Hydrology of

Hungry Horse Reservoir,

Northwestern Montana

By W. D. SIMONS and M. I. RORABAUGH

GEOLOGICAL SURVEY PROFESSIONAL PAPER 682

Prepared in cooperation with the 

Bonneville Power Administration

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1971
Hydrology of

Hungry Horse Reservoir,

Northwestern Montana

By W. D. SIMONS and M. I. RORABAUGH

GEOLOGICAL SURVEY PROFESSIONAL PAPER 682

Prepared in cooperation with the 

Bonneville Power Administration

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1971
UNITED STATES DEPARTMENT OF THE INTERIOR 

ROGERS C. B. MORTON, Secretary

GEOLOGICAL SURVEY 

William T. Pecora, Director

Library of Congress catalog-card No. 70-610287

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington, D.C. 20402 Price 65 cents (paper cover)
CONTENTS

Abstract ___-______.___._--__-__---_------_------

Introduction ____._-___________-__--._.-----------

Purpose and scope .__.__.._-_-_-_----_-------.

Background ---------------------------------

Hungry Horse Project .______-._-____-_--.

Location and description -------------

South Fork Flathead River drainage basin - 

Meteorological observations __.___--___--_. 

Hydrology _._..__.___.-____________-_._..

Previous investigations -------------------

Page

1

1

1

2

2

2

4

4

5 

8 

Acknowledgments ----------------------------- 11

Theoretical considerations -------------------------- 11

Inflow ----__--_.--..__---_---....------------- 11

Outflow ---_-----_----_--_---_----_--------._-- 12

Change in storage ----------------------------- 13

Data-collection program ___________________________ 15

Gaging-station networks ._-_-_-_--.--_._-______- 15

Drainage areas ---------------------------- 18

Change in reservoir contents _._--_____-__--_____ 20

Evaporation _._.___._______.__._____._-____._. 20

Ancillary meteorological observations ----------- 23

Ground-water observation wells -___._.____.-_.__ 23

Geology of the reservoir area ----------------------- 23

Consolidated rocks __--__--__---_----__---_-_-_- 23

Unconsolidated rocks -_-_------__--__-__-----_- 24

Analysis of data ___________________________________ 25

Approach to problem _.--__--____._______.._... 25

Water budget _-_..._____._.._..._______.__._._ 25

Inflow -----_---------------.---_.__-...__- 26

Primary gaging-station network ---___._ 26 

Secondary gaging-station network ______ 27

Ungaged areas _-----------__----__._-_ 29

Precipitation __________________________ 30

Total reservoir inflow -_____-__-___-__-. 30

Outflow -----_-_--------__-_____--_-.-_---_ 30

Change in reservoir contents --___._._______ 33

Water-budget residual -_------__.____.____. 33

Mathematical model .-----------.--_-_--__-__-_ 34

Page

Analysis of data Continued

Development of equations ------------------- 34

Volumes _.__-__-_--_----__----__------ 37

Selection of dimensional constants ------- 38

Hydrologic constants ---------------------- 38

Outwash, Dry Park area --------------- 38

Till, Canyon Creek area ---------------- 39

Till, Mclnernie-Riverside area ---------- 40

Theoretical solutions and comparison with

preliminary water budget ------------ 41

Trial Af, ------------------------------ 42

Trial Aft ------------------------------ 42

Water-budget modifications ----------------- 43

Revised water-budget computations --------- 46

Selection of model constants ---------------- 46

Single solutions ----------------------- 46

Reservoir stage as a parameter --------- 47

Significance of model characteristics _.__ 49 

Model solutions with two sets of constants ------------------------------ 49

Inherent errors in discharge records --_. 51

Sensitivity ____________________________ 53

Choice of model constants -------------- 53

Aquifer storage __--_____-______----__----_ 53

Use of the model __._-_-____.________-____- 54

Low-flow forecasts -------------------------------- 55

Natural conditions ----------------------------- 55

Regulated conditions -------------------------- 56

Inflow to Hungry Horse Reservoir ----------- 56

Recession characteristics -.___-__-._-___ 58

Inflow forecasts -__-___--__________-___ 59

Precipitation _______--_-__-____-_____-_____ 62

Evaporation ______________________________ 62

Storage changes --------------------------- 63

Water available _._..___.__....___..____.._ 63

Summary and conclusions __________________________ 64

References ________________________________________ 66

Index ----__----_-----____--_--_-----_-__.-_--_.... 66

m
IV CONTENTS

ILLUSTRATIONS

Page

FIGURE 1. Map showing location of the Hungry Horse Project ...--_____----___-_____------____--___---_------- 2

2. Summary hydrograph of daily discharges, South Fork Flathead River near Columbia Falls ------------ 5

3. Summary hydrographs of monthly mean discharges, South Fork Flathead River near Columbia Falls,

water years 1929-51 and 1952-68 ___-..-._..__.______._-._.____.__.__..--_____._______----____ 6

4. Hydrographs of water-surface elevations, Hungry Horse Reservoir, water years 1952-68 -------------- 7

5. Graph showing range of monthly change in contents, Hungry Horse Reservoir, water years 1952-68 - - - - 8 

6-11. Maps:

6. Location of gaging stations prior to the start of this investigation ____---__--______-________- 9

7. Location of gaging stations in primary network, water years 1965-67 ---------------------- 16

8. Location of gaging stations in secondary network, water years 1965-67 __-_-___-________----- 17

9. Drainage areas of subbasins in South Fork Flathead River basin, downstream from Spotted

Bear Ranger Station --__-.____-___-_____..___-_____.______-_______-__-_______--_-___ 19

10. Location of data-collection sites for energy budget study of evaporation .____-___--_----_____ 21

11. Location of ancillary meteorological observation sites and ground-water observation wells ____ 22

12. Graph showing vertical distribution of unconsolidated sediments adjacent to Hungry Horse Reservoir 25

13. Mass curve of accumulated water-budget residuals and month-end reservoir elevations ________---____- 34

14. Schematic sketches of aquifer showing assumed conditions ----------------------------------------- 35

15. Hydrographs showing comparison of ground-water levels with stage of Hungry Horse Reservoir ------- 40

16-28. Graphs:

16. Cumulative apparent gains to reservoir determined from unadjusted water budget and from

M2 and accumulated differences between water budget and M2 --------------------------- 42

17. Revised mass curve of accumulated water budget residuals and month-end reservoir elevations _ 46

18. Reservoir elevation versus cumulative difference of water-budget volumes and those computed

by M2 ______________________________________________________________________________ 48

19. Comparison of volumes of water from water-budget residuals and those computed by Af2 +230

cfs-days per foot of stage change __-___-______.___-____________---___-_________-----__ 48

20. Accumulated volume of ground-water outflow computed using M*+230 cf s-days per foot of

stage change ________________________________________________________________________ 49

21. Comparison of volumes of water from water-budget residuals and those computed using

0.6_tf,+0.4_tf« _________________________________________________________________________ 50

22. Comparison of volumes of water from water-budget residuals and those computed using

M2 +0.4M4 __________________________________________________________________________ 50

23. Accumulated volume of ground-water outflow computed using M2+OAMt --------------------- 51

24. Cumulative residuals for a sequence of assumed inherent errors _________-_---__-______-____ 52

25. Aquifer storage-capacity curves for solutions A, B, and C ___-----___---________--_-_---_--_ 53

26. Aquifer storage and storage capacity computed from solution B, 0.8(Af2 +0.4Af4) --------------- 54

27. Frequency diagrams of accumulated monthly runoff for various time periods, South Fork Flathead River near Columbia Falls, 1929-51 _______---_-__-__-_.-_--_----_--------------- 57

28. Ratio of evaporation amounts calculated by energy budget and by class A pan, Hungry Horse

Reservoir, 1965 and 1966 .______----___-_._.._____-_____-_---.__--------__--_-_------- 63
CONTENTS V

TABLES

Page

TABLE 1. Prime power benefits of the Hungry Horse Project at site and at existing downstream projects _________ 4

2. Summary of monthly meteorologic observations, Hungry Horse Dam, for water years 1948-68 .-_-____-___ 5

3. Summary of monthly and annual discharges, South Fork Flathead River near Columbia Falls _--_-_--_ - 7

4. Summary of monthly change in contents Hungry Horse Reservoir, water years 1952-68 ------------------ 8

5. Drainage areas of subbasins, South Fork Flathead River basin, downstream from Spotted Bear Ranger

Station _____._.____...___._____-.____-___--_.___......__._._____._-..____-.___-..--_---.------- 18

6. Vertical distribution of saturated unconsolidated material in the reservoir area ------------------------ 25

7. Summary of monthly runoff for gaging stations on east-side tributaries to Hungry Horse Reservoir _______ 26

8. Summary of monthly runoff for gaging stations on west-side tributaries to Hungry Horse Reservoir ______ 27

9. Summary of monthly inflow to Hungry Horse Reservoir from stations in primary gaging-station network -___-_____--------------_-_-------_--_____---___________--____-_--_---_------------------_ 27

10. Summary of monthly runoff for secondary-network stations on east side of Hungry Horse Reservoir ______ 28

11. Summary of monthly runoff for secondary-network stations on west side of Hungry Horse Reservoir _______ 28

12. Summary of monthly inflow to Hungry Horse Reservoir from stations in secondary gaging-station network _ _ 29

13. Summary of monthly inflow to Hungry Horse Reservoir from the ungaged areas ___-__-__---_-_-_---_-_- 29

14. Summary of monthly inflow to Hungry Horse Reservoir _-___________-___----_-_---___---_------------- 30

15. Comparison of average rates of evaporation from three sources: energy budget, mass transfer, and class

A pans, Hungry Horse Reservoir, 1965 and 1966 ____________________-_--____--____---__------_----- 31

16. Evaporation from Hungry Horse Reservoir, by energy-budget method, 1965 and 1966 _______----__-_-_--- 32

17. Summary of monthly outflow, Hungry Horse Reservoir -____-____________--___--___------_---_------- 32

18. Month-end reservoir elevations and monthly changes in reservoir stage and contents, Hungry Horse Reservoir 33

19. Components of water-budget computations for Hungry Horse Reservoir _-_______________--______-_-_--- 34

20. Symbols used in the mathematical model ___-__-_______-________________--____--..---_---_----._---_--_ 35

21. Lineated stage of Hungry Horse Reservoir and input constants to theoretical model --------------------- 41

22. Percentage deviations of high-water discharge measurements from rating tables, South Fork Flathead

River above Twin Creek near Hungry Horse __________________________________--___------------ 43

23. Monthly runoff, South Fork Flathead River above Twin Creek near Hungry Horse ---------------------- 44

24. Revised estimate of reservoir inflow from ungaged drainage area __-__-__---__-----_-_----_--_--------- 44

25. Percentage deviations of high-water discharge measurements from tentative rating table, South Fork Flathead River near Columbia Falls --___-_--__---._------__-_-_-_-_____-___.___--_--_----_------------ 45

26. Summary of percentage deviations of high-water discharge measurements from tentative rating tables,

South Fork Flathead River near Columbia Falls _____-____________________--______---_--------__--- 45

27. Monthly runoff, South Fork Flathead River near Columbia Falls .___--._-.__-__.__.___------_----------- 45

28. Revised components of water-budget computations Hungry Horse Reservoir .__________-_---___--_-__---_ 46

29. Volumes of bank storage computed from the M2, M3, and M4 ----------------------------------------- 47

30. Monthly runoff, South Fork Flathead River near Columbia Falls ____---____--__---__-------------------- 55

31. Accumulated monthly runoff through April, South Fork Flathead River near Columbia Falls ------------ 56

32. Estimated monthly inflow to Hungry Horse Reservoir __________________--_---_---__--_-_------------ 58

33. Accumulated monthly inflow through April to Hungry Horse Reservoir _._-_____--____--_---------__-_- 59

34. Recession index for the inflow to Hungry Horse Reservoir ________________-_--__--_-__--_----_-------_- 59

35. Monthly precipitation, Hungry Horse Dam ____._____.____._--_.____-_.---_--------------------------_ 60

36. Accumulated monthly precipitation through April, Hungry Horse Dam ._----_-_-----.------_---_.------- 60

37. Monthly degree days (65° F), Hungry Horse Dam _._____.___._____-__________-___-_--___---_-------- 61

38. Accumulated monthly degree days (65° F) through April, Hungry Horse Dam ___________.___-___---_--- 61

39. Summary of step-regression analysis, reservoir inflow versus recession index, precipitation, and degree

days (65° F) ...._-__._....___._.___._._....._.........._.._.._..__.._..._..__-.._.__-.__.._.__ 62

40. Monthly and seasonal evaporation, class A pan, Hungry Horse Dam ____._-.--_____-___--------_--------- 63

HYDROLOGY OF HUNGRY HORSE RESERVOIR, 

NORTHWESTERN MONTANA

By W. D. SIMONS and M. I. RORABAUGH

ABSTRACT

Hungry Horse Project, on the South Fork Flathead 

River in northwestern Montana, is an important element 

in the comprehensive water-resources-development plan for 

the Columbia River basin. It is used primarily for at-site and 

downstream power generation and local and downstream 

flood control. Hungry Horse Reservoir has a usable storage 

capacity of 2.98 million acre-feet for at-site production of 

electrical energy. Previous studies have indicated that there 

may be an additional increment of ground-water storage in 

the permeable bed and banks of the reservoir that responds 

to changes in reservoir elevation. This is referred to as bank 

storage.

The existence of an additional amount of usable bank 

storage was established by a comprehensive water-budget 

analysis of Hungry Horse Reservoir for the period October 

1964-April 1967. A theoretical model of the response of the 

aquifer adjacent to Hungry Horse Reservoir to changes in 

reservoir stage was developed. The constants used in the 

mathematical equations were based on the residuals from 

the water-budget computations.

A wide range of potential solutions is possible when the 

water-budget and model methods are used separately. But 

when they are used in conjunction with each other, the 

range of potential solutions can be reduced and a most 

probable solution inferred. The model solution, when used to 

predict additional water supplies available during drawdown periods or when used to adjust historical records for 

general hydrologic studies, is expected to give results which 

are within 25 percent of the true values of the bankstorage component.

The selected solution indicates that the ground-water 

storage in the alluvium adjacent to Hungry Horse Reservoir 

is 108,000 cfs-days between the elevations of 3,336 and 3,560 

feet above mean sea level. This amount of added storage 

is not totally available as reservoir inflow under normal 

patterns of regulation because of the time-lag and hysteresisloop effects of ground-water movement across the interface 

between the aquifer and the reservoir.

The computed additional inflows to Hungry Horse Reservoir from bank storage during the three drawdown periods 

studied are 34,000, 20,000, and 43,000 cfs-days. The amounts 

of ground-water inflow average about 60 percent of the 

corresponding ground-water storage. These are believed to be 

large enough to be considered in the operation of Hungry 

Horse Reservoir. Other patterns of reservoir regulation

could increase or decrease the amount of effluent groundwater 

indicated above.

Forecasts of water available for project use should include 

the following components: Reservoir inflow ( + ), precipitation on the reservoir ( + ), evaporation from the surface 

of the reservoir (-), changes in reservoir storage (±), and 

changes in ground-water storage adjacent to the reservoir 

(±). The reservoir inflow and changes in reservoir storage 

are the largest components, but precipitation, evaporation, 

and changes in ground-water storage should be evaluated in 

order to enhance the efficient operation of Hungry Horse 

Reservoir.

Step-regression analysis of the water-budget data indicates 

that the inflow to Hungry Horse Reservoir, except for 

precipitation, can be satisfactorily estimated by a two-station 

index. This index is based on the discharge data for South 

Fork Flathead River above Twin Creek and for Sullivan 

Creek. The recession characteristics of these two streams 

provide a means for forecasting the assured inflows to the 

reservoir during the low-flow periods. The use of precipitation 

and temperature data from Hungry Horse Dam provides 

a potential means of adding refinements to the forecasting 

procedures based on recession characteristics.

INTRODUCTION 

PURPOSE AND SCOPE

Hungry Horse Project, which includes a reservoir with total storage capacity of 3,468.000 acrefeet, is one of the major Federal multipurpose 

components of the water-development program in 

the Columbia River basin. It is used primarily for 

at-site and downstream power generation and for 

flood control. Since its completion in 1953, certain 

regulating problems dealing with an apparent imbalance between reservoir inflows and outflows have 

been encountered. Prior to this investigation several 

unsuccessful attempts were made to solve this 

problem. The hydrologic data collected during the 

period 1948-60 were inadequate to provide conclusive answers.

The basic objectives of this investigation were 

to determine more accurately the volume of water
HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

available at Hungry Horse Reservoir, including 

bank storage, and to improve the forecasting procedure for low-water periods. The keys to the success of this investigation were the accurate definition of the water budget for Hungry Horse Reservoir and the development of a suitable mathematical 

model of the ground-water movement in the aquifers 

adjacent to Hungry Horse Reservoir. The ability 

to assess and evaluate each of the variables involved 

led to the resolution of the apparent imbalance between reservoir inflows and outflows.

This study included (1) the collection of the 

data required to define accurately the inflow and 

outflow components of the hydrology of the reservoir and (2) the analysis of the water-budget components to improve the procedure for forecasting 

reservoir-inflow volumes during low-flow periods. 

The intensive data-collection program included direct measurement or an evaluation of the following: 

Surface inflow and outflow, change in reservoir 

contents, subsurface inflow including bank storage, 

and precipitation on, and evaporation from the 

water surface of the reservoir. Evaporation from 

the reservoir surface was determined by an energybudget procedure. A separate basic-data supplement 

summarizes the field data collected for this project 

(Simons, 1968).

In previous collaborative programs with the 

Bonneville Power Administration, the methods of 

relating ground water to surface water were explored. These explorations tested certain theoretical 

concepts and developed equations for expressing 

bank-storage effects in terms of the hydraulic 

characteristics of the alluvium adjacent to a stream 

channel and river stage. The current study expands 

these theoretical concepts to the unique characteristics of a large reservoir in a mountain valley.

The low-flow-forecasting section was developed 

as an expansion of previous studies of the base-flow 

characteristics of streams in the Columbia River 

basin. This, also, has been a part of the long range 

collaborative program of hydrologic investigation 

with the Bonneville Power Administration.

BACKGROUND

HUNGRY HORSE PROJECT 

LOCATION AND DESCRIPTION

The earliest investigations of hydroelectric power 

potentials in the South Fork Flathead River basin 

were carried on by the U.S. Geological Survey in 

1921 and were continued periodically over the next 

25 years. The U.S. Army Corps of Engineers made 

a preliminary study of this general area during

the early 1930's, and in 1939 a damsite at Devils 

Elbow, 1 mile downstream from Hungry Horse 

Dam, was investigated in more detail.

The Hungry Horse Project was authorized by 

Congress in 1944 and was constructed by the U.S. 

Bureau of Reclamation during the period April 

1948-July 1953. The initial storage of water began 

in September 1951, and full-pool elevation of 3,560 

feet above mean sea level was reached in July 1954. 

The first power was generated in October 1952.

The principal features of the Hungry Horse Project include a dam, reservoir, and powerhouse. 

These are in the lower reaches of the South Fork 

Flathead River in northwestern Montana (fig. 1). 

The dam is about 5 miles upstream from the confluence of the South Fork Flathead and Flathead 

Rivers, about 20 miles northeast of Kalispell. It 

is in a deep, narrow canyon and is a variable113°

113°

10 20 30MILES 

I

FIGURE 1. Location of the Hungry Horse Project.
INTRODUCTION

thickness concrete arch structure. The structural 

height of the dam is 564 feet, and it has a crest 

length of 2,115 feet.

The following tabulation lists elevations, in feet 

above mean sea level, of pertinent features of the 

project:

Feature Elevation

Top of dam _____-_-----_________- 3,565

Normal full pool _________________ 3,560

Crest of spillway ________________ 3,548

Limit of power storage ___________ 3,336

Penstock openings ________________ 3,319

Sill of river outlet openings ._.__- 3,196

Powerhouse floor ________________ 3,113

Maximum tail water _----_______-- 3,101

Minimum tail water _______________ 3,074

The powerhouse is at the toe of the dam and 

contains four generating units with a total nameplate capacity of 285,000 kilowatts. The switchyard 

for the powerhouse is about one-fourth mile downstream on the right bank.

The reservoir is about 33 miles long and extends 

upstream to a point a short distance below Twin 

Creek. The reservoir ranges from 1/2 to 3l/_; miles 

in width and covers an area of about 24,000 acres, 

or nearly 37 square miles. Maximum depth of water 

is about 490 feet, total storage capacity is 3,468,000 

acre-feet, and the usable storage for the production 

of electrical energy is 2,982,000 acre-feet between 

the elevations of 3,336 and 3,560 feet. The storage 

ratio (usable storage to average annual runoff) is 

1.27 years. Thus the reservoir can be operated in a 

"cyclic" manner in which the drawdown period 

extends over more than one low-water season.

Primary benefits from this project are production of hydroelectric energy, flood control, and recreation. The basic operating plan for Hungry 

Horse Reservoir is to store most of the runoff 

during the snowmelt period May, June, and 

July and to release this stored water over the 

balance of the year as needed. This plan of operation provides flood control during the high-runoff 

period and provides additional water for the generation of electrical energy during periods of heavy 

power demands. The size of this reservoir and its 

potential for being operated on a cycle that is 

longer than 1 year make it an important element 

in the long-range program for the control and 

utilization of the water of the Columbia River.

Multipurpose guidelines for the operation of the 

Hungry Horse Project were developed jointly by 

the Bureau of Reclamation, the Corps of Engineers, 

and the Bonneville Power Administration, acting in 

collaboration with the Water Management Subcommittee, Columbia Basin Inter-Agency Committee (CBIAC). These guidelines are formalized in 

Memorandums of Understanding between the 

Bureau of Reclamation and the Corps of Engineers 

for flood control, and between the Bureau of Reclamation and the Bonneville Power Administration for the generation of power. Frequent reviews 

and discussions of proposed operating schedules are 

maintained by these agencies and the Columbia 

River Water Management Group.

Hungry Horse Project is an integral part of the 

Federal Columbia River Power System, which is 

composed of the hydroelectric generating facilities 

constructed and operated by the Corps of Engineers and the Bureau of Reclamation and the 

transmission network built and maintained by the 

Bonneville Power Administration. The generating 

plants and the transmission facilities are operated 

as an integrated electrical system. The Bonneville 

Power Administration acts as marketing agent for 

the coordinated system.

In 1966-67 this system included 22 projects with 

installed generating capacity (nameplate rating) 

of 6,758,150 kilowatts. The associated usable storage capacity is 11,946 million acre-feet. Hungry 

Horse Project supplies 4.2 percent of the generating capacity and contains about 25 percent of the 

usable storage in the system. Only Franklin D. 

Roosevelt Lake contains more of the system's usable storage capacity.

The prime power benefits that can be directly 

attributed to Hungry Horse Project were estimated 

at 1,054,000 kilowatts by the Bonneville Power 

Administration. This was based on the actual 

1966-67 installed generating equipment and storage capacity and on the flows for the critical power 

year 1936-37. The details of this estimate are 

shown in table 1.

The gross head between the normal pool of 

Hungry Horse Reservoir, elevation 3,560 feet, and 

the tail water of Bonneville Dam, elevation 15 feet, 

is 3,545 feet. During power year 1967, the water 

released from Hungry Horse Reservoir passed 

through 17 powerplants utilizing a gross head of 

about 2,275 feet. Since that time, three additional 

powerplants have been put into operation and have 

increased the amount of head utilized to about 

2,710 feet, or more than 75 percent of the available 

gross head. Additional powerplant sites downstream from Hungry Horse are being studied which, 

if developed, would utilize several hundred additional feet of head, making a total of more than 

90 percent of the gross head.
HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

TABLE 1. Prime power benefits of the Hungry Horse 

Project at site and at existing downstream projects

[Average kilowatts, based on 1966-67 installations and minimum power 

year 1936-37. Includes U.S. plants only. From Bonneville Power Administration.]

Without With Increase

Hungry Hungry due to

Horse Horse Hungry Horse

Federal system plants:

Hungry Horse ----------

Albeni Falls ---._.-_--_--. 

Grand Coulee ------------

Chief Joseph ------------

McNary _.--..._.. .____

The Dalles ---_-._----__-.

Bonneville ---------------

Total -----.-....-_...

20,000

1,132.000

638,000

525,000

559,000

399,000

222,000

28,000

1,331.000

733,000

570,000

604,000

426,000

222,000

8,000

199,000

95,000

45,000

45,000

27.000

3,273,000 3,914,000 641,000

Non-Federal system plants: 

Kerr ---------____..__

Thompson Falls --..-_ 

Noxon Ranids ........

Cabinet Gorge ------

Box Canyon .........

Rocky Reach --------

Rock Island ..........

Wanapum --.-......

Priest Rapids --------

Total -.-.-.....---.

64,000

28,000

98,000

64,000

43,000

385,000

114,000

336,000

328.000

1,460,000

155,000

38,000

182,000

117.000

60,000

440,000

129,000

381.000

371,000

91,000

10,000

84,000

53,000

17,000

55,000

15000

45,000

43,000

1,873,000 413,000

Combined total .................. 4.733,000 5,787,000 1,054,000

The Bonneville Power Administration has estimated that each acre-foot of water at Hungry Horse 

Reservoir will produce at site and downstream 

about 1,700 kilowatt hours of firm power. Another 

way of expressing this is that a 1-percent increase 

in usable reservoir storage capacity is worth about 

$40,000 annually in firm power sales. Thus, the 

accurate determination of the amount of water 

available at Hungry Horse Project is important to 

the efficient operation of the Federal Columbia 

River Power System. That determination was the 

primary objective of this study.

SOUTH FORK FLATHEAD RIVER DRAINAGE BASIN

The South Fork Flathead River drains about 

1,700 square miles of area lying on the west side of 

the Continental Divide in northwestern Montana. 

This stream flows generally northwestward between the Swan and Flathead Ranges for about 

105 miles and joins the Flathead River about 10 

miles northeast of Columbia Falls. The elevation 

of the drainage basin ranges from about 3,000 feet 

at its junction with Flathead River to mountain 

peaks as much as 10,000 feet above mean sea level. 

Hungry Horse Reservoir occupies most of the lower 

part of the basin lying between 3,070 and 3,560 

feet.

The drainage basin of the South Fork Flathead 

River is almost exclusively within the boundaries 

of lands that are under the jurisdiction of the 

U.S. Forest Service. These lands are covered with 

moderate to sparse stands of evergreen trees, but 

the lower valleys have coverings of brush and some 

deciduous trees. Most of the drainage basin is in a 

natural state, although some logging has been and

is being done under the supervision of the Forest 

Service in the area immediately surrounding Hungry Horse Reservoir.

Except for a few recreational facilities, there is 

no commercial development in the South Fork 

Flathead River basin. Roads extend upstream on 

both banks only as far as Spotted Bear Ranger 

Station. There are two small landing strips for 

light planes in the basin upstream from Hungry 

Horse Reservoir.

METEOROLOGICAL OBSERVATIONS

When construction of the Hungry Horse Project 

was started, there were no meteorological observations being made in the South Fork Flathead River 

drainage basin except intermittent records collected 

by the Forest Service during the fire season. Longterm weather records were available at Kalispell 

and West Glacier. In order to get data that would 

be more representative of conditions at the project, 

a meteorological station was established about 4 

miles downstream from the dam in 1947 which 

provided daily observations of precipitation, maximum and minimum air temperatures, and evaporation (class A pan). This weather station was 

moved 3.3 miles upstream in December 1953 and 

was located within the switchyard of the project. 

Records for the two sites are considered to be 

equivalent.

Monthly data for this station for the water years 

1948-68 are summarized in table 2. Average wateryear precipitation at the dam is about 32 inches 

and during the period of record has ranged from 

about 22 to 42 inches. Larger amounts of precipitation occur in the high mountain ranges, especially to the west along the Swan Range. About 50 

percent of the annual precipitation occurs in the 

period October-February as a result of general 

winter storms. Only 10 percent of the annual precipitation occurs during July and August and is 

generally in the form of summer showers which 

have limited areal extent.

The estimated average annual temperature at 

Hungry Horse Dam is about 42° F. Monthly mean 

temperatures normally range from 21° F. to 66° F., 

although during the period of record these have 

varied from a low of 2.5° to a high of almost 72° F. 

Monthly mean temperatures of 32° F. or lower 

normally occur during the period NovemberMarch.

The usual period of evaporation at Hungry Horse 

Reservoir extends from May through October, although some evaporation may take place in April
INTRODUCTION

TABLE 2. Summary of monthly meteorologic observations, Hungry Horse Dam, for water years 1948-68

October November December January February March April May June July August September

Monthly precipitation, in inches

Average .. 

Maximum 

Minimum .

3.32

6.80

.29

3.48

7.37

.72

3.31

8.21

1.03

3.49

7.02

1.30

2.66

6.11

.91

2.15

3.17

.36

2.24

5.16

.57

2.54

5.03

.65

3.05

6.49

.53

1.57

3.90

.10

2.00 2.46

5.21 6.57

.00 .28

Monthly mean temperature, in °F

Average .. 

Maximum 

Minimum -

43.6

46.9

39.4

32.0

37.6

23.0

26.1

32.9

15.8

21.4

84.1

2.5

26.8

35.5

17.1

31.0

39.4

23.1

41.0

44.9

37.5

51.1

60.6

46.8

57.8

63.5

53.2

65.8

71.8

60.4

63.7 54.2

70.7 62.2

59.1 45.7

Monthly evaporation, in inches, based on partly estimated data 

(class A pan)

Average ..

