......................•••••.•.•.••.......•......••.. 

19. Double mass curve of measured runoff plotted against computed runoff for Missouri River at 

Fort Benton, Mont. • .................•...........•..•....••....•...•....•..•.•.•.•••... 

20. Relationship of effective annual precipitation to annual runoff of Madison River near West 

Yellowstone, Mont .•...•............•..........••...........•............•....•.....•.. 

21. Double mass curve of measured runoff plotted against computed runoff for Madison River 

near West Yellowstone, Mont •..•.........•.••.......•.......•...••.......••..•••.••..••• 

22. Relationship'of effective annual precipitation to annual runoff of Tenmile Creek near Rimini, 

Mont ................•....••...•......•...•....••..•........•.....•••...•••......•••••. 

23. Double mass curve of measured runoff plotted against computed runoff for Tenmile Creek 

near Rimini, Mont •.•..•...•....•....•.....•...•.•.....•.....•........•.....•....••..•. 

24. Relationship of effective annual precipitation to annual runoff of North Fork Sun River near 

Augusta, Mont. . ............•...••........•... _. ........•.........•...•...•.•.•••.. ~ •••• 

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Figure 25. 

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Double mass curve of measured runoff plotted against computed runoff for North Fork Sun 

River near Augusta, Mont ...................•............•...........•..•............. 

Relationship of effective annual precipitation to annual runoff of Marias River near Shelby, Mont. 

Double mass: curve of measured runoff plotted against computed runoff for Marias River near 

Shelby, Mont ...............••...•.......•....•..........•.•............•............ ,_ 

Relationship of effective annual precipitation to annuai runoff of Judith River near Utica, 

Mont ............................................................................... . 

Double mass curve of measured runoffplotted against computed runoff for Judith River 

near Utica, Mont .................................................................... . 

Relationship of effective annual precipitation to annual runoff of Musselshell River at 

Harlowton, Mont. . .................................................. : ............... . 

Double mass curve of measured runoff plotted against computed runoff for Musselshell 

River at Harlowton, Mont ............................................................ . 

Relationship of effective annual precipitation to annual runoff of Yellowstone River at Corwin 

Springs, Mont ...................................................................... . 

Double mass curve of measured runoff plotted against computed runoff for Yellowstone River 

at Corwin Springs, Mont ............................................................•. 

Relationship of effective annual precipitation to annual runoff of Bighorn River at Thermopolis, 

Wyo ............................................ : .................................. . 

Double mass curve of measured runoff plotted against computed runoff for Bighorn River at 

Thermopolis, Wyo .................................................................. . 

Relationship of effective annual precipitation to annual runoff of Powder River at Arvada, Wyo .. 

Double mass curve of measured runoff plotted against computed runoff for Powder River at 

Arvada, Wyo .................................... · .......•................•............ 

Relationship of effective annual precipitation to annual runoff of Little Missouri River near 

Alzada, Mont ........................................ ; ............. ' ......•........... 

Double mass curve of measured runoff plotted against computed runoff for Little Missouri 

River near Alzada, Mont ....................................................•......... 

Relationship of effective annual precipitation to annual runoff of Cannonball River at Breien,. 

N.Dak ............................................................................. · 

Double mass curve of measured runoff plotted against computed runoff for Cannonball River 

at Breien, N. Dak ............•.............................................•......... 

Relationship of effective anrtual precipitation to annual runoff of Moreau River at Promise, 

S. Dak ........•...•........•••••.••..•.... , .. , ......•.• , ... , • , • , . , , .. , . , ••.. , •• , •. , , . 

Double mass curve of measured ·runoff plotted against computed runoff for Moreau River at 

Promise, S. Dak ...... ;, ........ : ..............................•....................• 

Relationship of effective annual precipitation to annual runoff of Cheyenne River near Wasta, 

S.Dak ............................. , .............• , ........ , .......................• 

Double mass curve of measured runoff plotted against computed runoff for Cheyenne River 

near Wasta, S. Dak ..........................................•...........•........... 

Relationship of effective annual precipitation to annual runoff of Rapid Creek at Big Bend, 

S. Dak ............................................................................. . 

Double mass curve of measured runoff plotted against computed runoff for Rapid Creek at 

Big Bend, S. Dak ................................................................... . 

Relationship of effective annual precipitation to annual runoff of Belle Fourche River, near 

Belle Fourche, S. Dak ............................................................... . 

Double mass curve of measured runoff plotted against computed runoff for Belle Fourche 

River near Belle Fourche, S. Dak ........................................•............ 

Relationship of effective annual precipitation to annual runoff of Bad River near Fort Pierre, 

S.Dak ............................................................................. . 

Double mass curve of measured runoff plotted against computed runoff for Bad River near 

Fort Pierre, S. Dak ................................................................. . 

Relationship of effective annual precipitation to annual runoff of White River near qacoma, 

S. Dak ..... · ................................................................•....•.... 

Double mass curve of measured runoff plotted against computed runoff for White River near 

Oacoma, S. Dak ......•..•.............•............................................. 

Relationship of effective annual precipitation to annual runoff of Niobrara River at Dunlap, 

Nebr ...................................................................•............ 

Double mass curve of measured runoff plotted against computed runoff for Niobrara River at 

Dunlap, Nebr .............................................. · ......................... . 

Relationship of effective annual precipitation to annual runoff of James River near Scotland, 

S. Dak ................................................. ~ ..•......................... 

Double mass curve of measured runoff plotted against computed runoff for James River near 

Scotland, S. Dak. . ............................................................. · · .. · · 

Relationship of effective annual precipitation to annual runoff of Big Sioux River at Akron, Ia ... 

Double mass curve· of measured runoff plotted against computed runoff for Big Sioux River 

at A.kron, Ia ...........•............................................. · .. · · . · · · · · · · · · · 

Relationship o'f effective annual precipitation to annual runoff of North Platte River at 

Sarat?ga, Y'yo .......................................................... · · · · · · · · · · · · · 

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Figure 61. 

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9g. 

Double mass curve of measured runoff plotted against computed runoff tor North Platte River 

at Saratoga, Wyo .......•.............•.....•.......•...••..•............••.•••.•..••. 

Relationship of effective annual precipitation to annual runoff of North Fork South Platte River 

at South Platte, Colo. . ......•...........•.......... , ........••....•.•••.••••••••••.•• 

Double mass curve of measured runoff plottecfagaiiist computed runoff for North Fork South 

Platte River at South Platte, Colo .......•.........•.... ·, .•.........••..•.. ; •. , ..•.•••••• 

Relationship of effective annual precipitation to annual runoff of Clear Creek near Golden, 

Colo .....•.• , ..•.....•...• , ...................... , ..........• , . , ••.••.•.. , .••.••••• , 

Double mass curve of measured runoff plotted against computed runoff for Clear Creek near 

Golden, Colo .....•...........•..........•... , ........ , ..............••........•••••• 

Relationship of effective annual precipitation to annual runoff of Thompson River (below 

powerhouse) near Drake, Colo ........................•..................•...•..•..••. 

Double mass curve of measured runoff plotted against computed runoff for Thompson River 

(below powerhouse) near Drake, Colo ..............•....................... , ... , •...•.. 

Relationship of effective annual precipitation to annual runoff of Cache la Poudre River at 

mouth of canyon, near Fort Collins, Colo .......•.... , .•......•...............••...•...• 

Double mass curve of measured runoff plotted against computed runoff for Cache la Poudre 

River at mouth of canyon, near Fort Collins, Colo., ......................•.. , •...••.....• 

Relationship of effective annual precipitation to annual runoff of Loup River at (near) Columbus, 

Nebr ....•............•..........•..........................•.•...•.•...........•.•.• 

Double mass curve of measured runoff plotted against computed runoff for Loup River at (near) 

Columbus, Nebr. . ...........................•..................••........••...•..... 

Relationship of effective annual precipitation to annual runoff of Elkhorn River at Waterloo, 

Nebr ........•................................. · ......••...•...•••.•. , ...• , •..••...• , 

Double mass curve of measured runoff plotted against computed runoff for Elkhorn River at 

Waterloo, Nebr ......•..............•.....................•......•......•...•••.•.•.• 

Relationship of effective annual precipitation to annual runoff of Nishnabotna River above 

Hamburg, Ia .........................•........•........•.•......••..........••••.••• 

Double mass curve of measured runoff plotted against computed runoff for Nishnabotna River 

above Hamburg, Ia .......•....•...•...............•......... , .....•............•.•••. 

Relationship of effective annual precipitation to annual runoff of Nodaway River near 

Burlington Junction, Mo ...........................• , .......•.......•.••.• , . , ••. , ••.•• 

Double mass curve of measured runoff plotted against computed runoff for Nodaway River near 

Burlington Junction, Mo. , •..•... , ....................•..•.•..•....•. , ...••.•••••••••• 

Relationship of effective annual precipitation to annual runoff of Platte River near Agency, Mo •. 

Double mass curve of measured runoff plotted against computed runoff for Platte River near 

Agency, Mo .....•....................•......................•.•.••...••..•..••••.••• 

Relationship of effective an'nual precipitation to annual runoff of Arikaree River at Haigler, 

Nebr .................................•........•...•....•.•...••.....•••....•••••. • · · 

Double mass curve of measured runoff plotted against computed runoff for Arikaree River at 

Haigler, Nebr ............•...•...•...................•.•....•..........•. · · •• • · ·. •·• • • 

Relationship of effective annual precipitation to annual runoff of Smoky Hill River at Ellsworth, 

Kans .........•............•..........................................•.......•••.••. 

Double mass curve of measured runoff plotted against computed runoff for Smoky Hill River 

at Ellsworth, Kans .....................•..........•.........•............• : . .••.....• 

Relationship of effective annual precipitation to annual runoff of Saline River at Tescott, Kans .. 

Double mass curve of measured runoff plotted against computed runoff for Saline River at 

Tescott, Kans ............•.......................................................... 

Relationship of effective annual precipitation to annual runoff of Big Blue River at Randolph, 

Kans ..................•...............................................••.......•..•• 

Double mass curve of measured runoff plotted against computed r,unoff for Big Blue River at 

Randolph, Kans. . .......................•.............•••.................•.•.•••..•• 

Relationship of effective annual precipitation to annual runoff of Grand River near 9a11atin, Mo. 

Double mass curve of measured runoff plotted against computed runoffforGrand River near 

Gallatin, Mo .......................................•.....................•...•..•.•..• 

Relationship of effective annual precipitation to annual runoff of Sac River near Stockton, Mo .•. 

Double mass curve of measured runoff plotted against computed runoff for Sac River near 

Stockton, Mo ...................•................................•...•.....•...••.••.. 

Relationship of effective annual precipitation to annual runoff of Gasconade River near 

Waynesville, Mo ......•..............•.....•..••....••... ; ..•......•...•••.•.••.•••• 

Double mass curve of measured runoff plotted against computed runoff for Gasconade River 

· near Waynesville, Mo .......................•..........•.................••......••.. 

Relationship of effective annual precipitation to annual runoff of St. Mary River near Kimball, 

Alberta ..........................•.............•.........•.............•••..••.•.••. 

Double mass curve of measured runoff plotted against computed runoff for St. Mary River 

near Kimball, Alberta .....•.....................•......••..•........•.••.•..••....•.. 

Relationship of effective annual precipitation to annual runoff of Neosho River near Parsons, 

Kans ........•..... ·.o ••••••• o •••••••••••••••••••••••••••••••••••• o o •.••••••• o o •• o ••• ~. 

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Figure 97. Double mass curve of measured runoff plotted against comp'uted runoff for Neosho River near 

Parsons, Kans .........••....................................................... ·. . . . . 104 

98. Residual mass curves for Beaverhead River at Barratts, Mont. . . . . . . . . . . . . . . . . . • . . . . . . . . . • . 107 

99. Comparison of computed long-term effective precipitation with measured runoff of Beaverhead 

River Basin . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 

100. Decline of base flow during drought years as shown by Big Spring Creek near Lewistown, 

Mont............................................................................... 108 

101. Determination of limiting annual water loss for Nodaway River Basin above Burlington 

Junction, Mo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . • . . 109 

102. Relationship of winter precipitation to annual precipitation in Colorado, Wyoming.and 

Montana ...............................•......... , . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . 110 

103. Variation of limiting annual water loss with altitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 

104. Limiting annual water loss in the Missouri River Basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 

TABLES 

Tahle 1. Distribution of annual precipitation by decades for the months October to March and June 

to August ....•..•.....•..•..••.............•..............................•........ 17 

2. Tributary basins studied for trends in the precipitation--runoff relationship ....•...•..•..... 105 

ABSTRACT 

This report presents a study of trends in climate 

and in the relationship between precipitation and 

runoff in the Missouri River Basin for the period of 

available records. Long-term trends in annual precipitation are generally downward (or show a decline 

in precipitation) in the States of Montana, North 

Dakota, South Dakota, Nebraska, and Kansas, but 

seem to be indeterminate in the remainder of the 

basin. Long-term trends in mean annual temperature are generally upward (or show an increase in 

average temperature) for the entire basin. For the 

relatively short period of record available for study, 

trends in the precipitation-runoff relationship are 

found to exist for some basins draining the mountain 

ranges beginning usually about 1930, and indicate 

decreasing runoff yields under constant precipitation. The trends in the precipitation-runoff relationship are shown to be the result of concurrent 

trends in either or both temperature and groundwater outflow. A map of limiting annual water loss 

in the Missouri Basin is presented in this report. 

INTRODUCTION 

The existence of a basin-wide, long-term trend 

in annual precipitation indicating a continual decline 

in future precipitation would be a serious threat to 

agriculture. A widespread trend in the relationship 

between precipitation and runoff indicating a gradual decline in future runoff yields under equal precipitation would take out of production many irrigated 

acres in the basin. 

The Missouri Basin is shaped like a parallelogram 

with its major axis lying in a northwest-southeast 

direction. Along the western edge are the mountains of the Continental Divide; in Wyoming and 

Montana outlying mountain ranges lie roughly parallel to the Divide. Climate varies from arid in 

intermontane valleys of Wyoming to humid in Missouri. The high-altitude regions of the mountain 

ranges in the basin have a very different climate 

from that of the flat plains immediately adjacent; 

annual precipitation often exceeds 50 inches on the 

mountain peaks compared with annual totals of less 

than 10 inches in the plains. Mean annual temperature ranges, north to south, from 40 to 56 degrees 

over the Great Plains, and decreases with altitude 

in the mountains according to a definite lapse. rate 

for each locale. Because of the large areal extent 

of the Missouri Basin and of the range of climate, a 

satisfactory study of precipitation-runoff trends requires detailed investigation of many tributary basins. 

A detailed discussion of the hydrologic factors 

influencing annual runoff is beyond the scope of this 

study. One of the best concise reviews of the variables entering the runoff equation is contained in a 

recent publication of the Geological Survey.!/ The 

results of the study of trends in the precipitationrunoff relationship are explained in this report by 

citing the changes in climatic and cultural conditions 

that may have caused the observed trends. 

This report was compiled as part of the program 

of the Interior Department for development of the 

Missouri River Basin, by the staff of the Lincoln 

Regional Field Office, Special Reports an.d- Investigations Section of the Surface Water Branch, U. S. 

Geological Survey, J. V. B. Wells, Chief. 

W. B. Langl;lein · furnished valuable advice and 

constructive criticism on the method used in showing 

the trends in the precipitation-runoff relationship. 

PRECIPITATION 

Precipitation may be considered the starting point 

for studies of runoff. A study of the time trend 

of annual precipitation is a prerequisite to the study 

of trends in the precipitation- runoff relationship. 

In a subsequent section of this report the effect of 

long - term declining precipitation on ground water 

contributions to current runoff is discussed. The 

study of trends of annual precipitation was made 

with graphs of precipitation at selected long-term 

1 Langbein, W. B., and others, Annual runoff in 

the United States: U.S. Geol. Survey Circ. 52, 1949. 
weather stations to give a representative coverage 

for the basin. There are only a few long- term 

weather stations available in the western half of the 

basin; in the eastern half of the basin the available 

long-term weather stations are more numerous. 

Figures 1 to 7 show the plots of the 10 -year centered 

moving averages at the selected stations for the period of continuous record ending in 1948. A computed 

trend line was drawn through each plot. The trend 

line has a slightly different position from one computed using original unaveraged figures. Note the 

general decline in the basin precipitation during the 

decade 1930-40. 

The trend lines, only, have been plotted on a map 

(see fig. 8) to show a composite picture of the trends 

in annual precipitation for the entire Missouri Basin. 

Figure 8 indicates that there is a general downward 

trend in annual precipitation in the Great Plains but 

that there are mixed trends in humid Missouri and 

in areas in or adjacent to mountain ranges. The 

area extending in a north-south direction across the 

basin between the meridians of 96 and 100 degrees 

longitude has had a greater decline in annual precipitation than any other part of the basin. 

In general, climatic trends over long periods 

appear to follow a consistent worldwide pattern. 

Matthes.!/ has shown that glacial evidence indicates 

uniform long-term trends in world climate. Assuming that, over long periods of time, there is good 

correlation between precipitation trends in the world, 

a comparative study of the precipitation trends at a 

Missouri Basin. station with a long period of record 

and like trends at a station, located elsewhere, with 

much longer record may indicate possible trends in 

the Missouri Basin for a much longer period. 

Milan, Ital~, has the longest published record)./ 

continuous 1768- 1936, of annual precipitation for 

any weather station in the world. Figure 9 is a 

plot of 10-year centered moving average annual 

precipitation at Milan, Italy. For comparison with 

records in the Missouri Basin, the Milan record 

has been broken at the year 1833, and divided into 

two parts, so that the latter period, 1833 to end of 

record, will approximate the longest period of precipitation record in the Missouri Basin. Both the 

Milan record and Missouri Basin records show 

downward trends for the period 1833 to the present. 

However, the trend for the Milan record before 

1833 is upward, compensating for the later downward trend, and making the entire period at Milan 

show one significant level trend. It is apparent that 

the general downward trend of precipitation in the 

Missouri Basin reflects the period of record available. 

Variation of Precipitation Distribution 

Within the Year 

Annual precipitation is not only variable as to the 

total occurring in each year, but is also variable with 

2 Matthes, F. E., Hydrology (edited by 0. E. 

Meinzer), Glaciers, pp. 149-219, 1949. 

3 Clayton, H. H., World Weather Records, Smithsonian Misc. Colls., vols. 79, 90, and 105, 1944. 

5 

respect to the percentage of the annual total distributed to each month. Large changes in the distribution 

of the annual precipitation to the individual months 

have an important effect on the annual runoff produced, 

because an inch of precipitation in April will usually 

produce more runoff than the same quantity precipitated wrth equal intensity in July. Changes in the 

distribution of the annual precipitation such that a 

greater-than•normal percentage falls in the summer 

months of higher evapotranspiration demand usually 

result in annual runoff less than normal for the correspondin~ annual precipitation. 

Figure 10 shows graphically the average monthly 

distribution in percent of annual total by decades, 

from 1881 to 1940, for six weather stations in or adjacent to the basin. Table 1 is a list of the percentages of the annual total precipitated in the six months 

October to March, and the percentage of the annual 

total precipitated in the three months June to August 

averaged by ~ecades. 

No consistent variation appears to exist for the 

stations useq, and the average distribution percentages by decades vary only a minor amount from the 

average for the period 1881-1940. The percentage 

distribution within individual years, of course, varies 

widely from tihe long-term average. Apparently, there 

is no signifi<:ant trend in the seasonal distribution of 

the total annual precipitation. 

Areal Variation of Precipitation 

Precipitation measured at a single point is not a 

precise measure of the precipitation of the surrounding area. Tne accuracy with which point precipitation 

represents the precipitation on the surrounding area 

varies from • poor for individual storms to good for 

annual values. The degree of correlation found to 

exist between annual precipitation measured at two 

points indicates how well the annual precipitation 

measured at the one point represents the precipitation 

at the other. To define the areal variation in representativeness of point-measured precipitation, a key 

station was selected for the particular area under 

study, and correlations were made between precipitation measured at the. key station and that measured 

at surrounding stations. The results are graphically 

portrayed ort a map of the basin (see fig. 11) on which 

correlation roses are shown for the key stations, 

Great Falls, Mont., Bismarck, N. Dak., Cheyenne, 

Wyo., Omaha, Nebr., and Kansas City, Mo. The 

correlations are based on annual-precipitation values 

for the period 1920-48. · 

It is surprising to note how well the precipitation 

at Great Falls and Bismarck represents the precipitation for surrounding areas, compared with the results 

obtained at Omaha and Kansas City. The elongation 

of the corr¢lation. roses in particular directions is 

probably intimately associated with mean annual 

storm paths. Note that the correlation roses are not 

extended beyond the Continental Divide at Cheyenne 

and Great Falls; this was not done because of the 

lack of precipitation records at or near the Continental Divide. Actually there is an apparent continuation 

of the correlation in the area west of the mountains. 

The correlation roses show indirectly the optimum 

spacing of ·precipitation gages to obtain the same 
'6 

.. 

.&: • 

u 

.!: 50 

.!: - .... c Are lad Ia .. 45 . ... . 2 . . 0 . . . . . ~ 

- ·i ... 40 10 ·u .. • .&: • ct u 45 .e 

.!: ... .... . 40 c . . .... . .2 

Hermafl. ... ~ • ... 0 35 ~· Cit ·u • l .&: 

u 

.~ 40 30 

Kansas ity. . . . . . . . .... . . . . . . .5 . . .. . . . r!" 35 .2 . - 0 • . . . ·i 30 50 Cll ·u 

• .&: • ct ·. 45 u 

.!: .. . .!: 

lo 40 r::· .. .2 . .... ... 0 Kirk I ~ill. r • • . .. 35 I .&: • "' . ... u ... .5 40 30 

.5 .... . .... Ortgo • . ... . ... . r: ~5 . . 0 ... . . . . •t; ... . . .. . . .. . :a 30 . 50 ·u • • . . . . . . .&: • It .. 45 .I -!.. 

. .5 

St. Louis ~ 40 . . . .i . . . ... . ... . . . . . . ... ... . ..... . . ... . . 1; 

·i .. ... 35 - ·u 

! 

50 30 0.. 

Cit 

.&: • 

u 45 _._ .~ -= .. .5 S~tring eld . . .... . . .. . . . . . r: 40 

~ ... .2 

·a. 35 Cll ·u • • .&: 

ct . . . . . u 

30 . 40 .e . . . . .5 .... 35. r: warren sCI urg .. . . . . ~ 

2 30 ·a. 

·u 

! 

0.. 

1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 

Figure I.-Plots of 10-year centered movino averaoe annual precipitation with computed trend 

lines for selected weather stations in Missouri. 
7 

Ill 

!5 I: • 

u 

.E 

30 .5 

Concordia - .. ,; Ill . ·····. ~ • . 25 I: ... .E u .... . !E -- :~ 

.E 25 20 ~ 0.. r;.A Dodge City ........ . .. ··· . ~ 20 . = g .. .. ····· I: Q. u ·u 15 40 .E 

f 

0.. -~ .··· . . !5 r!' 

! .2 Emporia . u ! .. .. .5 45 30 :e. .. ·. u .5 ~ 

40 Fort iscott 0.. 

c 

0 ····· :;: .. = .E 35 30 I: 

:g. u 

u .5 

• a: ····· 25 .5 

HHS ... ... c ... ..... .2 

20 ~ ·a Ill ·u I: • 45 • u ct 

.!E 

40 . .!E .. ... . . lnd1 ~endence _._ ·. r!' .. .2 35 ······· ... Ill 

0 ! 

u 

:a. .5 

·a 30 40 • .5 

ct .. . . .. . .. ... i Lawrl riC I . · ... Ill .... ~ . 35 

• .2 I: ·a u 40 ·u .!E 30 • . 5 .. ·d: 

35 . ··· . . •____.__ .... ... •- c . . • . 2 . . . Leavenwo th ..... I: • 

2 ... u 

:g. 30 40 :!E 

u ·.~ • a: 35 c ... ~ Manha tan .E ...... 30 ·a ...... . . ·u 

• • 

• 35 ct I: 

u 

. 5 . .. ·~ 30 McP ~rson....: . . c 

0- ······· ~/ 25 . Ill 

-!!· .. . 1 ·a. u '(j 20 20 

.!E 

• a: . ... .5 

!wallace • . . . ..... .· .. . 15 r!' 

.2 

! 

10 :g. 

u 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 • 

trend 

ct 

Figure 2. -Plots of 10-yeor centered moving overage annual precipitatio" with computed 

lines for selected weather stations in Kansas. ' 
8 

en 

CIJ 

s:: 

Ainsw frth 

-.............. 

~ 

4 • • • • 

..... .. .. -----~~ .... ~~ 

• • • • I -

u 

.s 40 r--------+--------1-------~~------~--------+-------_,---------r~ 

·=· g 35 :0:: 

~ 

I 

I 

Auburn,. • 

.... .. 

······ 

.... . 

. 

.. 

30 

25 

20 

15 

en 

·a .! ·u 30 ~--------r---------r---------r---------r---------r---------r---~----r-~ 30 CIJ 

u 

.s 

0: 

en 

CIJ 

s:: 

u 

·= 

35 

.s 30 

c 

B< over Citv • 

Bioi,. • 

- . 

. . . . . 

.... 

... 

... . 

... 

. . ... 

... 

. ... .... 

. ... . .. 

. . 

0 

:0:: 

~ 25 ~---------+----------~----------~---------4----------~----------~--------~---~ 

.s 

25 ~ 

:0:: 

~ 

20 :~ 

CIJ 

0: 

·a 

·u • • • • • en 

~ 20 ~---------+----------~----------~---------4----~----~----------+---------~--~ 

.! 

u 

.s 

.s 

. ~ 

i 

~ 

·c:; 

ct 

.... .... . . . .. . . . . . ... ·.. . . ... .· 

30r--------r--------r-------~--~--~r-------~------_,--------~~ 

Columbus --•-.' ' • • • 

25 

20 

Crete . . . .. . . ... 

. 

. . . . 0 • 0 

...... .. ······· 

. .. . .. • 0 

.... .... 

. 

... . . 

. 

-

25 r--------r------~r-------~------~~------~------~--------~~ 

..... 20 I ~~-------t------~~~~;;;===~~·!4·~F====9.,~~~~~.r~··- Culber son , , , , , , , • .... ---t~~--====lr,.~~~ • • , , .. 15 • 0 • . . . . ........ . F rt Robinson ':.i..!'--...---f....!:_-•!.,!•.L.I ·+~ •. ';',-;,-r...!--t....!...:..J!.-:.&.-;,To·'":.~.~.:-. : ..... -r . . . . .. 

35 r-------~---------+--------~--------4---------~------~---------+~ ... Frer ont • ..... 30 . . ... . .. . 

. . .. . . 25 r---------~--------~~~·L------4----------4----------+----------~~-------+~ ...... 20 r-------~---------+--------~--------4---------r--------;---------+~ 

1870 1880 1890 1900 1910 1920 1930 1940 

Figure 3.-Plots of 10 -year 

with computed trend lines 

(Continued on fig. 4). 

centered moving average annual precipitation 

for selected weather stations in Nebraska 

.! 

20 .~ 

15 

10 

en 

~ 35 u 

.5 

30 .5 

25 

20 
en 

QJ 

.s:. 

(.) 

. S 

.S: 

c!' 

0 

+= 

~ 

·a. 

·c:; 

QJ 

.t 

KJ 

~ 

-~ 

.5 

c!' 

. 2 

.. 

.E 

-~ 

·u 

~ 

en 

QJ 

.s:. 

(.) 

.S 

.S 

c!' 

0 

+= 

.E 

·a. 

"2 

a: 

35 

30 

25 

20 

30 

25 

20 

15 

25 

20 

15 

10 

Genoa - .... ... 

Lin oln 

. . 

Nebraska City 

North Platte 

.. 

. 

. . . .. 

. .. . . . 

... . • .... 

. 

. . . . . 

. . -• .. 

. . . 

... . . 

. .. 

. . . .. 

. . . . ---~ o,~~ 

. . ... 

. ..... . .. . 

. . . .... . .. . . 

. . . . .... . . . . .. . . 

.. .···· .. . '• ~ ... . . . ~~ . .. 

. . . . Rave ~na :-:-; ••• . . . . . ... . . .... . . 

Scottt.,luff . . . . . . . . ..... . . . . . . 

Vale tine . . . . . . . . . . . . . . ..... 

. . . . . . ... 

....... 

.. ... . 

. . . . .. . . 

:-

.· 

. . . . . . .--. 

.. . .. . . .. 

. . . ... -

1870 1880 1890 1900 1910 1920 1930 1940 

35 

20 

25 

20 

35 

30 

25 

40 

20 

20 

15 

10 

Figure 4.- Plots of 10-year 

with computed trend lines 

(Continued from fig. 3). 

centered moving average annual precipitation 

for selected weather stations in Nebraska 

9 

en 

QJ 

.s:. 

() 

.s 

.s 

c!' 

-2 

.E 

·a. 

"() 

QJ 

.t 

en 

QJ 

.s:. 

() 

.s 

c:: 

c!' 

.2 

2 

·o. 

·u 

QJ 

CL "'" 

en 

QJ 

~ 

-~ 

.S 

c 

0 

+= 

~ 

·a. 

·c:; 

QJ 

a: 
10 

30 

25 

20 

15 

30 

~ berd.een ----=--~ _. _ ••• I ~~···· •• 

---~ . . . 

25 

. t----

...... r--.20 

Alex ndrj_Q. -• • •• 

.. -------~..-·--- ·~ I ~1---

. . .. ... 

15 

. • ----r--

~------~--------~-------+--------+--------+--------+--------+~25 

- ..... . I l -~~~~*··~··~···~~~ Broo ings 20 

·-... . . - . . ..... Ill 

cu 

.s:::. 

-~ ~ ~-------+--------~--------+--------4---------r--------+-------~--1 15 

-~ 

25 

20 

15 

10 

! 

Huron • 

......... . . . .... . . ~---------4----------~----------4-----------~--------~----------~~·~·~·~~--;-~ 30 

----------r----------:r:::~=====t~~·=·=·==·=·=·=·~~~~·=·:·::·~~~~~==~==~~~:l~] 25 ... ~ ilbonk •.. • • 

~---------+----------~----~.~.rr~----------~~--------+---------~~~.~.~.~.~~-+--~ 20 

~------~--------~------~--------~-------+--------~-------+~15 

. . . ... . . . . . 0 lrichs • • • • • •• , • • • • • 

20 

--~·=·=·=··::·:l·~·~~~~==t::P:i•=r~r~t~~j:·:·:·::·~!:~[!!!::::::~:·:•:•:,;:~~~;:::::==:;~~ • • • • • • • • • • • • ~ 15 

I • I I I I I I I I I I 

_g_ 20 ~--------~----------~----------4----r~----~-------r~~~·~·'LL-'----~--------~--~ . . . . . . . . . . . . 10 

·= r!' 15 . 2 

... 

.2 

:e. 10 (,) 

;_ 

Ill 

cu 

.s:::. 

~ 2~ 

5 

§ 20 

+= .E 

Rapid City 

... . . . ...... 

~------~-------+--------~------~------~--------+--------r~30 I I I I I I 

l----------1-------~Si~liio~UIL-~Fal~ll~==~!:'~•~•::::::::t:":•:!::~·~·~·l:.~·~•E!•;;~~!:~·~==·=·~=·=·~ 25 ... 

Speo fish • • ..... . . ..... 

.... . .. . . 

20 

... :~ 15 ~---------r----------~--------~----------~---------+----------~~-------+~ 30 cu 

0: Yankton:_ ... . . . . . . . .. . . . . . ..... . 25 .. ..... .-- - .... 20 

15 

1870 1880 1890 1900 1910 1920 1930 1940 

Ill 

! 

(,) 

.5 

·= .f 

... 

2 

:e,. 

(,) 

411 

~ 

a. 

Ill 

cu 

.s:::. 

u 

.5 

.5 

c 

-2 

2 

:e. 

u 

cu 

~ 

a. 

Ill 

cu 

.s:::. 

(,) 

.5 

·= i 

2 

:e. 

(,) 

i 

Ill 

.! 

.~ 

Ill 

.! 

.~ 

Ill 

cu 

.s:::. 

(,) 

·= 

.5 

c!' 

0 

+= 

.2 

·o. 

'ii 

cu 

a: 

Figure 5.-Plot of 10~ year centered moving average annual precipitation with 

computed trend lines for selected weather stations in South Dakota. 
11 

Montana 25 I 

.e Ill . c .1:. 

cu . 20 ~ u ... . ~ .e Bozema~ .. ... :2 . e 20 . . . . . 15 

c d: 0 

G ~ndive~· • ~ .... Ill 

15 cu .. .... .1:. 

:g. .. u u .. ..... .!: cu - 0: 10 15 .: 

Havre LL•_L . . ... . . ..... c: ......... 0 Ill . . . . . .. :0: ·cu c .1:. 20 10 :a u 

·= '(j 

·= cu 

c: 15 0: 

2 Helena. . . . . . ..... .. . .... . . Ill 

~ ..... .! ·a 10 20 u '(j .!: cu 

0: Kalis DeiiLL ___.. .... .e . .. 15 r:! Ill . . . . . . . . ... .2 cu 

.1:. 2 u 25 10 ·a .!: '(j 

.s cu 

0: c: 20 . _g --• ... Lewistown ... . .. . 2 ... .. .. . ·a . ... . ... Ill 

15 20 cu ·o .1:. 

~ u 

.: a.. ... . . . . . . 15 ·= Miles Cit, ... . .. , . .... . .... . . . .. . . . 8 . . . . . :0: 

. 10 s Ill :g. Cll 

.1:. ~ -~ 20 5 a.. 

.E 

c 15 - .......... . ....... .2 Missoula . . ... 2 . . . ·a ..... - ·o 10 Cll 

0: 

North Dakota 25 Ill 

Cll 

.1:. 

-~ 

Bismarck . . 20 ~ ...... . . :/ y -~ . • re .... ~ ...... ._, ...... . . ·~ ·-·" '"'"···. , .. . . .. . . it'·" IS: 

Ill . ..... ·a Cll '(j .1:. cu u 20 10 d: ·= 

.e . . . . . . .. c: llickin .. .2 15 . . . .. 2 . ... Cll 

Cll ·a .1:. 

·o 10 25 u. Cll .Et 

0: .s; mmestown- .. . . ..... . .. ... 20 gf Cll ... Cll - ·~f .1:. .... u ·a 20 15 

·= '2 

.s 0: 

c: ...... Williston 15 -... 2 . . . . . ..... . .. ~ .. . . . . .... :g. 10 u 

Cll 

0: 

1[ 

1870 1880 1890 1900 1910 1920 1930 1940 P-1 

Figure 6.-Piots of 10-year centered moving average annual precipitation L- I I 

I 

with computed trend lines for selected weather stations in Montana 

and North Dakota. 
12 

Wyoming 

= .s:: 

20 -~ 

II) 

(1.1 

.c 

.s 2o 

.S: 

c.~ 

0 

·.;: 

E 

a. 

·u 

(1.1 

a':: 

{f) 

Q) 

..c 

u 

15 

10 

...... ... Cheyenne • • ... 

. . . . . . Sheridan. . . - ... 

Yellowstone! Pork ~ 

. . . . .~ 20 

~ I . . ..... . c 

0 

.;::: 

E 

·a. 

·u 

Q) 

a':: 

15 

10 r i 

20 

15 

r----------

' 

Denver 

... 

Col oro do 

·----.. -.-. ····. 

. . 

. . ...... . 

........ 

. ... . . . . ...... . -

. ....... 

. .. . ..... 10 

• • • • .••••••••• 1 ••• 

1------+--- -----~-~ ---· -- -- : - -- ·------+----t---.__-+----~ 

I 

15 

10 

20 

15 

10 

15 

10 

5 

20 

i ---~- -- t'' .. ~ ~~: ____ ·_·_·_·-+-· _·_·_._·_·_·_· _· +---·-·_·_· -+-·-·_._, • ...., ....... _·--1 ._·_·-1 :: 

------.-.-.-.~~.-.~.-.-.--.~.-.-r----------+----------~.~. 5 ....... 

II) 

(1.1 

.c 

u 15 s: 

. S 

.; 

0 

:;: 

E 

·a. 

u 

(1.1 

rt 

<J) 

Q) 

.c 

u 

s 

.S 

c. 

0 

.;: 

E 

a. 

u 

(1.1 

a':: 

10 

5 

15 

. . 

1880 1890 1900 1910 1920 1930 1940 

Figure 7.- Plots of 10-year centered moving average annual precipitation 

with coftlputed trend lines for selected weather stations in Colorado 

and Wyoming. 

20 

.5 

.! 

u 

.5 

.5 

r£ 

.2 

~ :t: 

.9-

u 

~ Q. 

.! 

u 

.5 

.5 

r£ 

.2 

.. 

Sl 

·a 

'2 

~ 

a. 
1otf lOft' 104° «' 10rfl 98° 96° 40 92° 

EXPLANATION 

+50% 

u 

·~ "' c 

-- 0 0 u 

0 E 1-

0 

0 0 ~ 

u 

~ u 

~ a. 

- c c;:.:: 

0 

1-

108° 10ft' 

Figure 8.- Long-term trends in annual precipitation in the Missouri River Basin. 

9d' 

Of long-term 

trend line 

.... 

w 
(/) 

cv 

s= 

50 .--------.--------~------~--------~--------~------~--------~ 

.~ 45 

·= 

l~J i 

·~ 35 cv 

... 

a. 

30 ~------~---------L--------~--------~------~L-------~--------~ 1770 1780 1790 1800 1810 1820 1830 1840 

50 .--------r------~~------~-------,~------~------~r-------~------~r-------~------~~------~ 

(/) . . . . . .. . . . .. "5'45 • • ••••••• •••••••• •• • •• ·" - . . .-.. . . c •• • • • 

·-. • • • • • • I 

" 40 ~ • • • • • • • • • • .!! - . • • • • • • • • • • .E 

:g. 3!5 0 

~ 

a. 