Maximum

Minimum

1.55

4.00

.70

4.98

8.10

3.72

5.82

7.62

4.68

8.13

11.28

6.76

6.73 3.54

10.35 5.29

4.96 1.97

and November. The estimated seasonal evaporation from a class A pan at this site is 31 inches, 

about one-fourth of which occurs in July and more 

than two-thirds during the period June-August.

HYDROLOGY

When the Hungry Horse Project was authorized, 

there was only one gaging station in the South 

Fork Flathead River basin. Records for this station, 

South Fork Flathead River near Columbia Falls, 

are available as noted below:

Location 

Period (river mUe)

1910-28 _.._.__.__._._..___. 0.4

1928-52 ._.._..._..__..._.._ 2.1 

1952-present -.__.-_---__.__ 3.5

Type of record* 

Fragmentary. 

Continuous.

Do.

The current location is about 1% miles downstream 

from Hungry Horse Dam.

Records for this station provide a measure of 

the amount of water contributed to the Columbia 

River system by the South Fork Flathead River 

under both natural and controlled conditions. Initial storage of water in Hungry Horse Reservoir 

began on September 22, 1951. Thus all data prior 

to that date are a measure of the natural conditions 

that existed prior to the reservoir regulation. Subsequent data represent virtually completely controlled conditions, inasmuch as the active storage 

capacity of Hungry Horse Reservoir is larger than 

the average annual runoff.

Period of record 

May 1928 - September 1951

510152025 510152025 

JUNE I JULY

FIGURE 2. Summary of daily discharges, South Pork Flathead River near Columbia Falls. Adaptation of diagram from the 

Water Management Subcommittee, Columbia Basin Inter-Agency Committee.
HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

The natural runoff regimen for this gaging station is depicted in figure 2. This hydrograph shows 

the average, maximum, and minimum daily discharges for the period May 1928-September 1951. 

It was prepared by the Water Management Subcommittee of CBIAC in connection with its evaluation of runoff forecasts for this station.

The hydrograph shows that the natural discharge 

regimen of the South Fork Flathead River exhibits 

the usual characteristics of an alpine basin for this 

latitude. The stream is characterized by large 

discharges during the snowmelt period, May-July, 

followed by a gradual recession to low flows during 

wintertime. Minimum discharge commonly occurs 

during February. Flows during March and April 

usually exhibit slight or moderate rises as a result 

of the initial melting of accumulated snow and ice. 

During the late summer and early fall periods, 

increases in discharge are common as a result of 

localized showers or storms. There is an increase 

in discharge each fall with the lessening of evapotranspiration demands on the drainage basin. During an average winter there are times when the 

stage-discharge relationship is affected by the 

formation of ice in the stream channel. This effect

can last for a few days or weeks inasmuch as it 

varies with the length and magnitude of the 

sequence of below-freezing temperatures. During 

the period of maximum precipitation, NovemberFebruary, major increases in discharge are not 

common because the precipitation usually falls as 

snow and the cold temperatures prevent it from 

running off immediately.

Using water years 1929-51 as a measure of 

natural (unregulated) conditions, the average observed discharge was 3,297 cfs (cubic feet per 

second). The maximum discharge during this period was 43,400 cfs, which occurred during the 1948 

flood. The minimum observed flow was 206 cfs, 

which was measured during December 1935. However, discharge may have been less during periods 

of severe ice conditions which periodically affect 

this stream. A summary of the natural monthly 

discharges for this station is contained in table 3 

and shown in figure 3.

During construction of Hungry Horse Dam, the 

flow of the South Fork Flathead River was routed 

through a diversion tunnel on the right bank. On 

September 22, 1951, the tunnel was closed and 

storage of water in the reservoir area was initiated.

100,000

50,000 

JFMAM J J AS

100

WATER YEARS 1929-51

M A [ M | J | J | A | S 

WATER YEARS 1952-68

FIGURE 3. Summary of monthly mean discharges, South Fork Flathead River near Columbia Falls, water

years 1929-51 and 1952-68.
INTRODUCTION

TABLE 3. Summary of monthly and

Maximum ..

Minimum ..

Maximum --

Minimum - -

October

956

2,899

432

2,556

8,803

»387

November December

1,189

4,128

361

3,051

9,092

204

Discharges,

1,120

3,504

313

Discharges,

5,073

8,985

898

January

in cubic

843

2,729

266

in cubic

5,654

10,030

»768

annual discharges

February March

, South

April

feet per second, during natural

842

2,210

302

feet per

4,245

9,447

208

1,058

2,945

402

second, during

3,848

14,840

259

5,220

11,770

2,020

regulated

5,555

13,270

202

Fork Flathead

May

River near Columbia Falls

June July

period, water years

12,773

18,140

6,613

period, water

2,915

1 6,817

358

10,484

25,000

3,965

years

3,295

7,345

205

1929-51

3,308

9,717

1,152

1952-68

3,220

6,914

*535

August

1,018

2,282

557

1,104

1,650

»395

September Annual

667

978

493

1,954

5,540

1 955

3,297

4,650

1,647

3,535

5,326

1 1,012

1 Occurred during initial filling of Hungry Horse Reservoir.

By October 11, 1952, the stage had risen to an 

elevation of 3,215.4 feet and the flow was regulated 

through the river outlet tubes. During this period, 

the flow at the downstream gaging station averaged 

less than 20 cfs and the minimum observed was 

about 7 cfs.

The operation of Hungry Horse Reservoir has 

altered the pattern of water being added to the 

Columbia River system by the South Fork Flathead River. The largest flows below Hungry Horse 

Darn normally occur during December and January, and minimum flows occur during August. A

3600

3550

3500

>3450

summary of observed monthly flows for this station for water years 1952-68 is also shown in 

table 3 and figure 3. Except for the period of 

initial filling, the main effect of the operation of 

this project is a redistribution of the flows within 

the year.

The records for this station can be adjusted to 

approximate conditions by making adjustments for 

change in contents for Hungry Horse Reservoir. 

During construction and prior to May 1953, various 

nonrecording gages were used to measure the elevations of the water in the reservoir. Subsequent to

3400

3350

.^3300

z 3250

3200--

3150

3100

3050

DMJSDMJSDMJSDMJSDMJ 

1954 1955 1956 1957 1958

SDMJSDMJ S 

1952 1953

3400

SDMJSDMJSDMJSDMJSDMJSDMJSDMJS 

1962 1963 1964 1965 1966 1967 1968

FIGURE 4. Water-surface elevations, Hungry Horse Reservoir, water years 1952-68.
8 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

that date, continuous records of reservoir stage 

have been recorded by a gage in the south elevator 

tower of the dam.

A hydrograph of the water-surface elevations of 

Hungry Horse Reservoir is shown in figure 4. A 

summary of the monthly change in contents is 

given in table 4 and shown in figure 5. These 

changes are based on the midnight reservoir elevations and the capacity table furnished by the

TABLE 4. Summary of monthly change in contents, in 

acre-feet, Hungry Horse Reservoir, water years 1952-68

Range

May ...........

July -.--..--.--

Mean

----- -72,535

----- -93.970

--... -234,110

----- -282,730

----- -179,325

----- -162,950

----- -77,805

.-.-- +637,875

----- +668,750

..--. +60,810

.-.-. -690

----- -54,785

----- +204,380

Upper

1 +100,000

+32,000 1 -7,190

1 +1,720

1 +34,300

+27,000

+225,000

+991,100

+1,103,000

* +292,000

1 +46,000

1 +15,000

1 +1,807,400

Lower

-498,000

-495,000

-469,000

-555,000

-434,000

-803,000

-550,000

+392,000

+369,000

-12,000

-39,000

-294,000

-291,000

1 Occurred during period of initial filling, September 1951 through July 

1954.

1000 £

0+500

-500

O|N|DJFM|AM|J J|A s

1000 "

FIGURE 5. Range of monthly change in contents, 

Hungry Horse Reservoir, water years 1952-68.

Bureau of Reclamation. The range in monthly 

change in contents of Hungry Horse Reservoir 

has been from -803,000 acre-feet during March 

1965 to +1,103,000 acre-feet during June 1967. 

At the time of the initial construction of the 

Hungry Horse Project, six additional gaging stations were installed on tributaries to Hungry Horse 

Reservoir. During the construction period, a gaging 

station was established on Hungry Horse Reservoir 

to collect records of reservoir stage and contents. 

These gaging stations are listed below along with 

the periods of record prior to October 1964:

South Fork Flathead River at 

Spotted Bear Ranger Station near 

Hungry Horse ----------------

Spotted Bear River near Hungry 

Horse --__._-_-----------------

Twin Creek near Hungry Horse _ - _

Lower Twin Creek near Hungry 

Horse ..__---_-_---------------

Sullivan Creek near Hungry 

Horse -------------------------

Graves Creek near Hungry Horse 

Hungry Horse Reservoir near 

Hungry Horse _-----_------.

Sept. 1948-Sept. 1957; 

Sept. 1959-Sept. 1964.

Oct. 1948-Sept. 1956. 

Sept. 1948-Sept. 1956.

Do.

Oct. 1948-Sept. 1956;

Oct. 1959-Sept. 1964. 

Sept. 1948-Sept. 1956.

Sept. 1951-Sept. 1964.

The locations of these gaging stations are shown in 

figure 6.

About 80 percent of the drainage of the South 

Fork Flathead River near Columbia Falls is encompassed bv this upstream group of stream-gaging 

stations. The data for these stations exhibit the same 

general characteristics as the downstream station 

in its natural state.

PREVIOUS INVESTIGATIONS

During the early stages of the operation of 

Hungry Horse Project, the inflows to the reservoir 

were computed by adjusting the observed outflow 

for the changes in contents in the reservoir. When 

this was done on a daily basis, the resulting hydrograph was very irregular, especially during the fall 

and winter months. During these periods, water is 

withdrawn from storage to meet the large and 

sometimes variable electrical loads. The amount of 

stored water released is large in comparison to the 

actual inflow. Even a small difference in the observed stage of the reservoir could indicate a greatly 

different adjustment to project outflows.

Even under these conditions, it became apparent 

that the inflow computed by this procedure exhibited characteristics that were different from the 

characteristics of the tributaries flowing into the 

reservoir and of other nearby unregulated streams.
INTRODUCTION

114°00'

/South ForKflathead

 near Columbia Falls *.

I Hungry Horse ^». )

* Rpcorvoir ^^iT^-^l ^^

EXPLANATION

Graves Or.

A

Gaging station

Basin boundary

. Reservoir

48°15

48°00

. 48°00'

^.

113°45'*,

101234 SMILES 

1,111111 \

Spotted Bear R. \_ x 

South Fork Flathead R. \ 

at Spotted Bear Ranger Station

113°30'

FIGURE 6. Location of gaging stations prior to the start of this investigation.

The most noticeable difference appeared when large 

amounts of water were withdrawn from Hungry 

Horse Reservoir. Computed inflow increased even

though the discharge at other stations was continuing to follow a natural recession. When water was 

being stored in Hungry Horse Reservoir, the op-
10 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

posite effect was noticed, although to a lesser degree. 

This imbalance between inflows and outflows was 

apparently related to the change in contents of the 

reservoir.

In 1957, the Bonneville Power Administration 

requested the Geological Survey to make an examination of this phenomenon. A preliminary study 

of the problem was conducted by the Technical 

Coordination Branch office in Tacoma, Washington. 

Graphical correlations of monthly mean discharge 

for water years 1949-56 were made between the 

computed inflow (outflow ± change in contents) 

and the flow in tributary and nearby streams. The 

results of this analysis suggested the use of the 

following formula:

where 7 = natural monthly mean inflow to Hungry 

Horse Reservoir, in cubic feet per 

second,

Q! = monthly mean discharge, South Fork Flathead River at Spotted Bear Ranger Station, in cubic feet per second,

and Q2 = monthly mean discharge, Sullivan Creek 

near Hungry Horse, in cubic feet per 

second.

For purposes of that preliminary study, this index 

of the natural inflow to Hungry Horse Reservoir 

was considered satisfactory, even though some seasonal variation was evident.

Estimates of natural inflow were prepared for 

water years 1952-56 using the above formula and 

were compared to the inflow computed by adjusting 

the outflow for change in contents in Hungry Horse 

Reservoir. The comparison indicated that during 

periods of reservoir drawdown the adjusted outflow 

records showed more water than the index of inflow. 

During periods when the reservoir was full or being 

filled, the opposite effect was noted. Thus it was 

tentatively concluded that bank storage existed in 

Hungry Horse Reservoir and that additional studies 

would be needed to refine the index of inflow. Such 

studies should include a geologic examination of 

the reservoir area and the collection of data from 

ground-water observation wells around the periphery of the reservoir.

During 1959 and 1960, the Bonneville Power Administration made additional studies to define the 

cause of this phenomenon and the quantitative 

amount of the effect of reservoir operation on computed inflow to Hungry Horse Reservoir. These 

studies included the extension of the earlier Geological Survey studies to the winter of 1959-60 and

a special program of withdrawals from Hungry 

Horse Reservoir in which the reservoir was alternately drafted and held steady. The results of the 

studies indicated the existence of a difference of 

about 6 percent between the two methods of estimating reservoir inflow. This could be attributed 

to an error in the reservoir-capacity table or to 

excess ground-water inflow (bank storage). Corrections were made by computing a reservoir "use" 

table by multiplying the values in the existing 

storage-capacity table by a factor of 1.06. The Bonneville Power Administration recommended that 

this "use" table be used for all determination of 

power available from the Federal Columbia River 

Power System and that the reservoir inflow be 

computed by the index developed in earlier studies.

During 1961, the Bureau of Reclamation reviewed 

the studies by the Geological Survey and the Bonneville Power Administration and made several 

separate analyses and comparisons. One dealt specifically with the capacity table for the reservoir. 

The comparison indicated that the capacity of the 

reservoir between elevations of 3,360 and 3,500 

feet based on surveys made by the Geological Survey before the reservoir was cleared and by 

the Bureau of Reclamation after the reservoir was 

cleared differed by only one-fourth percent. Thus 

any difference between methods of computing the 

inflow to the reservoir was unlikely to be due to 

errors in the capacity table. Several inconsistencies 

in the data and related analysis suggested that 

there was insufficient evidence to justify making 

any changes in the capacity table at that time.

The Water Management Subcommittee of CBIAC 

reviewed in qualitative terms the results of the 

studies by the Geological Survey, the Bonneville 

Power Administration, and the Bureau of Reclamation. This review generally concluded that:

1. Bank storage probably existed in Hungry Horse 

Reservoir but quantity was unknown.

2. The capacity table was probably not in error.

3. Other hydrologic considerations such as wintertime precipitation, evaporation, and changes 

in hydrologic conditions were not evaluated 

as fully as possible.

4. Further study, including the collection of additional data, should be done before making any 

changes in the capacity table for this reservoir.

Therefore, in December 1961 the Water Management Subcommittee recommended that the original 

capacity table be used until such time as additional 

data could be collected and presented to this sub-
THEORETICAL CONSIDERATIONS 11

committee to prove or disprove the existence of 

the 6-percent factor recommended by the Bonneville Power Administration.

ACKNOWLEDGMENTS

This investigation is part of the long-range collaborative program of hydrologic investigations in 

the Columbia River basin undertaken by the Geological Survey and the Bonneville Power Administration. The Bonneville Power Administration 

requested the current study and furnished most of 

its financial support. It also furnished considerable 

background data and information, especially on the 

power aspects of the Hungry Horse Project and the 

operating problems. The authors wish to acknowledge the active participation of F. A. Limpert, 

Head, Hydrology Section, Bonneville Power Administration, in the overall guidance of the project.

The investigation was made by the Water Resources Division, U.S. Geological Survey, under the 

project leadership of M. I. Rorabaugh who developed the sections dealing with ground-water analyses, including the mathematical model and its 

optimization to the field setting. W. D. Simons was 

project coordinator and developed the sections dealing with the water-budget analyses and the runoffforecasting procedure. The energy-budget data on 

evaporation was developed under the leadership of 

J. S. Meyers, Denver, Colo. The collection of field 

data was primarily carried on by E. J. Blank, 

Kalispell, Mont., under the general supervision of 

C. W. Lane, District Chief, Water Resources Division, Montana. Part of the cost of the energy-budget 

study, test drilling, and ground-water analyses was 

financed by the Geological Survey.

The Bureau of Reclamation furnished financial 

support for the outflow and reservoir-stage gaging 

stations. It also furnished historical data on the 

Hungry Horse Project, observer services, and storage and work facilities at the dam. The Corps of Engineers, Seattle District, furnished meteorologic and 

water-temperature data for previous years and 

loaned some instruments used during this investigation. The Forest Service constructed the gaging 

station Goldie Creek near Hungry Horse and furnished some financial support for the miscellaneous 

discharge measurements. In addition, it supplied 

planimetric maps of the Flathead National Forest 

and ancillary precipitation data collected at Spotted 

Bear Ranger Station. The U.S. Weather Bureau 

furnished precipitation and evaporation instruments used for the ancillary meteorological observations. The Montana State Department of Fish and

Game supplied water-temperature data for the gaging station South Fork Flathead River near Columbia Falls.

THEORETICAL CONSIDERATIONS

The basic problem facing this investigation is the 

apparent imbalance between the two methods of 

computing the inflow to Hungry Horse Reservoir. 

In its simplest form, the problem requires solution 

of this basic relationship:

Inflow=outflow ± change in storage.

Each term in the equation is composed of many 

items which are often interrelated. A qualitative 

discussion of each of the items to be measured or 

evaluated in this investigation follows.

INFLOW

The inflow to Hungry Horse Reservoir is composed of surface and subsurface runoff from the 

area tributary to the reservoir and the precipitation 

that falls directly on the reservoir surface. The 

index of reservoir inflow developed from previous 

studies was based on data from six gaging stations 

that measured the runoff from about 1,310 square 

miles. Principal deficiencies of the index are that 

it was based on runoff from too small a proportion 

of the total drainage area and that records for 

critical periods were lost.

The drainage area above Hungry Horse Dam is 

about 1,654 square miles, the reservoir occupying 

about 37 square miles. The remaining 1,617 square 

miles is the land area that contributes the bulk of 

the inflow to Hungry Horse Reservoir.

A well-defined network of streams drains this 

area. The drainage basins range in size from about 

1,240 square miles, where the South Fork Flathead 

River enters the reservoir, to less than 1 square 

m'le. One of the simplest ways of measuring a 

larger part of the reservoir inflow was to establish 

a gaging station on the South Fork Flathead River 

as close to the reservoir as possible. Since it was 

not feasible to put a gaging station on all the remaining streams tributary to the reservoir, it was 

necessary to determine part of the inflow by indirect means.

One indirect method is to utilize a network concept in the gaging-station operation. In this procedure, a primary network of full-time gaging stations is established. This basic network is supported 

by subsidiary networks of stations where only partial data are collected. Data from these subsidiary 

networks can be expanded by correlation techniques
12 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

to provide larger areal coverage. This method was 

adopted for use in this study.

The primary network of gaging stations included 

those already in operation and eight additional stations to provide coverage of the different sizes, 

shapes, exposures, and terrains represented by the 

various segments of the tributary drainage area. 

Priority was given to the reestablishment of discontinued gaging stations and to the establishment 

of a station on the South Fork Flathead River as 

close to the reservoir as feasible.

The secondary network of partial-year gaging 

stations was composed of 20 locations selected to 

provide broad areal coverage of the remaining tributary area. At each location, the stage-discharge 

relationship was determined and supplemental stage 

records collected at periodic intervals. The time 

interval between observations was selected to cover 

the range in discharge for each location.

A tertiary network of observation points was 

established to provide partial coverage for the remaining or ungaged parts of the drainage basin. 

This network consisted of miscellaneous discharge 

determinations on all other streams entering the 

reservoir. Measurements were normally made during high- and low-flow periods only.

The areas not drained by surface streams are 

small, and their contribution to the reservoir inflow 

is correspondingly small. It was estimated that the 

yield of these areas may be similar to that of the 

small streams measured in the gaging-station networks. Thus the runoff from these areas was included in the estimates of runoff from the ungaged 

area which was sampled by the tertiary network 

of observation points.

Ground-water flow to the reservoir may be assumed to be accounted for in the runoff determinations. Ground-water movement in the hard rocks 

flanking the valley and seepage through the overlying soil cover are considered to be of minor importance. For the unconsolidated material adjacent 

to the reservoir, the assumption does not fully 

satisfy field conditions. In areas of high permeability, such as gravel terraces, water from precipitation and snowmelt recharges to the water table 

and then moves laterally to the reservoir. The timelag in the ground-water system ranges from a few 

days in the open gravels to many months in the 

fine-grained material. The estimates of reservoir 

inflow based on the gaging networks are considered 

to be reasonable on an annual basis; in other words, 

total yield is not greatly in error, although monthly 

values may be affected by the timelag in the groundwater system. In areas of very high permeability, 

where timelag is small, inflow to the reservoir as 

indexed is reasonable irrespective of whether it 

moved as surface runoff or by way of the subsurface route.

Precipitation falling directly on the surface of 

the reservoir immediately adds to the available 

water supply of the project. As such, it is a separate 

component of inflow to the reservoir. Snow falling 

on top of ice cover on the reservoir acts in the 

same fashion. Records of daily precipitation at 

Hungry Horse Dam were used to compute the portion of inflow from precipitation. The total inflow 

to Hungry Horse Reservoir is considered to be the 

sum of the inflows for the primary and secondary 

networks of gaging stations plus inflow from the 

ungaged area plus inflow resulting from precipitation on the reservoir.

OUTFLOW

The gaging station South Fork Flathead River 

near Columbia Falls measures all the water that 

flows past Hungry Horse Dam and includes runoff from the area between the dam and the gaging 

station. Flow at the downstream gaging station 

was modified for this latter factor using the flow 

of Aurora (Fawn) Creek as an index of the runoff 

from the intervening area.

The amount and seasonal variation of evaporation from the water surface of Hungry Horse Reservoir were not known in specific detail at the 

onset of this investigation. The Bureau of Reclamation had collected readings on a class A evaporation pan as part of their meteorological observations since 1948. Currently, the instruments for 

these observations are in the switchyard about onefourth mile downstream from the dam. Normally, 

reservoir evaporation is considered to be seventenths of the evaporation from a class A pan. Tests 

have indicated that this may be satisfactory on an 

annual basis, but it is subject to some variation for 

short periods of time. Thus, it was decided to make 

an energy-budget study of evaporation from Hungry 

Horse Reservoir as an integral part of the waterbudget analysis.

In the energy-budget procedure, the amount of 

evaporation for any time period is computed from 

the net change in energy content of the reservoir 

divided by the heat of vaporization. This method 

of computing evaporation was extensively tested at 

Lake Hefner (Anderson, 1954) and used in the 

water-loss studies at Lake Mead (Koberg, 1958).

A modified form of the basic equation is as follows:
THEORETICAL CONSIDERATIONS 13

a- Qar ~Qftg + Qv ~ Qv

L(l+R)+T0 

where E- Reservoir evaporation,

Qg = Solar radiation incident to the water

surface,

Qr = Reflected solar radiation, 

Qa = Long-wave radiation from the atmosphere,

Qar = Reflected long-wave radiation, 

Qz,g = Long-wave radiation from the reservoir, 

Qr =Net amount of heat added to the reservoir by advection, 

Qv = Increase in energy stored in the reservoir, 

L- Latent heat of vaporization of water

at temperature T0, 

To - Surf ace temperature of water in the

reservoir, 

and #=Bowen Ratio.

The Bowen Ratio is the ratio of the energy conducted to (or from) the air as sensible heat to the 

energy utilized for evaporation. For computation 

the above terms were expressed on a unit-area, 

unit-time basis in metric units.

Consumptive use of water from the reservoir by 

vegetation around the shoreline does occur in some 

areas; but the areal extent is not great owing in 

most part to the steep banks and the shallow root 

systems of the plants. The amount of water used 

consumptively after the reservoir was initially filled 

is probably less than that which was used in the 

natural state. The evaluation of this factor was 

not included in the project investigations. The total 

outflow from the Hungry Horse Reservoir is considered to be runoff as measured by the gaging 

station South Fork Flathead River near Columbia 

Falls, plus evaporation from the surface of the 

reservoir, minus runoff from the area between the 

dam and the gaging station.

CHANGE IN STORAGE

The change in reservoir storage for any period 

of time depends upon the change in water-surface 

elevation and the relation of the elevation to the 

amount of water stored within the topographically 

defined reservoir area. Each of these factors is 

briefly discussed below.

The capacity table for Hungry Horse Reservoir 

was based on surveys made by the Bureau of Reclamation immediately following the reservoirclearing operations. The mapping was done on the 

scale of 1 inch = 400 feet, the contour interval

was 10 feet, and intermediate contours at 5-foot 

intervals were determined in some places. The capacity table developed from these surveys was used 

throughout this investigation.

One procedure for estimating the inflow to 

Hungry Horse Reservoir is to adjust the measured 

outflow by the changes in reservoir contents. During the period July-April, this procedure frequently 

results in a very erratic hydrograph of daily inflows. 

The change in contents in the reservoir is frequently 

large in comparison to the estimated inflow, and 

a small difference in elevation of the reservoir can 

result in a large difference in the estimated inflow. 

A measure of the magnitude of the deviation, in 

equivalent cfs-days, that could be caused by a difference of 0.01 foot in determining the change in 

elevation of the water surface is shown in the 

following tabulation:

Reservoir elevation Deviation 

(feet above mean tea level) (cfs-days per 0.01 ft)

3,560 ...._._..._..__....-_.-...-..- 118

3,500 --__-_-_-._----_-_--_--_-__--- 89

3,450 -__..-_....._--_._._....-.---- 53

3,400 ....._........................ 45

3,336 --_-_--_--.-______--_-------_- 28

Continuous records of the water surface in 

Hungry Horse Reservoir are maintained by a floatoperated water-stage recorder at the dam. This gage 

is in the south elevator tower in block 14. A 24-inch 

gage well extends from elevation 3,300 to 3,570 

feet and is connected to the reservoir by a 4-inch 

brass-pipe inlet. The water-level recorder has a 1:6 

gage scale and a time scale of 9.2 inches per day. 

It is equipped with a selsyn attachment so that 

readings of the water levels in the reservoir may be 

made from the powerplant operator's headquarters. 

There is no outside gage, and prior to 1964 there 

was no regular program of comparing water-surface 

elevations in the reservoir to those in the gage well 

or to those indicated in the operator's headquarters.

In September 1963, the Bureau of Reclamation 

investigated the effect of the temperature-density 

profiles of water in the gage well and in the reservoir on the gaging of the reservoir-surface elevations. They found the water in the gage well to be 

0.09 foot higher than in the reservoir and estimated 

that a maximum difference of +0.16 foot would be 

possible during the period when the water in the 

reservoir was the coldest. The gage was reset in 

December 1963. A program of periodic checking of 

water elevations of the reservoir and in the gage 

well was started in 1964.

Change in storage of ground water is not directly 

evaluated and is included in the water-budget
14 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

residual along with errors and unevaluated minor 

items. The ground-water system for natural conditions (no regulation of reservoir) is represented by 

the following equation:

where GR is ground-water recharge, Gd is groundwater discharge, and &Sa is change in storage in the 

aquifer. Superimposed on the natural system is the 

effect of stage changes of the reservoir. For a simple 

case of a horizontal water table at reservoir level, 

water moves into or out of the permeable bed or 

banks of the reservoir in response to changes in reservoir elevation. When superimposed on a natural 

ground-water system, ground-water flow toward the 

reservoir may be slowed or delayed by the reduced 

gradients caused by a rise in reservoir stage. Thus, 

as the result of "underground backwater," aquifer 

water is stored in response to a rise in reservoir 

levels even though reservoir water may or may not 

have entered the aquifer. For a given change in reservoir stage, the amount of storage change in the 

aquifer is the same regardless of which type of water 

is stored, and no separation of water types is needed 

for this study. This change in storage (ASB)is referred to as bank storage.

For most reservoirs storage extends through the 

topographically defined bed and banks into the adjacent geologic formations. The amount of additional subterranean storage and the rate of movement in either direction between the reservoir and 

the formations are controlled by the areal extent 

and thickness of the formations, the water-bearing 

characteristics (hydraulic conductivity and specific 

storage) of the material, the degree of connection 

of permeable zones with the reservoir, and the timedependent natural ground-water gradients on which 

are superimposed the effects of time-stage manipulation of the reservoir. For equal volumes of 

material this added increment of storage may be 

small for tight materials such as consolidated rocks 

or glacial till and large for unconsolidated alluvium 

or glacial-outwash materials.

The rate at which reservoir water will enter the 

banks in response to a rising stage or return in 

response to a falling stage depends, in part, on the 

hydraulic conductivity and the hydraulic gradient. 

Thus movement would be sluggish in material of 

low hydraulic conductivity such as clay or till and 

rapid in materials of high hydraulic conductivity 

such as clean sand or gravel. The effect of a stage 

change in the reservoir is transmitted landward 

as a wave whose travel rate is controlled by the

aquifer characteristics. Thus it may take days, 

months, or years for complete response. For a reservoir with an adjacent aquifer of very large areal 

extent or one of sluggish characteristics, annual 

cycles of regulation may be too rapid for storage 

in or drainage of more than the part of the formation immediately adjacent to the reservoir. Storage 

in the remote area would be filled at a diminishing 

rate over a period of several or perhaps many 

years. This filling loss could not be recovered unless 

the reservoir were held at low stage for several 

years.

The manipulation of reservoir stage is an important control on movement of water to or from bank 

storage. The thickness of aquifer available for storage or release of water is directly related to the 

stage change in the reservoir. When the amount 

of drawdown is small, the amount of usable bank 

storage is small; when drawdown is large, the 

amount of usable bank storage could be large 

depending on the character of the adjacent materials.