_j 

30 L--------L--------~------~~-------L--------L-------~--------~--------._------~--------~------~ 

1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 

Figure 9.- Plot of 10-ye_or centered moving average annual precipitation with computed trend lines for 

two perio~s at Milan, Italy. 

-

"" 
c 

0 

:;: 

0 

~ 

·a. 

·u 

., 

15. 

1 

c 

c 

a. 

& 

0 

... 

., 

» 

0 

.... 

0 

~ 

c 

., 

" ... 

:. 

15 

10 

15 

10 

15 

5 

15 

0 

25rrTT,-rrr~~~trTTTIIIrTTT~TI-rrrTI~trrTrTTollrT~,-rrrrrTIIIIITTTirMMrrT~~rrTIII 

15 

10 

0 

1881-1890 1891-1900 1911-1920 1921-1930 1931-1940 

Figure 10.-Average monthly distribution of annual precipitation by decades 

for selected weather stations. 
0 

<llj 

.... 

,£> 

<t 

0""1 

""' 

. i 

0, 

~~-

I 

,. 

I 

0 

0, 

..... 

! 

~~--

1 

I 

:_4o 11~0 l_l...:" •qa· •96" IQ_4 o tQ2..:> IQO" 9_8° ___ 9_!)~--- 9!J0 ¥-:_ _______ 90° -- ---~~ -----. 

,-........... - ........ 

----........ "'----... ........ 

/'--~- . .. ---~'r- .. ·\ . _....--... 

( 

) 

~ ' 

Note: Numbers show degree of 

correlation computed fQf' 

period 1920 - 1948. 

,,. ··!m. 

j 

I 

I 

t' ···. - i . ...,. ..... ,} ' 1'--·- \ I 

' ) ------~, 

--r 

' l ~---------------.... I ~--~ I '. I ) -~ r ' I \ 1.-_ 

'\ 

, l 

'""'"""""' ~ =--._><--; 

( 

''t--- ) 

\_.J') 

\ 

\ 

\ f \ \ I\ 

~~' ~~ i '-- ~~) ' 

i --- ~~,~~ r ~ ,, 

(' 

t ...... ~, : ~ \ r- '-, l.; -- "--' ....... . _ _,..,.-"""-..,..... ...... _J 

"""-,"""' 

~'­-~' ,. ,., 

( 

' I 

I "", v ~""-~ 

j 

i 

I 

j,. 

:""o' 

I 

i 

! 

I 

I 

:,. 

1No 

I 

i 

~· I 

i 

I 

I 

~0 

-----,;-2~-------;-;-0°- ------,08" 'IQ6o _______ ---- 104° 102" 

-;o(,o ___ -- -- 98° ____ _ 96° 

I 94° ------g~------9'oo 

Figure 11.-Roses showing correlation of annual precipitation between selected weather stations and surrounding stations . 

. ~, .,------.,,,,,,,~-----.,,] .... ,.., ...,.,,,,--.,-.,.,,,, 

...... 

0) 
17 

Table 1. -Distribution of annual precipitation by decades for 

th th e mon s 0 c o t b er to March and June to Au_g_ust 

Station 1881-1940 1881-90 

(percent) (percent) 

October to March 

Kansas City 32 32 

North Platte 21 19 

Moorhead 25 25 

Huron 22 19 

Cheyenne 28 24 

Havre 27 28 

June to August 

Kansas City 34 36 

North Platte 44 45 

Moorhead 44 46 

Huron 44 48 

Cheyenne 34 39 

Havre 43 47 

relative accuracy of computed basin-average precipitation in drainage areas of identical shape and size 

in different geographic locations within the basin. 

It would be necessary to have precipitation stations 

more closely spaced near Omaha than near Bismarck 

to obtain the same accuracy of basin-average annual 

precipitation. 

TEMPERATURE TRENDS 

Figure 12 shows the long-term temperature trends 

found at selected stations in the basin. The trend 

lines are fitted to 10-year centered moving average 

plots of the mean annual temperature. The trend 

seems to be generally upward with the strongest upward tendency occurring in the Great Plains and arid 

intermontane valleys. The upward temperature trend 

is very likely associated with the downward trend in 

precipitation. Figure 13 shows computed regression 

lines between annual precipitation and mean annual 

temperature at selected long-term weather stations 

in or near the basin. Temperature was arbitrarily 

selected as the independent variable. The regression lines show a wide variation in slope throughout 

the basin, ranging from practically none at Williston, 

N. Dak., to a maximum 10-inch decrease in annual 

pre·cipitation for an 8- degree rise in mean annual 

temperature at Omaha, Nebr. Correlation between 

mean annual temperature and annual precipitation is 

low for the basin; at Omaha 0. 35 was the coefficient 

of correlation computed. Plotting points for individual years at Omaha have been shown to portray 

the wide scatter indicative of the practical absence 

of relationship. On the basis of the temperature 

trend to date and the relationship of annual temperature and annual precipitation, an assumption might 

be made that our climate will gradually become warmer and drier in the future. However, such anassumption would be groundless; our future climate cannot 

be accurately forecast on the basis of past performance. 

1891-1900 

(percent) 

30 

22 

26 

-25. 

28 

28 

38 

47 

46 

39 

36 

41 

1901-10 1911-20 1921-30 1931-40 

(percent) (percent) (percent) (percent) 

28 34 33 34 

20 25 22 19 

26 20 27 28 

23 20 24 25 

27 29 32 26 

24 30 23 29 

38 30 34 29 

47 39 44 42 

41 48 41 44 

45 46 45 40 

32 30 36 32 

43 39 45 45 

TRENDS IN THE PRECIPITATIONRUNOFF RELATIONSHIP 

A long - term upward or downward trend in the 

relation of annual precipitation and annual runoff in 

any portion of the Missouri Basin would be of general interest. As plans for further utilization of 

surface wat~rs for irrigation are carried out, the 

existence of a long-term downward trend- -that is, 

declining runoff yield under constant precipitation--

in the relationship of precipitation to runoff would 

become especially serious in those regions now supplied with barely sufficient water. Essentially, the 

investigations contained in this section were designed 

to determine whether equal yields of runoff resulted 

from identical annual precipitation at the beginning 

and end of the period of runoff record. If the study 

indicated a trend in the relationship for a particular 

tributary basin, further investigations were made to 

determine what changes in climatic or cultural conditions may have caused the trend. 

Unfortunately, neither the precipitation nor runoff . 

records available for the study of trends in the precipitation-runoff relationship are of ideal length or 

character. In the basin, runoff records of long duration are few. 'The number of gaging stations in 

operation prior to 1930 is hardly sufficient to define 

the variation of average annual runoff with geographic 

location. The runoff records used in the study have 

been tabulated from the published annual discharges 

corrected, where appropriate, for reductions in 

stream flow through irrigation. Some discharge 

records of long duration cannot be converted into 

usable runoff records because of uncertain amounts 

used for irrigation. Equally serious limitations apply 

to the precipitation records. In some basins enough 

weather stations were not available to allow computation of a reliable basin average annual precipitation. In tributary basins deriving their water from 

the high mountain ranges, the distribution of precipitation gages was also poor; almost all records were 
18 

J'-

i 

::J 

e 

• Q. 

e 

{!?. 

J'-

i 

2 I· 

Q. 

e 

~ 

o"-

i 

::J 

~ 

Q. • 

E 

~ 

58 

57 

56 . . .. .. 55 

47 

46 

45 

44 

4! 

42 

45 

44 

43 

42 

~~ 

Kom iCJs City, Mo. ----... 

.. . . . ' . . . .. St. Louis, Mo.- . .. 

-----.~~· .. · ....... Bism rck, N. Dok. ~ • • • 

. . . . . . . 

Huron, S. Oak. ,-:r 

Den~tr. Colo. 

~~·.· .... 

.... . .... 

. .. ... ~ 

. . . . · . 

... .. . . 

·-

. . .. .. .. 

. ... · :.:.:-:..~ 

... ~ ,. ~·_...,... 

.... . . . .. ...... 

.. -

Land r, Wyo. . ··~······ ~ . . . ...... . · -- . • • . . • • ----+------+-; 

. . ... .. Helena, Mont. ••• . . . . . ... ····· 

58 

57 ol&. 

i 

56 i 

E 

• 

55 a 

e 

f! 

54 

43 

o"- 42 .r 

::J "" 41 0 

"" • Q 

40 e 

~ 

39 

53 

01.1. 

52 ... 

z "' 

51 e 

! 

50 l 

49 

46 u • 

45 

44 

~---+--------~r----------+----------4-----------+---------~-----------+~·-·------~~---------+--------1--1 43 

1850 1860 1870 1860 1890 1900 1910 1920 1930 1940 

Figure 12 .-Plots of 10-year centered moving average annual mean temperature with computed 

trend lines for selected weather stations. 
40 

30 

20 

10 

0 

40 

30 

20 

10 

Cl) 0 

Cll 

&:. 

u 40 c: 

c: 

·-.. 30 c: 

~ c 

+-

:§. 

u 

~ Q. 

0 

:I 

c: 

c: 

~ 

20 

10 

0 

40 

30 

20 

10 

0 

40 

30 

20 

10 

0 

30 

Note: Regre 

tempe 

ssion lines have been computed on the basis of 

rature considered as the independent variable. 

19 

~----------+-------------r---------~ 

Denver~ Colo. 1874-1947 l 

Coefficient of correlation , •-0.31 

....... ~ 

- --..... 

St. Louis, Mo. 1839-1947 

r=-0.10 

Miles City, -----

Mont. 1892 -1947 

r =-0.30 

Bismarck, N. Oak. 1876-1947 

r =-0.21 

--.. 

------

Cheyenne, Wyo. 1874-1947 

~28 

40 50 6030 

Las Animas, Colo. 1868-1947 

r•-0.01 

-

Havre, Mont. 1882-1947 

............... r=-0.45 

~ 

........... ....... 

" North Platte, Nebr. 1876-1947 

r=-0.33 

Willisto.n, N. Oak. 1895-1947 

r =-0.01 

Lander, Wyo. 1893-1947 

.._ r=-0.45 

~ 

40 50 60 30 

Topeka, Kans. 1888-1947 

r•-0.21 

Helena, Mont. 1881-1947 

r=-0.37 

~ 

'- ·~ ~ .... . ,;-...,~ .. .· . ·' . 

Omaha, Nebr. 1874-1947 , =- 0.35 

Rapid City, S. Oak. 1889-1947 

!:.:-0.40 

Yellowstone Pork 1890 -1947 

-........... r = -0.22 

.............. 

40 50 

Mean annual temperature, in degrees Fahrenheit. 

Figure 13. -Relationship of annual precipitation to mean annual temperature 

at selected weather stations. 

60 
20 

collected at points on the valley floor or at points on 

the flat plains relatively distant from the mountains. 

It has been common practice to assume that the 

intrarelationship of the amounts of annual precipitation, occurring in the same basin at high altitudes 

and at the low altitudes of the weather stations, is 

such that although a true basin-average precipitation cannot be computed, the average computed from 

available low-altitude .weather stations accurately 

represents a constant relationship to the true basinaverage precipitation. Recently, several storagetype precipitation gages have been established at 

poi!lts along the Continental Divide; after these stations have been operated for a period of several 

years the assumed constancy of the relationship between high altitude and low altitude precipitation 

may be tested. 

The method used in this report for the study of 

trends in the relationship of precipitation and runoff 

is based on a graphical comparison of two variables. 

This plot, called the double mass curve, is constructed by plotting corresponding cumulative totals 

of measured annual runoff against computed annual 

runoff. The resulting double mass curve closely 

approximates a straight line if there is no change in 

the relationship between the two variables. If there 

is a change in the relationship between the two variables, the double mass curve will show the time of 

occurrence and magnitude of the change by an abrupt 

change of slope. 

Because annual runoff is a function of annual precipitation minu·s annual losses, it is necessary to 

use a synthetic quantity computed on the basis of the 

precipitation and roughly equivalent to measured 

runoff in the construction of the double mass curve. 

Briefly summarized, the procedure used for all tributary basins in this report was: preparation of a 

curve showing the average relationship between precipitation and runoff; listing of synthetic runoff values 

taken from that curve; and study of consistency of 

of computed runoff and measured runoff via double 

mass curve. 

The details of procedure are best shown by the 

study made on the Osage River Basin above the 

Geological Survey gage at Bagnell, Mo. Definitions 

of the algebraic terms used are: 

P - precipitation 

Pe - effective basin-average annual precipitation, computed from formula, 

Pe = aP0 + bP1 

P 0 - current year, basin-average precipitation 

P 1 - first antecedent year, basin-average 

precipitation 

a, b - constants such that sum of "a" plus "b" 

equals unity 

R - current-year measured runoff 

Rc - current-year computed runoff 

The values of "a" and "b" are determined by successive trial correlations so that the resulting values 

of Pe correlate best with the .corresponding values 

of R. For the Osage Basin Pe was found equal to 

0. 8 P 0 + 0. 2 P 1· The i11dividual year values of P e 

and R were used to define a curve of relationship as 

shown on figure 14. The values of synthetic runoff, 

Rc, were picked from this curve, entering with the 

known values of P e. Cumulative values of R and Rc 

were then plotted to show a double mass curve (see 

fig. 15). This plot shows no trend in the precipitation-runoff relationship in the Osage Basin. Shown 

at the top of figure 14 is a residual mass curve for 

the Osage Basin. The residual mass curve is constructed by plotting the cumulative R-Rc values 

against time. The residual mass curve is related 

to the double mass curve as follows; the changes in 

relationship between R and Rc (and hence between P 

and R) are magnified and the maximum or minimum 

point is· equivalent to the break in slope of the double 

mass curve. 

The procedure, as described above, was used on 

all the tributary basins studied for trends in the precipitation-runoff relationship. Figures 16 to 97 show 

the precipitation-runoff relationship curves and the 

double mass curves for the studies. See figure 17, 

the double mass curve for Beaverhead River at 

Barratts, Mont. , for an example of a basin in which 

a trend in the precipitation-runoff relationship was 

found. For that basin an almost uninterrupted decline in runoff relative to precipitation is indicated 

for the period since 1924. 

Table 2 contains a list ;Jf the basins studied showing the period of record, standard error of estimated 

Rc, and indicated trends in the precipitation-runoff 

relationship. With the exception of the Niobrara 

Basin, all tributary basins that showed a trend in 

the precipitation - runoff relationship drain from 

mountainous or semimountainous country. 

POSSIBLE EXPLANATION OF TRENDS 

The following hydrologic factors have important 

effect on the precipitation- runoff relationship and 

may be responsible for the indicated trends: 

Cli'matic -temperature, seasonal distribution 

of precipitation, variations in orographic effect, and long-term variations in ground-water storage; 

and 

Cultural-forest denudation, farming andconsumptive use. 

In a preceding section upward temperature trends, 

with sharp increases during the decade 1930-40, 

were shown to be general for the basin. As most of 

the declining yield trends in the precipitation-runoff 

relationship started at approximately the same time 

as ,the rapid increase in temperature, it would be 

logical to ascribe part of the trend to temperature 

effect. However, if temperature increases were 

alone responsible, generally declining yields of runoff from equal precipitation should be ·the rule for 

the entire Missouri Basin, a condition that does not 

exist. 

Seasonal variation of precipitation, discussed in a 

previous section, was shown to have remained relatively constant from 1880 to 1940 so the effect of this 

factor must be ruled out as a possible cause of the 

precipitation-runoff trends except in the mountain 
+10 

• 

I:. • 

u 

.~ 

+5 .~ 

,,; 

~ 

~ 0 0 Q. 

"0 • 

• 

~ 0 -5 

-; 

e 

3 

-lo 

1880 

60 

1892 

Cumulative 

1904 1916 

Year 1928 

departures of computed runoff from measured runoff 

21 

1940 19!52 

50r-----------~------------+-----------~-------------r------~~--------------~ 

~v ~45 t! 

21. ~ p, 815 

1!:4. .n • 

OR_ JO 44• I 8f _j.a"" ~~~~ 1!:9 

e.f ~~20. • . 09;.-~ • lfi JB ~ I a , 

~ 40r------------+------~~d~~~~~------~~----------~------------4-----------~ ~ •oo r.s .a :.!• t.;i •07 12 

~ ··~~· .~ ~ ~~~9.i,.......- .II ~ .. - J7 I! 4 

• .)~ •• Ll j /./'"40 ·,, Note: Year is lettered adjacent to plotted point • 

. 5 30 r-----~-~~.~ .• ----------~---------.~.0~.----------~----------------------~.~------------------------~~-------------------~~------------------~ 

EXPLANATION .~~ 

i 

. ·a 

u 

• 

~ 

• 

.! 20 t-------------------------1-- ~ IU 

Pe 

Effective basin-overage annual precipitation 

Po 

Current ·year, basin -overage annual precipitation 

P, 

First antecedent year, basin overage annual prec~pi tot ion 

IOr-------------~-------------;--------------+--------------r--------------~----------~ 

o~----------~4------------~8-------------~~2-------------,~6------------~2~o----------~24 

Annual runoff, in inches 

Figure 14. -Relationship of effective annual precipitation to annual runoff of 

Osage River near Bagnell, Mo. · 
750 ---------r 

I 

I 

----+---·--r c 

--0 

c 

~ 

----,------ 1 

+----------~----------~ 

l 1945 

'C 500 : ------ -- --- - ! 

::1 

Q. ---+------ E 

0 

u 

4,. 

~ 0 

:; 

E 

J 375 

250 

0 

0 

1 

t1 

I 

I I I _T ____ -- ~-- -----~-----~ 

--~------ _______ L_ _____________ -J_ _______ _L __ _ 12.5 250 375 500 625 750 

Cumulative measured runoff, in inches 

FigurP 15. -Double mass curve of measured runoff plotted against computed runoff for 

Osage River near Dagnell, Mo. 
., 

.c. " 

u 

.~ 

. ~ 

.,-

~ 

~ 0 

Q. 

~ " 

" > 

:;: 

0 

3 

e 

~ 

0 

07 

~ 

0 

+ 

ce 

CD 

0 

II 

~ 

., 

" .c. 

u 

.5 

5 

r:.-

2 

2 

a 

u 

~ Q. 

" :! 

u 

~ 1&.1 

+6 

+4 

+2 

0 

-2 

1900 

v 

1908 

v ~ 

J ~ v ........ 

~ / 

1916 1924 1932 

Yeor 

~ 

\ 

\../' 

1940 

Cumulative departures of computed runoff from measured runoff 

23 

- -

1948 

24r-------------~------------~--------------~-------------r------------~r-----------~ 

/ JS 

20r-------------r-------------+-------------~----~~~~~·~ ·~------~----+-----------~ ~~ 

1$ 

12 

8 

.41 

40 25. •1 21 .. 16 

... 10. ~ ... 2 .. , 

• ~ ~~ ;/~;s. P .22 

0 17 ;s .... JO 

Note: Year is lettered adjacent to plotted point. 