The amount of, and the time distribution of, available bank storage can be computed by a mathematical model from a knowledge of the geology of 

the bank materials, their hydraulic characteristics, 

and the stage fluctuations of the reservoir. Bank 

storage can also be computed from a water-budget 

analysis as a residual in the change-in-storage component :

Bank storage = outflow- inflow ± change in reservoir storage.

Separately, these methods are subject to a wide 

range in possible solutions; but when used in conjunction with each other, the range of potential solutions can be reduced.

A water budget for the combined reservoir and 

adjacent aquifer is:

where RT> = inflow from the drainage basin except 

for the alluvim adjoining the reservoir,

Ru = surf ace runoff from the alluvium, 

GR = ground- water recharge to the aquifer

adjacent to the reservoir, 

P= precipitation on the reservoir, 

0 = outflow including flow past the dam

and evaporation,

&Sr = change in reservoir storage, 

A«J?a = change in natural ground-water storage, 

and A&j= change in bank storage.
DATA COLLECTION PROGRAM 15

The sum of Ru and GR is water yield for the area 

adjacent to the reservoir. In the water budget for 

the reservoir, this area was indexed on the basis of 

measured flow of streams which, for the most part, 

drain areas that permit very little recharge to 

ground water. It is apparent that the three terms in 

parentheses are equal to the runoff-inflow item of 

the reservoir budget. Terms O, P, and ASr are identical in both budgets. Thus, for the reservoir water 

budget the residual includes (A/SB + ASa ) that is, 

changes in bank storage plus changes in storage 

which would have occurred in the natural groundwater system under unregulated conditions.

In a later section equations are derived to describe 

bank-storage responses to reservoir-stage changes. 

The mathematical model does not include changes 

in aquifer storage which would have occurred in 

the unregulated ground-water system. The residual 

of the water budget for the reservoir does include 

this item as well as bank storage and unevaluated 

minor items, so results by the two procedures are 

not exactly compatible. The effects of the difference 

will be discussed in a later section.

DATA-COLLECTION PROGRAM

During September 1962, representatives of the 

Bonneville Power Administration and the Geological 

Survey made a field reconnaissance of the Hungry 

Horse Project area. As a result of this inspection 

and subsequent discussions, the decision was made 

to initiate a detailed study of the hydrology of 

Hungry Horse Reservoir. This study would seek to 

furnish a definitive answer to the basic problem 

of an apparent imbalance between reservoir inflows 

and outflows. Such an investigation would, within 

the limits of funds available, utilize both the waterbudget and ground-water approaches previously discussed. The data-collection programs carried on for 

this investigation are outlined in the following sections.

During the summer of 1964, selection was made 

of the data-collection sites included in each of the 

various categories. Most of the construction and 

instrumentation was done at the same time. The 

data-collection program was started in October 1964, 

and was scheduled to continue until about November 

1966. However, it was extended through April 1967, 

when it appeared that the reservoir drawdown during water year 1967 could be the maximum of record.

GAGING-STATION NETWORKS

The following gaging stations were in operation 

at the start of the investigation:

South Fork Flathead River at Spotted Bear Ranger

Station near Hungry Horse 

Sullivan Creek near Hungry Horse 

Hungry Horse Reservoir near Hungry Horse 

South Fork Flathead River near Columbia Falls

Data from the station South Fork Flathead River 

near Columbia Falls were used as a measure of 

outflow from the project. Data from the stations 

South Fork Flathead River at Spotted Bear Ranger 

Station near Hungry Horse and Sullivan Creek 

near Hungry Horse were used in the computation 

of inflow to the reservoir. Changes in reservoir contents were determined from the station Hungry 

Horse Reservoir near Hungry Horse.

To supplement this sparse network of gaging stations, eight additional gaging stations were installed 

to provide data on the reservoir inflow. These included : 

South Fork Flathead River above Twin Creek near

Hungry Horse

Twin Creek near Hungry Horse 

Soldier Creek near Hungry Horse 

Graves Creek near Hungry Horse 

Canyon Creek near Hungry Horse 

Goldie Creek near Hungry Horse 

Wounded Buck Creek near Hungry Horse 

Emery Creek near Hungry Horse

The location of these sites is shown in figure 7.

The runoff from about 82 percent of the total 

drainage area above Hungry Horse Reservoir was 

measured by gaging stations in this network. Their 

locations were selected to represent different sizes, 

shapes, and orientations of streams tributary to the 

reservoir. The primary network of gaging stations 

for measurement of reservoir inflow includes all 

stations shown in figure 7 except South Fork Flathead River near Columbia Falls and Hungry Horse 

Reservoir near Hungry Horse.

All the new gaging stations were temporary-type 

stations and were run only during the period of 

investigation with the exception of the station South 

Fork Flathead River above Twin Creek. This station 

replaced the gaging station South Fork Flathead 

River at Spotted Bear Ranger Station near Hungry 

Horse as a primary inflow station to Hungry Horse 

Reservoir. These two stations were operated concurrently for water years 1965-67 to develop correlation between the data for the two sites. The 

gaging station South Fork Flathead River above 

Twin Creek includes about 200 square miles more 

drainage area and measures a larger percentage 

of the total inflow to the reservoir.
16 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

114°00

South Fork Flathead 

near Columbia Falls

\ Hungry Horse

. Reservoir

EXPLANATION

Graves Or.

A

Gaging station 

Basin boundary

48°15

South Fork 

Flathead R 

above Twin Cr.

48°00

1234 5 MILES 

I I I I I \

South Fork Flathead R.

at Spotted Bear Ranger Station

113°30' 

FIGURE 7. Location of gaging stations in primary network, water years 1965-67.

In addition to the primary network of regular 

gaging stations listed above, a secondary network 

of partial-year gaging stations was established

which included 20 sites. They are listed in table 5 

(Nos. 12-31) and shown in figure 8. 

Nineteen stations on streams directly tributary
DATA COLLECTION PROGRAM 17

EXPLANATION 

Battery Cr. 

Gaging station

Basin boundary

48°15

101234 SMILES 

1,1 I I I I__I

113°30'

FIGURE 8. Location of gaging stations in secondary network, water years 1965-67.

. 48°00'

to Hungry Horse Reservoir were selected to give 

broad areal coverage of the tributaries to Hungry 

Horse Reservoir not included in the primary gagingstation network. Size of drainage area, convenience 

of operation, and channel stability were the prime 

criteria used to select these sites. The drainage areas
18 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

for these stations range in size from about 1 square 

mile, for Dry Park Creek, to more than 23 square 

miles, for Hungry Horse Creek. Eleven of these 

sites were on streams entering the east bank of the 

reservoir with a total drainage area of about 83 

square miles. Eight sites were on streams entering 

the west bank with a total drainage area of about 

64 square miles.

Aurora Creek, which enters the South Fork Flathead River below Hungry Horse Dam and above the 

outflow gage, was included in this network. The 

drainage area at this site is about 6.5 square miles, 

and the records provide data for the refinement of 

the evaluation of the outflow from the reservoir.

A staff gage or reference point was established 

at each site in this secondary gaging-station network. A partial record of stream stage was collected. 

Discharge measurements were made at intervals 

chosen to provide data covering a wide range in 

flow conditions.

Supplementing the primary and secondary network of gaging stations, miscellaneous discharge 

measurements were made at 40 additional sites on 

streams tributary to the Hungry Horse Reservoir. 

Measurements were normally made during the highflow and low-flow periods only. Data collected at 

these sites were used as a guide in estimating the 

ungaged inflow to Hungry Horse Reservoir. The 

ungaged area encompasses about 125 square miles, 

of which 61 square miles is on the west side of the 

reservoir and 64 square miles on the east side.

DRAINAGE AREAS

During this investigation, the South Fork Flathead River basin was not completely covered by 

modern topographic maps. Earliest determinations 

of the drainage areas were computed from Forest 

Service planimetric maps at a scale of 

one-half inch=l mile. The area of primary concern 

of this investigation deals with the drainage basin 

extending from the gaging station South Fork Flathead River at Spotted Bear Ranger Station near 

Hungry Horse downstream to the gaging station 

South Fork Flathead River near Columbia Falls. 

This area is covered by Forest Service planimetric 

maps in 15-minute quadrangles which were compiled from aerial photographs at a scale of 1:31,680, 

or 2 inches = 1 mile. Generally, ridge lines and 

drainage direction were indicated on the maps. The 

individual drainage basins for the gaging stations 

in the primary and secondary networks and other 

miscellaneous areas used in this study were outlined 

on individual quadrangle maps. The subareas were

planimetered and balanced for each quadrangle 

sheet and are summarized in table 5 and shown in 

figure 9.

TABLE 5. Drainage areas of subbasins, South Fork Flathead 

River basin, downstream from Spotted Bear Ranger Station

No. Subbasin

1 South Fork Flathead 

River at Spotted Bear 

Ranger Station near

2 South Fork Flathead 

River above Twin 

Creek near Hungry

3 Between Hungry Horse 

Dam and South Fork 

Flathead River near 

Columbia Falls -- ---

4 Soldier Creek near

5 Sullivan Creek near 

Hungry Horse ...--, 

6 Graves Creek near 

Hungry Horse ------- 

7 Goldie Creek near 

Hungry Horse ----- 

8 Wounded Buck Creek 

near Hungry Horse --

Total -----------

9 Twin Creek near

10 Canyon Creek near 

Hungry Horse ------ 

11 Emery Creek near 

Hungry Horse ------

Total .------.--.

12 Clark Creek near

13 Battery Creek near 

Hungry Horse ----- 

14 Wheeler Creek near

15 Forest Creek near 

Hungry Horse ------- 

16 Clayton Creek near

17 Flossy Creek near

18 Lost Johnny Creek near

19 Doris Creek near 

Hungry Horse ------

Total -----------

20 Lower Twin Creek neai

21 Dry Park Creek near 

Hungry Horse ------ 

22 Hoke Creek near

23 Losran Creek near 

Hungry Horse ------- 

24 Felix Creek near 

Hungry Horse ------ 

25 H*rris Creek near

26 Deep Creek near 

Hungry Horse ----- 

27 McTnemie Creek near

28 Murray Creek near 

Hungry Horse 

29 Riverside Creek near 

Hungry Horse 

30 Hungry Horse Creek 

near Hungry Horse .

Total ------------

31 Aurora Creek near

33 . - -- do -----------

34 Reservoir at full

pool ----------------

Area 

(SQ mi)

958

160 

8.7

4.77

71.3 

27.0 

3.29 

13.6

120

47.0

5.8 

26.4

79.2

4.38

2.45 

22.2 

4.69 

6.13 

1.60 

9.51 

13.5

64.5 

22.4

1.11 

3.00 

6.73 

9.13 

2.79 

2.68 

2.57 

3.08 

5.83 

23.3

on c

6.5

61 

64

37.2

Side of 

Hungry Horse 

Reservoir

West --------

.-.. do ------- 

.... do ...... . 

.--. do .---.-- 

--.. do -------

..-. do -----.. 

-_ do -------

.... do ------- 

..-. do ------- 

.-_ do -------

..-- do ------- 

.... do ------- 

..-- do ------- 

,..- do -----

-._. do ------- 

..-- do -------

_--. do ------- 

.... do ------- 

,. do -------

__-_ do -------

--.- do -------

,- do -------

 _ do -------

do ------

tXTaet

Remarks

Primary 

network.

Do.

Primary 

network.

Do. 

Do. 

Do. 

Do.

Primary 

network.

Do. 

Do.

Secondary 

network.

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do.

Secondary 

network.

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do.

Secondary 

network.
DATA COLLECTION PROGRAM 19

48°15

EXPLANATION

South Fork Flathead River

Ungaged area

Basin boundary 

Subbasin boundary

48 "00

101234 SMILES

lil I I I I I

113°30'

48°00'

FIGURE 9. Drainage areas of subbasins in South Fork Flathead River basin, downstream from Spotted Bear Ranger

Station.

A part of this area was, at the time of this investigation, also covered by Geological Survey topographic maps. The drainage areas of 11 small 

tributary basins, common to both sets of maps, were
20 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

planimetered and compared. This indicated an overall degree of comparability of about 1 percent.

In the area of primary concern, the incremental 

drainage area computed from the recent Forest 

Service maps was about 14 square miles larger than 

that computed from data in "Water Resources Data 

for Montana Part 1, Surface Water Records" for 

water year 1965 (available from the U.S. Geol. 

Survey, Helena, Mont.). Since the Forest Service 

quadrangle maps were of a more recent edition and 

published at a larger scale, the drainage areas 

computed from them were used as needed throughout this report. The Bonneville Power Administration computed and furnished these drainage-area 

determinations as a contribution to the study.

CHANGE IN RESERVOIR CONTENTS

The collection of records at the gaging station 

Hungry Horse Reservoir near Hungry Horse was 

continued. The midnight reservoir elevations were 

furnished by the Bureau of Reclamation, and these 

were used to compute the change in contents of the 

reservoir.

Since 1964, direct determinations of the water 

level in the gage well and the reservoir have been 

made about twice a month by means of an electric 

tape gage. Thermal profiles of the water in the 

gage well and reservoir were made for various 

seasons of the year. Three temporary gages for recording the water-surface elevations of the reservoir 

were maintained for short periods of time to study 

local variations in water-surface elevations during 

periods of near-full pool.

EVAPORATION

The general procedures developed for the Lake 

Hefner and Lake Mead studies (p. 12) were adopted 

for use at Hungry Horse Reservoir. The inflow, outflow, and change-in-contents data needed were collected as part of the water-budget studies.

The measurements of radiation and vapor pressure were made at the south (left) elevator tower 

of the dam. Sensing elements consisting of an Eppley 

pyrheliometer, a flat-plate radiometer, and a thermocouple psychrometer were placed on the roof of the 

elevator tower. These were connected to an eightchannel recording potentiometer located inside the 

elevator tower. Observations of radiation and vapor 

pressure were recorded at 8-minute intervals on the 

potentiometer charts. Supplemental accumulating 

dials attached to each channel of the potentiometer 

were read daily.

The water-surface temperature and wind movement over the reservoir were recorded at two raft

stations. One raft was at the log boom about 1,000 

feet upstream from the dam, and the second was 

opposite the confluence of Graves Creek with the 

reservoir. These raft stations were serviced weekly. 

The mean daily water-surface temperatures were 

computed directly from the recorder charts. The 

wind movement at the 2-meter level was measured 

by an anemometer equipped with dials which accumulated the total wind movement in 10-mile units. 

In addition, the passage of each 10 miles of wind 

was recorded on the temperature-recorder charts by 

means of tick marks. Because daily wind records 

were not required in the energy-budget procedure, 

the total wind movement as determined by readings 

of the anemometer dials was used as the basic data.

Thermal surveys of the water stored in the reservoir were made at about 2-week intervals. Each 

thermal survey consisted of measuring the vertical 

water-temperature profile at 23 locations evenly 

spaced along the axis of the reservoir. The watertemperature observations were made from a boat 

utilizing a Whitney underwater thermometer. Additional thermal-profile data were collected at the log 

boom upstream from the dam to cover the balance 

of the period April 1966-ApriI 1967 not included 

in the energy-budget evaporation study.

Continuous records of the water temperatures of 

seven streams tributary to Hungry Horse Reservoir 

were maintained at the following gaging stations:

South Fork Flathead River above Twin Creek, near

Hungry Horse

Twin Creek near Hungry Horse 

Soldier Creek near Hungry Horse 

Sullivan Creek near Hungry Horse 

Graves Creek near Hungry Horse 

Canyon Creek near Hungry Horse 

Emery Creek near Hungry Horse

The location of these sites is shown in figure 10.

A recording thermometer was also maintained 

at the gaging station downstream from Hungry 

Horse Dam (South Fork Flathead River near Columbia Falls). When releases were small or intermittent, however, the temperature of the water leaving the reservoir could change appreciably while 

flowing down the stream channel from the dam 

to the gaging station. Mean outflow temperature 

was therefore derived from the three components 

of flow:

1. Power flow, withdrawn at an elevation of 3,319 

feet, whose temperature was measured as the 

water passed through the turbines.
DATA COLLECTION PROGRAM 21

EXPLANATION

 

Radiation station

 

Raft station

a 

Thermal-survey point

® Emery Cr.

Gaging station with watertemperature recorder

48° 15 Basin boundary

South Fork Flathead R.

near Columbia Falls * /k\EmeryC'r.

V -^V^'^/

South Fork 

Flathead R: 

above Twin Cr.

48°00

101234 SMILES 

1,111111 \

113"30'

FIGURE 10. Location of data-collection sites for energy-budget study of evaporation.

2. Spillway flow, from the surface of the full reservoir, whose temperature was measured by a 

recording thermometer on the instrument raft.

3. Reservoir release, withdrawn infrequently at an 

elevation of 3,196 feet, whose temperature was 

obtained from periodic reservoir surveys.
22 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

EXPLANATION

-(J)-

Precipitation, temperature, wind, 

and evaporation station

Radiation station

O

Precipitation station, temporary

Ground-water observation wells 

 ^^ ^ 

Basin boundary

§BettyCr. (

/^ r-i Ranger 

Station

South Fork 

Flathead R. 

above Twin Cr.

48 "00 . 48°00'

101234 SMILES i.i i i i i i

113°30'

FIGURE 11. Location of ancillary meteorological observation sites and ground-water observation wells.
GEOLOGY OF THE RESERVOIR AREA 23

ANCILLARY METEOROLOGICAL OBSERVATIONS

The Bureau of Reclamation has made daily 

weather observations at a site about one-fourth mile 

downstream from the dam in the project switchyard. Records for this station are included in the 

State Climatological Observations for the State of 

Montana as Hungry Horse Dam. Daily observations 

include maximum and minimum temperatures, precipitation, wind, and evaporation from a class A 

evaporation pan. The evaporation observations were 

normally made from about May through September. 

Since these observations might not be representative of the conditions at the surface of the reservoir, 

ancillary meteorological observations were made on 

the right abutment of the dam, just above the 

reservoir flow line. Daily temperature and humidity 

data were recorded in a standard Weather Bureau 

shelter. These were supplemented by observations of 

maximum and minimum air temperatures measured 

on Monday, Wednesday, and Friday of each week 

during the summertime period. Total solar radiation 

was also recorded at this site. On the Monday, Wednesday, and Friday schedule, observations were made 

of total wind movement at 5.5-foot and 11.5-foot 

levels, evaporation measurements were made from 

a class A pan, and precipitation amounts were 

measured in a standard 8-inch Weather Bureau 

gage.

Intermittent observations of precipitation were 

made by Geological Survey personnel during the 

summer seasons of 1965 and 1966 at the gaging 

stations Goldie Creek near Hungry Horse and South 

Fork Flathead River above Twin Creek and at Betty 

Creek Ranger Station. The Forest Service made 

daily observations of precipitation at the Spotted 

Bear Ranger Station during the fire seasons. The 

location of these ancillary meteorological observation sites is shown in figure 11.

GROUND-WATER OBSERVATION WELLS

During the summer of 1964, three ground-water 

observation wells were drilled in a 1500-foot-wide 

river terrace on the right bank of the reservoir 

about 2 miles downstream from the head of the 

reservoir and just upstream from Dry Park Creek. 

These wells were on a line which was perpendicular 

to the shore of the reservoir and extended toward 

the drainage divide on the eastern side of the reservoir. The wells were 195, 410, and 800 feet from 

the bank of the reservoir at full pool. Each of these 

wells was cased with steel pipe seated in gravel 

and equipped with a water-stage recorder.

During June 1966 three additional ground-water

observation wells were drilled on the right bank of 

the reservoir about 10 miles upstream from Hungry 

Horse Dam. One of these observation wells was near 

a Forest Service boat-landing area at the mouth 

of Riverside Creek about 210 feet from the reservoir. Two other observation wells were about onehalf mile upstream from the mouth of Mclnernie 

Creek, at distances of 115 and 340 feet from the 

reservoir. Each of these observation wells was 

cased with perforated steel pipe and equipped with 

a water-stage recorder.

The location of these ground-water observation 

wells is shown in figure 11. Geologic samples were 

obtained at each site. The thermal profiles of the 

water were measured at periodic intervals in the 

Dry Park and Riverside observation wells.

GEOLOGY OF THE RESERVOIR AREA 

CONSOLIDATED ROCKS

The basin of the South Fork Flathead River is 

underlain principally by sedimentary rocks of the 

Belt Supergroup (Ross, 1959). In the lower part of 

the basin three formations of the Belt Supergroup 

are of interest. The oldest, the Ravalli Group, includes the Grinnell Formation, which is about 4,000 

feet thick and consists of mostly siliceous argillite 

and a top unit of calcareous argillite. Overlying 

the Ravalli Group is the Piegan Group which includes the Siyeh Limestone, a laminated massive 

limestone about 5,000 feet thick having impurities 

of magnesia, silica, and argillaceous material. The 

Missoula Group, of much greater thickness, overlies 

the Piegan and consists of argillite, quartzitic argillite, and quartzite.

Major parallel faulting which trends northnorthwest, uplift, and tilting produced a topography 

of high mountains and troughs. Formations dip 

toward the east-northeast at about 2,000 feet per 

mile. Hungry Horse Reservoir occupies a structurally controlled trough. Vertical displacement in the 

fault zone is several miles, the upthrown side being 

on the east.

The oldest rocks, the Grinnell Formation, crop 

out along the high-mountain basin divide about 8 

miles west of the reservoir. Major streams entering 

the reservoir from the west head in the Grinnell 

flow across the younger Siyeh Limestone and thence 

across the Missoula Group. Main-channel valleys 

are partly filled with glacial-outwash deposits 

where they cross the Siyeh Limestone. Minor westside tributaries to the reservoir head in and flow 

across the Missoula Group. Principal streams on the
24 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

west side have tributary systems that are strongly 

influenced by the geologic dip. Westerly flowing 

secondary tributaries which flow across the bedding 

planes are short and have steep gradients. In contrast, easterly flowing secondary tributaries are 

longer, have less steep gradients, and have minor 

branches.

On the east side of the reservoir, the basin divide 

is in the upthrown Grinnell Formation and Siyeh 

Limestone. Tributaries to the reservoir flow westward across the bedding of the Grinnell. The eastside tributaries, compared to those on the west, are 

shorter, have steeper gradients, and contain much 

less glacial material in their valleys. An exception 

to the contrast in stream patterns is found in the 

headwater area on the east side where local faulting has produced a setting whereby Twin Creek 

and Lower Twin Creek have tributary systems 

which resemble Sullivan Creek on the west side.

Consolidated rocks which could be related to bank 

storage are (1) the Siyeh Limestone on which the 

dam was built and which forms the valley base and 

sides in the lowermost reaches of the reservoir and 

(2) part of the Missoula Group which is exposed 

along the western side of the valley and which 

underlies the alluvial fill in much of the reservoir 

area.

The limestone is generally resistant to solution. 

Joints which have been enlarged at the surface by 

weathering narrow with depth. They are commonly 

clay filled and in places have been filled with calcite. 

Very little movement of reservoir water to or from 

this limestone would be expected because of the 

very limited void space for storage and because only 

a small volume of this material is adjacent to the1 

reservoir.

Rocks of the Missoula Group are fairly tight, and 

only in weathered zones would they be expected to 

transmit significant quantities of water. They are in 

direct contact with the reservoir in very limited 

areas in the river bed near the head of pool and 

along the lower reaches of Graves, Hungry Horse, 

and Emery Creeks.

Because of limited exposure to the reservoir and 

small storage capability, these rocks are considered 

unimportant in the bank-storage studies. It is probable that there is a seepage zone at the contact of 

the soil zone and the top of the consolidated rocks. 

This would be consistent with observations of seeps 

and water in roadside ditches during a fairly dry 

period, September 24-27, 1962. Small amounts of 

water undoubtedly seep into the unconsolidated sediments adjacent to the reservoir.

UNCONSOLIDATED ROCKS

In the main valley of the South Fork Flathead 

River and in the lower reaches of some tributaries, 

rocks of the Belt Supergroup are covered by old 

alluvium and associated deposits. Ross (1959) 

grouped Tertiary and Pleistocene valley fill of sand, 

gravel, and silt as a unit. The map shows these 

materials as a 4-mile-wide deposit reaching an elevation of about 3,800 feet near the dam and about 

4,300 feet near the head of the lake. The river 

flows through this material, and is flanked by 

modern alluvium of gravel, sand, and silt in a band 

ranging from one-fourth to 1 mile in width.

At the time the reservoir area was cleared, A. F. 

Bateman, Jr., Conservation Division, Geological 

Survey, mapped the unconsolidated deposits in and 

adjacent to the reservoir. He also constructed 80 

cross sections. Very few subsurface data were available; hence these sections represent a large degree 

of interpretation. This unpublished material was of 

considerable value in the project studies.

Bateman (unpub. data, 1951-52) classified the unconsolidated material as follows:

Pleistocene till made up of well-graded mixtures of 

angular to rounded boulders, cobbles, pebbles, and 

sand with a matrix of silt or silty clay.

Pleistocene outwash consisting of glaciofluvial deposits underlying terraces from 10 to 150 feet 

above the Flathead River or associated with tributary streams. Mostly unconsolidated mixtures 

of gravel and sand with cobbles and boulders 

and minor amounts of interbedded sands and silts.

Pleistocene ponded deposits of laminated clay, silt, 

or interbedded clay and silt, mostly of very limited 

areal extent.

Holocene terrace gravel, reworked glacial-outwash 

material redeposited on terraces, consisting of 

clean mixtures of gravel and sand with minor 

amounts of interbedded silt and clay.

Holocene inactive alluvium consisting of coarse 

gravel-sand mixtures containing cobbles and 

boulders and in places silt with interbedded sand 

and silt, located in streambanks and beds below 

the depth of scour and in alluvial fans and cones.

Holocene active alluvium of similar character and 

location as the inactive alluvium but occasionally 

reworked during floods.

Alluvial deposits of slope wash, talus, and landslide 

deposits. Amounts of material in these classes 

are small.

The unconsolidated materials under and adjacent 

to the reservoir are by far the most important part
WATER BUDGET 25

of the bank-storage problem. Distribution of the 

types of material is complex. Using Bateman's unpublished map and sections, sediments were lumped 

into two groups, (1) those predominantly gravel and 

sand which might be expected to have a large storage 

coefficient and moderate to high hydraulic conductivity (permeability), and (2) till, which would be 

expected to have a low hydraulic conductivity. Volumes of saturated sediments were computed for the 

two groups by 20-foot increments of elevation for 

reservoir elevations between 3,560 and 3,320 feet 

(table 6 and fig. 12).

In the operating range of elevations of the power 

pool (above 3,336 feet), there are about 250,000 

acre-feet of material of high bank-storage potential 

and about 1 million acre-feet of material of low 

bank-storage potential.

TABLE 6. Vertical distribution of saturated unconsolidated material in the reservoir area

Range of 

elevation 

(feet above 

mean sea 

level)

8,560-8,540 .........

3,540-8,520 .........

3,520-3,500 _-----._.

3,500-8,480 .........

3,480-3,460 ---------

3,460-8,440 _____---.

3,440-8,420 -..-._.._

3,420-3400 -.--.--..

3,400-3,380 -.-...-..

3,380-8,360 ----- _ .

3.360-3.340 ........

3,340-3,820 ---------

Volume of material between 

given elevations 

(thousands of acre-feet)

Sand and 

gravel

1-8 *>

91 1

22.5

24.1

25.4

23.4

19.8

11 Q

15.3

171

IK 9

16.7

Till

84.4 

97.0 

98.4 

101.9 

104.6 

96.8 

82.9 

75.4 

71.0 

66.6 

59.4 

52.3

Total

102.6 

118.1

120.9 

126.0 

130.0 

120.2 

102.7 

90.3 

86.3 

83.7 

75.6 

69.0

Total ............. 234.7 990.7 1,225.4

> 3OOU

Ul

<

ui -aeon en oo^u

<

Ul

^ 3480

Ul

co 3440

<

Ul

u 3400

z

§ 3360

H

<

^ 3320

I

1

Sand

and

gravel

|

|

|

Till

|

1

|

1

|

J

|

J

] 40 20 0 20 40 60 80 100 120 

VOLUME IN THOUSANDS OF ACRE-FEET

FIGURE 12. Vertical distribution of unconsolidated sediments 

adjacent to Hungry Horse Reservoir.

ANALYSIS OF DATA 

APPROACH TO PROBLEM

The apparent bank-storage effect was computed 

by two independent methods, (1) water budget and 

(2) mathematical model.

In the water-budget method, after all measured 

and (or) estimated components have been evaluated, 

the residual represents the bank-storage effect plus 

or minus the total accumulation of the errors in 

the components. The true value of bank storage may 

be masked by the error accumulation to such an 

extent that the results would be unusable. For the 

mathematical model, the aquifer constants are unknown and must be assumed. By the theoretical approach, any number of solutions can be computed, 

depending on the input constants assumed.

Either method taken alone will produce bankstorage values having a wide range of uncertainty. 

The two methods, when used jointly, provide a powerful tool for reducing some of the uncertainties 

in the bank-storage determination. Comparison of 

theoretical models with field data pointed to discrepancies which led to correction of several mistakes in record calculation, reanalysis of two rating 

curves, and reestimate of ungaged inflow. The range 

of values for the aquifer constants in the mathematical model was narrowed on the basis of the 

modified field data. The principal purpose for constructing and refining the mathematical model was 

to provide a working tool for predicting availability 

of water for power generation, both for this study 

and for application at other sites.

WATER BUDGET

Bank-storage estimates were computed by the 

water-budget method as one approach in this investigation. Basically, the procedure involves balancing the measured and (or) estimated inflows 

against the outflows modified for changes in reservoir content. This is simple in theory, but many 

complications are inherent when the object is the 

degree of accuracy required to evaluate the potential 

magnitude of bank storage.

The computations for the water budget were made 

in terms of monthly runoff volumes, expressed as 

cfs-days. The monthly volumes were derived from 

daily records or estimates.

Monthly totals were computed to the same number of significant figures used in the publication of 

the data and were then rounded off to the nearest 

cfs-day. These monthly values were used throughout 

the study until the final values were selected. This 

produced a greater number of significant figures in
26 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

the basin totals than might be warranted, but 

excessive rounding of the larger components of the 

budget could distort the final values beyond usable 

limits.

Most of the basic data for this study have been 

presented in "Water Resources Data for Montana 

Part 1, Surface Water Records" and "Part 2, Water 

Quality Records," for water years 1965, 1966, and 

1967 (available from the U.S. Geol. Survey, Helena, 

Mont.). A basic-data supplement containing these 

and other data collected for this study was released 

to open file in 1968 (Simons, 1968).

INFLOW

The inflow to Hungry Horse Reservoir was assumed to be the runoff from the tributary streams 

included in the primary and secondary gaging-station 

networks plus the runoff from the ungaged area 

plus that resulting from precipitation on the surface 

of the reservoir. Each component of reservoir inflow is outlined in the following sections.

PRIMARY GAGING-STATION NETWORK

Part of the inflow to Hungry Horse Reservoir 

was measured at nine stations in the primary gaging-station network. These stations have a combined drainage area of about 1,360 square miles 

and include one station on the South Fork Flathead 

River, three stations on east-side tributaries, and 

five stations on west-side tributaries.

The following are the gaging stations on the 

east-side tributaries:

Twin Creek near Hungry Horse 

Canyon Creek near Hungry Horse 

Emery Creek near Hungry Horse

These stations have a total drainage area of 79.2 

square miles (see table 5). The discharge records 

for these stations are complete for the period of 

study and have been used as published. They are 

summarized in table 7.

The following are the gaging stations on the 

westside tributaries:

Soldier Creek near Hungry Horse 

Sullivan Creek near Hungry Horse 

Graves Creek near Hungry Horse 

Goldie Creek near Hungry Horse 

Wounded Buck Creek near Hungry Horse

These stations have a combined drainage area of 

120 square miles (see table 5). The records for 

these stations are complete for the period of study 

and were used as published except as noted below.

TABLE 7. Summary of monthly runoff for gaging 

stations on east-side tributaries to Hungry Horse 

Reservoir

Monthly runoff

1964

Oct .-----..-.

Nov

Dec ---.---_,

1965

Jan - -

Feb ---------

Mar -..-.-..

Apr ------

May - -

June --- _ -

July --------

Aug _ . -. _

Sept --------

Oct ---------

Nov _ Dec ---------

1966

Jan . -. -

Feb -.---__..

Mar ---------

Apr - -

May -_-_---.

June - - -

July --------

Aug

Sept --------

Oct ---------

Nov __--.--_

Dec ---------

1967

Jan . .

Feb __--_.--_

Mar -.--.--_

Apr -----

Total -.--

(cfs-days)

Twin

Creek

..--- 1,231

.-..- 1,005

.--_- 1,465

.--- 1,160

.-.-- 1,075

.-.-. 1,126

_.-- 7,253

-.-_ 15,027

---_ 12,686

..--- 2,446

.--.. 926

----- 1,880

..--- 1,155

.---. 952

..--- 1,091

...-- 594

...-- 432

.---. 1,388

.--- 6,499

--.- 15,378

-_.- 10,015

----- 1,935

----- 612

----- 360

----- 352

----- 503

------ 789

----- 705

----- 800

----- 863

----- 3,294

---_ 94,997

Canyon

Creek

121.7

107.1

133.6

72.2

74.7

81.3

456.8

1,249

1,810

376.4

136.7

187.9

144.1

90.8

75.3

58.8

41.6

109.3

338.1

1,266.3

1,032

302.3

106.2

62.1

61.6

69.9

104.0

84.5

78.8

62.5

201.7

9,097.3

Emery

Creek

274.6

257.2

532

348.8

289.9

423

2,926

4,648

2,608

726

359

340

295.9

227.7

237.4

170.9

132.2

268.3

1,689

2,893

2,604

924

362.2

214.4

190.1

190.3

314.5

311.5

398

316.6

750

26,022.5

Total

(rounded)

1,628

1,369

2,131

1,581

1,440

1,630

10.436

20,924

17,104

3,548

1,422

2,408

1,595

1,271

1,403

824

606

1,765

8,526

19,537

13,651

3,161

1,080

636

604

763

1,207

1,101

1,277

1,244

4,246

130,118

The low-water records for Graves Creek near 

Hungry Horse were revised for the period October 

1, 1964 April 19, 1965. The rating curve used during this period lacked definition below 45 cfs. Lowwater measurements made during water years 1966 

and 1967 indicated that a redefinition of the lower 

end of that rating curve was justified.

The discharge records for the gaging station 

Goldie Creek near Hungry Horse were not collected 

prior to May 1965. Daily discharges for October 

1964-April 1965 were estimated by means of correlation with the daily discharges for Graves and 

Sullivan Creeks. The comparisons between these 

stations were of good quality, and the runoff estimated by the above method is comparable in accuracy to later runoff determinations.

The daily discharge records for Wounded Buck 

Creek near Hungry Horse during August and September 1966 were corrected for purposes of this 

study. Summaries of monthly runoff for this group 

of gaging stations are shown in table 8.

The remaining gaging station in the primary 

network is the South Fork Flathead River above 

Twin Creek. This station, with a drainage area of
WATER BUDGET 27

TABLE 8. Summary of monthly runoff for gaging stations on 

west-side tributaries to Hungry Horse Reservoir

Monthly runoff 

(cfs-days)

Month

1964 

Oct -----...

Nov -------

Dec .---.-.

1965

Feb --------

Mar ......

May ...-.--

July ......

Sept ..----

Oct -------

Nov .....--

Dec .......

1966

Feb ........

Mar

May ......

July .......

Sept ------

Oct -------

Nov -------

Dec ......

1967

Feb .-.-...

Mar .......

Apr .

Soldier 

Creek

130.0

146.4

414.5

229.9

178.1

164.9

893.2

1,491

872

237.2

148.9

145.8

123.1

180.9

185.6

131.8

89.3 

224.5

801

1,226

665.9

223.6

115.9

86.6

89.8

105.4

214.8

189.1

186.1

143.1

431.0

Sullivan 

Creek

3.646

3,041

4,843

2,438

2,084

2,065

11.708

26,701

27,088

5,989

2,957

5,368

2.737

2,476

2,236

1,359

938 

2,347

10,519

24.407

20,061

5,996

1.440

951

1,110

1,451

2,413

1,866

1 7AQ

1 QR.O

3,803

Graves 

Creek

1 2.125

1 2,297

» 3,275

1 1,197

!888

'939

1 4,942

12,379

18,741

6,018

1,375

3,034

1,369

1,940

1,162

and

519

Q71

4,183

191 RQ

12,131

4

1 O1

R9Q

512

786

1,241

1 QRK

1 QfkA

1,094

rjetft

1,579

Goldie 

Creek

*186

«193

*254

M10 *89

»95

2 593

1,636

1,612

298.3

75.2

136.2

72.8

177.8

128.9

76.2

39.1

1flQ Q

428.5

1,401

1 AfiQ

236.3

61.7

40.5

67.6

105.9

91 7 7

1ft1 8

134.9

102.0

1C0 Q

Wounded 

Buck 

Creek <

1.296

1,271

9 91 A

1,031

801

823

2,950

7,225

10,448

4,452

1,617

1,302

Q9R

1,061

806

fiRQ

472

£»QC

O jirje.

C Cf Q

C QQQ

9 fiQQ

1 1,297 1720

Gift

QQ9

1 94Q

1 Aft J

o jl

fi97

QOA

Total 

'rounded)

7,382

P.OJ8

11,000

5,006

4,040

4,087

21,086

49,432

58,761

16,994

6,674

9,986

5,227

5,836

4

K1Q

3,034

2,057

A 9OQ

18,406

45,811

40 920

1Q O7ft

9 TAA

9 4in

o oao

9 TOR

6,050

4,581

4 QtrQ

9 QQ9

6,905

Total -.-. 10.466:4 187,094 107,047 10,070.6 67,233 381,909

1 Revised. 

1 Estimated.

1,160 square miles, replaced the station at Spotted 

Bear Ranger Station as the main inflow gage. It 

measures a larger part of the inflow to Hungry 

Horse Reservoir, has better physical and hydraulic 

characteristics, and should in the long run provide 

a better index of reservoir inflow. The exposed location of this gaging station and its channel characteristics should tend to decrease the number and 

frequency of ice-affected periods. The two rating 

curves used for the computation of high-water records showed some divergence in shape, and the 

low-water periods were affected slightly by roadconstruction activities. But for the initial comparison, no revisions in published data were made. The 

total inflow to the reservoir as indicated by the 

primary network of gaging stations is summarized 

in table 9.

SECONDARY GAGING-STATION NETWORK

Another part of the inflow to Hungry Horse 

Reservoir was measured at 19 sites included in the 

secondary gaging-station network. Eleven of these 

sites, with a total drainage area of 82.6 square 

miles, were on streams entering the east side of the 

reservoir. Eight sites, with a total drainage area 

of 64.5 square miles, were on west-side tributary 

streams.

Discharge measurements were made to define the

TABLE 9. Summary of monthly inflow to Hungry 

Horse Reservoir from stations in primary gagingstation network

Monthly runoff 

(cfs-days)

Month

1964 

Oct __--.----.

Nov ..........

1965

Feb -....----.

Mar -.....--.

May ..----..--

June

July ..-..-....

Sept __ ......

Oct -.--.-.-..

Nov ..---.--.

1966 

Jan ..-.....-.

Peb ..........

Mar ..........

July .-......-

Sept ......-.-

Nov ---------

1967

Feb ..-------.

Mar ----------

Total ------

South Fork 

Flathead 

River 

above 

Twin Creek

25,968

18,596

25,932

18,751

14,160

16,794

87,746

.... 264,480

. . . . 346,460

...- 118,010

35,559

.... 47,496

30,939

18,811

.... 16,374

12,773

9,657

15,642

.... 75,620

... 254,450

.... 202,610

66,592

20,119

12,703

10,783

11,390

12,327

11,903

11,737

11,896

28,389

.... 1,854,667

East-side 

gaging 

stations

1,628 

1,369 

2,131

1,581 

1.440 

1,630 

10.436 

20.924 

17,104 

3,548 

1,422 

2.408 

1,595 

1,271 

1.403

824 

606 

1,765 

8,526 

19,537 

13,651 

3,161 

1,080 

636 

604 

763 

1,207

1,101 

1,277 

1,244 

4,246

130,118

West-side 

gaging 

stations

7,382 

6,948 

11,000

5,006 

4,040 

4,087 

21,086 

49,432 

58,761 

16,994 

6.674 

9.986 

5,227 

5.836 

4,519

3.034 

2.057 

4,238 

18,406 

45,811 

40,920 

13,276 

3,744 

2,310 

2,863 

3,785 

6,050

4,581 

3,959 

2,992 

6,905

381,909

Total

34.978 

26,913 

39,063

25,338 

19,640 

22,511 

119,268 

334,836 

422,325 

138,552 

43,655 

59,890 

87,761 

25,918 

22,296

16,631 

12,320 

21,645 

102,552 

319,798 

257,181 

83,029 

24.943 

15.649 

14,250 

15,938 

19,584

17.585 

16.973 

16,132 

39,540

2,366,694

stage-discharge relationship at each site. The average number of discharge measurements made at 

each location was 15. Most of the stage-discharge 

curves were of good to excellent quality, and a few 

maintained a single relationship during the entire 

period of study. However, a few streams, notably 

Lower Twin and Deep Creeks, shifted almost continuously as a result of channel modifications caused 

by the 1964 high water.

Stage readings at each site were made at irregular intervals throughout the year, the largest 

number being made during periods of high runoff. 

Fewer readings were made during the recession and 

base-flow periods.

A partial record of daily discharges for each site 

was computed from these discharge and stage data. 

These partial-year discharge records were graphically compared to the discharge records for all 

stations in the primary gaging-station network. 

Most of these secondary stations correlated well 

with one or more of the stations in the primary 

network. A complete record of daily discharges for 

each secondary site was developed from these comparisons, using a consistent pattern for the 31 

months studied.
28 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

TABLE 10. Summary of monthly runoff for secondary-network stations on east side

of Hungry Horse Reservoir

Month

1964 

Oct _.

Nov .--

1965

Feb ...

Mar ...

July ...

Sept . .

Oct ...

Nov ...

1966

Feb --.

Mar _..

July ...

Sept ..

Oct _..

Nov ...

Dec

1967

Feb ...

Mar ...

Total

Lower 

Twin 

Creek

.--. 793

. . - - 700

.... 1,042

.... 747

.... 695

.... 729

.... 4,149

---. 7,865

.... 9,310

.... 1,988

---. 707

--.. 1,180

- ... 877

-.-. 727

.... 826

---. 448

.... 337

.-.. 839

---. 3,700

.... 8,545

---. 5,807

.... 1,328

.... 440

.... 253

.... 242

.... 344

.... 555

.... 517

-... 563

-... 610

.... 2,198

-... 59,061

Monthly runoff 

(cfs-days)

Dry 

Park 

Creek

28 

23 

34

26 

25 

25 

161 

334 

294 

80 

41 

61 

36 

30 

35

20 

16 

28 

75 

178 

148 

59 

22 

10 

9 

12 

20

18 

19 

20

84

1,971

Hoke 

Creek

186 

167 

240

147 

112 

114 

302 

630 

989 

488 

233 

176 

118 

96 

81

65 

47 

106 

287 

619 

708 

346 

157 

98 

86 

95 

146

125 

108 

72 

103

7,247

Loi?an 

Creek

155 

136 

169

93 

96 

106 

726 

1,861 

2,551 

567 

201 

274 

192 

122 

101

78 

54 

136 

414 

1,619 

1,507 

479 

121 

72 

86 

99 

145

114 

114 

91

262

12,741

Felix 

Creek

294 

245 

381

272 

248 

282 

1,738 

3,670 

3,657 

765 

226 

309 

251 

211 

225

132 

101 

262 

1,048 

2,779 

2,049 

528 

187 

108 

96 

125 

196

179 

211 

200

684

21,659

Harris 

Creek

140 

116 

170

90 

87 

96 

380 

736 

1,097 

276 

120 

119 

121 

93 

86

72 

51 

115 

282 

614 

736 

257 

111 

78 

75 

84 

122

100 

93 

72 

204

6,793

Daer Mclnernie Murray 

Creek Creek Creek

97 

86 

107

52 

54 

60 

279 

726 

1,136 

297 

107 

149 

114 

71 

57

42 

29 

82 

260 

892 

731 

224 

82 

49 

41 

46 

71

62 

60 

47 

143

6,253

70 

57 

90

64 

60 

63 

376 

920 

722 

134 

54 

104 

73 

45 

39

32 

23 

68 

312 

808 

570 

101 

35 

27 

31 

38 

62

55 

64 

63 

213

5,373

67 

59 

75

41 

42 

47 

309 

877 

1,290 

245 

80 

130 

90 

55 

44

33 

23 

67 

342 

820 

448 

125 

48 

36 

38 

41 

54

41 

36 

36 

123

5,762

Riverside 

Creek

116 

101 

129

69 

70 

77 

404 

1,114 

2,175 

532 

171 

272 

194 

117 

88

59 

39 

149 

588 

2,388 

1,728 

351 

100 

57 

54 

60 

88

73 

67 

54 

160

11,644

Hungry 

Horse 

Creek

636 

530 

830

604 

540 

619 

3,739 

8,382 

6,507 

1,442 

557 

859 

443 

345 

320

253 

178 

554 

2,622 

5,825 

4,624 

1,078 

341 

202 

181 

227 

361

327 

384 

374 

1,273

45,157

Total

2,582 

2,220 

3,267

2,205 

2,029 

2,218 

12,563 

27,115 

29,728 

6,814 

2,497 

3,633 

2,509 

1,912 

1,902

1,234 

898 

2,406 

9,930 

25,087 

19,056 

4,876 

1,644 

990 

939 

1,171 

1,820

1,611 

1,719 

1,639 

5,447

183,661

TABLE 11. Summary of monthly runoff for secondary-network stations on west side

of Hungry Horse Reservoir

[Values for Aurora not included in total values]

Monthly runoff 

(cfs-days)

Month

1964 

Oct .........

Nov .........

Dec .........

1965

Feb --------

Mar -------

May -------

July ........

Sept -----...

Oct .----.--.

Nov -.--....

1966

Feb ...----..

Mar --------

July -..---..

Sept .----...

Oct ---...-..

Nov -----....

Dec ---..-...

1967

Feb .........

Mar .........

Total --....

Clark 

Creek

85.6

98.6

... 293.3

.-- 154.7

... 119.4

... 112.2

._- 841.4

.-- 1,635

.-- 995

... 193.1

92.3

... 137

90.1

--. 121.6

..- 123

88.2

58.4

.-. 159.6

. - - 688

... 1,485

- - 839

... 176

81.8

51.8

66.1

78.8

... 158.0

... 136.8

... 138.2

... 104.4

... 310.5

... 9,712.9

Battery 

Creek

99.1 

106.1 

201.2

106.5 

85.3 

79.4 

425.4 

964 

1,041 

277.8 

117.1 

111.3 

99.5 

123 

103

79.0 

47.5 

81.5 

278.0 

827 

592.6 

179.5 

94.0 

65.0 

72.0 

88.3 

175.5

151.1 

153.4 

117.2 

344.8

7,286.1

Wheeler 

Creek

1,398 

1,313 

2,283

937 

814 

790 

4,344 

9,775 

12,330 

3,193 

1,443 

2,078 

1,153 

1,095 

807

564 

368 

713 

3,352 

9,710 

7,908 

2,884 

679 

446 

442 

570 

966

735 

682 

528 

1,463

75,763

Forest 

Creek'

333 

279 

439.5

215.5 

182.0 

181.0 

1,042.5 

2,308 

2,103 

518.3 

183.2 

202.7 

147.9 

166.1 

138.5

113.5 

91.5 

187.0 

673 

1,560 

1,329 

370.5 

141.5 

89.0 

101 

130.5 

295.3

216.6 

244.4 

207.4 

420.4

14,610.8

Clayton 

Creek

453.6

484.1 

675.6

269.2 

225.1 

223.2 

1,384 

3,591 

3,675 

845.8 

236.9 

307.8 

189.9 

305.6 

181.6

147.3 

99.6 

202.5 

903 

2,554 

2,303 

667.1 

136.1 

124.1 

162.6 

201.3 

342.6

296.0 

241.8 

178.0 

419.4

22,026.8

Flossy 

Creek

92.4 

96.5 

126.8

55.3

44.5 

47.3 

251.2 

728.2 

647.3 

85.3 

32.3 

69.2 

43.3 

102.4 

73.7

43.6 

22.1 

55.8 

194.3 

704.5 

427.1 

67.6 

11.5 

7.1 

12.9 

20.4 

41.7

31.5 

26.5 

19.2 

30

4,201.5

Lost 

Johnny 

Creek

502 

496

874

402 

317 

325.6 

1,106.9 

2,898 

4,216 

1,738 

586 

512 

256.5 

317.1 

223.4

180.4 

128.1 

190.5 

787 

2,557 

3,169 

989 

334.3 

193.5 

202.5 

220.5 

312.2

266.0 

210.2 

156.8 

232.5

24,900

Doris 

Creek

610 

592 

1,047

480 

373 

382.5 

1,376 

3,394 

5,120 

2,198 

932 

767 

588 

631 

451

365 

262.5 

375.7 

1,353 

3,642 

3,896 

1,513 

691 

371 

336.6 

354.2 

506

428 

343 

254.8 

374.0

34,007.3

Total 

(rounded)

3,574 

3,465 

5,940

2,620 

2,160 

2,141 

10,771 

25,293 

30,127 

9,049 

3,623 

4,175 

2,568 

2,862 

2,101

1,581 

1,078 

1,966 

8,228 

23,040 

20,464 

6,847 

2,169 

1,348 

1,396 

1,664 

2,797

2,261 

2,040 

1,566 

3,595

192,509

Aurora 

Creek

207.1 

204.8 

362.7

168.8 

132.0 

136.5 

498.9 

1,621 

2,266 

847 

312.2 

300.1 

217.6 

207.9 

130.7

106.6 

76.7 

98.6 

353.0 

1,583 

1,964 

733 

294.3 

158.3 

147.3 

158.3 

223.4

189.7 

152.3 

114.4 

165.0

14,131.2
WATER BUDGET 29

Monthly runoff for each site, in cfs-days and in 

inches, was computed from the daily discharges. 

All stations in the primary and secondary networks 

were compared as a test of regional homogeneity, 

and adjustments were made where justified. Estimates of the inflow to the reservoir from this 

secondary network of stations are considered to be 

good and are almost as reliable as the runoff derived from the stations in the primary network. 

The results of these computations are summarized 

in tables 10,11, and 12.

TABLE 12. Summary of monthly inflow to 

Hungry Horse Reservoir from stations in 

secondary gaging-station network

Monthly inflow

Month

1964.

Oct --------

Nov -------

Dec -------

1965

Jan . -

Feb -------

Mar -------

Apr -------

May -------

June ------

July -------

Aug ..---..

Sept ------

Oct -------

Nov -------

Dec -------

1966

Jan -------

Feb -------

Mar -----..

Apr - - . - 

May -------

June ------

July -------

Aug -------

Sept ------

Oct ....---

Nov ...--.-

Dec -------

1967

Jan -------

Feb .......

Mar .-...--

Apr -------

Total ..-.

East side

----- 2,582

-.-.. 2,220

.- _ 3,267

----- 2,205

----- 2,029

----- 2,218

----- 12,563

----- 27,115

----- 29,728

----- 6,814

.-.-- 2,497

----- 3,633

----- 2,509

----- 1,912

----- 1,902

-..-. 1,234

----- 898

----- 2,406

9,930 

....- 25,087

----- 19,056

----- 4,876

----- 1,644

--..- 990

.-.-- 939

----- 1,171

----- 1,820

----- 1,611

.-.-. 1,719

----- 1,639

----- 5,447

----- 183,661

(cfs-days)

West side

3,574

3,465

5,940

2,620

2,160

2,141

10,771

25,293

30,127

9,049

3,623

4,175

2,568

2,862

2,101

1,581

1,078

1,966

8,228 

23,040

20,464

6,847

2,169

1,348

1,396

1,664

2,797

2,261

2,040

1,566

3,595

192,509

Total

6,156

5,685

9,207

4,825

4,189

4,859

23,334

52,408

59,855

15,863

6,120

7,808

5,077

4,774

4,003

2,815

1,976

4,372

18,158 

48,127

39,520

11,723

3,813

2,388

2,335

2,835

4,617

3.872

3,759

3,205

9,042

376,170

UNCAGED AREAS

Figure 9 shows the ungaged areas interspersed 

between streams in the primary and secondary 

gaging-station networks and around the periphery 

of Hungry Horse Reservoir. Miscellaneous discharge 

measurements made at 40 locations in these areas, 

sampled the runoff from about one-half of the 

residual area were considered to be representative 

of the entire ungaged area.

Discharge measurements at these locations were 

made during high-flow and low-flow periods only, 

each miscellaneous set being made within a period 

of a few days. Estimates of reservoir inflow from 

various segments of the ungaged drainage area 

were based on these data. Composite estimates were 

prepared for the ungaged inflow from the east-side

and west-side areas separately and were compared 

to individual station's and groups of stations in the 

primary and secondary networks.

For the drainage area on the east side of the 

reservoir, a coefficient of 0.75 times the total inflow 

of the east-side stations in the secondary gagingstation network provided the best apparent mean^ 

of computing this segment of reservoir inflow. The 

ratio of the east-side drainage areas for the ungaged 

and secondary networks is 64/82.6 or 0.775. The 

coefficient of 0.75 is slightly smaller than the drainage-area ratio and was used to compute the reservoir inflow from the east-bank ungaged area.

On the west bank, a coefficient of 0.9 times the 

total inflow of the west-bank secondary stations 

appeared to give the best results. The drainage-area 

ratio for the west-side ungaged and secondarynetwork areas is 61/64.5, or 0.946. The coefficient 

of 0.9 was used to compute reservoir inflow from 

this residual area.

The total reservoir inflow frbm the ungaged area 

was assumed to be the sum of the east-side and 

west-side estimates. These are summarized in table 

13. Estimates of the reservoir inflow for other combinations of segments of the ungaged drainage area 

were prepared, but no significant differences from

TABLE 13. Summary of monthly inflow to 

Hungry Horse Reservoir from the ungaged areas

[Based on 0.75 X 2 east-side secondary stations 

and on 0.9 X % west-side secondary stations]

Monthly inflow

Month

1964

Oct -..---.

Nov -------

Dec -------

1965

Jan ----- -

Feb -------

Mar -------

Apr ----_-.

May -------

June -----

July -------

Aug -------

Sept ------

Oct -------

Nov -------

Dec ------

1966

Jan -------

Feb -------

Mar -------

Apr -------

May -------

June ------

July -------

Aug -------

Sept ------

Oct -------

Nov -------

Dec -------

Feb -------

Mar -------

Apr -------

Total -..-

East side

.-...- 1,936

.-..-. 1,665

.-. 2,450

----- 1,654

----- 1,522

----- 1,664

----- 9,422 

--.-. 20,836

----- 22,296

.-.-- 5,110

----- 1,873

----- 2,725

----- 1,882

----- 1,434

----- 1,426

----- 926

----- 674

-..-- 1,804

----- 7,448

---.. 18,815

----- 14,292

----- 3,657

..--- 1,233

.---. 742

----- 704

---.. 878

----- 1,365

----- 1,208

----- 1,289

----- 1,229

----- 4,085

----- 137,744

(cfs-days)

West side

3,217

3,118

5,346

2,358

1,944

1,927

9,694 

22,764

27,114

8,144

3,260

3,758

2,311

2,576

1,890

1,423

970

1,769

7,405

20,736

18,418

6,162

1,952

1,212

1,256

1,498

2,517

2,035

1,836

1,409

3,236

173,255

Total

5,153

4,783

7,796

4,012

3,466

3,591

19,116 

43,100

49,410

13,254

5,133

6,483

4,193

4,010

3,316

2,349

1,644

3,573

14,853

39,551

32,710

9,819

3,185

1,954

1,960

2,376

3,882

3,243

8,125

2,638

7,321

310,999
30 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

those shown in table 13 were indicated. Thus it was 

assumed that the above procedure provides reasonable estimates of this segment of the inflow to 

Hungry Horse Reservoir.

PRECIPITATION

In the water-budget studies, precipitation falling 

directly on the reservoir was treated as an inflow 

component and was added to other increments of 

inflow. The precipitation data for Hungry Horse 

Dam, the only complete year-round record available 

within the drainage basin, were used in these 

computations. Comparison with short-term precipitation records collected at the top of the dam, on 

the right abutment, at Spotted Bear Ranger Station, at South Fork Flathead River above Twin 

Creek, at Goldie Creek, and at Betty Ranger Station 

indicates that these data are fairly representative. 

Some variations are known to exist, but data are 

insufficient to make any real distinctions.

Daily estimates of inflow to the reservoir were 

prepared by applying the observed precipitation 

amounts to the area of the full reservoir pool 

(24,000 acres). Monthly totals were computed from 

the daily values. This procedure was modified during the period December-April to account for snow 

accumulation on that part of the reservoir area 

between actual water surface and reservoir flow 

line. During this period, daily inflow amounts were 

computed using the actual water-surface area. The 

precipitation falling on the remaining area below 

the flow line and above the reservoir surface was 

assumed to be snow which did not contribute immediately to reservoir inflow. This amount was accumulated for the period December-March and was 

assumed to melt during April and to become effective reservoir inflow at that time. Thus for April 

the inflow would be the effective precipitation falling on the total surface of the reservoir plus the 

December-March accumulation. This is not precise 

but for purposes of this study was assumed to be 

satisfactory.

TOTAL RESERVOIR INFLOW

The total monthly inflow to Hungry Horse Reservoir is assumed to be the sum of the runoff 

measured by the gaging-station networks, plus that 

estimated for the ungaged area, plus that for precipitation falling on the reservoir surface. The inflow for the period of study is summarized in table 

14.

OUTFLOW

The determination of the outflows from the

TABLE 14. Summary of monthly inflow to 

Hungry Horse Reservoir

Monthly inflow 

(cfs-days)

Month From From From Subtotal

primary secondary ungaged (columns Precipnetwork network area 2 4) itation

Total

1964 

Oct ------

Nov -----

Dec ------

1965

Feb -----

Mar ------

May -----

July ----.

Oct ......