EXPLANATION 

Pe 

Effective basin -overage annual prec t pi tot ion 

Po 

Current year, basin-average annual precipitation 

P, 

First antecedent year, bas•n average annual precipitation 

4r-------------~-------------;--------------+--------------+--------------r-------------; 

0~----------~------------~------------~------------~------------~----------~ 0 2 3 4 5 6 

Annual runoff, in inches 

Figure 16. -Relationship of effective annual precipitation to annual runoff of 

Beaverhead River at Barratts, Mont.· 
24 

12 0 

: 100 .c 

u 

c: 

c: 

~ 

~ 

0 

c: 

~ 

"0 80 

:! 

:I 

Q. 

E 

0 

u 

1 

.5! 

! 

a so 

40 

20 

1----

0 

0 

l/1945 

1940 

v 

/ 0 

v 

/ .. 

/ 

l4o 

v 

20 40 60 80 100 

Cumulative measured runoff, in inches 

Figure 1 7. -Double mass curve of measured runoff plotted against computed runoff for 

Beaverhead River at Barratts, Mont. 

. 

120 
"' G 

J::. 

u 

-~ 

.: 

"'~. 

~ 

~ 

0 

Cl. 

G 

"1:1 

G 

~ 0 

:; 

E 

:I 

(.) 

C? 

ID 

+4 

+2 

0 

/ 

-2 

1895 

"' hi ~ ~ ~ 

j\ lJ v \ J ~(\ 

IV v 

1905 1915 1935 1945 

Cumulative 

1925 Year 

departures of computed runoff from measured runoff 

25 

20r-----------~-------------+------------~------~/L-·--~-------------+------------~ 

·:~s 

10 e9EI • 12 

.es 

e21. • 07 

~ 16 

26e :~15e 27• el7 

18e el4 e24 

,oe• .21~,~ 22 

48 or •4 •:e42 • d 

II 

& 

..... 

.e 

e41 • ~ 00 

... . ~v . 11• /oe 

"· 5I 

e04 

40. ~o· • 

Sle 12 .eo 12r-----------~--------~~-+----~~----~------------~------------+-------~--~ 

y::: Note: Year is lettered adjacent to plotted point. 

The measured runoff values used in this plot are. computed from reyised figures published in 

Geological Survey Circular 108, 

er-----------~-------------+--~ I 

EXPLANATION 

Pe 

Effective basin-overage annual precipitation 

Po 

Current year, basin -overpge annual precipitation 

P, 

4t-----------~- First antecedent year, basin overage annual precipitation ------+--------~ 

o~------------~----------~·~-------------~-------------~------------~-------------~ 0 2 4 

Annual. runo~f. in inches 

8 

Figure 18. -Relationship of effective annual precipitation to annual runoff of 

Missouri River at Fort Benton, Mont. 
2f1 

300 

~250 

.c 

u 

c: 

!200 

;;) 

Q. 

E 

0 

u 

100 

50 

1----··-

-~·----

190~ 

/ .... 0 

93!5 

1150 

11'' ... 15" 

.. 

1120 

1~1!5 

1910 

·-

1900 

0 

0 50 100 150 200 250 

Cumulative measured runoff, in inches 

Figure 19.-Double mass curve of measured runoff plotted against computed runoff for 

Missouri River at Fort Benton, Mont. 

I 

300 
., 

.t:. • 

u 

.!: 

+20 

+10 

.!:. 

"' • 0 

+ cP. 

U) 

d 

II 

~ 

., 

.t:. • 

u 

.5 

.5 

c.· 

0 

~ a 

·u 

• a. 

• 

-~ u 

~ 

w 

19 10 

24 

.20 

16 

12 

8 

4 

0 

0 

/ ~ ~ --........... ~ ~ 

""" '\ v---

/ 1'---

1916 1922 1928 1934 1940 

Yeor 

Cumulative departures of computed runoff .from measured runoff 

/ 

1/ J4 

!'4 t-5 

v,:~ •8. J7 .26 

,)9 !'5 8 

40. 

.. /. •5 •• e• 

p 19 .22 

••• 

~·~ b .20 

2 

. 

34 • • 31 3 

36 

I "35 

' 

Note: Yeor is lettered odjocent to plotted point. 

I EXPLANATION 

Pe 

Effective basin -overage c;mnuol preci pitotion 

Po 

Current year, basin -overage annual precipit~tion 

P, 

First antecedent year, basin overage annual precipitation 

4 8 12 16 20 

Annuol runof~ in inches 

Figure 20.-Relationship of effective annual precipitation to annual runoff of 

Madison River near West Yellowstone, Mont. 

27 

) 

" ,. 

19 46 

24 
! 

I 

---------- -----t------t------+------+--'-----4------~ 

600~-------------T-------------~------------~-------------+-------------4------------~ 

I 

:: 500 l ------ I 

I 

--- ------·----l .c 

u 

c: 

c: 

--

0 

c: 

~ 

1945 

I 

~400 t··- T7 :I 

Q. 

e 

0 

u 

/

. ·----· . Ill v --·-~--

200 1·---"-~-- -~---··------ " .... -------·- ·---1~-------+-........;-------1 i ~25 

191!0 

100 -------···· I t-""·--· --·-·--.-----~--. -· ---+---....:...----+-------

1 

1915 I 

I

I 

o~-----------~-----------L_ __________ L_ ___________ ~----------~--------~ 

0 100 200 300 40_0 500 

Cumulative. measured runoff, in inches 

Figure 21.-Double mass curve of measured runoff plotted against computed runoff _for 

Madison River near West Yellowstone. Mont. 

600 
• ! 

u 

c. 

·- +20 

.5 

i? 

0 16 + 

n.o 

m 

d 

" 

~ 

.. 

.s= " 

u 

.5 

5 12 

g· 

:;: 

2 

·a 

·u 

~ Q. 

·~ 8 u • t 

w 

4 

0 

/ 

./"'.. k/\~ 

v ~ 

t L/ ~ "'---

) 

91:; 

0 

~ 

~ \___, 

19ZO 1925 1930 1935 1540 

Year 

Cumulative dtpar tures of computed runoff from measured runoff 

~ v 

J6 

J8 7 

.n / 

fl j!5 

26, 

~ 

~6 143 

;;·/ 42 )0 

.ae 

.40 .ao 

21 

:14e f2 v .45 

II ~7 

.24 Note: Year is lettered adjacent to plotted point. 

~~ .ss 

I " EXPLANATION 

Pe 

Effective bosin-overoge onnuol prec i pi to tion 

Po 

Current year, basin -overage onnuol precipitation 

PI 

First antecedent year, bas•n overage annual precipi to tion 

4 8 12 16 20 

Annual runoff, in inches 

Figure 22.-Relationship of effective annual precipitation to annual runoff of 

Tenmile Creek near Rimini, Mont'. 

29 

~·· 

I! 45 

.. 7 

24 
30 

300 

:: 250 .c 

0 

c 

c 

--

0 

c 

~ 

~ 200 

!! 

;:) 

~ 

e 

0 

u 

·! 0 

1 a 1so 

100 

50 

--

t--

t----~· -- -·--" -~·-

·---...... --

~----------

I 

v·· .. 1940 

ItS 

1----·. 

[/'· 

/ v ... 

I / -

v 

0 v 

0 50 100 

-· 

150 200 250 

Cumulative measured runoff, in inches 

Figure 23.-Double mass curve of measured runoff plotted against computed runoff for 

Tenmile Creek near Rimini, Mont. 

300 
+5 

• "' 

~ 

u 

.5 

0 . 5 

.~ 

~ 

~ 

0 -5 Q. 

, • 

A 

I 

• > 

:; -tO 

3 

e 

3 

30 

25 

. ~ - 10 

~ w 

5 

/ ~ /\ / .... " v 

/\ I 1\/ \ v 

"'----7 \ V" / ., 

\ 

v 

1910 . 1926 

Cumulative 

1914 1918 1922 

Year 

departures of computed runoff from measured runoff 

First 

•oe 

/ 

v ~0 

EXPLANATION 

Pe 

... 

Note: Year is let ered adjacent to p btted point . 

Effective basin -overage annual preci pi tat ion 

Po 

Current year, bos•n -overage on nuol precipitation 

p; 

antecedent year, basin overage annual precipitation 

31 

1930 

•• 

0 o~------------~s~------------~,2--------------~,a--------------2L4--------------30~----------~~36 

Annual runoff, in inches 

Figure 24. -Relationship of effective annual precipitation to annual runoff of 

North Fork Sun River near Augusta. Mont. 
32 

1: 

.... 

.... 

0 

1: 

2 

60 0 

0 

200 

100 

0 

0 

I 

f 

I 

I litH! 

1/1928 

110 

j v 

1110 

100 200 300 400 !500 

Cumulative measured runoff, in inches 

Figure 25.-Double mass curve of measured runoff plotted against computed runoff for 

North Fork Sun River near Augusta, Mont. 

600 
lit 

I: • 

u 

.5 

.5 

.. -. 

~ 

~ 0 

Q. 

"0 • 

• > 

:0: 

0 

:; 

e 

.::J 

(.) 

c 

• 0 

+ rP 

U» 

d 

II 

~ ..... 

= I: u 

.5 

.5 

t 

0 

"i 

·u 

• 

~ 

. ~ 

i 

w 

+12 

+8 

+4 

0 ~ 

\ 

-4 

1912 

24 

20 

16 

12 

8 

4 

0 

vv ---....... 

/ ~ \ !/ ~ 

l/ '--

~ 

1\ 

I \ II"-

v 

1918 

fl 

~P..,, 

':t4 

2 

1924 1930 1936 

Yeor 

Cumulative departures of computed runoff from measured runoff 

/~ • 

"15 .a• "24 .211 

.,42 

•s .ra 

.a• 2 21., 

.a • 

"14 

.,17 II., ·'"- .,41 •at ao. Jl .. Ill 

"ltl 

... ' .ae.18 

Note• Year· is lettered adjacent 

.ae /-.1 

~10 

... , 

EXPLANATION 

Pe 

Effective basin-overage annual' precipitation 

Po 

Current year, basin -overage annual prec ipi totion 

~. First antecedent yeor, basin overage annual precipi to tion 

4 6 8 

Annual runoff, in inches 

1942 

to plotted 

10 

Figure 26.-Relationship of effective annual precipitation to annual runoff of 

Marias River near Shelby, Mont. 

33 

1948 

.,27 

point. 

12 
34 

r--

240 

:200 t------ - ·-- .,;: 

u 

c; 

c; 

.... 

0 

c; 

~ 

'0 

! 

::J 

Q. 

e 

0 

u 

Gl 

.~ 

B 

::J 

e 

::J 

u 

r-----------r------- - 160 !.t_I94!S 

I 

0 

120 r----- ----~----- I I 

I 

I 

eo 

40 1-------

0 

0 

/ 

/ose 

/ v 

v-1920 

I i 

40 80 120 160 200 

Cumulative measured runoff, in inches 

Figure 2 7.-Double mass curve of measured runoff plotted against computed runoff for 

Marias River near Shelby, Mont. 

240 
• "' s:. 

u 

-~ 

-~ •. 

~ 

~ 0 

Q. 

., •

• > 

:s 

:; 

e 

:I 

0 

~ II 

~ 

• "' s:. 

u 

.5 

~ 

r;· 

-~ 

~ ·a 

·u 

~ Q. 

• 

~ u 

~ 11.1 

+12 

+8 

+4 

0 .......~ 

1920 

20 •4t 

15 

.40 

·" 

.37 

/JI.ae 

10 

/' ~ 

I ~ ~ 

v \ ~ r1926 1932 1938 .1944 

Year 

Cumulative departures of computed runoff from measured runoff 

~ )'5 

}9 

.21 45_ 

.H 

.29 

14 

4~ 1-'5 

se. 

~'5 

·2~5 .28 ~2 28 

~0 .24 

Note: Year is lettered adjacent to plotted point. 

EXPLANATION 

Pe 

I 

Effective basin -overage annual prec i p itotion 

Po 

5t------- Current year, basin -average annual precipitation 

p• 

First antecedent year, basin average annual precipitation 

35 

1950 

o~--------~------------~2-----------~3~~----------4~------------~5------------~6 

Annual runof~ in inches 

Figure 28.-Relationship of effective annual precipitation to annual runoff of 

Judith River near Utica, Mont. 
36 

Ill 

4b 

~ 

u 

c 

.~ 

.... 

.... 

0 

c 

~ 

'a 

: 

:I 

Q. 

E 

0 

u 

I • I 

u 

60 

/1945 

v 50 

40 

~,.a 

!0 I 

Ill 

1110 

/ v 20 

10 

0 l/ 

0 

/ 

10 ~0 30 40 eo 

C.umulative measured runoff, in inches 

Figure 29. -Double mass curve of measured runoff plotted against computed l'Unoff for 

Judith River near Utica, Mont. 

eo 
Ill 

J: • 

u 

.!: 

.!: •. 

~ 

~ Cl 

Q. 

~ • 

·> • 

:;: 

Cl 

:; 

e 

:I 

0 

C? 

If) 

0 

ce 

... 

d 

II 

! 

= J: u 

.5 

e 

.~ 0 

·i 

'ij 

! 

Q. 

.~ 

u • :t: 

I&J 

+16 

+12 

+8 

+4 , 

+01 904 1912 1920 1928 1936 

Year 

Cumulative departures of ·computed runoff from measured runoff 

37 

1544 IS !52 

25r-----------~-----------r----~-----+------------~----------4-----------~ 

20 

15 

10 

.o7 

J7 

ei !7.14 · zo 

1.

3_7' 'A.. .r· :y Jl Nolo• Y- II lotion d adjacent to plotted point. 

EXPLANATION 

Pe 

E fective basin-overage annual precipitation 

Po 

Curr~nt year, basin -average annual precipitation 

P, 

5~------------~---------- First ant~cedent year, basin average annual precipitation------~ 

o~------------~2------------~4------~----~6~------------~e------------~~o------------~ 

1 nnuol runoff. in inches 

Figure 30.-Relationship o effective annual precipitat~on to annual runoff of 

Mussels.~ell River at Harlowton, Mont. 
38 

... 

., 

.c: 

Co> 

c: 

c: 

-

0 

c: 

~ 

, 

: 

:I 

Q. 

e 

0 

Co> 

., 

> 

+= 0 

-; 

E 

:a 

u 

120 

100 

I /'- -···----~· 

I ;·~ 

1 

/ 

/-

/ ~ 

80 

60 

40 

20 

0 / 

0 

/ 

20 40 60 80 100 

Cumuloti ve measured runoff in inches 

Figure 31.-Double mass curve of measured runoff plotted against computed runoff for 

Musselshell River at Harlowton, Mont. 

120 
+20 

IIJ 

! 

u 

.5 

+15 . 5 

.-· 

f 

! +10 a 

Q. 

'0 • 

I 

; +5 - i 

3 

0 1910 

30 

25 

i? 

"' 0 20 + tP 

CD 

~ 

~ 

., 

CD 

.c 

u 

.5 

.5 15 

rt 

0 

~ Q. 

u 

~ Q. 

CD 

-~ 

u 10 CD 

~ 

5 

/\ 

J "--v ....... 'I\ -/ ~'----~ 

I v \ 

- ~ I \ v v \ 

1916 1922 1928 1934 1940 

Ytor 

Cumulative departures of . computed runoff from measured runoff 

y·•s 

.15 0 17 ••• ·" ••• 44 'I ·•• . ~s 

. ·~ r.. 40 10 51 

50•41 J.C .a• .s1 ~? •• ••• ·" 

•aa 

Iii a 

/ . . .. .(" •50 s/•,, 

Note: Year is lettered adjacent to plotted point. 

EXPLANATION 

Pe 

Effective basin -overage annual prec i pi tot ion 

Po 

Current year, basin -overage annual precipitation 

P, 

First antecedent year, basin overage annual precip ito tion 

~ 

4 8 12 16 20 

Annual runoff, in inches 

Figure 32.-Relationship of effective annual precipitation to annual runoff of 

Yellowstone River at Corwin Springs, Mont. 

39 

IS 

24 
40 

::500 

.s:: 

u 

c:: 

c:: 

--

0 

c:: 

2 

~--

I 

l- -- -

I 

200 

100 l 

I 

I 

I 

I 

I 

I 

I 

I 

0 

0 

/1945 

/' 

940 

/ 

v 

0 ~----. 

/ 

v 

I 

/ 

I 

1915 

100 200 300 400 500 

Cumulative measured runoff, in inches 

Figure 33.-Double mass curve of measured runoff plotted against computed runoff for 

Yellowstone River at Corwin Springs, Mont. 

600 
• 

&:. • 

u 

.!: 

.!: 

,; 

~ 

t 

0 

a. 

"0 • 

• 

~ 0 

"5 

E 

::ll 

(,) 

i' 

II) 

c:i 

II) 

~ 

d 

II 

~ 

lit 

&:. • 

.~ 

.5 

.~· 

0 

i 

·u 

f 

a. 

• . ! 

~. I&J 

+8 

+4 /~ I"-~ 

---1\ vv / "\ ~ _.........._ ' / 0 '-......./' ~ 

-4 

1900 

25 

20 

is 

JO 

5 

1908 

F ~rst 

1916 1924 1932 

Year 

Cumulative departures of computed runoff from measured runoff 

0~ 

··~ 

•e ••. oe J 4 

~' / • 21 44 .• ot. 

·us ••a ... a~ -~~ . 07. 

a•. .a• ,.,i •II 

e22 

10. ar. II 

ee• .ao •a 

•at ••• •tl5 

!4~p ir. oa. ~~ sa .17 

oz. i ~ .32 

.315 

1940 

II 

..o• 

Note: Year is lettered adjacent to plotted point. 

EXPLANATION 

Pe 

Effective basin -overage annual precipitation 

Po 

Current year, basin -overage annual precipitation 

PI 

antecedent year, basin overage annual precipitation 

2 j 4 5 

Annual runoff, in inches 

Figure 34.-Relationship of effective annual precipitation to annual runoff of 

Bighorn River at Thermopolis, Wyo. 

r"-.. 

1948 

. 

24 

6 
180 

:: 150 .1: 

u 

c 

c 

... 

0 

c 

~ 

'a 120 ~ ~ 

Q. 

e 

0 

u 

.~ 

s 

~ a go 

60 

30 

I 

0 

0 

V"~ 

940 

193& 

7 

/ & 

v 

191& 

1910 

1905 

30 60 90 !20 150 

Cl.!mulotive meosureG r~JOOff, in inches 

Figure 35.-Double mass curve of measured runoff plotted against computed runoff for 

Bighorn River at Thermopolis. Wyo. 

180 
lA 

" .t:. 

u 

.~ 

.~ 

f/1-

~ 

z 

0 

Q. 

'"0 • 

~ " 

0 

~ 

E 

::J 

(.) 

C? 

It) 

0 

+ rP 

d """ 

II 

~ 

lA 

.t:. • 

u 

.~ 

.~ 

r:.· 

.2 

:2 

·a 

·c:; 

• 

~ 

• 

~ u 

l 

w 

+4 

+3 

+2 

+I 

0 

1915 

25 

20 

15 

10 

5 

:',.. 