Dec -----

1966 

Jan ----- 

Feb ------

Mar ------

Apr ----- 

May ---- 

June ----- 

July .-_- 

Aug ----- 

Sept ----- 

Oct ------

Nov ----- 

Dec ------

1967

Feb ----- 

Mar ----- 

Apr -----

34,978

26,913

39,063

25,338

19,640

22,511

119,268

334,836

422,325

138,552

43,655

59,890

37,761

25,918

22,296

16,631 

12,320

21,645

102,552 

319,798 

257,181 

83.029 

24,943 

15,649 

14,250

15,938 

19,584

17,585

16,973 

16,132 

39,540

6,156

5,685

9,207

4,825

4,189

4,359

23,334

52,408

59,855

15,863

6.120

7,808

5,077

4,774

4,003

2,815 

1,976

4,372

18,158 

48,127 

39,520 

11,723 

3,813 

2,338 

2,335

2,835 

4,617

3,872

3,759 

3,205 

9,042

5,153

4,783

7,796

4,012

3,466

3,591

19,116

43,100

49,410

13,254

5,133

6,483

4,193

4,010

3,316

2,349 

1,644

3,573

14,853 

39.551 

32,710 

9,819 

3,185 

1,954 

1,960

2,376 

3,882

3,243

3,125 

2,638 

7,321

46,287

37,381

56,066

34,175

27,295

30,461

161,718

430,344

531,590

167,669

54,908

74,181

47,031

34,702

29,615

21,795 

15,940

29,590

135,563 

407,476 

329,411 

104,571 

31,941 

19,941 

18.545

21,149 

28,083

24,700

23,857 

21,975 

55,903

2,928

4,881

7,931

3,485

2,612

212

5.067

1,730

3,771

1,246

4,331

3,558

907

3.253

1,552

2,922 

1,308

9 978

3,937 

2,166 

6,518 

1,579 

2,153 

641 

3,360

5,428 

2,945

4,068

G61 

1,236 

6,034

49,215

42,262

63,997

37,660

29,907

30,673

166,785

432,074

535,361

168,915

59.239

77,739

47,938

37,955

31,167

24,717 

17,248

31,868

139,500 

409,642 

335,929 

106,150 

34,094 

20,582 

21,905

26,577 

31,028

28,768

24,718 

23,211 

61,937

Total -- 2,366,694 376,170 310,999 3.053,863 94,898 3,148,761

Hungry Horse Project requires the consideration 

of three items: (1) runoff measured at the gaging 

station South Fork Flathead River near Columbia 

Falls, (2) runoff from the intervening area between 

Hungry Horse Dam and the outflow gaging station, 

and (3) evaporation from the water surface of 

Hungry Horse Reservoir. The last two are small 

in comparison to the measured discharge at the 

gaging station, except during the summer months 

when minimum releases are being made from the 

reservoir.

The gaging station South Fork Flathead River 

near Columbia Falls has been considered as measuring the outflow from the Hungry Horse Project 

and has been at its present site, 134 miles downstream from the dam, since October 1953. The 

control section and the stage-discharge relationship 

for this gaging station has remained very stable, 

and most records have been rated as excellent. Two 

stage-discharge relation curves, with a spread of 

about 3 percent, were used in the computation of 

daily discharges during the period of this investigation. There were no periods of ice-affected record 

during the period of study. Records for the period 

October 9-22, 1964, were revised to correct for a 

minor instrument malfunction. Other than this, the 

published records were used in the preliminary 

water-budget computations.
WATER BUDGET

The amount of channel storage between the dam 

and the gaging station was evaluated by considering 

the range in stage and the average areas of the 

channel in its 1%-mile length. This would amount 

to about 12 cfs per foot of range in stage at the 

tail water of the dam. This could be a factor that 

should be included if modifications were made on 

a daily basis when the change in stage would 

amount to 8 or 12 feet, but on a monthly basis 

the potential amount of channel storage is minor. 

Thus in this investigation it was not considered.

The record for the downstream gaging station 

includes not only the water discharged past the 

dam but also the runoff from the 8.7 square miles 

of intervening area. Consideration was given to the 

possibility of moving the outflow gaging station upstream to a point where the intervening drainage 

area would be much smaller, but it was not considered feasible at that time. In lieu thereof, the 

contribution of this intervening drainage area was 

estimated by use of a partial-year gaging station 

on Aurora Creek. The drainage area of Aurora 

Creek amounts to 6.5 square miles. The contribution for the total 8.7 square miles was estimated 

by multiplying the contribution in Aurora Creek 

by a factor of 1.34. This amount was subtracted 

from the runoff for the station at South Fork 

Flathead River near Columbia Falls, giving a more 

precise measure of the flow passing Hungry Horse 

Dam.

Evaporation from the water surface of Hungry 

Horse Reservoir was computed by the energy-budget 

method for 23 periods extending from May 11 to 

October 20, 1965, and from May 11 to November 

2, 1966. These computations produced small negative values for evaporation during periods 1 (May 

11-26, 1965) and 13 (May 25-June 2, 1966). Inflow volumes and changes in stored energy were 

very large for both of these periods, and conditions 

were unfavorable. Also, the balance motor in the 

recording potentiometer for the radiation station 

burned out during period 13 and had to be replaced. 

Most of the radiation and humidity data for period 

13 were estimated rather than observed.

Evaporation was also computed by the masstransfer formula, developed by the Lake Hefner 

studies, which has the form

where E evaporation from reservoir,

«=wind speed over the reservior, 

Ae= vapor-pressure difference between air

and

31

over the reservoir and water in the 

reservoir, 

= an empirical coefficient.

The coefficient was determined from the values of 

evaporation computed by the energy-budget method, 

and it varies depending upon whether the metric 

or the English system of units is used.

Evaporation data for class A pans are available 

for stations in the switchyard at the foot of the 

dam and on the right abutment at the top of the 

dam. The average rates of evaporation for these 

stations are compared to those for energy-budget 

and mass-transfer computations in table 15.

TABLE 15. Comparison of average rates of evaporation from 

three sources: energy budget, mass transfer, and class A 

pans, Hungry Horse Reservoir, 1965 and 1966

Average rates of evaporation 

(inches per day)

Class A pan

Date of 

thermal 

survey

Period Days Energy 

budget

Mass 

transfer

Top 

of dam

Foot 

of dam

1965 

May 11

May 26 

June 9 

June 23 

July 7 

July 21 

Aug. 4 

Aug. 18 

Sept. 1 

Sept. 16 

Oct. 5

Oct. 20

1966 

May 11

May 25 

June 2 

June 15 

June 29 

July 20 

Aug. 3 

Aug. 17 

Aug. 31 

Sept. 14 

Oct. 5 

Oct. 19 

Nov. 2

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

15

14

14

14

14

14

14

14

15

19

15

14

8

13

14

21

14

14

14

14

21

14

14

0.122

.101

.086

.128

.161

.201

.102

.089

.118

.058

.096

.068

.085

.158

.229

.209

.142

.142

.116

.118

.041

0.046 

.086 

.097 

.084 

.139 

.151 

.155 

.127 

.144 

.101- 

.073

.079

.081

.075

.118

.125

.191

.196

.177

.131

.120

.128

.086

.172

.246

.247

.211

.108

.070

.076

.074

.149

.209

1.162

.172

.223

.291

.246

.169

.185

.107

.058

.056

0.149

.214

.214

.178

.255

.254

.227

.094

.073

.055

.055

.144

.231

.143

.203

.124

.304

.257

.161

.167

.079

.050

.036

*Pan overflowed on June 4, 1966.

The evaporation from Hungry Horse Reservoir 

for the 23 periods, derived by energy-budget computations, is shown in table 16. Monthly totals of 

evaporation, in cfs-days, were computed from the
32 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

TABLE 16. Evaporation from Hungry 

Horse Reservoir, by energy-budget method, 1965 and 1966

Date of 

thermal

survey

1965

May 11

May 26

June 9

June 23

July 7

July 21

Aug. 4

Aug. 18

Sept. 1

Sept. 16

Oct 5

Oct. 22

Season total

1966

May 11

May 25

June 2

June 15

June 29

July 20

Aug. 3

Aug. 17

Aug. 31

Sept. 14

Oct. 5

Oct. 19

Nov. 2

Season total

Period

1

2

3

4

5

6

7

8

9

10

11

11

12

13

14

15

16

17

18

19

20

21

22

23

12

Days

15

14

14

14

14

14

14

14

15

19

15

162

14

8

13

14

21

14

14

14

14

21

14

14

175

Evaporat'on 

for period

(acre-feet)

843

2,600

2,490

2,300

3,500

4,420

5,490

2,790

2,600

4,400

1,690

83,123

2,350

1,221

1,700

2,320

6,450

6,260

5,710

3,870

3,850

4,640

2,950

980

42,301

data in table 16. Daily records from the class A 

pan in the switchyard were used to prorate a period 

total for parts of 2 months. The energy-budget 

study did not cover the complete May-October period of each year, and estimates were made for 

October 1964; May 1-10 and October 21-31, 1965; 

and May 1-10,1966.

The normal period of evaporation from Hungry 

Horse Reservoir is believed to be from May through 

October. The exact beginning and ending dates are 

subject to variation each year. However, the use of 

evaporation data in reservoir-operation studies 

could well be limited to the above period.

For the period May-October, approximately 20 

inches of evaporation from the water surface of the 

reservoir is indicated by the 2 years' study. This 

amounts to about 20,000 cfs-days or an approximate 

daily average of 100 cfs-days. However, from the 

data at hand it appears that 50 percent of the

seasonal total occurs during July and August, 30 

percent during September and October, and 20 percent during May and June.

Evaporation amounts computed by the energybudget and mass-transfer procedures were nearly 

equal. The use of one or the other would not greatly 

change the results of the water-budget study. There 

seemed to be a small seasonal bias; that is, the masstransfer values were lower when the reservoir was 

warming and higher when the reservoir was cooling. The overall differences are not considered significant at this stage of the analysis.

Comparisons were also made of the data from 

the evaporation pan below the dam in the switchyard and near the spillway on the right abutment. 

Seasonal totals were in very close agreement, but 

there is an indication of a small seasonal bias. The 

readings from the evaporation pan in the switchyard were higher when the reservoir was warming 

and lower when the reservoir was cooling.

The outflow from Hungry Horse Reservoir is the 

sum of the runoff at gaging station South Fork 

Flathead River near Columbia Falls, plus the evaporation, minus the runoff from the intervening area. 

These components are summarized in table 17.

TABLE 17. Summary of monthly outflow, Hungry 

Horse Reservoir

Monthly outflow 

(cfs-days)

Month

1964 

Oct ----...

Nov -----

1965

Feb .......

Mar -----

July ------

Sept ---....

Oct .......

Nov ---.-..

1966

Feb -------

Mar .--.--.

May -------

July ------

Sept ------

Nov ------

1967

Feb ------

Mar -------

Total

Runoff at 

South Fork 

Flathead 

River near 

Columbia 

Falls

1 44,530 

59,430

162,534

254,850

264,520 

459,960

183,625

80,230 

6,144

84,793

51,144

75,190 

89,519 

68,204 

255,420

258,771 

74,835 

66,636 

29,526 

85,460 

130,670 

102,933 

48,587 

146,886 

272,900 

230,377 

151,092

129,177 

69,404 

125,196 

176,049

4,238,592

Runoff from 

area between 

gaging station 

and reservoir

278 

274 

486

226 

177 

183 

669 

2,172 

3,036 

1,135 

418 

402 

291 

278 

175

143 

104 

130 

470 

2,119 

2,632 

931 

393 

212 

200 

211 

298

254 

204 

153 

217

18,921

Evaporation

2,200

"979 

2,652 

4,134 

4,557 

2,904 

2,074

2~266 

2,227 

5,520 

5,555 

3,906 

2,275

41,249

Total 

outflow

46,452 

59,156 

162,048

254,624 

264,343 

459,777 

182,956 

79,037 

5,760 

87,792 

55,283 

77,692 

91,302 

67,926 

255,245

258,628 

74,731 

66,506 

29,056 

85,607 

130,265 

107,472 

53,749 

150,580 

274,975 

230,166 

150,794

128,923 

69,200 

125,043 

175,832

4,260,920

1 Revised.
WATER BUDGET 33

CHANGE IN RESERVOIR CONTENTS

The change in reservoir contents is the third major 

item in the water budget. This was computed from 

the midnight (11:59 p.m.) stage readings of 

Hungry Horse Reservoir and the table of reservoir contents dated Ocotber 19, 1953. The data have 

been used as published.

The published daily stage readings are determined from the gage in the operator's control room, 

which is electrically connected to the water-stage 

recorded in the south elevator tower. A correction of 

-0.10 foot was made in December 1963, presumably

TABLE 18. Month-end reservoir elevations 

and monthly changes in reservoir stage 

and contents, Hungry Horse Reservoir

[Month-end reservoir elevation: Add 3,000 to obtain 

elevat'on, in feet above mean sea level]

Date

1964

Sept

Oct

Nov

Dec

1965

Jan

Feb

Mar

Apr

May

June

July

Aug

Sept

Oct

Nov

Dec

1966

Jan

Feb

Mar

Apr

May

June

July

Aug

Sept

Oct

Nov

Dec

1967

Jan

Feb

Mar

Apr

Month-end

reservoir

elevation

(feet)

560.53

560.55

------ 559.03

------ 551.15

...... 532.33

------ 510.13

------ 460.02

------ 459.77

-...-- 503.32

------ 553.98

------ 560.50

.--- . 560.50

------ 560.08

------ 556.29

------ 553.73

------ 533.68

------ 510.67

------ 504.83

------ 501.60

------ 513.74

------ 543.33

----- 560.29

------ 560.17

----- 558.50

------ 547.48

----- 524.10

-..- . 502.85

------ 489.66

------ 477.83

472.67

----- 458.79

------ 441.28

Change in

reservoir

stage

(feet)

+0.02

-1.52

-7.88

-18.82

-22.20

-50.11

-.25

+43.55

+ 50.66

+ 6.52

0

-.42

-3.79

-2.56

-20.05

-23.01

-5.84

-3.23

+ 12.14

+29.59

+16.96

-.12

-1.67

-11.02

-23.38

-21.25

-13.19

-11.83

-5.16

- 13.88

-17.51

Change in

reservoir

contents

(cfs-days)

+242

-17,904

-92,885

-207,478

-222,067

-404,940

-1,650

+343,213

+ 525,733

+76,867

0

-5,082

-44,492

-80,190

-223,280

-231,186

- 54,849

-29,309

+113,568

+306,181

+195,939

-1,452

-19,704

-128,279

-250,807

-204.089

-113,305

-93,920

-39,946

-98,202

-109,866

based on levels and the temperature profiles run in 

September 1963. Comparative readings have been 

made of the water surface in the reservoir and 

that indicated by the control-room gage since May 

1964. The differences range from +0.078 to -0.045 

foot, and the average during the period of this 

study was +0.020 foot. There does not appear to be 

any definite seasonal trend in these differences, and 

they were assumed to be of a random nature for 

purposes of this study. No other corrections have 

been applied, nor was the recorder chart used in 

the determination of midnight readings. The monthend reservoir elevations and the monthly changes 

in reservoir stage and contents are summarized in 

table 18.

The period of study covers three drawdown and 

two refill periods. These are summarized in the following tabulation:

Change in stage Change in contents 

Period (feet) (cfs-days)

September 1964-October 1964 .- +.02 +242

November 1964-April 1965 .._. -100.78 -946,424

May 1965-August 1965 ------- +100.73 +945,813

September 1965-March 1966 .._ -58.90 -618,388

April 1966-June 1966 -------- +58.69 +615,638

July 1966-April 1967 _________ -119.01 -1,059,570

The drawdown periods for water years 1965 and 

1967 are the two largest since the reservoir was 

filled during July, 1954. This was fortunate for this 

study, as it permitted a wider range of values to be 

examined for bank-storage potentials.

WATER-BUDGET RESIDUAL

The three components of the water budget just 

discussed were algebraically combined on a monthly 

basis to give a preliminary evaluation of potential 

bank storage in Hungry Horse Reservoir. These 

components and the residuals are shown in table 19. 

A plus sign signifies that more water is available 

than is indicated by the water budget, and a negative sign signifies that less water is available. These 

values range from +24,164 cfs-days in March 1965 

to -17,904 cfs-days in May 1965.

The water-budget residuals were accumulated on 

a monthly basis over the 31-month period and plotted against month-end reservoir elevations. This is 

shown in figure 13. This plot reveals several inconsistencies which suggest that further study of the 

data used in this method should be made.

If the reservoir and ground-water storage had 

reached a state of equilibrium prior to the start of 

each drawdown period, then the residual of the 

water-budget computations for a drawdown period 

should be approximately balanced by that computed
34 HYDROLOGY OF HUNGRY HORSE RESERVOIR. NORTHWESTERN MONTANA

TABLE 19. Components of water-budget computations, in 

cfs-days, for Hungry Horse Reservoir

Month

1964

Oct ----- 

Nov -.--- 

Dec -----

1965

Jan ----- 

Feb ----- 

Mar ----- 

Apr ----- 

May ----- 

June

July .-.- 

Aug

Sept ----- 

Oct ----- 

Nov ----- 

Dec -----

1966

Jan ----- 

Feb ----- 

Mar ----- 

Apr ----- 

May ---.. 

June

July -.... 

Aug ---.. 

Sept ----- 

Oct ----- 

Nov ----- 

Dec -----

1967

Jan -.-._ 

Feb ----- 

Mar ----- 

Apr -----

3540

3520

3500

3480

5 3460

3440

Outflow Inflow Change in 

contents

Residual

Accumuulated 

residuals

46,452

59,156

162,048

254,624

264,343

459,777

182,956

79,037

5,760

87,792

55,283

77,692

91,302

67,926

255,245

258,628

74,731

66,506

29,056

85,607

130,265

107,472

53,749

150,580

274,975

230,166

150,794

128,923

69,200

125,043

175,832

49,215

42,262

63,997

37,660

29,907

30,673

166,785

432,074

535,361

168,915

59,239

77,739

47,938

37,955

31,167

24,717

17,248

31,868

139,500

409,642

335,929

106,150

34,094

20,582

21,905

26,577

31,028

28,768

24,718

23,211

61,937

+ 242

-17,904

-92,385

-207,478

-222,067

-404,940

-1,650

+343,213

+ 525,733

+76,867

0

-5,082

-44,492

-30,190

-223,280

-231,186

-54,849

-29,309 

+ 113,568 

+306,131 

+ 196,939

-1,452

-19,704

-128,279

-250,807

-204,089

-113,305

-93,920

-39,946

-98,202

-109,866

-2,521

-1,010 

+ 5,666

+9,486 

+ 12,369 

+24,164 

+ 14,521

-9,824

-3,868

-4,256

-3,956

-5,129

-1,128

-219 

+798

+2,725 

+ 2,634 

+ 5,329 

+ 3,124 

-17,904

-9,725

-130

-49

+ 1.719

+2,263

-500 

+6,461

+6,235 

+4,536 

+3,630 

+4,029

-2,521

-3,531 

+ 2,135

+ 11,621 

+ 23,990 

+48,154 

+ 62,675 

+ 52,851 

+48,983 

+44,727 

+40,771 

+35,642 

+ 34,514 

+34,295 

+35,093

+37,818 

+40,452 

+45,781 

+48,905 

+81,001 

+ 21,276 

+21,146 

+ 21,097 

+ 22,816 

+25,079 

+ 24,579 

+31,040

+ 37,275 

+41,811

+ 45,441 

+ 49,470

Total 4,260.920 3,148,761 -1.062,689 +49,470 

3570

3560

-10 0 +10 20 30 40 50 60 

ACCUMULATED VOLUME, IN THOUSANDS OF CFS-DAYS

70

FIGURE 13. Mass curve of accumulated water-budget 

residuals and month-end reservoir elevations.

for the following refill period. In the two complete 

cycles of drawdown and refill studies, this is not 

the case. In the 1965 cycle the residual was + 66,206 

cfs-days on the drawdown and only -28,380 cfsdays on the refill. During the 1966 cycle, the situation was reversed with a residual of +14,610 cfsdays on the drawdown and -27,808 cfs-days on 

the refill. Even if the two seasons were considered 

together, there was a residual of 21,097 cfs-days 

more water on drawdown cycles than on refill cycles.

The apparent inconsistencies, which might be related to nonequilibrium ground-water conditions and 

unaccounted-for ground-water inflow, will be considered in relation to theoretical concepts.

The residual of the water-budget computations 

was divided by the range in reservoir stage for 

each drawdown and refill period. The average volumes, in cfs-days per foot of change in reservoir 

stage, are shown in the following tabulation:

Year

1965

1966

1967

Drawdown

.- 657

.- 248

.- 238

Refill

282

474

These values also suggest a lack of consistency that 

needs further study.

MATHEMATICAL MODEL

DEVELOPMENT OF EQUATIONS

Bank-storage changes in response to reservoir 

fluctuations can be calculated. In the section which 

follows, theoretical ground-water concepts are used 

to derive a mathematical model which relates reservoir-stage fluctuations both to movement of water 

across the boundary between the reservoir and adjacent geologic materials and to changes in bank 

storage. The reliability of results, when applied to a 

field situation, depends on how closely the dimensions and characteristics of the aquifer match those 

of the theoretical model.

Assumptions are made as follows:

1. The unconsolidated material adjacent to the reservoir is the principal aquifer in which bank 

storage takes place.

2. The aquifer shape can be described as two 

identical wedges separated by the reservoir 

(see fig. 14).

3. There is a free hydraulic connection through the 

vertical planes forming the boundaries between the reservoir and aquifer.

4. The vertical planes forming the landward 

boundaries between the aquifer and the consolidated rocks flanking the valley are parallel 

to the reservoir boundaries and are impervious.

5. The planes forming the bottom and downstream 

ends of the aquifer are impervious.

6. There is no vertical recharge to the aquifer.

7. Material is homogeneous and isotropic. Initially, 

ground-water level is everywhere at initial reservoir level.

For convenience, most of the mathematical symbols are listed in table 20. Some are explained where
DEVELOPMENT OF EQUATIONS 35

VNN

SECTION B

FIGURE 14. Schematic sketches of aquifer showing assumed conditions.

first introduced in the text. Schematic sketches of 

the aquifer shape showing assumed conditions are 

shown in figure 14.

TABLE 20. Symbols and dimensions used in the 

mathematical model

Symbol Description Dimensions

a -_-_-__ Distance from reservoir to valley 

wall __-__-_--_-_--_-_-______

C ______ Rate of change of reservoir level;

C^dh/dt ____________________

e --_-_.- Napierian log base, 2.71828 _______ None

L ______ Length of reservoir pool at beginning of any change _____________ L

L, ______ Distance from head of pool to section in unponded reach ___.__. 

m _----. Slope of reservoir bed ___________

Q --.___ Flow to ( + ) or from (-) the 

aquifer for both sides of the 

reservoir ______________________ UT~l

q, qt, q* _ _ _ Flow to (+) or from ( ) the 

aquifer per unit length for one 

side of reservoir _______________ L'T~'

S -_--._ Coefficient of storage of aquifer ___ None

L

None

Symbol Description Dimensions 

T ______ Transmissivity of the aquifer ______ UT~l

t _______ Time from beginning of change in

reservoir level ________________ T

tf _______ Time from cessation of change in

reservoir level _________.--__--__ T

*i --_.--_ Duration of a constant rate change

in reservoir level ____-__--_-_--_ T

V --_.-- Volume gain ( + ) or loss ( ) of

water in aquifer _-_--------__-_ L3

«_----__ A descriptor of the aquifer shape 

and its hydrologic characteristics;

For the stated assumptions, a drawdown is imposed on the reservoir at a constant rate, dh/dt=C, 

where dh/dt is the slope of the time hydrograph of 

reservoir elevation. Coordinates are oriented so that 

dh/dt and C are positive for a rising stage and 

negative for a falling stage.

For these conditions, ground water flows to the 

reservoir. At a section in the portion of the reservoir 

downstream from head of pool where ponded conditions still prevail, the equation of flow per unit
36 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

length of reservoir from one side is (Rorabaugh, 

1964, p. 435, eq 5)

dx J x=( = CaS

00

1-4-

, (1)

where qd is the rate of flow across the boundary between the aquifer and the reservoir for a unit length 

and for one side of the ponded reach of the reservoir; 

a is the distance from the reservoir to valley wall; 

S is the coefficient of storage of the aquifer; t is time 

from beginning of change in reservoir level; a, which 

equals 7r2T/4a2S, is a descriptor of the aquifer shape 

and its hydrologic characteristics; T, the transmissivity of the aquifer; and dh/dx is the hydraulic 

gradient at the aquifer-reservoir boundary. In this 

equation and those following, flow is positive for 

movement from the reservoir to the aquifer and negative for ground-water discharge to the reservoir.

It should be noted that equation 1 was originally 

derived using a heat-flow equation as a starting 

point and that the analogy between heat flow and 

ground-water movement is used in some of the derivations that follow. Corresponding items in the analogy are listed below.

Heat conduction Ground-water movement

Concept Notation Concept Notation

Temperature --------

Specific heat of

material times its

density. 

Thermal conductivity --

Diffusivity -----------

Head ____--_-------. h

Specific storage ----- S«

K

K/cp

One dimensional a 2v

equation of con- - =

duction of heat. d *2

Hydraulic conductivity.

Diffusivity ----------

For diffusivity of 

an aquifer, inclusion 

of aquifer thickness 

results in the ratio 

transmissivity divided by storage 

coefficient.

One dimensional ? 

equation of 

ground-water 

movement

k/S, 

T/S

da;2

Since the basic differential equations are of the 

same form, the solution for a problem in one field 

will be the same as in the other field for similar 

boundary conditions, the only difference being notation.

At a section in the upstream part of the reservoir 

between the original head of pool and the new head 

of pool, ponded water has been depleted and stream 

level prevents any additional drawdown. The flow 

per unit unponded length of reservoir for one side 

is (Rorabaugh, 1964, p. 435, eq 7)

00

SCaS

(2n-l) 2

(2)

where qu is the rate of flow across the boundary between the aquifer and the reservoir for a unit length 

and for one side of the unponded reach of the reservoir, and f is the time since the cessation of change 

in reservoir level at a section in the unponded reach. 

To obtain the flow for the total length of the 

reservoir, inflows from the ponded and unponded 

reaches are added and multiplied by two to account 

for both sides of the reservoir. For the ponded reach, 

equation 1 is multiplied by the ponded length at time 

t. Unponded length is drawdown, Ct, divided by 

bed slope, m. Ponded length is initial length, L, 

minus Ct/m. Flow for the unponded reach is obtained by integrating equation 2 with respect to 

length. Limits of integration are Lv =0 at initial 

condition and Lr =Ct/m at time t. Note that the 

variable unponded length, L,,, is equal to C(t-t')/m. 

From this relation, the variable V in equation 2 is 

replaced by its equivalent, tf-t-Lvm/C. Total flow

s

Ct/m

qwdLt

when this is integrated, we have

Q=2LCaSl

ct r

00 i_ A V* c-<««-*> at

TTZ 2-» (2n-l) 2

n=l

Lm

96

IT

00 -(2n-i)'

(2rc-l) 4

. (3)

Equation 3 was derived for the case of a falling 

reservoir stage. For a rising stage, total flow is the 

sum of the flows of the ponded and unponded 

reaches, doubled to account for both sides of the 

reservoir. Ponded length is initial length, L. Flow at 

a section is given by equation 1; thus, total flow in 

the ponded reach is 2Lqd. As the reservoir rises, 

the head of pool moves upstream into an unponded 

reach. At a section in this reach a distance Lv upstream, flow to the aquifer is expressed by equation 

1, in which time begins when the moving head of 

pool reaches the section. This time for pool to arrive 

at the section is Lrm/C. Therefore, t in equation 1 

is replaced by (t-Lvm/C). The equation is then integrated with respect to length. Limits of integration, in the positive direction of length, are from 

Ct/m to zero. Results are multiplied by two to account for both sides of the reservoir. Thus

I qddLv ).

J Ct/m /

Integration results in equation 3, which applies 

to either a lowering or a raising of the reservoir
DEVELOPMENT OF EQUATIONS 37

level. C is positive for a rising reservoir level 

and negative for a falling level. The sign of Q indicates the direction of flow, a positive Q for flow 

from the reservoir to the aquifer and a negative Q 

for flow of ground water to the reservoir.

Inspection of equation 3 shows that for large 

values of time, series terms become very small. When 

a£>7r2 /20 (or Tt/a*S>0.2), all but the first series 

terms may be neglected. Equation 3 is modified for 

a£>7r2 /20 as follows:

I yin. ri±. 9.

Q=2LCaS\ 1-

L

Lm Lm' I2at

Lm at .

J

When time is small enough that the aquifer response has not reached the valley wall, the system is 

behaving as semi-infinite. From the solution for 

head in a semi-infinite aquifer given by Hantush 

(1961, p. 1311, eq 24) or from translation of the 

heat-flow equation of Carslaw and Jaeger (1959, p. 

63, eq 4), we find that for a section for one side 

of the ponded reach of the reservoir

dx

and, by superposition, for a section for one side of 

the unponded reach of the reservoir

Total flow, for at<^2 /2Q, is

r r 

Q=2 j(L-CVw) qd+J

when this is integrated, we find

ct/m

Periods of drawdown or fill followed by constant 

levels are experienced in reservoir operation. Also 

in computing effects of a series of regulations on 

a future time, it is convenient to have expressions 

for the condition of a constant change in stage 

dh/dt = C -for time t^ followed by a constant level 

from time £, to time t. Expressions are developed 

by superposition.

For constant rate of drawdown or fill followed by 

stationary levels,

00

e,-(zn-i) -(zn-i 2«*

(2n-

_5L1

Lm a

00

E

-(2n-i)

(2n-l)*

00 -(2n-i) 2 a*

(4)

For Tt/a*S>Q.2 and

(4a)

For Tt/a?S<0.2, 

Qt>t^ .JLJ/1--??*-) /-?*

V

a z S

For n/a2S>0.2 and T(t-tJ/a2S<O.I,

(46)

. Lm at **

Lm

3Lm

VOLUMES

Equations 3-4c are useful in computing rates of 

movement to and from bank storage. For large 

increments of time, as in monthly values, it is more 

convenient to compute cumulative storage changes. 