/ ~ - v --./ 

~ ~ 

I ~ 

) " f\ 

l/ __./ \ 

1921 1927 ~33 1939 1945 

Cumulative departures of . comput:'d runoff from measured runoff 

~ 

/ 

/ 

v 

~4 

~s .24 

.4'5 28 :,

~ 8 ·" .20 • 26 

v ~~/ 

3'5 .25 2 ~30 

s .17 40"3S 

~ 2 

. 

5e Note: Year is let ered adjacent to plotted point: 

EXPLANATION 

Pe 

Effective basin-overage annual precipitation 

Po 

Current year, basin -overage annual precipitation 

P, 

First antecedent year, basin overage onnuol precipi to tion 

2 

AMuol runoff. in inches 

Figure 36.-Relationship of effective annual precipitation to annual runoff of 

Powder River at Arvada, Wyo. · 

43 

.2'5 

3 
44 

.., 

" .1: 

u 

c: 

c: 

~ 

~ 

0 

c: 

~ 

, 

~ :I 

Q. 

E 

0 

u 

" Ill 

i 

:I 

E 

:I 

u 

.-----------...------------...-

-- ------ ----------+---

I 

i 

30 ---- - ----+---------+----------t---------t--------+ 

I 

25 -- --------------t----------- ---- ---+----+--

20 

IS ----------~---

5r------------r-~---------+------------~-------------+-------------4------------~ 

o~------------~----------~------------~------------~--------------~------------~ 

0 5 10 15 20 25 

~umulotive measured runoff, in inches 

Figure 37. -Double mass curve of measured runoff plotted against computed runoff for 

Powder River at Arvada. Wyo. 

30 
., 

s: • 

u 

.!: 

.!: 

ID 

+6 

; 

0 0 

3 

E 

c3 

30 

25 

C? 

~ 20 

o? 

en 

d 

II 

~ 

., 

ID 

s: 

u 

.5 

.5 

15 

r:;~ 

.2 

:2 

·a. 

·u 

f! 

Q. 

ID 

-~ 10 

~ w 

5 

(\ 

, 

.31 35 

·'9 .34 

.31 

45 

............. 

j '1 I ~ r ~ 

v v V' 

. I 

.·~ " 

v 

1920 1930 1940 1950 

Year 

J1 

Cumulative departures of computed runoff from measured runoff 

Note: Year is lettered adjacent to plotted point. 

EXPLANATION 

Pe 

. ·------------~--------------~ 

Effective basin -overage annual precipitation 

Po 

Current year, basin -overage annual precipitation 

P, 

First antecedent year, basin overage annual precipitation 

0 o~------------~2--------------~4--------------~6--------------e~------------~~~o------------~~2 

Anriual runof~ in inches 

Figure 38.-Relationship of effective annual precipitation to annual runoff of 

Little Missouri River near Alzada, Mont. 
46 

• ., 

r. 

u 

.~ 

c: 

--

0 

c 

~ 

, 

:! 

:a 

Q. 

E 

0 

u 

• .! 

i 

i 

:I 

u 

t---

I 

I 

120 ---1 I 

I I 

I I 

I 

I -----~-------- i 

---------·-t ------ -·- l ------

I 

100 

I 

I 

I 

! 

! i 

I i I 

j ___ -- ----~- ~---r-- - -

I 

I v·· .. -·--.. -- -~~. --~- 1--·---·--·--··-

80 

60 

1940 

1955 

1950 

40 

1925 

20 

v 5 

0 

0 

v 

20 40 60 80 100 

C_umulotive measured runoff, in inches 

Figure 39.-Double mass curve of measured runoff plotted against computed runoff for 

Little Missouri River near Alzada, Mont. 

120 
., 

CD 

s::. 

u 

·= 

·= 

.,-

Ill 

~ 0 

a. 

CD 

~ 

CD 

~ 0 

3 

E 

:I 

u 

-tl 

0 

-r 

-2 

-3 

1910 

30 

25 

5 

~ 

\ 

~ 

1920 

--......,... y \ r ~ r -~ ~ \I 

v 

1930 1940 1950 

Year 

Cumulative depar1ures of computed runoff from measured runoff 

}1 

J5 

Note: Year is lettered adjacent to plotted· point. 

EXPLANATION 

Pe 

Effective basin -overage annua I precipitation 

Po 

Current year, basin -overage annual precipitation 

P, 

First antecedent year, basin overage annual precipitation 

47 

o o=-------------~------------~------------~------------~2------------~------------~3 

Annual runof~ in ~ches 

Figure 40.-Relationship of effective annual precipitation to annual runoff of 

Cannonball River at Breien, N. Dak .. 
Ill 

u 

.c: 

u 

c 

-~ 

.... 

.... 

0 

c 

~ 

, 

:! 

:I 

Q, 

E 

0 

u 

1 

a 

-; 

e 

:I 

u 

25 

20 

15 

10 

5 

0 

0 

1145 

1140/ 

.~ 1935 

1930 

/' 

1925 

19,.... 1922 

1915 

5 10 15 20 25 

Cumulative measured runoff, in inches 

Figure 41.-Double mass curve of measured runoff plotted against computed runoff for 

Cannonball River at Breien, N. Oak. 

30 
+2 

.. 

&. • 

u 

.5 

+I 

.5 

.... 

~ 

~ 

5 0 Q. 

, • 

• > 

; -I 

I 

3 

25 

C? 

., 

o2o 

+ rP 

,.. 

d 

II 

~ 

15 

.~ i 10 

~ 

5 

0 

........ 

"""'~----. 

0 

-

1932 

- ~ """-

~ """ I ~ 

l 

\ v 

1936 1940 1944 

Ylar 

Cumulative departures of computed runoff from measured runoff 

Note: Year is lettered adjacent to plotted point. 

EXP.LANATION 

Effective basin-overage annual precipitation· 

Po 

Current year, basin -overage annual precipitation 

P, 

First antecedent year, basin overage annual precipitation 

2 

Annual runoff, in inches 

1948 

Figure 42. -Relationship of effective annual precipitation to annual runoff of 

Moreau River at Promise, S. Dak. · 

49 
50 

., 

" .I: 

u 

c 

c 

.... 

-

0 

c 

~ 

, 

! 

::. 

Q, 

E 

0 

u 

: 

j 

i 

:I 

u 

12 

10 

8 

6 

4 

2 

0 

0 

l/1945 

/ 

/ 

r 

I 

1940 

II 

/ 

v 1930 

2 4 6 8 10 

Cumulative measured runoff, in inches 

Figure 43.-Doublt: mass curve of measured runoff plotted against computed runoff for 

Moreau River at Promise. S. Dak. 

12 
Ill 

Ill 

s:. 

0 

-~ 

-~ 

,.~ 

~ 

z 

0 

Q. 

Ill 

, 

Ill 

> 

:; 

:; 

E 

:J 

0 

C? 

0 

+ 

0.0 

en 

d 

II 

If 

Ill 

Ill 

s:. 

0 

5 

5 

r::.~ 

~ 

E 

Q 

u 

Ill 

li 

Ill 

·~ 0 

Ill 

;: 

w 

+.6 

+.4 

+.2 

0 

-.2 

1928 

25 

20 

15 

10 

5 

0 

0 

/ 

- /"' v~ 

~ I\ 

~ v-v \! ~ 1\ 

\ 

\ 

19:32 19:36 1940 1944 

Year 

as. 

Cumulot•ve departures of computed runoff from measured runoff 

.,. ~ 

v~ 

... y~, Note: Year is 

EXPLANATION 

Pe 

lettered adjacent to plotted point. 

I 

I 

Effect•ve basin-overage annual precipitation 

Po 

Current year, basin -overage annual precipitation 

P, 

51 

1948 

First antecedent year, bas•n overage annual precipitation +---------+----------1 

0.2 Q4 0.6 

Annual runof~ in inches 

0.8 1.0 

Figure 44.-Relationship of effective annual precipitation to annual runoff of 

Cheyenne River near Wasta, S. Dak. · 

1.2 
52 

Ill) 

., 

.c:: 

u 

c: 

.~ 

-

0 

c: 

~ 

, 

: 

~ 

Q. 

e 

0 

u 

• 

~ !2 

i 

~ 

u 

12 

10 

/~ 

/ 

/ 

/940 

8 

6 

,. .. / 

/ 

/ 

4 

2 

0 v 

0 

v 

2 4 6 8 10 

Cumuloti ve measured runoff, in inches 

Figure 45. -Double mass curve of measured runoff plotted against computed runoff for 

Cheyenne River near Wasta, S. Dak. 

12 
.. 

u 

s:. 

u 

.!: 

.!: 

.. -

~ 

~ 0 

Q. 

u 

"0' 

I) 

> 

:;::: 

0 

3 

.E ::1 

0 

'i 

• 0 

cf 

co 

d 

II 

~ 

s:. = u 

.E 

.5 

.~-

c; 

"i ·u 

! 

Q. 

·~ u 

~ I&J 

... a 

+4 v 

0 

( ~ N' 

-4 

1915. 1921 

30 

25 

20 

,, 

V\v-,...__.-....., 

/ ~ I--- ......... 

"" ~ . 

1927 1933 1939 

Yeor 

Cumulative departures of computed runoff from measured runoff 

1,- ~7 

.. .26 / 15 . . . v .e 

v 

.. ftl ·~ ... 

·" •• 

,. all 

••• 

1945 

.to 

., .11 I'\ v Note: Year it I ttered adjacent to plotted point. 

IS 

4o 

10 

5 

. ./ .JI 

"IT 

EXPLANATION 

Pe 

Effective basin-overoQe on.nuol preci pitotion ,. 

Po 

· Current year, basin -overoQe annual precipi totion 

PI 

First antecedent year, basin overage annual precipi tot ion 

3 6 

Annuol runoff, in inches 

Figure 46.-Relationship of effective annual precipitation to annual runoff of 

Rapid Creek at Big Bend, S. Oak. · 

53 

9 
54 

120 

Ill 

., 100 z: 

u 

c 

c 

--

0 

c 

~ 

'a 80 ~ 

::1 

Q, 

E 

0 

u 

40 

20 I 

0 

0 

~-- ------------

1915 

/ .... --~-- /940 

------- -- -- 195 ./ 

/ 

v 

1/ 

/o2s 

20 40 60 80 100 

Cumulative measured runoff, in inches 

Figure 4 7. -Double mass curve of measured runoff plotted against computed runoff for 

Rapid Creek at Big Bend, S. Dak. 

:--

120 
• 

s:. • 

u 

.~ 

.~ 

.,.· 

~ 

~ 0 

c. 

, • 

• > 

:;:: 

0 

3 

E 

::J 

0 

a: 

• 0 

+ rP 

CD 

d 

II 

~ 

• 

s:. • 

u 

.5 

.e 

t 

Cl 

i ·u 

• 

~ 

• . ~ 

~ ~ 

+2 

+I 

- / 

0 

-I 

L ~ 

1916 

vv 

1\ I 1\ 

\I \ 

\ I r\. 

1922 1928 1934 

Year 

---" 

Cumulative departures of computed runoff from measured runoff 

. 55 

~ 

1940 1946 

30r-------------------,---------------~--------------------~---------------r----------------------r---------------~ 

25r-------------r-------------+-------------~------------~-------------+------------~ 

20 

IS 

10 

.23 

.• 27 

.~ 

~ ... 

Note: Year Is 

EXPLANATION 

Pe 

adjacent to plott'ed point. 

Effective basin -average annual precipitation 

Po 

Current year, basin-average annual precipitation 

P, 

First antecedent year, basin overage annual precipitation 

5r------------------+--------------~------------~r--------------+--------~----~------------_, 

o~------------.~6----~------~~~.2~--------~-~~.8~----------~2~.4~----------~3~.o~----------~3.6 

Annual runoff, in inches 

Figure 48.-Relationship of effective annual precipitation to annual runoff of 

Belle Fourche River, near Belle Fourche, S. Dak. 
56 

., 

" .c 

u 

c: 

c: 

--

0 

c: 

~ 

"0 

! 

::. 

Q. 

e 

0 

u 

.! " 

0 

1 

::. 

u 

60 

50 

40 

30 

20 

10 

v 

0 

0 

v 

10 

1920 

-·-

ll.·~ 5 

b 

V 19Zl5 

20 30 40 50 

Cumulative me.osured runoff, in inches 

Figure ·49.-Double mass curve of measured runoff plotted against computed runoff for 

· Belle Fourche River near Belle Fourche, S. Dak. 

·--

60 
-t-1.5 

+1.0 -~ 

.,.~ 

~ :::J 

~+0.5 Q, 

'Q • 

• 

~ 0 0 

3 

E 

:::J 

0 

( ~ 

J".. / 

LJ - '\V ............. ..,.... r---

-0.5 1925 1929 1933 1937 1941 

Year 

1945 

cc 

0 

+ rP 

en 

d 

II 

~ ..... 

• 

1: • 

.~· 

.e 

.J~ 

~ ·a 

·u 

f 

Q, 

• 

-~ u • :t: 

1.aJ 

20 .t:l/ ~1 IS u'f' • ••a 

1'" 

10 lt.· •as 

5t-------

Cumulative departures of . computed runoff f;om measured runoff 

Note: Year is. lettered adjacent to plotted point. 

EXPLANATION 

Pe 

Effective basin-average annual precipitation 

Po 

Current year, basin -overage on nuol precipitation 

PI 

F~rst antecedent year, bosin overage annual precipitation 

. 57• 

0 o~-----------~------------~2------------~3~------------4~------------~5------------~6 

Annual runoff, in inches 

Figure 50.-Relationship of effeative annual precipitation to annual runoff of 

Bad River near Fort Pierre, S. Dak. 
58 

2 

:: 10 J:. 

u 

.: 

.: 

-0 

c: 

~ 

, 8 

~ 

:::1 

a. 

e 

0 

u 

G.l 

> 

.. 

0 

:; 

~ 6 u 

4 

2 

194fl 

/ 

/ 

v 

/. 

v 

/ 

l/ 

/ 

1930 

2 4 6 8 10 

Cumulative measured runoff, in inches 

Figure 51. -Double mass curve of measured runoff plotted against computed runoff for 

Bad River near Fort Pierre, S. Dak. 

12 
59 

+.4 

!" .~ 

-- . ~ 

~ 0 

a. 

, • 

• 

+.2 

0 I \ I 

/ h I 

v I \ I r~ \V ~ 0 -.2 -; 

! 

;_o 

" 

~ 

lit 

.c • 

u 

.5 

~ 

r;· 

0 

~ a. 

·u 

~ a. 

• 

~ u 

~ LLI 

-.4 

19 25 ~ (\ 

1929 \;._../ 1933 !£37 1941 1945 or Cumulative departures of computed runoff from measured runoff . 

30~----------~------------~------------~-------------r------------~----------~ 

25~----------~-------------+-------------+~--------~~-r------------~----------~ 

.J-~~ 

.... ~ / 

20 

15 

.40 

~4 .H 

10 

/ .44 

Note: Yeor is lettered adjacent to plotted 

EXPLANATION 

Pe 

Effective basin -ave.rage annuo 1 precipitation 

Po 

Current year, basin -overage annual precipitation 

P, 

· First antecedent year, basin o~eroge annual precipitation 

point. 

5~-------------------+---------------------;----------------------~-------------------+---------------------~-------------------; 

2 

Annual runoff, in inches 

Figure 52.-Relationship of effective annual precipitation to annual runoff of 

White River near Oacoma, S. Dak. · 

3 
110 

., 

., 

.s::. 

u 

c 

.~ 

-

0 

c 

2 

'I 

.. 

~ 

Q, 

e 

0 

u 

., 

,. 

j 

~ 

E 

~ 

u 

12 

10 

8 

6 

4 

2 

0 

0 

/~·· 

v 

v 

/ 

1~40 

/ 

19~ v 

2 4 6 8 10 

Cumulative measured runoff, in inches 

Figure 53.-Double mass curve of measured runoff plotted against computed runoff for 

White River near Oacoma, S. Oak. 

12 
-t0.6 

.,. 

.c • 

u 

·c 

·- +0.4 

.: 

.,.~ . 

~ ::I 

~+0.2 

Q. 

"0 • 

• > 

-~ 0 

3 

E 

::I 

0 

cc 

In 

25 

;; 20 

r:f 

It) 

Cf! 

~ 

= .c 

-~ 15 

.5 

5 

/ 

0 0 

/ -----~ 

1928 

~ ~ 

-

v-~ 

~ 

~ 

1932 1936 1940 

Year 

Cumulative departures of computed runoff from measured runoff 

1944 

··~· 

v 

y 

F~rst 

••• 

,41 ,aa 

,58 / •s• ,25 

•39 

~ ,ae 

3~ 

• 

~0 / 7 

Note: Year is lettered adjacent to plotted 

EXPLANATION 

Pe 

Effective basin -overage annual prec i pi tot ion 

Po 

Current year, basin -overage annual precipitation 

P, 

antecedent year, basin average annual precipitation 

.10 .20 .30 .40 .50 

Annual runoff, in inches 

Figure 54.-Relationship of effective annual precipitation to annual runoff of 

Niobrara River at Dunlap, Nebr. 

••• 

point. 

.60 
62 

en 

Ql 

.1: 

u 

c: 

c: 

... 

... 

0 

c: 

2 

, 

! 

:t 

Q. 

e 

0 

u 

Ql 

> 

i 

i 

:t 

u 

12 I 

I 

10 

8 ··-·-- Jt42 

940 

6 ----·-·--- -

4 

2 

0 

0 

v 

/ I 

I 

I -· 

/~ ,/ r --- --

I 1925 I I 

I , I 

I I , I 

I 

---------~------------_1__ _________ ___L__- I 

2 4 6 8 10 

Cumulative measured runoff, in inches 

Figure 55. -Double mass curve of measured runoff plotted against computed runoff for 

~hobrara River at Dunlap, Nebr. 

I 

12 
., 

II) 

~ 

u 

.~ 

.~ 

.,·. 

~ 

~ 0 

Q. 

II) 

"C 

II) 

~ 0 

3 

E 

:I 

0 

£ 

If) 

0 

+ rP 

.... 

d 

II 

~ 

., 

II) 

~ 

u 

.5 

.5 

r:t 

2 

~ a 

·u 

II) 

Q. 

II) 

~ u 

~ 

w 

63 

+4 

+3 

+2 

+I 

A 

/~ ~ j\ 

v""--"" u \ If 

~ \ I 

v 

1930 1935 1940 1945 

Year 

Cumulative departures of computed runoff from measured runoff 

24~------------r-------------~------------~------------~,~--~4 ~2~ ~-------r~~~------~~ 

~ 

15 ~ 

~·'" 

20~----------~~--------~~~~-----------+------------~--------~--~------------; 1' v--

16 

12 

8 

se. • 

)lv~ 

4d -----------4------------+------------+--~--------~--------~~ 

~ )7 Note: Year is le:t ~red adjacent to plotted point. 