Flow equations are integrated with respect to time 

to produce the following volume equations:
38 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

For constant rate of drawdown or fill,

V=2LCaSt .f \AJ AJ | JL O

3Tt ~at^

n=l

Lm

'1 a2£ 2/a2£\ 

2 3T* 15\r*/

(5)

For Tt/azS>0.2,

Ct

2Lm

2 . Ct(a 

15 Lm\

ZS\ 2 

TJ

J'

For 2Va2S<0.2,

(5a)

5Lm)' < 5& > 

For drawdown or fill followed by stationary level,

____._8_ 2Lm~r at, ' **

Lm

00

E

-(2n-i) a(t-t*) r*+ 1 e______* ^EI *

n= l (2n-l) 4 Lm ' at.

00

(6)

For Tt/a*S>Q.2 and

- . 

Lm

Ct.Ct,

For Tt/a2S<Q.2, 

V 4 Kf>« -

For Tt/azS>0.2 and

-

t>_ t -

a*S,Ct a*

15'Lm\n/ 

.-

at\ Lm at**

4

5Lm

LmJ

Hand calculation of flow by equations 3 and 4 

and volume by equations 5 and 6 is too cumbersome. 

These equations lend themselves to computer solution, and a computer would be used if daily calculations were required. For this problem the modified 

equations 3a, 3&, 4a, 4&, and 4c for discharge and 

5a, 5&, 6a, 6&, and 6c) for volume are not too cumbersome for hand calculation on a monthly basis.

SELECTION OF DIMENSIONAL CONSTANTS

The length of the reservoir at full pool, at an 

elevation of 3,560.5 feet, was determined as 32.5 

miles (171,600 feet). This is based on maps and 

sections by Bateman (unpub. data, 1952). It is 

somewhat shorter than river mileage because some 

of the minor meanders are not considered.

The average bed slope (from sections) is 15.48 

feet per mile or a ratio of 0.00293. Note from the 

orientation sketch (fig. 14) that the origin is at 

head of pool (at any pool level) and that m is negative.

The length, L (feet), at the start of any fluctuation 

is determined from reservoir and full-pool elevations 

(feet above mean sea level), and slope.

L = 171,600- 

or 

L =

reservoir elevation 3,560.5

-0.00293 

3,057.5 reservoir elevation

-0.00293

The term Lm (feet) is determined as follows: 

Lm- -503- (reservoir elevation-3,560.5) 

=3,057.5 reservoir elevation.

The distance from reservoir to valley wall was 

computed as 851 feet on the basis of the geometry 

of the wedge and volume of material computed from 

the unpublished cross sections.

HYDROLOGIC CONSTANTS 

OUTWASH, DRY PARK AREA

In August 1964, three observation wells were installed in a line perpendicular to the reservoir to
HYDROLOGIC CONSTANTS 39

sample conditions in outwash deposits. The location 

is near Dry Park Creek on a 1,500-foot-wide terrace 

on the east side of the reservoir and about 2 miles 

downstream from the head of pool. These wells were 

drilled using 6-inch steel casing without a screen. 

Well information is summarized below:

Dry Park well 1, located 195 feet east of reservoir 

at full pool

Material

Silt, tan, sandy _____. ___________.

Sand and gravel, well-rounded, 

washed; silt and clay ._._______.

Gravel and sand, clean, loose _--..- 

Sand, fine; silt __________________

Clay, silt, sand, some gravel; hole 

stood open ____________________

Deep interval 

(feet)

0-1

1-15

15-41.5 

41.5-50

50-57

Casing was pulled back to 38 feet below land surface to 

place the end of the casing in clean gravel. After developing, 

well was pumped at 70 gpm (gallons per minute) for 15 

minutes with a drawdown of 08 foot. Land surface is at an 

elevation of 3,561.0 feet, and bottom of casing is at 3,523.5 

feet.

Dry Park well 2, located 410 feet east of reservoir 

at full pool

Material

Silt, sandy; top soil _____________

Gravel and sand, very loose, wellwashed ; more sand and silt than 

in well 1.

Depth interval 

(feet)

0-3 

3-59

Well was pumped at 40 gpm for 3 hours with a drawdown 

of 5 feet. Land surface is at an elevation of 3,561.9 feet, and 

bottom of casing is at 3,502.8 feet.

Dry Park well 3, located 800 feet east of reservoir 

at full pool

Material 

Soil, cobbles, silt _______..

Silt, clay, sand ___________

Sand and gravel, some silt 

Gravel, sand, some silt ___ 

Gravel, sand, some silt ___ 

Sand, silt __-_--__-_--_-__

Depth interval 

(feet)

0-3

3-6

6-18 

18-30 

30-46 

46-51

Casing was pulled back to 45 feet below land surface. 

Well was pumped at 70 gpm with a drawdown of less than 

1.5 feet. Land surface is at an elevation of 3,563.6 feet, and 

bottom of casing is at 3,518.6 feet.

At this section the streambed is at an elevation 

of about 3,520 feet. When the reservoir is lowered, 

beds of clean boulders, gravel, and sand are exposed 

on the steep bank. Following a rapid drawdown, 

freely flowing discharge from the outwash deposits 

to the river was observed just above river level.

Waterlevel recorders were installed in each observation well and operated from October 1, 1964, 

to November 1966. Well 1 did not record below an 

elevation of 3.524 feet. Considerable records were 

lost during the winter months because of severe 

weather and inability to service the recorders.

Water levels in all three observation wells responded to changes in reservoir level. Seiches in 

the reservoir, frequently having an amplitude of 

about 0.2 foot and a period of 96 minutes, were 

recorded with small timelag at all three wells. During reservoir-drawdown periods, ground-water levels 

dropped at almost the same rate as the surface of the 

reservoir. During a reservoir recession of 0.7 foot 

per day, a ground-water profile with about 0.2 foot 

of head from well 3 to the reservoir was established 

and changed little during the first 30 feet of drawdown. Below an elevation of 3,530 feet and as the 

pool approached river-bed level, gradients steepened, 

reflecting effects of reduced transmissivity caused 

by unwatering of the highly permeable material at 

the higher elevations.

Theoretical analyses of the response of the aquifer 

to seiches and also of the ground-water profile during rapid drawdown produce very large values for 

diffusivity (T/S). Inasmuch as the values of head 

are very small, the results of this approach have a 

wide range of error. All the evidence leads to the 

conclusion that this outwash material is highly permeable and that drainage or filling response time is 

so rapid that timelag is negligible except when 

dealing with very small increments of time. On the 

basis of experience gained from outwash and river 

deposits of similar nature, the storage coefficient of 

this material would be expected to be 0.20 or perhaps somewhat larger.

TILL, CANYON CREEK AREA

A field inspection was made on May 11, 1966, 

when reservoir-pool level was about 3,525 feet and 

was rising at the rate of 1.5 feet per day. An area 

of the reservoir bed on the east side between Deep 

Creek and Canyon Creek and mapped as till was inspected in some detail. A small pond, perhaps 40 

feet in diameter and at an elevation of about 3,550 

feet, had a water level about 2 feet below its outlet. 

A small stream was flowing into the pond. Eros'on 

at the outlet showed that there had been substantial 

overflow when the lower elevation snow had melted 

a few weeks earlier. The fact that pond level had 

receded 2 feet during a time when there was inflow 

shows that at this location vertical infiltration rates
40 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

into the till, although not high, may be of some 

importance in the analysis. A small pit was dug 

about 1 foot from the pond and about 2 feet below 

pond level. Material was cobbles in a matrix of fine 

sand and silt. Inspection an hour later showed no 

water in the pit, a clear indication that the pond 

was perched, that unsaturated flow existed below 

the pond, and that the vertical hydraulic conductivity of the till was greater than that of the pond bed. 

A small pit was dug adjacent to the reservoir 

pool. Material was cobbles and fine sand. When 

bailed the pit filled in a few minutes indicating 

that, locally, the horizontal hydraulic conductivity 

is considerably better than that of the till generally. 

When a small ditch was dug to connect the pit to the 

reservoir, flow from the pit to the reservoir was observed. At this location vertical recharge from snowmelt and rain in the exposed reservoir bed and areas 

adjacent to the reservoir was large enough to maintain ground-water head above reservoir level during 

a period of rising reservoir levels.

This is an example of "ground-water backwater." 

Rising reservoir stage reduced ground-water gra3580

3560

3540

dients and reduced flow from the aquifer to the reservoir. Water which originated as ground-water 

recharge was slowed on its way toward the reservoir and was accumulated as bank storage.

TILL, MCINERNIE-RIVERSIDE AREA

Three 6-inch observation wells were drilled (June 

1966) in the till on the east side of the reservoir 

and about 10 miles upstream from the dam. Material 

penetrated was till, mainly clay with various mixes 

of boulders, cobbles, and gravel. During drilling the 

only place where permeability was high enough to 

permit ground-water to enter the well in noticeable 

amounts was at the Riverside site at an elevation 

of 3,512-16 feet.

As shown on figure 15, water levels in Mclnernie 

wells 1 and 2 rose very slowly during the year following drilling, demonstrating that the till at the 

location had very low hydraulic conductivity. Water 

levels in the Riverside well recovered slowly (fig. 

15), requiring about a month to rise 78 feet. This 

slow rise demonstrates a very low hydraulic conductivity. During the following year, while reservoir

3520

o

GQ

3500

3480

3460

3440

J FMAMJ JASONDJ FMAMJ J ASOND JFMAMJJASOND

1964 1967

FIGURE 15. Comparison of ground-water levels with stage of Hungry Horse Reservoir.
THEORETICAL SOLUTIONS AND COMPARISON WITH PRELIMINARY WATER BUDGETS 41

TABLE 21. Lineated stage of Hungry Horse 

Reservoir and input constants to theoretical model

[Stage: Add 3,000 to obtain elevation, in feet above mean 

sea level]

Date

196$

Dec 8 .--..

1964

Feb 5

May 8 -------

June 20 -----

Nov 16

Nov 25 ------

Dec 7 ------

1965

Jan 9 ------

Mar 5 ------

Mar 25

Apr 9 ------

May 8

June 25 --- -

July 10

Oct 25

Nov 2

Nov 29

Dec 7

Dec 13 ----..

1966

Jan 27

Mar 16

Mar 29

Apr 24

May 3

May 14

May 24

June 4

June 21 ..-..

Aug 28

Oct 3 -----

Nov 14

Nov 18

Dec 15

1967

Jan 1

Jan 9 ------

Jan 25

Feb 14

Feb 20

Mar 8

Mar 22

Apr 8

Apr 28 .--.

Stage

(feet)

560.5

511.5

486.5

560.5

560.5

559.0

559.0

548.5

505.8

464.9

453.4

463.0

550.0

560.5

560.5

554.5

554.5

548.5

548.5

512.0

500.2

500.2

513.2

513.2

531.0

531.0

548.8

560.3

560.5

547.0

514.5

514.5

487.5

490.0

482.0

477.5

477.5

473.0

473.0

458.5

458.5

---- 441.0

Change of

stage

(feet)

-49

-25

+74

0

-1.5

0

-10.5

-42.7

-40.9

-11.5

+9.6

+87.0

+ 10.5

0

-6.0

0

-6.0

0

-36.5

-11.8

0

+13.0

0

+ 17.8

0

+ 17.8

+ 11.5

+0.2

-18.5

-32.5

0

-27.0

+ 2.5

-8.0

-4.5

0

-4.5

0

-14.5

0

-17.5

Duration,

t, (days)

59

93

43

149

9

12

33

55

20

15

29

48

15

107

8

27

8

6

45

48

13

26

9

11

10

11

17

68

36

42

4

27

17

8

16

20

6

16

14

17

20

Bate of

change of

stage, C

(ft per day)

-0.8305

-.2688

+ 1.721

0

-.1667

0

-.3182

-.7764

-2.045

-.7667

+.3310

+ 1.8125

+.700

0

-.750

0

-.750

0

-.8111

-.2458

0

+ .500

0

+ 1.618

0

+ 1.618

+.6765

+.0029

-.3750

-.7738

0

-1.000

+.1471

-1.000

-.2813

0

-.750

0

- 1.038

0

-.875

levels dropped 120 feet and then returned to full 

pool, water level in this well fluctuated about 2 feet.

Ground-water level rose several feet above full-pool 

stage, indicating recharge. Movement of ground 

water toward the reservoir is very slow at this site.

From the foregoing evidence it is clear that hydraulic conductivity is highly variable from place 

to place, ranging from near zero in parts of the till 

to very high values in open-work gravels. The storage coefficients also appear to range from near zero 

to greater than 0.2. Frequently, when dealing with 

heterogeneous material, the problem can be adequately handled by treating in bulk lumping segments of the problem into one or more groups and 

treating each group on an average basis. A number 

of theoretical solutions were computed and tested 

against observed data.

The unknown (or uncertain) constants appear in 

the equations in two groupings, aS and T/a?S. An 

average value for a of 851 feet was determined from 

the volume and the geometry of the unconsolidated 

material. It must be kept in mind that this figure 

is approximate. Using the equations, assumed values 

for T, S, and a, and the reservoir-stage record, movement of water to and from its banks and volume of 

storage in the aquifer are calculated. The term S 

or aS appears as a multiplier in all the equations. 

Once a calculation is made for the period of record, 

the model solution obtained may be expanded into a 

family by multiplying by constants. If the multiplier is considered a change in storage coefficient, 

it also requires a similar change in transmissivity 

so that the term T/a?S remains the same in the 

internal parts of the equation. If the multiplier is 

considered as a change in term a, then transmissivity has been altered by the square of the multiplier.

The reservoir-stage record, which is the boundary 

input to the model, was approximated as a sequence 

of straight lines each having a constant rate of 

change of stage, C. Table 21 lists the segments 

of the lineated hydrograph and the rate of change 

of stage constants.

THEORETICAL SOLUTIONS AND COMPARISONS WITH 

PRELIMINARY WATER BUDGET

Equations 3-6c constitute a general model for 

bank-storage relations for the assumed geometry. 

For this particular problem several trials were made 

using groups of selected constants. Subscripts are 

used to designate the trial groups of selected constants. For example, M2 indicates that the model 

was used with the following constants: a=851 feet, 

5=0.15, and T/a*S=0.003 per day.

The equations are in dimensionless form. In the 

calculations for this problem, all length and eleva-
42 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

tion values were expressed in feet; all time values, 

in days; changes of reservoir level, in feet per day; 

and transmissivity, in square feet per day. Storage 

coefficient and slope are dimensionless. Use of these 

units produces values of flow in cubic feet per day 

and volumes in cubic feet; division of these values 

by 86,400 seconds per day yields flow in cubic feet 

per second and volume in cf s-days.

TRIAL M,

In the first trial very low values of diffusivity 

were assumed. A partial calculation yielded very 

small bank-storage values. The comparison with unadjusted water-budget residuals was so poor that 

this set of assumptions was abandoned.

TRIAL M2

For Ms the assumed constants were

and

a=851ft, 

5=0.15, 

T/a?S=0.003 per day.

These constants define T as 326 square feet per 

day, or 2,444 gallons per day per foot. Calculations 

were made on a volume basis using equations 5& 

and 6& for intervals shorter than 67 days (Tt/azS 

<0.2) and equations 5a and 6a for intervals equal 

to or greater than 67 days. It should be noted that 

the later equations tail as straight lines on semilog plots, and graphical methods may be used to 

shorten the calculations. For each recession segment 

(table 21) the cumulative ground-water storage gain 

or loss was computed at the end of each month from 

the beginning of the segment until the effect of the 

event became negligible. Total storage change at the 

end of any month is the algebraic sum of the effects 

at that time of all preceding changes in stage.

Water-budget calculations were computed so that 

negative residuals designate reservoir water going 

into bank storage, and positive, water moving from 

the aquifer to the reservoir. The equations were derived from the aquifer viewpoint, so negative signs 

in the theoretical model indicate ground-water outflow, and positive, flow the aquifer. For compatibility 

the signs of the model calculations were reversed. In 

addition, a constant was subtracted from the model 

in order to orient the model to the water-budget 

value of zero at midnight, September 30,1964.

Accumulated gains to the reservoir for the unadjusted water budget and those from M2 are 

shown in figure 16. Also shown are the accumulated 

differences of monthly water-budget residuals and 

calculated values from M2 . It is obvious that M2

-20

1967

FIGURE 16. Cumulative apparent gains to reservoir determined from unadjusted water budget and from Af2 and 

accumulated differences between water budget and M2.

alone cannot be modified to satisfy the water-budget 

data. A large multiplier would be needed to satisfy 

the three periods of drawdown. This would imply a 

storage coefficient unreasonably large and would not 

improve the relation at times of full pool (JulySept.). If M2 were combined with another model 

solution using different constants, the combined 

solution would have to satisfy the difference in relationship in the lower graph. This is not possible. 

The water-budget data on this illustration and on 

the plot against elevation (fig. 13) are incompatible 

with theory and cannot be approximated by use of 

any reasonable combination of constants in the 

model. In 1965 a gain of 64,000 cfs-days occurred 

during a draft of 100 feet, but in 1966-67 only
WATER-BUDGET MODIFICATIONS 43

30,000 cfs-days was gained during a draft of 120 

feet. In 1964-65, from full pool to full pool, return 

to ground-water storage was only 40 percent of the 

yield. For the 1965-66 pool-to-pool cycle, indicated 

return to the aquifer was double the yield. Thus the 

theoretical understanding points to the need to restudy the water budget for possible errors. The 

accumulated-difference graph indicates that a reduction of about 30,000 cfs-days in the period December 1964-March 1965 and an increase of about 

10,000 cfs-days in May-June 1966 would be~required 

to satisfy M2 approximately. During the first period, 

total inflow to the reservoir was about 162,000 cfsdays; change in contents, about 930,000 cfs-days; 

and outflow, about 1,140,0000 cfs-days. The accumulation is about 20 percent of the inflow and about 3 

percent of change in contents and outflow. For 

March the accumulation of 16,000 cfs-days is 50 

percent of the inflow. The inflow records could not 

account for this item. The capacity table, which 

undoubtedly contains some error, cannot by itself 

be the source of difference. If it were adjusted, the 

other periods of rise and fall of reservoir levels 

would become incompatible. The outflow record for 

the period is within close limits of measurements 

and could not logically be shifted as much as 3 percent.

During March, which includes the large drawdown period March 6-24, 1965, the accumulation 

of 16,000 cfs-days is about 4 percent of the monthly 

flow. Four discharge measurements made during this 

period show that it is very unlikely that records 

could be 4 percent in error.

At this stage in the analysis, a reexamination 

was made of rating curves and record analyses used 

in the water-budget analysis. In order to avoid bias, 

results of the theoretical approach and the waterbudget review were obtained independently.

WATER-BUDGET MODIFICATIONS

In the previous sections, it was pointed out that 

a considerable difference existed between the estimates of bank-storage effect made by the waterbudget procedure and those made by the mathematical models. The results of the water-budget 

study did not conform in some aspects to mathematical theory or hydrologic reasoning. Therefore, 

all the basic data and computational procedures used 

in the water-budget study were reviewed in detail. 

The purpose of this review was to ascertain whether 

or not any modifications should be made in the 

various components of the water budget. This review revealed that minor modifications could be

made in every item of the water budget. However, 

almost all such modifications would be of such a 

nature that they would not indicate superiority in 

either basic assumption or computational procedure.

There were three items that appeared to be 

worthy of further study: (1) the high-water rating 

for the gaging station South Fork Flathead River 

above Twin Creek near Hungry Horse (2) the 

high-water rating for the gaging station South 

Fork Flathead River near Columbia Falls, and (3) 

the estimate of reservoir inflow from the ungaged 

areas. A discussion of these items follows.

The upper end of the rating curve for the gaging 

station South Fork Flathead River above Twin 

Creek near Hungry Horse was reviewed in detail. 

Because this main inflow gaging station was newly 

established, some instability in the definition of the 

stage-discharge relationship might be expected. A 

review of the gage-height record did not reveal any 

periods where changes should be made. During the 

period of study, two rating tables had been used in 

the computation of daily discharges. These rating 

tables were identical up to a gage height of 8.7 feet, 

discharge 5,150 cfs. Above this stage, the two tables 

tended to diverge, and at a stage of 12.0 feet the 

difference amounted to about 7 percent. Three highwater measurements were made during each of the 

water years 1965, 1966, and 1967, and two were 

made during water year 1968. A slope-area measurement of the peak of the 1964 flood had also been 

made.

The channel characteristics at this gaging station 

suggest that a single stage-discharge relationship 

would be logical. Thus, the 12 measurements above 

a gage height of 8.7 feet were used to develop a 

mean high-water rating. Table 22 shows the percentage deviations of each of these measurements 

from the tentative rating table developed in this

TABLE 22. Percentage deviations of high-water 

discharge measurements from rating tables, South 

Fork Flathead River above Twin Creek near 

Hungry Horse

Measurement Date

1 

7 

8 

9 

21 

23 

24 

33 

34 

35 

46 

47

»6-64 

4-29-65 

5-14-65 

6- 7-65 

5- 6-66 

5-26-66 

5-30-66 

5-24-67 

6-14-67 

7- 7-67 

5-21-68 

6-19-68

Gage 

height 

(feet)

20.87 

9.77 

11.55 

12.16 

11.15 

9.83 

12.03 

13.41 

10.88 

9.35 

10.57 

11.17

Discharge 

(cfs)

50,900 

7,430 

13,000 

15,100 

11,900 

8,160 

15,500 

19,700 

10,500 

6,450 

9,730 

11,700

Percentage deviation 

from indicated rating 

table

1

0 

+ 1.2 

-1.2

-4.~8 

til ta

2

-0~2 

+4.2 

0.0

Tentative

-2.9 

-0.8 

-1.9 

+2.2 

+4.5 

+4.0 

-2.2 

-2.0 

-2.4 

-0.3 -0.1

1 Slope-area measurement taken.
44 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

review and the tables used in the computation of 

the published discharge record.

The overall balance of the 12 discharge measurements is very good; the total plus deviation from 

the tentative rating table is 10.7 percent, and the 

total minus deviation is 12.6 percent. The individual 

deviations ranged from +4.5 percent to 2.9 percent, the average deviation being 2.1 percent. If 

these are considered algebraically, the weighted 

average deviation amounts to -0.2 percent. There 

is some tendency for the measurements to cluster 

by years, but the total percentage deviations are 

well within the limits that characterize a good stagedischarge rating of a natural stream. The balance 

of these groups of measurements, by stage, is good; 

and in each range the plus and minus deviation approximately balance each other. The tentative 

rating table developed in this analysis was adopted 

for use in computing the 1968 discharge records. 

The use of this mean table was assumed to be appropriate for the entire period of record available 

at this station.

This rating table would be applicable during the 

period April-July 1965 and May-June 1966. It 

would modify the computed runoff by +16,750 cfsdays in water year 1965 and -6,050 cfs-days in 

water year 1966. These changes are in the right direction to improve the estimate of bank-storage effect on the reservoir-refill periods and were judged 

to be a better evaluation of runoff during the highwater periods. This alternative computation of runoff was adopted for use in the revised water-budget 

part of this analysis, and computed values of 

monthly runoff are shown in table 23.

TABLE 23. Monthly runoff, South Fork 

Flathead River above Twin Creek near 

Hungry Horse

Monthly runoff for 

indicated water year 

(cfs-days)

Month

Oct .......

Nov ---...

Dec ........

Feb ......

Mar ......

July ------

Sept .......

1965

-.---. 25,968

--.--. 18,596

...... 25,932

------ 18,751

------ 14,160

------ 16,794

..--- » 88,356

-...- 1 273,410

--,-. 1 353,290

.--.-1118,390

------ 35,559

...... 47,496

1966

30,939 

18,811 

16,374 

12,773 

9,657 

15,642 

75,620 

1 249,900 

1 201,110 

66,592 

20,119 

12,703

1967

10,783 

11,390 

12,327 

11,903 

11,737 

11,896 

28,389

1 Revised.

The inflow to Hungry Horse Reservoir from the 

ungaged drainage area was reviewed for consistency with the inflow from other parts of the drainage basin. For the area on the east side of the

reservoir, the inflow was assumed to be 0.75 times 

the sum of the inflow derived from the east-side 

secondary gaging-station network. The drainagearea ratio of the east-side ungaged drainage area 

and secondary gaging-station drainage areas is 

0.775. Since the original coefficient is so very close 

to the ratio of the drainage areas, there is sufficient 

justification to recompute the reservoir inflow from 

the ungaged area using the coefficient of 0.775. 

This in effect would give the same runoff per 

square mile as for the secondary-network drainage 

area. An inspection of figure 9 shows that the two 

areas are intermingled to such an extent that this 

assumption appears to have hydrologic justification. 

In a similar manner, the reservoir inflow from the 

west-side ungaged area was recomputed using a coefficient of 0.946 in place of 0.90. The revised estimates of inflow for the ungaged drainage areas on 

the east and west banks of the reservoir are shown 

in table 24. The revised estimate is 14,158 cfs-days 

more than was estimated for the preliminary waterbudget and has been used in the reevaluation of the 

water budget.

TABLE 24. Revised estimate of reservoir 

inflow from, ungaged drainage area

Monthly runoff for 

indicated water year 

(cfs-days)

Month

Oct -.--....

Nov .......

IW

Feb ........

Mar ...---.

May -----..

July -------

Sept .......

1965

...... 5,382

....... 4,998

....... 8,151

.--.... 4,187

....... 3,615

.-..--- 3,744

....... 19,925

....... 44,941

....... 52,123

....... 13,841

....... 5,362

...... 6,863

1966

4,373 

4,189 

3,492 

2.452 

1,716 

3,725 

15,480 

41,238 

34,127 

10,256 

3,326 

2,042

1967

2,049 

2,482 

4,056 

3,387 

3,262 

2,751 

7,622

The records for the main outflow station South 

Fork Flathead River near Columbia Falls were also 

reviewed in detail. The high-water discharge occurs 

during periods of heavy drawdown which normally 

occur from September through April but most consistently from November through February. The 

gage height record for the period of this study 

was reviewed, and no further changes appeared to 

be justified. Review of the flows during the drawdown periods for water years 1965, 1966, and 1967 

showed that two rating tables had been used, one 

for water year 1965 and the second for water years 

1966 and 1967. These were virtually the same at a 

discharge of 9,000 cfs and below, but above that 

point they tended to spread until the variation was 

about 3 percent.

An examination of these two rating tables and
WATER-BUDGET MODIFICATIONS 45

all the high-wafer discharge measurements that 

were made since 1954 suggests that a single rating 

for the entire period of record could be developed 

which would be an approximate mean of the two 

tables used. The deviations of the high-water discharge measurements from a tentative table are between +2.5 percent and 2.8 percent; the average 

deviation is 1.24 percent. Thus it appears that the 

use of a single rating is justified.

The deviations from the tentative rating table 

are shown in table 25. The stage-discharge relationship at this station, as judged by the 36 high-water 

measurements, appears to be extremely stable. The 

high flows that occurred during the period March

TABLE 25. Percentage deviations of high-water 

discharge measurements from tentative rating 

table, South Fork Flathead River near Columbia 

Falls

Measurement

270

274

275

278

289

292

312

313

322

323

338

339

341

348

349

353

365

366

367

376

397

898

407

412

413

414

415

416

417

424

426

432

433

443

444

448

Date

2-23-54

4-16-54

4-19-54

7-18-54

4-20-55

7- 8-55

11-20-56

12-28-56

11-12-57

12-10-57

3-24-59

4-24-59

6-22-59

1-15-60

2- 1-60

4-14-60

2-24-61

3-27-61

4-18-61

1-25-62

12-17-63

1-17-64

6-29-64

1-11-65

2-10-65

3- 8-65

3- 8-65

3-10-65

3-15-65

10-29-65

12-20-65

9-15-66

11- 9-67

12-19-67

1-24-68

6-13-68

Gage height 

(feet)

9.82

11.29

11.40

14.55

10.50

9.80

9.96

10.12

10.06

10.25

12.68

11.04

14.09

12.20

14.69

11.08

9.86

11.60

12.31

10.16

9.96

10.11

10.94

9.96

9.96

13.14

13.14

14.05

14.06

9.96

10.00

9.91

10.13

10.20

10.50

11.24

Discharge 

(cfs)

9,140

12,600

13,000

21,400

10,300

9,070

9,470

9,820

9,690

10,200

16,500

12,200

19,500

14,600

21,400

12,100

9,160

13,500

15,400

9,960

9,370

9,460

11.500

9,570

9,390

17,200

17,000

19,400

20,200

9,360

9,280

9,000

9,500

9,970

10,600

12,500

Deviations 

(percent)

+ 1.0

0

+.8

+1.9

-2.8

+.7

+ 1.2

+.9

+ 1.0

+ 2.0

+2.5

+ 1.7

-1.5

-2.0

0

0

+.2

+.7

+ 1.3

+ 1.4

+.1

-2.5

-1.8

+2.2

+ 3

 .6

-1.7

-1.5

+2.5

0

-1.8

-2.7

-2.6

+.6

0

0

10-23,1965, were the highest flows since 1960. Thus, 

if there were to be any major changes they would 

have occurred during this period.

For purposes of this analysis, all measurements 

made prior to water year 1965 were in one group 

and those made during and after 1965 were in a 

second group. A summary of these percentage deviations for different gage-height ranges and time 

periods is shown in table 26. There is a slight 

tendency for the measurements for the two time 

periods to cluster. However, in long-term perspective 

it is felt that a single rating is satisfactory for use 

in this study.