EXPLANATION 

Pe 

Effective basin -overage annual prec i p itotion 

Po 

Current year, bos!n -overage annual precipitation 

P, 

First antecedent year, basin overage annual precipitation 

4~------------~------------~--------------+--------------+--------------~------------; 

.I .2 .3 .4 .5 

Annual runoff, in inches 

Figure 56.-Relationship of effective annual precipitation to annual runoff of 

James River near Scotland, S. Dak. 

.6 
II) 

Cll 

s:. 

u 

c: 

c: 

-

0 

c: 

~ 

"0 

~ ~ 

Q. 

e 

0 

u 

64 

3r--------------+--------------4---------------r-------------~---------------r------------~ 

2 ------------- ··----------+----

-····-· --- ----- - --·------ --. - ....• - ..... . 

v ----------~ -·---+-------

/ 

9!5 

/ 

1940 

_ __._ --1----·-----

2 

Cumulative measured runoff, in inches 

Figure 57 .. -Double mass curve of measured runoff plotted against computed runoff for 

James River near Scotland, S. Dak. 

3 
+I 

• 

1:. • 

u 

·= +.~ 

·= •.. 

~ 

~ 0 0 

Q. 

"0 • 

• 

·~ 0 -.5 

3 

E 

::I 

0 

30 

25 

(? 

., 

0 20 + cf 

.... 

0 

II 

~ 

., 

1:. • 

u 

.5 

15 

.5 

5 

00 

I ~ ~ I/ 

"'-. v '\ L/ ~ .......... i'... I 

"---\} 

.1930 1932 1934 1936 1938 1940 1942 1944 1946 

Year 

.JI 

Cumulative departures of computed runoff from measured runoff 

42. / ~4 

v \5 

y .as 

.39 

315. 

~ .37 . 

• 33 

0 Note: Year is lettered adjacent to' plotted point . 

4 

y 

/ .36 

EXPLANATION 

Pe 

Effective basin -overage annual precipitation 

Po 

Current year, basin -average annual precipitation 

P, 

First antecedent yea~, basin overage annual precipitation. 

2 

Annual runoff, in inches 

Figure 58. -Relationship of effective annual precipit.ation to annual runoff of 

Big Sioux River at Akron, Iowa. 

65 

3 
66 

• 

..c:: • 

u· 

c: 

c: 

-

0 

c: 

e 

't:l 

: 

~ 

0. 

E 

0 

u 

• . ~ 

i 

~ 

E 

~ 

u 

30 

25 

20 

15 

10 

5 

0 

0 

1930 

VM 

v 

940 

193,.. : 

5 10 15 20 25 

Cumulative measured runoff, in inches 

Figure 59. -Double mass curve of measured runoff plotted against computed runoff for 

Big Sioux River at Akron, Iowa. 

30 
+20 

Ill 

., 

&. 

u 

c 

-- +15 

.!: 

" > 

0 t5 ~ 

E 

':1 

u 

( ~ 

~I ---·~---- -, 1912 

/"'-' ~~ ~ 

/ v ~ '\. 

I I 

~ 

1920 1928 1936 

Yeor 

\ 

"--

1944 

Cumulot•ve departures of computed runoff from measured runoff 

.--------~-----r-------------~---------------r-1~----

i 

67 

1952 

2or-----------~----------~------~--~------------4--------~---4----~----~ 

~ N 

0 

+ 

0.0 

CD 

0 

II 

~ 

Ill 

., 

~ 

u 

5 

5 

i. 

~ 

Q. 

u 

~ Q. 

., 

> 

~ 

~ " \;J 

II 

,!4 

12 

8 

.17 

u, 04 

3~·· .· ... 41~ 42 .oe 

;11!1 •• •,!8 / • 

,!1 ,4o ;;.!;• 4 ,!1 

!II, I 

/ 

10

44 1 

NQte; Year it lettered adjacent to plotted point. 

·" 

EXPLANATION 

Pe 

Effective basin -overooe on nuo 1 prec i pitotion 

Po 

Current year, basin -overooe annual precipitation 

PI 

First antecedent year, basin overage annual precipitation 

4j----------r----------~--------~----------~---------+--------~ 

on-----------~------------~-------------L------------~,~o------------~----------~,5 

Annual runoff, in inches 

Figure 60. -Relationship of effective annual precipitation to annual runoff of 

North Platte River at Saratoga, Wyo.· 
68 

.!: 

--

0 

c 

f! 

.~ 

i 

30 0 

u 

~ 150 

100 

50 

1940 

/ 

/ 

V"" 

/ 

/-

v 

v 

/ 

0 

0 

v 

V'•o 

50 100 150 -- ~00 250 

Cumulative measured runoff, in inches 

Figure 61.-Double mass curve of measured runoff plotted against computed runoff for 

· North Platte River at Saratoga,· Wyo. 

1945 

300 
., 

u 

&:. 

u 

.5 

.5 

.,·. 

~ 

z 

0 

Q. 

~ • 

u 

~ 0 

-; 

E 

::J 

0 

C? 

~ 

0 

+ rP 

co 

Ci 

" 

~ 

., 

u 

&:. 

u 

.5 

-~ 

c· 

.2 

~ ·a 

·u 

Gl 

~ 

Gl 

.~ 

u 

~ 1.1.1 

+8 

+4 

0 \ 

'--/ 

-4 

1910 1916 

/ 

r ~, ~ 

v ~ t"-

1922 1928 1934 

Year 

- - ~ r---_, 

1940 

Cumulative departures of computed runc-ff from measured runoff 

69 

~-

1946 

24r-------------~------------r-------------~-------------~------------~------------, 

20~------------4--------------+------------~~-----------,~~~------------+-------------4 • ~s I ~38 ~ 

16 

40. 

12 

8 

v .. .. : 27 X: . . .. ~:45 •17 

.• 14 

Note: Year is lettered adjacent to plotted point. 

/ 

EXPLANATION 

Pe 

Effective basin -overage annual precipitation 

Po 

Current year, basin -overage an nuol precipitation 

PI 

First antecedent year, basin average annual precipitation 

4~------------~-------------+--------------~------------~-------------+------------_, 

2 4 6 8 10 

Annual runof~ in inches 

Figure 62. -Relationship of effective annual precipitation to annual runoff of 

North Fork South Platte River at South Platte, Colo. 

12 
70 

., 

.. 

.c 

u 

c: 

.!: 

... 

... 

0 

c: 

::t 

... 

~ 

~ ::t 

Q. 

E 

0 

u 

.. 

> 

~ 

.9 

:::1 

E 

::t 

u 

150 

125 

100 

75 

50 

25 

0 

0 

191 

v···· 1940 

v 

955 

/feao 

lJ.'925 

22 

v 

25 50 75 100 125 150 

Cumulative measured runoff, in inches 

Figure 63. -Double mass curve of measured runoff plotted against computed runoff for 

· North Fork South Platte River at South Platte, Colo. 
• 

.c • 

u 

.5 

.5 

•· 

~ 

~ 

0 

Q. 

, • 

• > 

; 

:; 

E 

::J 

(.) 

C? 

N 

d 

+ 

~ co 

~ 

~ 

• 

.c • 

u 

.5 

.5 

rt 

.2 

~ ·a 

·;:; 

~ Q. 

• 

~ u 

~ 1&.1 

+16 

+12 

•8 

+4 

( ~ 

~ ,...-rl901 

1915 

~ ,) \ ..... A.. 

/ " ·~ 

~) 

1921 1927 1933 Year 

-

Cumulative departures of computed runoff from measured runoff 

71 

/ 1\ 

\ 

" \ 

1939 1945 

24~------------~------------~------------r-------------~~----------~------------, 

20~------------+--------------r------------~--------------+--------------r------------~ 

16 

12 

8 

41 

. 

•4e 

~· !5 

a4 .. 41 / 12 

.ae 22 

If. 

a f5 29 

••• .,7 

40. .a• a7 .se ~ .• .28 

ae• v 

I .as 

Note: Year is letttred adjacent to plotted point. 

EXPLANATION 

Pe 

Effective basin-overage annual precipitation 

Po 

Current year, basin -overage annual precipitation 

PI 

4r-------------~~----.... First onfecedent year, basin overage onnuol precipitation 

o~----------~3------------~s------------~9~----------~~2~----------~,~s~----------~,8 

Annual runoff, in inches 

Figure 64 ..... Relationship of effective annual precipitation to annual runoff of 

Clear Creek near Golden, Colo. 
72 

300 

: 250 s::. 

u 

c: 

c: 

.... 

0 

c: 

: 

t 

i 

I 

(,J 1!50 

100 

50 

;~·· 

v 

v 115 

1150 

v 

./ 

/ v 

v 8 

0 

0 

K,, 

50 100 150 200 250 

Cumulative measured runoff, in inches 

Figure 65. -Double mass curve of measured runoff plotted against computed runoff for 

Clear Creek near Golden, Colo. 

300 
.. 

~ • 

u 

.!: 

.!: 

.•. 

~ 

~ 

0 

a. 

"0 • 

• 

~ 0 

3 

e 

3 

i? 

~ ~ 

d 

II 

! 

~ = .K 

.s 

-~· 0 

i ·u 

f 

a. 

-~ i ll:. 

"' 

73 

+10 

+5 

0 

v rI 1'--- ~ 

u , " ~ 

~'-__ ~ -5 

19 15 15:21 1927 1933 1939 194~ 

Year 

Cumulative departures of computed runoff from measured runoff 

36r-----------------r---------------------r---------------~--------------~--------------~------------~ 

aa/ 30r-----------~------~-----r------------~------------~------------~~--------~ 

/v~ 24 

18 

12 

24 

Note: Year is lettered. adjacent to plotted point. 

EXPLANATION 

Pe 

Effective basin -overage annual prec i p itotion 

Po 

Current ye_or, basin -overage annual precipitation 

P, 

sr-------------~------------ First antecedent year, basin overage annual precipitation 

o=-------------3~------------~s------------~9--------~--~~2~------------~~5------------~~e 

Annuol runoff, in inches 

Figure 66. -Relationship of effective annual precipitation to annual runoff of 

Thompson River (below powerhouse) near Drake, Colo. 
'74 

c 

--

0 

c 

2 

300 

100 

50 

0 

0 

/ .... 

, 

1940 

/ 

/ 

0 

v Vl929 

5 

1920 

50 100 150 200 250 

Cumulative meosuced runoff, in inches 

Figure 67, -Double mass curve of measured runoff plotted against computed runoff for 

Thompson River (below powerhouse) near Drake, Colo. 

300 
• "' .c 

u 

-~ 

-~ 

.,.-. 

~ 

~ 0 

a. 

"0 • 

• 

-~ 0 

:; 

E 

:I 

(,) 

..... O• a: 

.... -

~ ..... 

, 

.c • 

u 

.5 

-~ 

r::.-

.2 

~ ·a 

·c:; 

~ a. 

• 

-~ 

u 

~ ·w 

+e 

+4 

0 f\.. 

"'--./ 

-4 

1911 

I lrv' 

~ 1/ 

J~ J 

u -

1917 1923 

v ~ 

1929 

Year 

~ v\ V\ ~ 

1935 1941 

Cumulative departures of computed runoff from measured runoff 

75 

~ \ 

1947 

24r-------------.-----------~.-------------~------------~------------,-------------~ 

.us .sa / ror-----------;------------+------------T-----------~~--------~~----------4 V .l4 

16 

12 

8 

.so 

.se 

9 .27/ 

Not .. (eor is lettered 

EXPLANATION 

Pe 

.21 

.28 

to plotted p int. 

Effective basin-overage annual precipitation 

Po 

Current year, basin -overage annual precipitation 

PI 

First o ntecedent year, ·basin overage o nnua I precipi to tion. 

4r------------;---------------+--------------~------------~------------+-----------~ 

o~----------~2-------------L4------------~6~----------~e------------~,o------------~,2 

Annual runoff, in inches 

Figure 68.-Relationship of effective annual precipitation to annual runoff of 

Cache la Poudre River at mouth of canyon, near Fort Collins, Colo. 
76 

240 

:200 

.1:: 

u 

c: 

c: 

.... 

.... 

0 

c: 

2 

'V 

• ; 

Q. 

E 

0 

u 

• . ! 

s 

i 

:I 

u 

160 

120 

80 

40 

0 

0 

lf1947 

1945 

194 

v 

lfeao 

/ 

191!0 

1915 

40 80 120 160 200 

Cumulative measured runoff, in inches 

Figure 69 .. -Double mass curve of measured runoff plotted against computed runoff for 

Cache la Poudre River at mouth of canyon, near Fort Collins, Colo. 

240 
1-3 

• CD 

~ 

u 

.~ 

+2 .~ 

.-. 

~ 

~ -+1 0 

a. 

CD 

'0 

CD 

> 

~ 

0 0 

3 

E 

:I 

0 

-·1890 

36 

30 

2 

., 

0 24 + 

0.0 

~ 

d 

" 

~ 

CD • 

~ 

u 

. 5 

.5 

18 

c· 

.2 

! 

ii ·u 

~ a. 

CD 

.:: 

u 12 CD 

:t: 

"-' 

6 

~ \ 

\J 

1900 

(\ 

I _j ' \ r-0 

/. 

1910 1920 1930 

Year 

/ ~ 

1940 

Cumulative departures of computed runoff from measured runoff 

.•5 

/ 

v p5 

~3 

p2 

v·~ 

¥p ~ ~· 

45 10 • 7 

.... .DI!I 

~··" 44 e .o9 ~5 . J2 41 5 J5 :s"e 30•J!9 

... )5 II. 