A review was also made of the relationship of 

power-generation, head, and turbine discharge for 

periods of full load (300 megawatts or more) and 

no flow through the spillway or river outlets. This 

review lends support to the contention that a single 

rating table might be applicable during the entire 

period of this study.

This mean rating table was used in the subsequent 

water-budget computations. Changes in the computed runoff for South Fork Flathead River near 

Columbia Falls were made for December 1964-May 

1965, October 1965-January, 1966, and July 1966- 

April 1967. These revisions indicate an increase in 

monthly outflow of 28,520 cfs-days for the entire

TABLE 27. Monthly runoff, South Fork 

Flathead River near Columbia Falls

Monthly runoff for indicated water year 

(cfs-days)

Month

Oct .--..

Nov .--.

Feb -----

Mar --..

May --..

July ---

1965

44,530

59,430

... 1 162,234

... * 253,510

... * 262,710

... * 456,210

... * 183,225

... * 79,930

6,144

84,793

51,144

75,190

1966

1 90,639 

» 68.774 

1 260,630 

1 264,741 

74,835 

66,636 

29,526 

85,460 

130,670 

1 103,123 

1 48,757 

1 148,356

1967

* 277,160 

1 236,207 

* 156,342 

1 132,047 

1 70,044 

1 126,326 

1 177,789

1 Revised.

TABLE 26. Summary of percentage deviations of high-water discharge measurements from tentative rating table, South Fork

Flathead River near Columbia Falls

1954-1968

range

9.82-10.00

10.11-10.50

10.94-11.60 

12.20-13.14 

14.05-14.69 

9.82-14.69

Max

deviation

Deviation (percent) l

No.

10

9

7 

5 

5 

36

--

Plus

5.7

5.9

3.2 

3.8 

4.4 

23.0

2.5

Minus

4.5

7.9

1.8 

4.3 

3.0 

21.5

2.8

Weightad

+ 1.2

-2.0

+ 1.4 

-.5 

+1.4 

+ 1.5

....

Avg

+0.1

_ 2

+.2

+.'3

<+.05

....

No.

5

5

5 

3 

3 

3

--

Plus

3.2

5.3

3.2 

3.8 

1.9 

1.9

2.5

1954-1963

Deviation (percent) 2

Minus

0

2.8

0 

2.0 

1.5

1.5

2.8

Weighted

+3.2

+2.5

+3.2

+1.8 

+ 1.4

+ .4

----

Avg

+0.6

+.5

+ .6 

+.6

K

....

No.

5

4

2 

2 

2 

15

--

1964-1968

Deviation (percent) *

Plus

2.5

.6

0 

0 

2.5 

5.6

2.5

Minus

4.5

5.1

1.8 

2.3 

1.5 

15.2

2.7

Weighted

-2.0

-4.5

-1.8 

-2.3 

+1.0 

-9.6

----

Avg

-0.4

-1.1

-.9 

-1.2

----

1 Avg deviation, 1.24. z Avg deviation, 1.13. 3 Avg deviation, 1.38.
46 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

period of study and are in a direction which would 

make the residuals of the water-budget study conform in general shape to those computed by the 

mathematical model. These revised flows are summarized in table 27.

REVISED WATER-BUDGET COMPUTATIONS

The water-budget computations were revised and 

are shown in table 28, which incorporates the modifications to reservoir inflow and outflow discussed

TABLE 28. Revised components of water-budget 

computations, Hungry Horse Reservoir

[Values in cfs-days, except as indicated]

Month Outflow Inflow

Change Accumu- Residual

in lated (cf s-days

contents Residual residual X 10-3 )

1964

Oct ------ 46,452 49,444

Nov ----- 59,156 42,477

Dec ------ 161,748 64,352

1965

Jan ----- 253,284 37,835

Feb .-.-.- 262,533 30,056

Mar ----- 456,028 30,826

Apr ------ 182,556 168,204

May ----- 78,737 443,003

June ----- 5,760 544,904

July ----- 87,792 169,882

Aug ----- 55,283 59,468

Sept ----- 77,692 78,119

Oct ------ 92,422 48,118

Nov .--.-- 68,496 38,134

Dec ------ 260,455 31,313

1966

Jan ------ 264,598 24,820

Feb .----. 74,731 17,320

Mar ----- 66,506 32,020

Apr -..--. 29,056 140,127

May ----- 85,607 406,779

June ----- 130,265 335,846

July ----- 107,662 106,587

Aug ----- 53,919 34,235

Sept ----- 152,050 20,670

Oct ------ 279,225 21,994

Nov ------ 235,996 26,683

Dec -.-.-. 156,044 31,202

1967

Jan ------ 131,793 28,912

Feb ------ 69,840 24,855

Mar -.---. 126,173 23,324

Apr -.-.- 177,572 62,238

+242 -2,750 -2,750 -2.8

-17,904 -1,225 -3,975 -1.2

-92,385 +5,011 +1,036 +5.0

-207,478

-222,067

-404,940

-1,650

+343,213

+ 525,733

+76,867

0

-5,082

-44,492

-30,190

-223,280

-231,186

-54,849

-29,309 

+ 113,568 

+306,131 

+ 195,939

-1,452

-19,704

-128,279

-250,807

-204,089

-113,305

-93,920

-39,946

-98,202

-109,866

+7,971 

+ 10,410 

+20,262 

+ 12,702

-21,053

-13,411

-5,223

-4,185

- 5,509

-188

+172

+5,862

+8,592 

+ 2,562 

+ 5,177 

+ 2,497

-15,041

-9,642

-377

-20

+ 3,100

+ 6,424

+ 5,224

+ 11,537

+8,961 

+ 5,039 

+4,647 

+ 5,468

+9,007

+ 19,417

+ 39,679

+52,387

+31,328

+ 17,917

+ 12,694

+ 8,509

+3,000

+ 2,812

+ 2,984

+8,846

+ 17,438

+ 20,000

+ 25,177

+ 27,674

+ 12,633

+2,991

+2,614

+2,594

+ 5,695

+ 12,119

+ 17,343

+ 28,880

+ 37,841 

+42,880 

+47,527 

+52,995

+8.0 

+ 10.4 

+20.3 

+ 12.7

-21.1

-13.4

-5.2

-4.2

-5.5

-0.2 

+0.2 

+ 5.8

+8.6 

+2.6 

+ 5.2 

+2.5

-15.1

-9.6

-0.4

0.0

+3.1

+ 6.4

+ 5.2

+ 11.6

+8.9 

+ 5.1 

+4.6 

+ 5.5

Total-- 4,289,431 3,173,747 -1,062,689 +52,995

in the previous sections. A mass curve of these revised monthly residuals from the water budget and 

month-end reservoir elevations was prepared and 

is shown in figure 17. The computations cited above 

correct many of the questionable periods which 

were discussed previously. The magnitudes of the 

residuals approximately balance each other for the 

two complete cycles of drawdown and refill. In fact, 

there is a slightly larger residual in the 1966 refill 

period than during the drawdown period. The slopes 

of the various mass-curve segments for drawdown 

and refill periods are about the same. The average 

water-budget residuals, in cfs-days per foot of 

change in reservoir stage, are shown in the following 

tabulation:

Year

1965

1966

1967

Drawdown

- 559

- 422 

. 424

Refitt

492

427

30/U

3560 

3540 

3520 

3500 

3480 

3460 

3440

3420

2

\

X^N\

vx

>

x\

N>^S\

^

\ \

V- ^

' X \

\

0 -10 0 +10 20 30 40 50 60 7(

ACCUMULATED VOLUME, IN THOUSANDS OF CFS-DAYS

FIGURE 17. Revised mass curve of accumulated water-budget 

residuals and month-end reservoir elevations.

These estimates are more consistent than those 

from the preliminary water budget and for all practical purposes are about as consistent as can be 

achieved by water-budget analysis. Further testing 

by mathematical model will be discussed in the succeeding sections.

SELECTION OF MODEL CONSTANTS

Water-budget data resulting from the reanalysis 

of records were adopted as a basis for trial solutions 

for constants in the equations. The field model was 

calculated on a systematic basis, and although application of some judgment and experience was necessary, the results are considered to be unbiased.

SINGLE SOLUTIONS

Although conditions are highly variable, the possibility that a single solution of the model could be 

used was studied. A double mass plot of cumulative 

residual volumes from the water budget and from 

M2 has a mean slope of about one-half. If M2 were 

to be used alone, all values would be multiplied by 2. 

This would imply an average storage coefficient of 

0.3, which would be unreasonably large.

Two additional model computations were made 

with assumptions as follows:

M, ..._

a 

(feet)

.._. 851

..... 851

s

0.2

.2

T/a2S 

(dajr»)

0.0064

.0256

T 

(ft2 per day)

927

3,710

Monthly and cumulative volumes calculated from 

M2, M3 , and M4 are given in table 29.
SELECTION OF MODEL CONSTANTS 47

TABLE 29. Volumes of bank storage 

computed from M*, M3, and M<

[Plus, to reservoir; minus, from reservoir]

Volumes of bank storage 

(1000 cfs-days)

M3

Month

Cumulative

Cumu- CumuMonthly lative Monthly lative Monthly

1984 

Oct .--.

Nov ...

Dec ---.

1965

Feb ----

Mar ----

July --.

Sept . . .

Oct ....

Nov ---.

Dec ---.

1966

Feb .--.

Mar ---.

May ....

July -..-

Oct

Nov ....

Dec ....

1967

Feb

Mar ....

.... -1.3

.--. -2.2

.... -2.0

.... +.3

 . +4.5

--.. +13.1

.... +19.6

.... +19.8

.... +13.6

.... +8.5

-.-. +5.4

-.-. +3.2

1 t C

.... +1.0

---. +2.6

---- +6.7

-..- +10.0

.... +13.1

.... +13.7

J-11 9

---- +6.5

---- +3.7

 . +1.8

1 1 O

J-i Q

--.- +8.5

---- +13.7

---. +18.4

--.. +21.7

.--. +26.2

.--. +31.0

-1.3

-.9

+ 0

+2.3

+4.2

+8.6

+ 6.5

+.2 -6.2

-5.1

-3.1

-2.2

-1.6

-.6

i i e

+4.1

+ 3.3

t Q 1

+.6

2.5 -4.7

-2.8

-1.9

0

+2.5

+4.2

ICO

+4.7

+3.3

+4.5

+4.8

 1 7

-2.5

-1.3

+ 3.9

+ 12.3

+27.5

+40.1

+38.9

+ 24.2

+ 12.7

+6.1

I o 1

0

+.1 1 4 Q

+13.0

+20.0

+25.6

+25.4

J-1Q Q

+ 10.0

+4.4

+ 1.1

i i a

i n c

+ 16.3

+ 26.4

+34.5

+40.0

+46.4

+ 53.4

-1.7

-.8

t 1 O

+ 5.2

+8.4

+ 15.2

+ 12.6

-1.2

14.7

-11.5 -6.6

-4.0

2.1

+ .1

+4.1

t O O

+7.0

+5.6

.2

5.5

Q Q

5.6

3.3

1 Q

+5.7

+8.7

+10.1

1 Q 1

+ 5.5

+6.4

+7.0

0

+ D

+4.0

+13.7

+26.5

+ 51.3

+60.5

+46.0

+16.4

+2.3

t O V+ Q

I q 7

-1_1S> Q

1 OK Q

+33.3

+37.4

I OO Q

+ 19.5

+4.0

+.7

+.4

+5.5

i 17 o

+30.5

+42.5

U-4Q 7

1 ro rj

+ 59.4

+66.9

0

+.6

+3.4

i a 7

+ 12.8

+24.8

+9.2

14.5

29.6

14.1

2.0

.3

-1. Q

+2.8

+8.6

t 1 Q e

+7.5

+4.1

5.1

1 9 Q

15.5

3.3

.3

+5.1

+ 11.8

t 10 9

+ 12.0

+ 7.2

+3.0

* rj K

Model M3, because of higher transmissivity, permits 

a more rapid drainage than M2 . This solution would 

require a multiplier of about 1.2 for an average fit 

to the water budget. The inferred storage coefficient 

is 0.24, which is unreasonably large if it represents 

only the aquifer.

M4, with a transmissivity greater than those for 

M2 and M3 , permits very rapid drainage. The match 

with field data requires that the model solution be 

multiplied by about 0.8 and that the storage coefficient be about 0.16. If we assume that the storage 

coefficient for the 20 percent of the material 

classified as open gravel and sand is 0.2, the remaining 80 percent of the material consisting mostly of 

till would have a coefficient of about 0.15. Although 

not impossible in view of the fact that more fine 

sand than anticipated was found in the till, the 

value is higher than would be expected. The rapid 

drainage feature of this solution minimizes timelag 

and narrows the loop effect. The solution produces 

a better fit to the water budget than M2 or M3 

in the lower part of the draft periods but a much 

poorer fit during the late stages of filling and following return to full pool.

Study of the characteristics of bank-storage responses calculated by use of several sets of constants in the model indicates the following:

1. No single application of the theoretical model is 

completely accurate.

2. Large inferred storage coefficients point to the 

need to consider other segments of the problem 

such as errors in the storage table and errors 

in the water budget.

The conclusion that a single model solution would 

not be adequate became evident when comparing 

computed results from M2, M3 , M4 with the field 

water budget. On a seasonal basis a slow lag such 

as is contained in M2 is needed; on a short-time 

basis quick response such as is contained in 

M4 is needed. Because of the wide range of 

hydrologic characteristics of the aquifer, it would 

seem appropriate to subdivide the aquifer into several or many units and assign T, S, and a 

values to each. Calculations for such a system would 

become very lengthy, and a more refined solution 

might result. In view of all the uncertainties, there 

is very little justification for over-refinement of the 

computations. In the following sections, the problem 

has been lumped into two groupings of characteristics.

RESERVOIR STAGE AS A PARAMETER

Solutions were computed on the basis of a mathematical model solution plus an increment for change 

in reservoir stage. The stage increment is determined from the slope of a plot of reservoir stage 

versus the cumulated differences of the waterbudget and the model results. This procedure lumps 

errors from the capacity table with the yield of 

highly permeable parts of the aquifer which respond with a small timelag.

Each of the three model solutions was expanded 

into a family of curves by multiplying by constants 

(thus varying storage coefficient and transmissivity). Cumulative differences of water-budget and 

model volumes when plotted against stage produced 

a sequence of graphs for each of the three cases. 

The graphs in each of the three sequences had 

similar characteristics. As the multiplier was 

varied, loops varied from positive through zero to 

negative. However, timing was different at different 

stages. A best solution was selected on the basis of 

mean monthly error. The plot for this solution is 

shown in figure 18.

This analysis indicates that bank storage can be 

calculated or predicted by the relation

Bank-storage volume=Volume computed from Af2

+ 230 cfs-days per foot of 

change of stage in the reservoir.
48 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

UJ 00/U

y 3560 

Soo

1 3540

Lul

§ 3520 

£

Lul

z 3500

o 

5 3480

Lul 

Lul

1 3460

>ce

Lul

co

* 3440

_

N?X^ I

vN\

^

wr>

^

^~^/x

\^\\

^

>

v

^w^ r

\ >

-Slope= 230 cfs-days 

\ per foot

\

j 0+5 10 15 20 25 30 3

VOLUME, IN THOUSANDS OF CFS-DAYS

FIGURE 18. Reservoir elevation versus cumulative difference 

of water-budget volumes and those computed by Ms.

Using stage record as input, the relation was 

computed for the period of study. Comparison of 

computed and water-budget results is shown in figure 19.

The overall agreement of computed and observed 

results is good. Monthly differences are within 

limits of ±5,000 cfs-days for 28 of the 31 months 

and within limits of ±3,000 cfs-days for 21 of the 

31 months. The mean deviation of monthly differences is 2,400 cfs-days. The cumulative-difference 

graph shows fluctuations which are balanced in relation to the zero baseline and which deviate more 

than 5,000 cfs-days only twice in the 31-month 

period. For yearly cyclic periods, from full pool to 

full pool, differences are very small.

Some of the larger monthly differences are to be 

expected. During the smowmelt and reservoir-filling 

periods, problems of timing should be evident. The 

theory assumes horizontal flow from the reservoir 

to the aquifer. During rapid filling, terraces are 

covered and some recharge takes place downward. 

This would make observed movement to bank storage larger than that predicted. Also during snowmelt, water from snow on the exposed reservoir 

bed and on the adjacent areas enters the aquifer. 

This volume of water was included in the value for 

precipitation on the reservoir bed and in the estimates for the ungaged areas. Estimates were based 

on gaged areas, and while the quantity is probably 

closed approximated, the timing is delayed by 

routing through the aquifer. At least part of the 

monthly differences in May 1965 and 1966 is related

ACCUMULATED VOLUMES

co

Q 

Z

< 

CO D 

O

I

-+10

/\

i i i i 1 I I I I l I I LJ I Mill I I I

CUMULATIVE DIFFERENCE 

(water budget minus computed)

10

-10 

0

+ 10 

1 964

_

1965

t -

*""

1966

^r -

1967

MONTHLY DIFFERENCE 

(Water budget minus computed)

FIGURE 19. Comparison of volumes of water from waterbudget residuals and those computed by Afs+230 cfs-days 

per foot of stage change.

to these effects. Further, excessive recharge in May 

leaves less storage capacity to be filled in later 

months, and field observations should be smaller 

than values computed from the model. Data for 

June-July 1965 and July-September 1966 are consistent with this expectation.
SELECTION OF MODEL CONSTANTS 49

Channel storage between the main inflow station 

and head of pool was neglected. This item is estimated to be about 1,000 cfs-days in May 1965 and 

contributes to the deviation for that month.

During May, the model calls for flow to bank 

storage downstream from head of pool and drainage 

in the reach upstream from head of pool. In May 

1965 the river rose about 7 feet in the reach upstream from head of pool, and movement to bank 

storage occurred. This is confirmed by the rise in 

observation wells at Dry Park. Here again, the 

model is deficient. However, although this segment 

could be calculated, its magnitude is about 2,000 

cfs-days (May 1965) and is small enough to be 

neglected. Problems related to filling periods have 

been discussed to explain major deviations.

The difference of 6,000 cfs-days in April 1965 

might be an indication that the mix of parameters 

is deficient. Reservoir stages at the beginning and 

end of April were nearly the same so that the portion of the model related to stage was not operating. 

This parameter lumps errors from the capacity table 

and part of the aquifer component. For April, only 

M2 is effective. The data suggest that M2 is inadequate and that we need to consider a mix of model 

solutions.

SIGNIFICANCE OF MODEL CHARACTERISTICS

An estimate of the model components is as follows:

1. The sand and gravel part of the aquifer (fig. 

12) has a volume of about 1,150 acre-ft per 

foot of elevation. For an estimated storage 

coefficient of 0.2, this accounts for about 115 

cfs-days per ft.

2. The remainder of the 230 cfs-days per ft in the 

model equals about 115 cfs-days per ft chargeable to error in the capacity table. In the top 

100 feet of storage, capacity would average 

1.2 percent greater than table values.

3. M2 has a storage coefficient of 0.15. For this 

interpretation the value 0.15 is applicable to 

80 percent of the volume of the aquifer, and 

the inferred coefficient is about 0.19. This is 

higher than expected for this type of material.

The accumulated volume of ground-water outflow 

computed from the model is plotted against reservoir stages in fig. 20. In general, the plot compares 

favorably with the similar plot from the water 

budget (fig. 17).

3570

3560

3540

3520

3500

3480

3460

3440-10 +10 20 30 40 

VOLUME, IN THOUSANDS OF CFS-DAYS

50 60

FIGURE 20. Accumulated volume of ground-water outflow 

computed using Ms +230 cfs-days per foot of stage 

change.

MODEL SOLUTIONS WITH TWO SETS OF CONSTANTS

Using two sets of constants in the model, a systematic analysis was made to seek the best combination to fit the field data.

One solution is

Volume=0.6M2 +0.4M4.

Comparison of values computed from this relation with those of the water budget is given in 

figure 21. Mean monthly deviation is about 2,800 

cfs-days. Monthly differences are within limits of 

±5,000 cfs-days for 26 months and are within 

±3,000 cfs-days for 22 months. Cumulative-difference values deviate by more than 5,000 cfs-days 

five times during the 31-month period.

Another solution is

Volume=M2 + 0.4M4.

Results of this solution are compared with the 

water-budget results in figure 22. Mean monthly 

deviation is about 2,600 cfs-days. Monthly differences are within limits of ±5,000 cfs-days for 28 

months and within ±3,000 cfs-days for 21 months. 

Cumulative difference values deviation by more than 

5,000 cfs-days five times during the 31-month period. This solution is somewhat better than the 

previous one.

The solution implies a storage coefficient for the 

till of about 0.19, and for the gravel and sand, about
50 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

30

-20

1 hrl i 1

.-_ 

Mill

 Wate 

 Com

 '

MONTHLY 

Mill

>r budget 

puted

_

VOLUMES 

1 1 1 1 1 1 1 1

15

-10

co

Q

CO 

LJ_ 

O

+ 10

-10

Mill

MONTHLY DIFFERENCE | 

(Water budget minus computed)

1 1 II 1 1 1 1 1 1 1 1 1 1 1 1 1 1

5+20

40

60 

-10

I I

Water budget

___\_

Computed

CUMULA IVE DIFFERENCE

I i I I I I I I I 1 I I I I I I I I 1 I I I I 1 I I

+ 10

/\

1964

CUMULATIVE DIFFERENCE 

(Water budget minus computed) 

l i i i I I i i i i i I i i i i i I i i i i i

1965 1966 1967

FIGURE 21. Comparison of volumes of water from waterbudget residuals and those computed using 0.6M8 +0.4Af4.

-20

+ 20

20

-10

1 1

* »^

11-411

-

T 

I 1 I II

 Water bu 

 Compute

__Ti.

MONTHLY 

Mill

1

dget 

d

-a.

VOLUMES 

1 1 1 1 i

T .

1 1 1

CO

> 

<

Q

CO 

Ll_

o

+ 10 1 1 J 1 1 II

MONT

(Water buc

i 1 1 i i

HLY DIFFEF 

get minus c

Mill

?ENCE

:omputed)

1 1 i 1 1

_ ____

1 1 1

ACCUMULATED VOLUMES

60 II I I I I I I i I ii I I I ! 1 1 I I I I I I I III

-10

+ 10 1964

A

CUMULATIVE DIFFERENCE 

(Water budget minus computed) 

i i i i i i I i i i I i i i i i ill

1965 1966 1967

FIGURE 22. Comparison of volumes of water from waterbudget residuals and those computed using
SELECTION OF MODEL CONSTANTS 51

0.4. Although these storage coefficients are larger 

than expected for these materials, the values are 

regarded as reasonable because of the following 

considerations: The assumption that the capacity 

table has no errors is probably too rigid, and computation of the aquifer width a from geologic cross 

sections was based on limited data. Errors introduced by these two items plus the errors in elements 

of the water budget are all reflected in the implied 

storage coefficients.

Accumulated volume for the solution ~ M2 +0.4 

M4 is plotted against reservoir stage in figure 23.

3570

3560

3540

3520

3500

3480

3460

3440

-10 0 +10 20 30 40 50 

VOLUME, IN THOUSANDS OF CFS-DAYS

60

FIGURE 23. Accumulated volume of ground-water outflow 

computed using Af2 +0.4Af4.

This curve has a wider loop than that for M2 +230 

cfs-days per ft (fig. 19) or for the water budget 

(fig. 17). The water-budget curve is short circuited 

on the rising-stage part because of vertical recharge 

discussed previously. The curve based on M2 + 

0.4M4 is statistically not as good as that for M2 + 

230 cfs-days per ft. However, the statistics are distorted because of comparison to conditions in the 

field that differ from those of the model. The solution M2 + 0.4 M4 fits better in,April and June 1965. 

This solution is considered superior because of the 

likelihood that it will give better results when projected to lower elevations for which data are not 

available. Such a projection based on the solution 

M2 + 0.4M4 will have a diminishing characteristic 

related to the wedge shape of the aquifer. In the 

solution M2 + 230 cfs-days per ft, the first term has 

the wedge effect but the second term does not. 

Use of the second term would depict a condition of

an increasing error in capacity as the reservoir 

became smaller.

INHERENT ERRORS IN DISCHARGE RECORDS

All the relations to this point in the analysis are 

based on the assumption that the reworked station 

records are without error. Solutions developed are 

well within the limitations of the data. However, the 

implied storage coefficient for the till and associated 

deposits appears to be larger than that to be expected on the basis of experience.

The fact that the yearly (full pool to full pool) 

values correlate extremely well verifies that the records are generally of high quality. The yearly figures 

provide only a broad look at the overall quality of 

records. Many errors affecting individual months 

are eliminated in this comparison. Those related to 

the capacity table and to the reservoir-stage readings self-compensate, and those related to vertical 

recharge of the aquifer, channel storage, stage effect on bank storage in the reach upstream from 

head of pool, and snow and ice storage on the unwatered bed of the reservoir and on the lake are 

nearly balanced out by midsummer.

Stream-flow measurements at all stations were 

made by standard Geological Survey methods. Personnel and equipment were rotated so that the records should be consistent and unbiased. If there 

were an inherent error in the procedure, it would 

balance out on an annual basis. On a seasonal basis, 

it could be significant since large inflows occur in 

spring and large withdrawals occur in the fall and 

winter. Since annual figures are in balance, any inherent error should be considered as being the same 

at all stations and also should be applied to ungaged 

estimates based on records. By judgment based on 

a large implied storage coefficient, it is concluded 

that solutions thus far obtained are probably high; 

that is, their use for predicting additional water 

for power would have more chance of overpredicting 

than underpredicting. Accordingly, in studying the 

sensitivity of the model to inherent errors in gaging 

it was assumed that measured flows might be too 

large. The water budget was recalculated for a 

sequence of assumed errors. For each member of 

the sequence, a constant percentage reduction was 

made in all measured flows and in all estimated 

flows derived from measured flows. Four waterbudgets were calculated by this procedure for assumed flow reductions of 0, 1, 2, and 5 percent. 

Slopes from double mass plots of cumulated waterbudget residuals versus cumulative volumes deter-
52 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

mined from M2 + QAM4 yield multipliers to be applied to the model values.

Model solutions corresponding to each of the 

water budgets calculated to include inherent errors 

are listed below:

Reduction of flow

(percent) Model solutions

A ._._____

B .........

C .........

D ._.......

0

1

.--__-..- 2

5

M2 +0.4M«

0.8(M2 +0.4M«)

0.6(M2 +0.4M4)

Cumulative differences of water-budget residuals 

calculated to include the listed assumed errors 

minus the volumes calculated by the corresponding 

model solution are plotted in figure 24. The graph 

shows that individual loops at middle and lower 

elevations open up as the assumed error increases 

and also that the spread of points increases at fullpool level. At lower elevations, data for the two

drawdown periods move closer together, then 

spread. At midrange, points for different years 

move closer together and then spread.

Results for these assumed conditions for 31 

months are summarized below:

A -----

B -----

C -----

Number of months 

for which monthly 

difference was 

within the range 

indicated

±5.000 ±3.000 

cfs-days cfs-days

..--- 28 21

----- 28 23

.-.-- 27 22

Number of 

times during 

period that 

cumulative

within ±5,000 

cfs-days

26

28

26

Mean

deviation 

cfs-days

2,600

2,500

2,600

Trial B appears to be the best solution, although 

trials A and C are acceptable. Trial A, based on 

M2 + 0.4M4 , was discussed previously and, although 

based on a reasonable match to field data, it was 

judged to be high because of high implied storage 

coefficients. Trial C, based on an assumed inherent

3440

10 -5 0 +5 10 10 -5 0 +5 10 10 -5 0 +5 10 15 

CUMULATIVE DIFFERENCES, IN THOUSANDS OF CFS-DAYS

FIGURE 24. Cumulative residuals for a sequence of assumed inherent errors. Diagrams are cumulative differences: 

(water-budget residuals minus indicated assumed error) minus (multiples of M2 +0.4/lf4). A, No inherent error 

and Mt+0.4Mt; B, 1 percent error and 0.8(M2 +0.4M«) ; C, 2 percent error and 0.6 (Af2 +0.4Af4); and D, 5 percent 

error alone.
SELECTION OF MODEL CONSTANTS 53

error of 2 percent and using 0.6(Af2 +0.4M4 ), fits 

the data about as well as Trial A. Calculated storage 

coefficients are about 0.12 for 75 percent of the material (till) and 0.20 for 25 percent of the material 

(sand and gravel). Trial B, using 1 percent assumed 

error and 0.8(Af2 +0.4M4 ), fits field data somewhat 

better than A or C. The storage coefficients are 

about 0.15 for 80 percent of the material (till) 

and 0.32 for 20 percent of the material (sand and 

gravel), or 0.18 for 68 percent of the material and 

0.2 for 32 percent. If an allowance were made for 

error in the capacity table, these coefficients would 

be smaller.

SENSITIVITY

A complete sensitivity analysis is not possible 

because range-of-error values cannot be determined 

for many of the items in the problem. The spread 

from diagrams A to D in figure 24 is 5 percent, 

while the corresponding effect on bank-storage values is from about 50,000 cfs-days to zero. Thus 

each 1 percent assumed inherent error causes a 

20-percent change in the bank-storage results.

The same relation (1 percent assumed error 

causes 20-percent change in bank-storage results) 

would be approximated if the errors were assumed 

to be in the capacity table. However, a 5-percent 

adjustment to the table will produce a graph very 

nearly like D. This graph shows a pronounced loop 

related to the aquifer response. Expressing bank 

storage as a percentage adjustment to the capacity 

table can modify only the slope of the loop, not the 

loop itself. On an average basis, solutions A, B, and C, 

give results approximately equivalent to 5, 4, and 

3 percent, respectively, of the capacity table.