v43 

~~~ . 

.95 

(: "37 

Note: Year is lettered adjacent to plotted point. 

I ., 

EXPLANATION 

Pe 

Effective basin -average annual precipitation 

Po 

Current year • basin -overage annual precipitation 

P, 

First antecedent year, basin overage annual precipitation 

2 3 4 5 

Annual runoff, in inches 

. Figure 70. -Relationship of effective anm.~al precipitation to annual runoff of 

Loup River at (near) Columbus, Nebr.· 

77 

\ 

1950 

6 
• • &. 

u 

c 

c 

... 

... 

0 

c: 

~ 

, 

~ :I 

Q. 

E 

0 

u 

.! " 

i 

~ :I 

u 

180 

150 

120 

90 

60 

30 

0 

0 

1895 

v, ... I 

958 

·no 

928 

1920 

1918 

Note• For years 1916-1928 value of Rc 

substituted for R for yean of 

non·measurect runoff. 

1910 

11~0~ 

1900 

30 60 90 120 150 180 

Cumulative measured runoff, in i~ches 

Figure 71. -Double mass curve of measured runoff plotted against computed runoff for 

· Loup River at (near) Columbus. Nebr. 
1.0 

• 

~ • 

u 

.5 

0 

.5 

• 

~ 

~ 1.0 0 

Q. 

, • 

• 

~ 0 2.0 

:; 

E 

3 

192~ 

30 

2~ 

C? 

N 

0 20 + tP 

CD 

d 

" & 

, 

.c • 

u 

~ 

.!: I~ 

ct 

.2 

~ ·a 

·u 

~ Q. 

• 

~ 10 u 

~ w First 

~ 

v--r---r---r--- ~ ~ ~ .-. I 

"----v ..... 1'--1' 

1929 1933 1937 1941 

Year 

Cumulative departures of computed runoff from meosureC! runoff 

~ ~ 

·.~ 44 

f1 ... 2 /.52 

il / 

~· 

.ao.n 

35• .... ,,. 

"· 

7 

~., 

''· 10 •• 34 Note: Year is lettered adjacent to plotted point. 

EXPLANATION 

Pe 

Effective basin -overage annual precipitation 

Po 

Current year, basin -overage annual precipitation 

P, 

antecedent year, basin overage annual precipitation 

2 3 

Annual runoff, in -inches 

4 

194~ 

~ 

Figure 72. -Relat-ionship of effective ann~al precipitation to annual runoff of 

Elkhorn River at Waterloo, Nebr. 

79 

1949 

~ 

~ 
80 

.. ., 

.c: 

u 

c: 

c: 

... 

... 

0 

C:, 

e 

"1::1 

~ :I 

Q. 

E 

0 

u 

., 

~ 0 

'S 

e 

:I 

u 

60 

50 

40 

30 

20 

10 

0 

0 

V'"47 1945/ 

1940 

193!5 

e 

1930 

10 20 30 50 60 

Cumulative measured runoff, in inches 

Figure 73.-Double mass curve of ceasured runoff plotted against computed runoff for 

· Elkhorn River at Waterloo, Nebr. 
"' .., 

.t::. 

u 

.s 

.s 

IIi 

~ 

~ Cl 

Q. 

'0 •

I 

i 

(.) 

~ 

+2 

0 1\ 

-2 

-4 

1925 1929 

" 

~ 

/\· ·/ ~ 1\ v \ 

r------v 

1933 1937 1941 

Ytor 

\ 

\ 

/ 

v 

1945 

Cumulative deporturll of computed runoff from measured runoff 

81 

36r-----------~------------~-------------r-------------r~~~------~----------~ 

r------~ 

30~----------4-----~'---~------------4------------+------------+-----------~ 

/~ 

V .H 

.a• 

IO 

/

.ae .at 

C? ~7 V') 

~ 24r-------.--~~-~~~------------~-------------+--------------+--------------r------------~ 

! ~· . Note• Year ;s lettlred odjocent to plotted pO;nt, 

"' .., 

.t::. 

u 

.5 

18r-------------~------------~--------------+--------------+--------------~----------~ 

12 ,_ _____ _ 

EXPLANATION 

Pe 

Effective basin -overage annual precipitation 

Po 

Current year, basin -overage annual precipitation 

P, 

First antecedent year, basin overage annual precipitation 

I 

&r-------------+-------------~------------~--._---------r-------------+------------~ 

o~------------~2------~----~4------------~6--------------~e------------~.o~----------~ 

Annual ruhoff, in inches 

Figure 74. -Relationship of effec~ive annual precipitation to annual runoff of 

Nishnabotna River above Hamburg, Iowa .. 
82 

f72 

: 60 -'= u 

c: 

c: 

-

0 

c: 

e 

"0 

! 

:II 

D. 

E 

0 

u 

., 

,. 

~ 

.s 

! 

:II 

u 

48 

36 

24 

12 

I 

0 

0 

I 

-

v 

;, v 

v 

V-40 

IIU.., 

1150 

12 24 36 48 60 

Cumulative measured runoff, in· inche~ 

Figure 75. -Double mass curve of measured runoff plotted against computed runoff for 

Nishnabotna River above Hamburg, Iowa. 

72. 
+4 

., 

., 

.c. 

u 

.~ 

+2 .~ 

.,· 

~ 

~ 

0 0 a. 

., 

'0 

., 

~ 0 -2 :; 

E 

::J 

0 

50 

C? 

N 

0 40 + 

0.0 

co 

d 

II 

~ 

Ill 

fll 

.c. 

u 

.5 

!: 30 

c" 

!2 

~ a 

u 

f 

a. 

., 

~ 20 ti 

~ LLJ 

10 

0 

,., 

1/" ~ 

1925 

)r\ 

I ' 1\ / "'I L-J "" J 

1929 1933 1937 

Yeor 

"'----A 

1941 

Cumulative departures of computed runoff from measured runoff 

.32 _.........--:: 1--

~ .. ~ 

~ 45 J.9 

~ ~ 41 

. 23 • 

8 .31 t35 .24 

33••4 k,•3e.30 

./ 7 •39 

•37 

Note: Year is lettered adjacent to plotted point. 

I 34 

I EXPLANATION 

Pe 

Effective basin -overage annual precipitation 

Po 

Current year, basin -average annual prec ip i tat ion 

P, 

Ftrst antecedent year, basin average onnuo! precipitation 

5 10 

Annual runof~ in inches 

Figure 76. -Relationship of ~ffective annual precipitation to annual runoff of 

Nodaway River near Burlington Junction, -Mo. 

8.3 

I 

v 

1945 

' 

15 
84 

VI 

411 

.c: 

u 

c: 

c: 

-

0 

c 

e 

~ ., 

-; 

Q. 

e 

0 

u 

., 

.!: 

a 

i 

:a 

u 

I 

! 

I 

e--

120 

I 

100 

/1945 

80 - --

I 840 

I 

I 

60 ------- ~ --------l-------- ~·----···-"-

I 

I 

I ·- I 40 

1810 

I 

I I 

I 

-~/ t I I 

·-.. -· ··--···-- ______ ..:__ -~·· ··- ............ ---·-+-·--- ~-·-··-----·----. 

I I 

I ! U __ 

20 

0 

0 ------~----1 _________ 

l 

20 40 60 80 100 

Cumulative measured runoff, '" inches 

Figure 77. -Double mass curve of measured runoff plotted against computed runoff for 

Nodaway River near Burlington Junction, Mo. 

I 

_j 

120 
Ill 

.&: • 

u 

.5 

+5 

.5 

•• • 

: "" 

"" 0 0 

Q. 

• 

/ 

___/ , 

• ,. 

; -5 

I 

1925 

J '\ /~ ~ 

1929 

'"" l-/ .......... 

~ ~ -

193! 1937 194.1 

Ytor 

Cumulative deportur11 of computed runoff from measured runoff 

85 

-

1945 

' 50~----------~------------~-------------+-------------r------------~----------~ 

a:-

N 

0 

+ rP 

co 

d 

~ 

" 

Ill 

.t:. • 

u 

·= 

: 

c· 

.2 

2 

:~ u 

~ Q. 

• > 

-~ 

~ w 

40 

30 

20 

···~ ·•• ':?~v 

29 

Note: Year is lettered adjacent to plotted point. 

EXPLANATION 

Pe 

Effective basin -average annual prec i pi tot ion 

Po 

Current year, basin -overage on nuol precipitation 

p• 

lOt------- First antecedent year, basin average annual precipitation -------+---------t 

4 12 Annual runoff, in inches 

8 16 

Figure 78. -Relationship of effective annual precipitation to annual runoff of 

Platte River near Agency. Mo. 
86 

lit 

., 

s:; 

u 

c: 

.: 

... 

-0 

c: 

2 

, 

~ ':1 

Q. 

E 

0 

u 

.~ 

s 

~ ':1 

u 

150 

125 

100 

7S 

eo 

25 

0 

0 

1925 

/ 1945 

~ 

840 

IUS 

19!p 

25 eo 100 125 

Cumulative measured runoff, in inches 

Figure 79. -Double mass curve of measured runoff plotted against computed runoff for 

Platte River near Agency, Mo. 

ISO 
87 

+1.0 

i.o. 

0 

.!: 

on- . 

~ 

I 

~ v --- - r--

::::1 --- - ~ +1.0 0. 

til 

'0 

til 

--~ 0 

:; 

E 

::::1 

(..) 

~ II 

~ 

on 

til 

s:. 

u 

.5 

: 

rt 

.2 

~ ·a 

·u 

~ 0. 

til 

.~ 

u 

~ ILl 

1924 1928 1932 1936 1940 

Year 

Cumulative departures of computed runoff from measured runoff 

1944 1948 

24~------------~--------------~------------~~----~------~--------------~------------~ 

~ 

. I' 

. 

41 

20~----------~~----+--------+--------------~----~------~------------~~----------~ 14 II" 

16 

12 

8 

.27 

.t4 

2\ 

I 

114. 

.. 

.u 

Note: is lettered adjacent to plotted point. 

EXPLANATION 

Pe 

Effective basin-overage annual preci pitotion 

Po 

Current year, basin -overage annual precipitation 

PI 

First antecedent year, basin overage o~nuol precipito tion 

.ss 

4r-------------~------------~--------------+--------------r--------------r-------------~ 

o~------------~.2--------------.~4--------------.~6--------------.~8------------~~.~o~----------~~~.2 

Annual runoff, in inches 

Figure 80. -Relationship of effective annual precipitation to annual runoff of 

Arikaree River at Haigler, Nebr. · 
88 

6 

: 5 .c: 

u 

c: 

c: 

.... 

.... 

0 

c: 

~ 

.. 4 

2 

I 

0 

0 

1925 

/194S 

/ ~ 

~ lt{. 

/ 

v-

/ 

2 4 5 

Cumulative measured runoff, in inches 

Figure 81. -Double mass curve of measured runoff plotted against computed runoff for 

Arikaree River at Haigler, Nebr. 

6 
., 

s; • 

u 

-~ 

-~ 

+.50 

0 

.,.~ . 

~ 

.:· . 0 -:50 Q. 

"l:J • 

30 

25 

i? 

0 20 + rf 

en 

d 

II 

~ 

Ill 

s; • 

u 

.5 

.5 15 

r:.~ 

~ 

.2 

a ·u 

~ Q. 

• . ? 

u 10 

.! 

w 

5 

0 

\~ 

... 1921 

,.. 

1! .eo 

25 

40. 

.2. 'H 

~ " 

r v 

I l) 

~ t-. 

) 

'V "-../ 

1927 1933 1939 

Year 

~ 

1945 

Cumulative departures of computed runoff from measured runoff 

2\ v.44· ~2 ~· / '"Ell 

II '1 

so. 

)2 

.45 ~· •2t 

)8 

.. 4 

..... ss 

)5 

~· 

/ •s1 

.s4 Note: Year is lettered adjacent to plotted point. 

First 

EXPLANATION 

Pe 

Effective basin -average annual precipitation 

Po 

Current year, basin -overage annual precipitation 

P, 

antecedent year, basin average annual precipitation 

.2 .4 .6 .a 1.0 

Annual runoff, in ·inches 

Figure 82.-Relationship of effective annual precipitation to annual runoff of 

Smoky Hill River at Ellsworth, Kans.· 

89 

.. 
90 

., 

., 

s:. 

u 

c 

c 

-

0 

c 

: 

, 

~ :I 

Q. 

E 

0 

u 

., 

» 

~ 

Ji 

i 

:I 

u 

12 

10 

8 

6 

4 

2 

0 

0 

91!0 

/ .... 

19 0 

/ / 

L' 

/ 

v 

7 

2 4 6 8 10 

Cumulative measured runoff, in inches 

Figure 83 .. -Double mass curve of measured runoff plotted against computed runoff for 

Smoky Hill River at Ellsworth, Kans. 

12, 
+I 

., 

tl 

.1: 

u 

.~ 

0 .~ 

.,· 

~ 

~ -I 0 

Q. 

tl 

, 

tl 

> 

·~ 

0 -2 

3 

E 

::J 

(.) 

36 

30 

C? 

0 24 + ce 

0 

" rf! 

., 

tl 

.c 

u 

.5 

18 

5 

r:" 

2 

~ ·o. 

u 

~ Q. 

tl 

.~ 

u 12 Q) 

::: 

LLI 

6 

0 

I'\ L-/ ~ ~ v !::_ 

0 

' 

~ L 

"--' 

1926 

• 23 

~ ~ I ~ 

1932 1938 1944 

Year 

Cumulative departures of computed runoff from measured runoff 

~0 

·/~ .. 

/ ... 31.JO' 

32. .29 

.43 

.21 

2~ 

25 • 35 

1950 

e24 22. 

.33 4'?._ 

2 I 

&. ;·36 

1 .34 

.39 Note: Year is lettered adjacent to p'otted point. 

EXPLANATION 

Pe 

E.ffective basin-average annual preci pitotion 

Po 

Current year, basin -overage annual precipitation 

P, 

First antecedent year, basin overage annual precipitation 

2 

Annual runoff, in .inches 

Figure 84. -Relationship of effective annual precipitation to annual runoff of 

Saline River at Tescott, Kans. 

91 

3 
92 

., 

., 

&. 

u 

c 

c 

... 

0 

c 

e 

"a 

! 

:a 

Q. 

E 

0 

u 

" :! 

s 

I 

:a 

u 

24 

20 

16 

12 

8 

4 

0 

0 

1920 

.I 

v··~ 

~ v IIIII . 

l/ 

/ 

~ v 

4 8 12 16 20 

Cumulative measured runoff, in inches 

Figure 85. -Double mass curve of measured runoff plotted against computed runoff for 

Saline River at Tescott, Kans. 

2~ 
.. 

u 

s:. 

u 

.~ 

.~ 

,r 

~ 

~ 0 

Q. 

., 

'0 

u 

> 

~ 

0 

3 

E 

:::J 

(.) 

C? 

N 

0 

+ 

0.0 

Cl) 

0 

II 

~ 

Ill 

u 

s:. 

u 

.5 

.5 

r:.· 

0 

~ ·a. 

·c:; 

~ Q. 

u 

.~ 

u 

u 

;: 

L&J 

+2 

0 

-2 

-4 

1915 

36 

30 

24 

18 

12 

6 

0 

0 

"' 1\v 

1921 

rv ./ 

~ ~ f--- __/ 

1927 1933 1939 

Yeor · 

) 

v 

1945 

Cumulative departures of computed runoff from measured runoff 

.•9 

./~ 23. 

v. 

v 0 .27 

.20 

)I .21 .38 I 

/ . 33 .29 

v~ 43 

2~ 8 

f .39 

.36 Note: Year is lettered adjacent to plotted point. 

l 4 

EXPLANATION 

Pe 

Effective basin -overage annual precipitation 

Po 

Current yeor, basin -overage annual precipitation 

P, 

F.rst antecedent year, basin overage onnuol precipitation 

2 3 .. 4 5 

Annual runoff, in inches 

Figure 86. -Relationship of effective annual precipitation to annual runoff of 

Big Blue River at Randolph, Kans. · 

93 

45 

'• 

6 
94 

., • 

.c 

C) 

.! 

.! 

.... 

0 

c: 

2 

~ 

: 

:I 

Q, 

e 

0 

u 

., 

> 

i 

-; 

e 

:I 

u 

60 

50 

40 

30 

20 

10 

0 

0 

/ 

/, ... 

v 

/ 

/ 

z··o 

193& 

/ v. 

I 

v 

1920 

10 20 30 40 50 

Cumulative measured runoff, in inches 

Figure 87. -Double mass curve of measured runoff plotted against computed runoff for 

Big Blue River at Randolph, Kans. 

60 
Ill "' 

s; 

u 

-~ 

-~ 

.,.· 

~ 

~ 

0 

0. 

Ill 

"0 

Ill 

-~ 

0 

:; 

E 

:I 

(.) 

cc 

N 

0 

+ rP 

CD 

d 

II 

~ 

"' Ill 

s; 

u 

.5 

!:: 

c." 

.9 

~ 

:9-

u 

• Q. 

Ill 

.::: 

u 

£ 

I.LJ 

i-12 

+8 

+4 

0 

-4 

1921 ""' 

I 

v--v 

1925 

I ~ / "'--~ u \ 

~ Ll I'---/ 

1929 1933 1937 

Year 

"' f\. 

1941 

Cumulative departures of computed runoff from measured runof.f 

95 

/ 

" v 

I 

1945 

sor-_..__..___.._..__.._-+_..___.._..___.._..__.._+-_..___.._.._ __ _..__.._~_..__..__..__..__.._~_..__.._ __ _.._ __ _._.4-_._._..__..__..__.._~ 

40 

30 •40 

34 

20 

,. 

Note: Year is lettered adjacent to plotted point. 

EXPLANATION 

Pe 

Effective basin-average annual precipitation 

Po 

Current year, basin -average annual precipitation 

P, 

First antecedent year, basin average annual precipitation 

IOr-------------+-------------4-------------~-------------+-------------4------------~ 

o=------------------~4~---------------~a-.-------------------~~2-------------------~~s------------------2Lo----------------~ 

Annual run-off, in inches 

Figure 88. -Relationship of effective annual precipitation to annual runoff of 

Grand River near Gallatin, Mo. 
96 

II) 

~ " u 

.~ 

.~ 

~ 

-0 

c 

~ 

'a 

~ :a 

Q. 

E 

0 

u 

" > 

:§ 

i 

:a 

u 

180 

150 

120 

90 

60 

30 

0 

0 

' 

/1945 

v 

/ 

lt:S ./ 

1100/ 

v 

v 

v 

1925 

I 

30 60 90 120 150 

Cumulative measured runoff, in inches 

Figure 89 .. -Double mass curve of measured runoff plotted against computed runoff for 

Grand River near Gallatin, Mo. 

180 
+5 

Ill 

" 1: 

u 

-~ 0 -~ 

~~~R 

t 

~ -5 0 

Q. 

" , 

" 

~ 0 -10 ~ 

E 

:::J 

(.) 

1921 

60 

50 

C? 

d "' 

+ 40 

0.0 

CD 

0 

II 

~ 

Ill 

" .c: 

u 

.e 

.e 30 

~-

.2 

·a 

·u 

f 

Q. 

-~ " 20 0 

£ 

IJJ 

10 

97 

" .1~ '"-

"' ~ "' / v ~ J ~ / ~ t-o.. __ 

~ / 

\ u· v 

1925 

~"""--" . 

1929 1933 1937 

Yeor 

1941 

Cumulative departures of computed runoff from measured runoff 

24 

281 / v ~ 43" 

/< .35 . 

• 37 

25.\4 

/ 

9 

·2~ 

I 

5 I y . 

..;/ 14 Note: Year is lettered adjacent to plotted point 

4 

EXPLANATION 

Pe 

Effective bas in -average annual precipitation 

Po 

Current year, basin ·-average annual p rec ip ito tion 

' P, 

First antecedent yeor, basin overage annual precipitation 

•' 

6 12 18 24 30 

Annual runoff, in inches 

Figure 90.-Relationship of effective annual precipitation to annual runoff. of 

Sac River near Stockton, Mo. · 

1945 

. 27 

. 36 
98 

:eoo 

.11: 

c.. 

.! 

.! 

. ... 

... 

0 

c: 

~ 

.. 

"E400 

~ Q. 

e 

0 

u 

.! " 

i 

:I 

E 

<3300 

200 

100 

0 

0 

vl945 

1940 

-- 19~5 

1930 

1925 

100 200 300 400 500 

Cumula-tive measured runoff, in inches 

Figure 91. -Double mass curve of measured runoff plotted against computed runoff for 

Sac River near Stockton. Mo. 
• ! 

u .. 5 

0 

.5 

,; 

~ 

~· 

0 -~ Q. 

, • 

1\ 

\ .....-

1926 

'"" ~ ~ r ~ 

1\_ 1r v 

1930 1934 1938 

Year 

~ v 

1942 

Cumulative departures of computed runoff from measured runoff 

99 

.;..... / 

"""'lo"" 

1946 

60 r-----------------~---------------~------------------~------------------r------------------~~-. ---------.~7.--~ 

~V< 

I 

. ~ 

.e 

Note: Yeor 11 lettered adJacent to ~lotted point . 

~ ~----------~~----------~-------------+-------------+-------------+----------~ 

.~· EXPLANATION 

0 ~ 

"i Effective basin-averaQe annual precipitation 'i 

a ~ Current year, basin -averaQe annual precipitation 

.I 20 t---- P, 

~ First antecedent year, basin averaQe annual precipitation 

"" 

10 ~--------~------~--------+------------+---------+----------~ 

o=-----------------~5------------------~,o~---------------~~5~--------------~2~o~----------~25~--------------~3o 

Annual runoff, in inches 

Figure 92. -Relationship of effective annual precipitation to annual runoff of 

Gasconade River near Waynesville. Mo.· 
100 

.!: 

... 

0 

c: 

:::t 

... 

300 

1200 

.. :::t 

.Q, 

e 

8 

: 

j 

I 3 ISO 

100 

50 

0 

0 

v·-

/ 

/ 

v 1930 

1925 

50 100 150 200 250 

Cumulative measured runoff, in inches 

Figure 93. -Double mass curve of measured runoff plotted against computed runoff for 

Gasconade River near Waynesville. Mo. 

3oq 
+:50 

• .! 

u 

.5 

+20 

.5 

.-. 

e 

~ 0 

0. 

'V •

+10 

0 

-10 19 

~~ 

. I 

/ \_ v-v 

10 1916 1922 

101 

~ II"---I'-\. ~---

·; 

v \ u \ 

'V IV I\; '--

1928 1~134 " ~ fS 

Ytor 

Cumulative departures of comJX,Jftd runoff from measured runoff 

30r-----------r-----------~----------~----------~--------------------~ 

• 

.II! •

u 

.5 

.5 

~ 

J5 

.42 

J'l. a a. 

.t.4. 

aa.,._5 

8 J1 

.vJ· 

.r:r 

e. 

J3 

~~ 

.M 

EXPLANATION 

Pe 

; •10 1-------~------+-

~ 

Effective basin -average annual precipitation 

LU Po 

Current year, basin-average annual precipitation 

P, 

First antecedent ¥ear, basin overage annual precipitation 

5r---------~--------~--------------------~~------------------~----------------~------~--------4-----------~ 

o~--------~~------------2~o--------------30~----------40L-----------~so~-----------~&o 

Annual runoff, in inches 

Figure 94. -Relationship of effective annual precipitation to annual runoff of 

St. Mary River near Kimball, Alberta:. 
102 

900 

.... 

0 

c 

2 

~600 

~ :s 

Q, 

e 

0 

u 

300 

150 

0 

0 

/1945 

1940 

/ 

v 

/ v~·!O 

v 

1920 

1915 

150 300 450 600 750 

Cumulative measured runoff, in inches 

Figure 95. :-Double mass curve of measured runoff plotted against computed runoff for 

St. Mary River near Kimball, Alberta. 

90Q 
+8 

"' cu 

s:. 

CJ 

£ 

+4 .~ 

.;. 

~ 

z 

0 0 Q. 

cu 

"tl 

' " cu 

~ 0 -4 

3 

E 

::II 

0 

1922 

/ 

~ ~ 

1926 

-..... / 

I'-- ~ 

1930 1934 1938 

Year 

-

"--

"'--

1942 

Cum~o~lative departures of computed runoff from measured runoff 

i03 

' "' 

1946 

60~------------r-------------~------------~------------,-------------~------------~ 

45. ./ 

50~------------~-------------+------------~~----------~·~~~~~----------~-----------~ 

Q7 

~ N 

~ 40 

CD 

d 

~ 

y·· ... . ~II Note: Year It lettered adJacent to plotted paint. 

J ·,y::l· .. ~ ~ ... . li I .5 50~--~~~···~m-----~------------~-----------+------------~----------~----------~ /·=4 f 1 

UP~ANATION 

l Efftctive boain·overo:~ onnuol preci pitotion 

Po 

.I 201------ Currtnt year, basin ·overogt onnuol precipitation 

~ ~ Ll.l First antecedent year, boain overage onnuol precipitation 

I0~----------~-------------+------------~------------~------------1-----·------~ 

o~-----------4~----------~a------------~~2~----------~,~6----------~2~o~----------=24 

Annual runoft in inches 

Figure ~li. -Relationship of effective annual precipitation to annual runoff of 

Neosho River near Parsons, Kans. 
104 

c: 

... 

... 

0 

c: 

e 

240 

v 160 ~ :II 

Q, 

E 

8 

.. 

~ 0 

:; 

E 

3120 

80 

40 

0 

() 

1925 

1945 

940 

1935 

1930 

40 80 120 160 200 

Cumulative measured runoff, in inches 

Figure 97,. -Double mass curve of measured runoff plotted against computed runoff for 

Neosho River near Parsons, Kans. 

240 
105 

Table 2. -Tributary basins studied for trends in precipitation-runoff relationship 

Standard Indicated changes in 

Figure Period of error of precipitation- runoff 

no. Tributary basin record e~!!~~ relationship 

(Percent -- - - - - 7 

-- of mean) f i Period Direction - •• "'• r -----1 

14 Osage - Bagnell, Mo_. 1881-1945 24 -- --

16 Beaverhead - Barratts, Mont. 1908-45 18 .1925-41 -R 

18 Missouri - Ft. Benton, Mont. 1910-45 12 -- -- 20 Madison -West Yellowstone, Mont. 1914-45 13 1931-45 -R 

22 Tenmile - Rimini, Mont. 1915-45 47 1927-41 -R 

24 North Fork Sun - Augusta, Mont. 1906-28 21 -- -- 26 Marias -Shelby, Mont. 1912-45 40 1935-42 -R 

28 Judith - Utica, Mont. 1920-45 58 1930-41 -R 

30 Musselshell -Harlowton,· Mont. 1907-45 45 1928-45 -R 

32 Yellowstone - Corwin Springs, Mont. 1911-45 16 -- -- 34 Bighorn - Thermopolis, Wyo. 1901-45 21 1931-41 -R 

36 Powder - Arvada, Wyo. 1917-45 37 1934-45 -R 

38 Little Missouri - Alzada, Mont. 1912-45 70 -- -- 40 Canno~ball - Breien, N. Dak. 1912-18 84 -- -- 1922-45 

42 Moreau - Promise,S. Dak. 1929-45 75- -- -- 44 Cheyenne -Wasta, S. Dak. 1929-45 30 1937-45 ·R 

46 Rapid - Big Bend, S. Dak. 1915-42 39 1919-25 +R 

1938-42 -R 

48 Belle Fourche - Belle Fourche, S.Dak. 1912-40 49 -- -- 50 Bad - Fort Pierre, S. Dak. 1929-45 35 -- -- 52 White -Oacoma, S. Dak. 1929-45 33 -- --· 

54 Niobrara - Dunlap, Nebr. 1924-42 21 1937-42 -R 

56 James - Scotland, S. Dak. 1929-45 69 -- -- 58 Big Sioux - Akron, Iowa 1929-45 29 -- --

60 North Platte -Saratoga, Wyo. 1904-45 21 1928-45 -R 

62 North Fork South Platte - South Platte, 1914-22 28 -- -- Colo. 1925-45 

64 Clear - Golden, Colo. 1912-22 21 -- -- 1925-45 

66 Thompson- Drake, Colo. 1918-26 21 -- -- 1929-45 

68 Cache la Poudre - Ft. Collins, Colo. 1910-45 32 -- --
106 

Table 2.-Tributary basins studied for trends in precipitation-runoff relationship--continued 

Figure Tributary basin no. 

70 Loup - Columbus, Nebr. 

72 Elkhorn -Waterloo, Nebr. 

74 Nishnabotna - Hamburg, Iowa 

76 Nodaway - Burlington Jet., Mo. 

78 Platte - Agency, Mo. 

80 Arickaree - Haigler, Nebr. 

82 Smoky Hill - Ellsworth, Kans. 

84 Saline - Tescott, Kans. 

86 Big Blue - Randolph, Kans. 

88 Grand - Gallatin, Mo. 

90 Sac - Stockton, Mo. 

92 Gasconade - Waynesville, Mo. 

' 94 St. Mary - Kimball, Alberta 

96 Neosho - Parsons, Kans. 

regions where data on high altitude precipitation are 

lacking. The effect of this factor must remain unknown. Variations in the orographic effect must 

also remain an unknown until adequate precipitation 

records from high-altitude stations are available. 

Long-term variations in water tables have been 

classified as climatic factors because, in basins 

where ground water is not extensively used for irrigation, most changes in ground -water levels may 

generally be ascribed to long -term variations in 

precipitation. The full effect of below-normal precipitation on water tables may not be apparent until 

many years later - the actual lag in any tributary 

basin is related to geologic conditions. McDonald 

and Langbein 4/ showed that, in the Columbia Basin, 

precipitation fur many years back is effective in determining the current year runoff. Unfortunately, 

lack of long records of precipitation hampers the 

full exploration of long-term, carry-over effects in 

some of the tributary basins of the Missouri Valley 

that showed trends in the precipitation-runoff relationship. 

4 McDonald, C. C., and Langbein, W. B., Trends 

in runoff in the Pacific Northwest: Am. Geophys. 

Union Trans., vol. 29, pp. 387-397, 1948. 

Standard Indicated changes in 

error of precipitation - runoff 

Period of estimate relationship record 

(Percent Period Direction 1 of mean) 

1895-1915 14 -- -- 1929-45 

1929-45 22 -- --

1929-45 37 -- --

1923-45 33 -- --

1922-45 32 -- --

1924-45 91 -- --

1919-45 52 -- --

1920-45 57 -- --

1919-45 35 -- --

1922-45 39 -- --

1922-45 19 -- --

1922-45 18 -- --

1912-45 19 -- --

1923-45 17 -- --

Forest denudation has been shown 5/ to materially increase runoff yield for the first few ye~rs 

after cutting of trees. After the second growth 

reaches a moderate stage of development the yields 

will begin to return to normal. In a large drainage 

basin deforestation would need be on a large scale 

to show a noticeable effect on the runoff. 

Changes in consumptive use due to altered farming methods, new crop types requi.~ing more irrigation water, and .the increased growth of wasteful 

plants in canals and seeped areas could cause an 

apparent modification in the prc:cipitation - runoff 

relationship if the increased use were unreported. 

The extensive construction of small stock ponds 

may be the cause of part of the declining yield ratio 

in the Cheyenne River Basin. 

Further computations were made in all tributary 

basins showing a ·precipitation-runoff relationship 

trend to determine, if possible, the factors responsible for the change. Figure 98 shows the 

residual mass curve for the Beaverhead Basin after 

5 Hoyt, W. G., and Troxell, H. C., Forests and 

stream flow: Am. Soc. Civil Eng. Trans., vol. 99, 

pp. 1-111, 1934. 
+6 

+!5 

+4. 

c .. 

·-.. +3 Ill 

f 

f 

I 

~ 

. +2 

~ a 

~ d +I 

KeJ 

: /.) ;I 

1: 

/~; 

p I 

~;/\ ,, 

I \ 

I -, I \ 

i~j 'I \.-, " ' J 

, 

r .. ~ 

\ 

' 0 

\V 

\I ~ 

\ 

r-""""'' ~ ..... ..., ..... , \ I -

' I \ 

/I \ 

\ ' \ 

\ 

--- Accumulated residuals from multiple correlation of runoff against short term 

\ 

' ~-, ~ ~ \.J ''./ '~ \ l'j/' 0 

Ill 

z: • 

u 

£ 

.!: 

::: 

0 

c 

~ 

a:: 

effective precipitation and temperature. 

-- Accumulated residuals fro11t correlation of short term effective PreCipitation 

against ·runoff. 

---- Accumulated residuals from multiple correlation of rllftaff against short and ,, •I 

1900 

10 

5 

0 

1900 

long term 'fftctive precipitation. l_ _l l .. 1910 1920 1930 1940 

Figure 98.-Residual mass curves for Beaverhead River at Barratts, Mont. 

v-- ~ - --v ~ ~ / ~ 

Long term effective precipitation 

"--~ ~ ~ Measured runoff 

"------r--_1 ..,--v--' - 1910 1920 1930 1940 

Figure 99.-Comparison of computed long term effective precipitation with measured 

runoff of Beaverhead River Basin. 

107 

1150 

20 

• 

4:: • 

u 

.s 

.s 

1!5 c 

.2 

s 

·a 

'2 

a: 

10 

1950 
108 

mean annual temperature was included in a multiple 

regression with Pe and R. For comparative purposes the former residual mass curve is drawn on 

the figure as a dotted line to show the very slight 

improvement due to inclusion of temperature effects. 

Another factor of importance in determining runoff yields in the Beaverhead Basin is fluctuations in 

water tables. No observation well records for the 

period 1908-45 are available to appraise the watertable fluctuations in the basin, so an indirect method 

of showing the probable variations in water table was 

used. Water-table levels, and hence ground-water 

contributions to stream flow, are probably determined by precipitation amounts for many years 

back. A long-term, carry-over effect of precipitation was computed by the use of die -away coefficients 

as outlined in an article by McDonald and Langbein.6/ 

Figure 99 shows the computed long-term component 

of precipitation for the Beaverhead Basin as related 

to measured runoff. If this long-term component, 

considered to represent ground-water contributions 

to stream flow, is included in a multiple regression 

of observed runoff against annual precipitation, the 

trend in the precipitation-runoff relationship, found 

previously, vanishes, indicating that it was due to a 

combination of declining water-table and temperature effects. The residual mass curve of R vs Rc 

resulting from the multiple regression, is shown on 

figure 98. 

Similar procedures were used to evaluate the ap-

\ 

parent trends in precipitation-runoff relationship in 

the other tributary basins and all were found due to 

either or both temperature and declining water-table 

effects. Figure 100 shows the mean annual discharge plotted as a time series for Big Spring Creek 

near Lewist')wn, Mont. The flow measured at this 

station is almost all spring discharge and is therefore a good indicator of ground-water levels. Follansbee measured the discharge of Big Spring Creek 

prior to 1~09 as 140 c. f. s. The plot shows the rapid 

decline of the water table for the period 1933-41, 

and illustrates the time lag between annual precipitation and ground-water outflow by comparison with 

the Lewistown precipitation record included on the 

plot. This graphic account of declining ground -water 

contributions to stream flow in one area of Montana 

is included to show the importance of an adequate 

observation-well program in forecasting changes in 

base flow. 

MAP OF LIMITING WATER LOSS 

The term 11water loss" as used herein refers to 

that portion of precipitation that does not appear in 

streams as runoff. Water loss as computed in this 

way differs from evapotranspiration by ( 1 ) the 

amount of changes in ground-water and soil-moisture 

storage and (2) the amount of subsurface discharge 

in or out of a basin. However, changes in storage 

tend to be compensating. 

In an arid or semi-arid climate a larger annual 

precipitation results usually in a larger annual water 

loss. But for wet years in ·a humid climate the 

6 McDonald, C. C. , and Langbein, W. B .. Trends 

in runoff in the Pacific Northwest: Am. Geophys. 

Union Trans., pp. 387-397, 1948. 

water loss tends to remain constant regardless of 

further increase in precipitation. This water loss, 

which is close in meaning to Thornthwaite's 8/ potential evapotranspiration, is termed limiting -water 

loss. Although a limiting water loss may be presumed to exist in an arid or semi-arid climate, it 

may never be reached because precipitation is 

usually insufficient for all demands. The difference 

between the limiting water loss and the annual water 

loss is an indication of the amount of water needed 

to be supplied by irrigation to fully meet the requirements of. vegetation. 

In the Missouri Basin only the eastern end and 

the high-altitude regions of the mountains regularly 

receive sufficient precipitation to approximate limiting annual water loss during years of high precipitation and runoff. In the greater part of the basin, the 

limiting annual water loss is seldom, if ever, exceeded by the annual precipitation. If the water 

from the rapidly melting snow and thunderstorms 

that produce most of the runoff were made available 

more slowly no runoff would occur. 

; 

~20 -7 

"0 140 ~ c u 0 

.: u 

.. .: "' c .: .2 or 2 l!l :; "' 120 ·a. 

·u ~ ~ :.0 Q. 

i c 

0 

Ql 0 E ,;10 - 100 31 0 Ql 

~ ..J 

<t 

eo 

'"5 1930 1935 1940 IM!l 

Figure 100.-Decline of base flow during drought years 

as shown by Big Spring Creek near Lewistown, Mont. 

Figure 101 shows the method used to define the 

limiting annual water loss in the Nodaway River 

Basin of Iowa-Missouri, as an example for all tributary basins in the humid and subhumid zones. 

Because of the lack of rain gages in the tributary 

basins deriving their water from the high mountains, 

approximate loss values were calculated by using 

data at mountain snow courses .. Figure 102 shows 

three plots illustrating the relationships of winter 

precipitation to the total annual precipitation at various rain-gage stations in Colorado, Wyoming, and 

Montana. These graphs were used to convert snowsurvey water contents into usable values of annual 

precipitation at high altitudes.' Figure 103 shows a 

composite plot of limiting annual water loss against 

altitude for tributary basins in the Missouri River 

Basin deriving their water from the mountains. For 

the semiarid and arid plains region, limiting annual water loss was defined by a temperature-loss 

relationship modified in light of the known geology 

of the basin. 

8 Thornthwaite, C. W., in Rept. of Committee on 

Transpiration and Evaporation, Am. Geophys. Union 

Trans., val. 25, pt. 5, pp. 686-693, 1944. 
en 

«» 

~ 

(.J 

c: 

c: 

c 

0 

+= 0 

.. :§. 

(.J 

«» 

... 

Q. 

0 

~ 

c: 

c: 

c:t 

45 

I 

1 1942. 

40~-----4-------+------~------4----+,--~~----r-----~------~ 

I J929 .1945 

35 ' 

I J 

Note: Above roughly 37" annual precipitatio~ losses are i 

~1944 el943 

completely satisfied -increase in roi~foll results ,..lj in an equal increase in runoff. 

l 1926 

v 1 1923 1928. 

I 

1924. 

, .. l.j ,. ..931 30 ' 

Ill :if 1

, 1140 ... 

I .~~~~ 1117• 911 

1

11111 v 

ltJ'I', y 2~ ;; / ~ 

en 

'j 

/ ~I 1ft - ., 1ft 

I -.., ~ 

v !1!-~~ .., 

.. 1ft 

.., . g .., 

.. U) s .c: 

~N u 

193'\ / 20 

~-~~~ / .., 

e ·e > ·.::. cl 

i 

15 ~----------._ __________ ~--------~--~.----~--------~--------_. ________ _. ________ ~ 

15 20 25 30 

Annual water-loss, in inches 

Figure 101.-DeterminatiQn of limiting annual water-loss for 

Nodaway River basin ¢1bove Burlington Junction; Mo. 

35 

109 
110 

40 

J 

. II . . 

Key ~I ---Colorado 

A ---Montano 

--Wyoming 

. . 

. 0/ J . I 

: . . . I . 

~ ,/ ·/' . V'' • : / .. . . . . ~': ./ / .·. / . .. . ~-.. .. v/ 

/. : . . . . : . . . . . / ::> . . .. "0: v~- .. . . ....... .. : . . 0.:. .:.~, ... . . . . : "/ .. . . . . ! : . . . . . · .... ~· . . 

30 

Ill 

Ill 

.1: 

u 

.!: 

c: 

• 25 > 

·~ 

c:; 

.!: 

.1: 

~ 0 

:1 

I 

.. 

Ill 20 .a 

E 

Ill 

> 

0 

! 

c 

~ 

2 

'Q. 

·u ,, .. 

~ 

.. 

! 

c 

i 

10 

. 

~ ~:" ... ··· . . . .. : .. . . .. Note: Points plotted for Colorado data only. 

• • •• i . : . .. . : . . . .. . :·: ··~ . . . . . . . . .. k.~·· . : 

~- --· v: / 0 0 --- 10 20 ~ ~ ~ 60 70 

Rotio of winter to annual precipitation, in percent 

Figure 102.-Relationship of winter precipitation to annual precipitation in Colorado, Wyoming, and Montana. 
4P·~--------~--------~--------._------~ 10 eo ;50 

Limiting annual water loss, in inches 

Fioure 103.-Voriotion of li.mitino· annual 

water 1011 with altitude. 

Figure 104, a map of the Missouri Basin, show$ 

the variation of limiting annual water loss in the 

basin by means of lines of equal limiting annua,J. 

water loss. The line locations are roughly similaf 

to the location of lines of equal potential evapotrans~ 

piration as defined by Thornthwaite. However, the 

limiting water loss values were approximated largely 

from measured runoff, and hence the factors of geolr 

ogy, topography, and surface-drainage patterns are 

111 

inherent in the loss values. Note the low values 

surrounding the sand-hill region of Nebraska, and 

the difference in values on the east and west sides 

of the Missouri River in the Dakotas; clearly the 

re.sult of different geologic and topographic conditions. The lines of equal limiting annual water loss 

on figure 104 are generalized because of local variations and because of the lack of sufficient· rl'moff 

records. 

CONC~ USIONS 

During the period of records, annual precipitation has had a downward trend through much of the 

Missouri :Basin. The downward trend may be considered to end with the dry 1930's. Mean annual 

temperature has trended upward during the period 

of record. The trend was sharpest during the decade 

1930-40. Annual precipitation and mean annualtemperature are related although the correlation is poor. 

If in the future, annual precipitation trends upward, 

mean annual temperatures may be expected to decline. 

There have been long-term trends in the yield of 

annual runoff from equal annual precipitation during 

t.he period of runoff records in several tributary 

basins of the Missouri Basin. All such trends in 

the precipitation-runoff relationship we.re explained f 

by concurrent changes in variables other than current year precipitation, considering ground-water 

outflow as related to precipitation, for many antecedent years. · · 

The runoff records available for this study were 

not of sufficient duration really to define long-term 

trends in the precipitation-runoff relationship, Desirable length of runoff record is at least half a 

century. Continued gaging at several long-term 

stations should be considered a necessity for proper 

evaluation of trends in our water resources. An 

adequate observation-well program should be maintained to forecast future variations in base flow. 
112 

--42° 

- -- .. - ... -

~ -- - 40° 

----- --~ -~~ 

/' 

I - ~ 

·;: 

:s 

0 

en 

en 

i 

Q) 

.c. 

-.5; 

.; 

CD 

.c. 

u 

.5 

.5 
REFERENCES CITED 

Clayton, H. H., World weather records, Smithsonian Misc. Cols., vols. 79, 190,,and 105, 1944. 

Davenport, R. W., Prediction of runoff in Hydrology (edited by 0. E. Meinzer), pp. 526-530, Dover Pubs., 

1949. 

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