CHOICE OF MODEL CONSTANTS

While solution B appears to be the best fit, the 

implied coefficients seem high. Part of the determination relates to the distance from reservoir to 

valley wall. The value used (851 ft) is an average 

value computed from the volume of valley fill which 

was determined from poorly controlled geologic 

sections. The opportunity for error in the width 

is substantial, and it is very possible that the volume 

of material is larger than estimated. Another item 

which was neglected is storage in the hard rocks 

flanking the unconsolidated fill. Storage space in 

these rocks is probably less than 1 percent by 

volume; however, as there is no way of arriving 

at a reasonable volume of material involved, quantitative evaluation was not attempted. The effect 

of omitting this item is to make the apparent

storage coefficients slightly larger than the true 

coefficients for the unconsolidated material.

In view of all the uncertainties, a final selection 

of model constants must be determined on the basis 

of judgment. Solution B is recommended as representing a reasonable approximation of true conditions. Solutions A and C which represent solution 

B ±25 percent are considered reasonable limits 

bracketing the zone within which the true solution 

probably lies.

Solution B is recommended for use in general 

studies where adjustment for bank storage needs 

to be used. For predicting water volume for power 

generation, solution B is recommended.

AQUIFER STORAGE

Aquifer storage capacity at any reservoir level 

is equivalent to ground-water storage for the condition of constant level for a long enough time 

either to drain or to fill the aquifer to that level. 

It can be computed from the geometry of the 

aquifer and the storage coefficient. 

 a,Sh2

where

-m

h- reservoir elevation-3,057.5 feet,

a=851 feet,

and m=- 0.00293. 

For combined models a weighted S value is used.

Curves of aquifer storage capacity were computed using constants for recommended solution B 

and for ±25 percent bracketing solutions A and 

C. Under normal operating conditions the reservoir

20 40 60 80 100 120 140

AQUIFER STORAGE, IN THOUSANDS OF CFS-DAYS

FIGURE 25. Aquifer storage-capacity curves for solutions 

A, B, and C.
54 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

will not be drawn down below an elevation of 

3,336 feet (bottom of power pool). Ground-water 

storage in the part of the aquifer below this elevation includes dead storage below the lowest outlet 

at elevation 3,196 feet, and inactive storage between elevations 3,196 and 3,336 feet (not available 

under normal operating conditions). Curves of 

aquifer storage capacity for reservoir stages between 3,336 feet and 3560.5 feet are shown in 

figure 25. These curves are for "active" aquifer 

storage capacity inasmuch as they define the 

aquifer storage capacity in which water may be 

stored or withdrawn for beneficial use. The 

weighted storage coefficient, the dead and inactive 

aquifer storage capacity, and the active aquifer 

storage capacity are listed below:

Aquifer storage capacity 

(cfs-days)

Dead and 

Weighted S inactive Active Total

0.23

.184

.138

60,100 135,400 195,500

48,100 108,300 156,400

36,100 81,200 117,300

Figure 25 also shows a plot of the cumulative 

water-budget residuals oriented to the aquifer 

storage-capacity curve for solution A, the solution 

which best matched field data. The starting point 

for this loop was calculated on the basis of the 

model. The average slope of the field loop is steeper 

than that of the capacity curve. The fit is very 

much in accordance with that to be expected. During drawdown, loops cross the capacity curve and 

reflect the lag in movement of ground water to the 

reservoir. If drawdown stops and stage is held constant, the loop curve should move to the left at a 

decreasing rate and approach the capacity curve 

as a limit. On a rising stage loops cross left of the 

curve, reflecting lag in filling of the aquifer. After 

reaching pool level, water continues to move to 

ground-water storage at a diminishing rate and the 

loop approaches the capacity curve as a limit. Thus, 

a very simple seasonal cycle consisting of (1) a 

constant rate of drawdown, (2) a stationary stage 

for several months, (3) a constant rate of fill, and 

(4) a stationary stage for several months, would 

lie inside a diamond-shaped limiting "box." The 

capacity curve would be the diagonal of the box, 

and rising and falling limbs would have slopes 

related to the rate of change of reservoir stage.

The aquifer storage-capacity curve for the recommended solution (B) and the storage loop 

calculated from this solution, 0.8(M2 + 0.4M4 ), 

are shown in figure 26. The loop on the rising-stage

3400

3360

3336 <- 

3320

20 40 60 80 100 

AQUIFER STORAGE, IN THOUSANDS OF CFS-DAYS

FIGURE 26. Aquifer storage and storage capacity computed 

from solution B, 0.8(M2 +0.4M4).

positions is wider than the observed loop in the 

preceding figure because the theoretical loop does 

not include the effect of vertical recharge which 

flattens the observed loop. The deviations of the 

storage loops from the aquifer storage-capacity 

curves in figures 25 and 26 clearly demonstrate 

the transient nature of ground-water storage and 

demonstrate that bank storage cannot be accurately defined by a single curve.

USE OF THE MODEL

The solution 0.8(M2 + 0.4M4 ), can be used to 

evaluate changes in ground-water movement or 

storage changes occurring in response to stage 

changes of the reservoir. Inspection of the equations 

shows that there are too many variables to permit 

drawing a simple working curve or family of curves. 

As shown by the analysis, simple relations attempting to use stage or a flat percentage of the capacity 

table can only approximate the average slope of 

the loop curve and cannot account for the timedependent effects which control the spread of the 

loop.

Computations in this report were made on a 

monthly basis by desk calculator. Time was reduced by using mathematical and graphical shortcuts. The equations lend themselves to computer 

solution; if used to any great extent, they should 

be programmed for the computer.
HYDROLOGY OF HUNGRY HORSE RESEVOIR, NORTHWESTERN MONTANA 55

LOW-FLOW FORECASTS

As previously indicated, the primary objectives 

of the Hungry Horse Project are to provide at-site 

and downstream power generation and local and 

downstream flood control. The power operations 

are based on bringing Hungry Horse Reservoir to 

its highest stage during July of each year and 

withdrawing water during the period August-April 

as needed. The amount of drawdown will depend 

upon the loads to be met and the stage of development of the power system. The flood-control operations are based on having the reservoir drawn 

down to a stage on May 1 which will provide for 

storing most of the inflow to Hungry Horse Reservoir during May, June, and July. During years 

of high-runoff potential, the flood-control parameters may indicate the need for withdrawing more 

water from storage than is needed for power 

generation.

The efficient operation of this reservoir to meet 

these dual objectives requires careful planning because the storage may be used on a "cyclic" or 

multiyear basis, as well as on a seasonal basis. The 

accurate evaluation of future inflows to the reservoir plays an important part in this planning 

procedure. A method for forecasting the inflow to 

Hungry Horse Reservoir for use during the period 

January-July was developed under the auspices of 

the Water Management Subcommittee of CBIAC 

in November 1964. This forecast is used as a parameter in the operation of this reservoir, primarily 

during the refill period. An accurate evaluation of 

potential reservoir inflows during the low-flow

period would improve the seasonal operations during the reservoir-drawdown period. The second 

phase of this investigation reviews the July-April 

runoff data for both natural and regulated conditions and develops a method of forecasting the 

reservoir inflows during the low-flow period.

NATURAL CONDITIONS

The initial storage of water in Hungry Horse 

Reservoir occurred in September 1951. Prior to 

this date the observed runoff records for South 

Fork Flathead River near Columbia Falls are assumed to be the inflow to the reservoir. Summaries 

of these data for the months of July-April for 

power years 1929-51 are listed in table 30. (A 

power year ends June 30 of the year indicated). 

The accumulated monthly runoff through April of 

each power year is shown in table 31. Frequency 

diagrams for the time periods listed in table 31 

are shown in figure 27. Power year 1937 had the 

lowest runoff during power years 1929-51 for all 

time periods except for the month of April when 

it had the second lowest.

Evaluations of "assured" runoff for some of these 

periods had previously been made utilizing recession curves developed from discharge records of 

the gaging station South Fork Flathead River near 

Columbia Falls. Frequency curves of increments of 

flow derived from concurrent weather conditions 

were used for other levels of flow probabilities. 

Dependable flow curves (Sachs, 1957) are also 

available for use in evaluating the potential runoff 

during the fall and winter months.

TABLE 30. Monthly runoff, South Fork Flathead River near Columbia Falls

Power 

year

1929 .--..--....

1930 ...........

1931 ...........

1932 ------.--..

1933 .-..--.-...

1934 ...........

1935 --------...

1936 --.-..-....

1937 ...........

1938 ..........

1939 ---.--.-.-

1940 ---.-----..

1941 ...........

1942 ...........

1943 ..--.-....

1944 ....... ...

1945 .--.-.-....

1946 ...........

1947 ..---..-...

1948 ...........

1949 ..........

1950 ...........

1951 ..........

Avg .......

Max

Min .......

Monthly runoff 

(cfs-days)

July

... 172,960

77,190

57,660

42,470

. . . 107,880

... 167,400

59,117

... 99,610

48,364

71 190

81,290

84,530

41,106

... 35,712

... 109,530

... 256,700

51,696

... 102,160

... 108,640

... 115,560

93,560

... 57,340

... 301,240

... 101,692

... 301,240

35,712

Aug

46,090 

25,141 

21,390 

19,158 

35,340 

44,330 

24,025 

29,892 

20,952 

27,065 

27,688 

25,791 

18,817 

17,267 

31,436 

51,760 

23,376 

28,259 

35,024 

38,080 

38,707 

23,628 

70,730

31,476 

70,730 

17,267

Sept

21,461 

14,790 

16,740 

20,730 

21,570 

26,100 

16,170 

17,214 

14,934 

15,110 

17,032 

16,205 

14,970 

23,550 

20,534 

24,991 

20,247 

20,005 

21,464 

29,343 

19,126 

18,646 

28,122

19,959 

29,343 

14,790

Oct

28,365 

13,795 

28,582 

19,065 

25,792 

89,869 

27,258 

13,991 

13,402 

17,066 

17,747 

14,477 

15,748 

47,180 

16,211 

23,025 

19,524 

28,587 

47,715 

77,320 

14,948 

21,780 

60,302

29,641 

89,869 

13,402

Nov

22,200 

11,760 

30,000 

24,600 

68,700 

123,840 

61,920 

11,873 

10,844 

24,717 

16,872 

14,310 

14,730 

35,755 

32,505 

19,162 

17,933 

57,480 

51,750 

42,870 

14,023 

41,805 

70,991

35,680 

123,840 

10,844

Dec

16,368 

11,532 

23,498 

24,428 

59,210 

108,624 

30,902 

9,716 

12,720 

29,798 

24,219 

21,607 

14,787 

73,070 

34,050 

19,107 

18,292 

35,040 

60,040 

29,436 

13,602 

45,770 

82,790

34,722 

108,624 

9,716

Jan

14,043 

9,579 

21,514 

17.112 

36,270 

84,519 

28,633 

10,725 

8,244 

29,663 

23,370 

17,236 

14,415 

29,710 

23,270 

13,960 

25,190 

27,195 

45,700 

28,905 

11.040 

29,980 

50,672

26,131 

84,579 

8,244

Feb

12,040 

15,064 

21,140 

41,760 

25,480 

57,176 

28,804 

10,125 

8,444 

26,493 

14,430 

16,791 

13,916 

16,920 

20,680 

11,090 

20,200 

20,172 

49,000 

20,100 

9,990 

24,150 

61,916

23,734 

61,916 

8,444

Mar

18,786 

14,570 

37,200 

66,030 

27,218 

91,295 

39,695 

14,683 

12,457 

29,109 

40,365 

42,718 

29,543 

19,311 

28,900 

13,960 

23,105 

41,094 

58,060 

19,650 

17,936 

34,000 

34,316

32,783 

91,295 

12,457

Apr

63,256 

254,610 

99,150 

165,540 

119,225 

353,050 

91,726 

216,657 

60,606 

159,345 

228,550 

136,820 

97,660 

163,810 

294,160 

77,729 

55,068 

215,290 

195,480 

119,167 

168,595 

104,700 

161,600

156,600 

353,050 

55,068
56 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

TABLE 31. Accumulated monthly runoff through April, South Fork 

Flathead River near Columbia Falls

Power 

year

1929 ---------

1930 .........

1931 ---------

1932 ---------

1933 ---------

1934 ---..--_-

1935 ---------

1936 .----..-.

1937 ---------

1938 ---------

1939 ---------

1940 ---------

1941 .........

1942 ---------

1943 ---------

1944 ---------

1945 ---------

1946 ---------

1947 ---------

1948 .........

1949 ---------

1950 ---------

1951 ---------

Max --.-.

Min .--..-

Accumulated monthly runoff 

(cfs-days)

JulyApr

.-- 415,569

... 448,031

... 356,874

--. 44D.893

- - - 526,685

--- 1,146,263

-.- 408,250

... 434,486

..- 210,967

- - . 429,556

--- 491,563

.-- 390,485

--- 275,692

... 462,285

.-- 611,276

--_ 507,484

--- 274,631

..- 575,282

._- 672,873

.-- 520,431

--. 401,527

--- 401,799

. - - 922,679

4Q9 417

--- 1,146,263

... 210,967

Aug^ 

Apr

242,609 

370,841 

299,214 

398,423 

418,305 

978,863 

349,133 

334,876 

162,603 

358,366 

410,273 

305,955 

234,586 

426,573 

501,746 

254,784 

222,935 

473,122 

564,233 

404,871 

307,967 

344,459 

621,439

391,160 

978,863 

162,603

SeptApr

196,519 

345,700 

277,824 

379,265 

383,465 

934,533 

325,103 

304,984 

141.651 

331,301 

382,585 

280,164 

215,769 

409,306 

470,310 

203,024 

199,559 

444,863 

529,209 

366,791 

269,260 

320,831 

550,709

359,249 

934,533 

141,651

Oci^

Apr

175,058 

330,910 

261,034 

353,535 

361,895 

908,433 

308,933 

287,770 

126,717 

316,191 

365,553 

263,959 

200,799 

385,756 

449,776 

178,033 

179,312 

424,858 

507,745 

337,448 

250,134 

302,185 

522,587

339,290 

908,433 

126,717

NovApr

146,693 

317,115 

232,502 

339,470 

336,103 

318,564 

281,680 

273,779 

113,315 

299,125 

347,806 

249,482 

185,051 

338,576 

433,565 

155,008 

159,788 

396,271 

460,030 

260,128 

235,186 

280,405 

462,285

309,649 

318,564 

113,315

DecApp

124,493 

305,355 

202,502 

314,870 

267,403 

694,724 

219,760 

261,906 

102,471 

274,408 

330,934 

235,172 

170,321 

302,821 

401,060 

135,846 

141,855 

338,791 

408,280 

217,258 

221,163 

238,600 

391,294

273,969 

694,724 

102,471

JanApr

108,125 

293,823 

179,004 

290,442 

208,193 

586,100 

183,858 

252,190 

89,751 

244,610 

306,715 

213,565 

155,534 

229,751 

367,010 

116,739 

123,563 

303,751 

348,240 

187,822 

207,561 

192,830 

308,504

239,247 

586,100 

89,751

FebApr

94,082 

284,244 

157,490 

237,330 

171,923 

501,521 

160,225 

241,465 

81,507 

214,947 

283,345 

196,329 

141,119 

200,041 

343,740 

102,779 

98,373 

276,556 

302,540 

158,917 

196,521 

162,850 

257,832

211,551 

501,521 

81,507

MarApr

82,042 

269,180 

136,350 

231,570 

146,443 

444,345 

131,421 

231,340 

73,063 

188,454 

268,915 

179,538 

127,203 

183,121 

323,060 

91,689 

78,173 

256,384 

253,540 

138,817 

186,531 

138,700 

195,916

189,382 

444,345 

73,063

Apr

63,256 

251,610 

99,150 

165,540 

119,225 

353,050 

91,726 

216,657 

60,606 

159,345 

228,550 

136,820 

97,660 

163,810 

294,160 

77,729 

55,068 

215,290 

195,480 

119,167 

168,595 

104,700 

161,600

156,600 

353,050 

55,068

REGULATED CONDITIONS

Subsequent to September 1951, the amount of 

water available for project use includes the net 

inflow to the reservoir plus or minus the change in 

storage. The net inflow includes runoff from the 

land area tributary to the reservoir plus precipitation falling on the reservoir area minus evaporation from the reservoir surface. The change in 

system storage includes the water stored within 

the limits of the topographic reservoir and the 

component stored in the aquifers adjacent to the 

reservoir. Each of these factors must be evaluated 

in order to arrive at the actual volume of water 

available for project use.

Initially the inflow to Hungry Horse Reservoir 

was estimated by adjusting the measured outflow 

for change in reservoir contents. The hydrographs 

of daily inflows computed in this manner are very 

irregular during months of low inflow and during 

periods of rapid drawdown. The potential reservoir inflows were evaluated by selecting a base-flow 

value for the beginning of each forecast period 

and using the recession curve previously developed 

for the outflow gaging station. The resulting flow 

projections were highly irregular primarily because 

of the difficulty in selecting the proper base-flow 

value. Theoretically, the recession curves developed 

for the downstream station should not be used 

with the reservoir inflow computed in this manner 

since they are not completely compatible. The 

characteristics of the natural hydrologic system 

were greatly modified because of the construction

of Hungry Horse Reservoir. The index of inflow 

developed by the 1959 studies was not completely 

satisfactory, and daily reporting facilities were 

never installed.

INFLOW TO HUNGRY HORSE RESERVOIR

In the water-budget studies, the reservoir inflow 

from the land area was in effect a measured quantity. But for other periods of time, it can be computed by an index based on records from upstream 

gaging stations.

A step-regression analysis was made using the 

water-budget data to derive an index of reservoir 

inflow from the land area for use after April 1967. 

In this analysis the reservoir inflow, except for 

precipitation, was the dependent variable. The independent variables included the runoffs from following upstream stations:

South Fork Flathead River above Twin Creek near

Hungry Horse

Sullivan Creek near Hungry Horse 

Twin Creek near Hungry Horse 

Soldier Creek near Hungry Horse 

Graves Creek near Hungry Horse 

Canyon Creek near Hungry Horse 

Goldie Creek near Hungry Horse 

Wounded Buck Creek near Hungry Horse 

Emery Creek near Hungry Horse 

Hungry Horse Creek near Hungry Horse

Reservoir-inflow volumes and runoff from the 

above gaging stations were expressed as total cfs-
LOW-FLOW FORECASTS 57

July-Apr

Aug-Apr

Sept-Apr

Oct-Apr

Nov-Apr

Dec-Apr

Jan-Apr 

Feb-Apr

Mar-Apr 

Apr

5 10 20 30 40 50 60 70 80 90 95 98 99

PERCENTAGE OF TIME ACCUMULATED MONTHLY RUNOFF WAS EQUALED OR EXCEEDED

FIGURE 27. Frequency diagrams of accumulated monthly runoff for various time periods, South Fork Flathead River 

near Columbia Falls, 1929-51. The plotting positions of the lowest 4 power years are indicated on the curve for 

each time period.

days for each of the 31 months used in this analysis. Both linear and logarithmic relationships were 

examined. The linear equations were slightly better 

than the logarithmic equations in their ability to 

reproduce the original data for the dependent 

variable.

The equation selected on the basis of the analysis is

Xx = 1.18X2 + 4.47X3 +1,246,

where Xi = monthly reservoir inflow except for precipitation, in cfs-days,

X2 =monthly runoff at South Fork Flathead 

River above Twin Creek near Hungry 

Horse, in cfs-days,

and X3 =monthly runoff of Sullivan Creek near 

Hungry Horse, in cfs-days.

This equation has a correlation coefficient of 

0.9999 and a standard error of estimate of 2,230 

cfs-days. When the reservoir inflows computed by 

the above equation were compared with the waterbudget data, the differences ranged from -6,740 

to +5,310 cfs-days and had an average deviation 

of 1,470 cfs-days.

The addition of the other independent variables 

listed above did not increase the correlation coefficient but did tend to reduce slightly the standard 

error of estimate. This is to be expected because 

the dependent variable is composed primarily of 

the sum of the independent variables selected for 

this step-regression analysis. However, in view of 

the accuracy indicated by the two-station index, it
58 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

is recommended that no more components be included in the index. The use of this index is judged to 

be a practical and economical method of evaluating 

the reservoir inflow from the tributary land area. 

Another step-regression analysis was made for 

computation of reservoir inflow from the land area 

prior to October 1964. In this analysis the dependent variable was the same reservoir inflow used 

previously but the independent variables included 

runoffs from the following stations:

South Fork Flathead River at Spotted Bear Ranger

Station near Hungry Horse 

Sullivan Creek near Hungry Horse 

Twin Creek near Hungry Horse 

Graves Creek near Hungry Horse

These gaging stations were in operation for part 

of the period between 1951 and 1964 and during 

the period of the present study.

The equation selected from this analysis was

Xi = 1.20Z2 + 6.94*3 - 777,

where Xl = monthly reservoir inflow except for precipitation, in cfs-days, 

X2 = monthly runoff, South Fork Flathead 

River at Spotted Bear Ranger Station 

near Hungry Horse, in cfs-days, 

and Xz =monthly runoff, Sullivan Creek near

Hungry Horse, in cfs-days.

The correlation coefficient of this equation is 

0.9994, and the standard error of estimate is 4,747 

cfs-days. This equation has almost the same correlation coefficient as the index based on South 

Fork Flathead River above Twin Creek near 

Hungry Horse, but it has about double the standard

error of estimate. The average deviation is 2,830 

cfs-days, and deviations range from +13,730 to 

-11,590 cfs-days.

Both of these index procedures were able to 

duplicate the water-budget data very well. For the 

31 months the accumulated differences were 

+ 1,380 and +1,840 cfs-days, respectively, for the 

above Twin Creek and Spotted Bear indexes.

An estimate of the monthly inflow to Hungry 

Horse Reservoir was developed by use of these two 

index procedures for the period 1949-68 when data 

for the indexes were available. In the period prior 

to the start of intensive data collection, October 

1964, the reservoir inflow was based on the index 

equation for South Fork Flathead River at Spotted 

Bear Ranger Station near Hungry Horse and 

Sullivan Creek near Hungry Horse. For the period 

after April 1967, the index developed on the combination of the values for South Fork Flathead 

River above Twin Creek near Hungry Horse and 

Sullivan Creek near Hungry Horse was used. During the period of the study, October 1964-April 

1967, the water-budget data were used. These inflows are shown in tables 32 and 33.

RECESSION CHARACTERISTICS

The recession characteristics of the inflow to 

Hungry Horse Reservoir from the land area were 

determined, using the recession characteristics 

previously developed for the stations South Fork 

Flathead River at Spotted Bear Ranger Station 

near Hungry Horse and South Fork Flathead River 

above Twin Creek near Hungry Horse as guides. 

These characteristics indicate that one curve could 

be used throughout the year. The inflow follows

TABLE 32. Estimated monthly inflow to Hungry Horse Reservoir

[Excluding precipitation on reservoir surface]

Water 

year

1949 .----.-..

1950 ---.--_..

1951 .........

1952 --_._____

1953 .........

1954 .........

1955 -...-....

1956 ..........

1959 .---......

1960 ---.......

1961 ..........

1962 ----......

1963 .-..--...

1964 --........

1965 --.-.---..

1966 ..........

1967 ... _ ....

1968 ---..-....

Max .....

Min -----

Estiimated monthly inflow 

(1,000 cfs-days)

October

.... 15.1

1Q Q

---. 66.2

.... 70.8

12.5

.... 13.6

.... 46.9

...- 52.5

.... 159.4

.... 21.8

---. 48.3

.... 43.0

--.- 15.2

.... 46.5

.... 47.2

-.-- 18.6

.... 26.5

---. 42.6

.... 159.4

.... 12.5

November

15.1 

44.7 

76.9 

43.7 

10.0 

15.5 

43.7 

51.5

95.0 

26.9 

29.4 

47.0 

14.5 

37.6 

34.9 

21.3 

52.7

38.8 

95.0 

10.0

December

13.3 

34.4 

87.6 

32.7 

10.5 

16.6 

29.5 

47.5

57.7 

20.6 

20.0 

44.4 

11.7 

56.4 

29.8 

28.3 

27.9

33.5 

87.6 

10.5

January February

10.8 

20.1 

46.1 

21.5 

25.7 

13.7 

18.0 

30.1

31.6 

18.6 

18.2 

25.4 

13.7 

34.4 

21.9 

24.8 

29.0

23.7 

46.1 

10.8

10.5 

20.2 

57.9 

18.3 

24.9 

16.8 

13.1 

17.7

21.9 

44.3 

20.6 

57.8 

11.3 

27.4 

16.0 

24.0 

37.1

25.9 

57.9 

10.5

March

18.0 

34.4 

30.0 

18.8 

22.5 

27.2 

14.6 

26.6

57.3 

45.2 

26.0 

38.9 

11.0 

30.6 

29.7 

22.1 

62.0

30.3 

62.0 

11.0

April

149.8 

95.6 

154.4 

215.2 

102.0 

85.5 

44.2 

160.8

172.6 

112.1 

227.8 

96.2 

54.0 

163.1 

136.2 

56.2 

60.3

122.7 

227.8 

44.2

May

512.6 

383.2 

475.5 

462.0 

341.1 

545.7 

294.7 

540.9

300.1 

484.1 

453.8 

333.7 

377.7 

441.1 

404.6 

437.2 

334.7

419.0 

545.7 

294.7

June

248.5 

612.2 

332.6 

267.8 

513.1 

462.0 

489.5 

460.0

468.4 

478.3 

426.2 

281.7 

643.3 

541.1 

329.3 

655.1 

425.6

450.1 

655.0 

284.5

July

54.7 

309.4 

183.0 

80.8 

166.1 

267.0 

166.8 

103.8

124.9 

72.8 

111.9 

95.7 

150.9 

168.6 

105.0 

180.6 

122.7

145.0 

309.4 

54.7

August

21.6 

75.8 

46.9 

29.8 

37.8 

51.6 

40.0 

34.8

38.8 

25.7 

36.0 

28.8 

39.8 

55.1 

32.1 

37.6 

43.2

39.7 

75.8 

21.6

September

16.8 

27.3 

35.0 

17.9 

19.0 

33.4 

19.9 

21.1 

58.7 

21.6 

21.6 

21.7 

19.0 

55.6 

74.6 

20.0 

20.1 

77.3

32.4 

58.7 

16.8
LOW-FLOW FORECASTS 59

TABLE 33. Accumulated monthly inflow through April to Hungry Horse Reservoir

Power 

year

1949 ----__-..

1950 -------

1951 --------

1952 --------

1953 --------

1954 --------

1955 --------

1956 .........

1960 --------

1961 -.---....

1962 -----...

1963 --------

1964 --..-...

1965 ...._....

1966 ---.--.-.

1967 .........

1968 --------

Max .....

Min .....

Accumulated 

(1,000

JulyApril

362.4

931.5

686.0

336.4

.- 411.7

-- 562.0

613.4

474 9

512.1

530.2

274.8

.- 642.4

614.0

352.4

533.8

.- 522.5

931.5

.. 274.8

AugustApril

307.7 

622.1 

502.9 

255.7 

245.7 

295.0 

446.6

350.0 

439.3 

410.3 

179.1 

491.5 

445.4 

247.4 

353.2

372.8 

622.1

245.7

SeptemberApril

286.1 

546.3 

456.0 

225.9 

207.9 

243.5 

406.6 

654.2 

311.1 

413.6 

374.3 

150.2 

451.6 

390.3 

215.3 

315.7

353.0 

654.2 

150.2

OctoberApril

232.6 

269.3 

519.0 

421.0 

208.0 

188.9 

210.0 

386.7 

595.5 

289.6 

390.3 

352.6 

131.3 

396.1 

315.7 

195.3 

295.5

317.5 

595.5 

131.3

NovemberApril

217.5 

249.4 

452.9 

350.2 

195.6 

175.3 

163.1 

334.2 

436.1 

267.7 

342.0 

309.6 

116.1 

349.6 

268.3 

176.6 

269.0

274.9 

452.9 

116.1

monthly inflow 

cfs-daya)

DecemberApril

202.4 

204.6 

375.9 

306.5 

185.6 

159.8 

119.5 

282.7 

341.1 

240.8 

312.6 

262.6 

101.6 

312.0 

233.6 

155.4 

216.3

236.1 

375.9 

101.6

JanuaryApril

189.1 

170.2 

288.4 

273.8 

175.1 

143.2 

90.0 

235.2 

283.4 

220.2 

292.6 

218.3 

89.9 

255.5 

203.8 

127.1 

188.5

202.6 

292.6 

89.9

FebruaryApril

178.3 

150.1 

242.3 

252.3 

149.5 

129.5 

72.0 

205.0 

251.8 

201.6 

274.4 

192.9 

76.2 

221.2 

181.9 

102.3 

159.5

178.9 

274.4 

72.0

March167.8 

130.0 

184.4 

234.0 

124.5 

112.7 

58.8 

187.3 

229.9 

157.4 

253.8 

135.1 

65.0 

193.8 

165.9 

78.3 

122.3

153.0 

253.8 

58.8

April

149.8 

95.6 

154.4 

215.2 

102.0 

85.5 

44.2 

160.8 

172.6 

112.1 

227.8 

96.2 

53.9 

163.1 

136.2 

56.2 

60.3

122.7 

227.8 

44.2

this curve for periods of a few days to several 

weeks at a time.

This curve is steeper than the recession curves 

developed for the station South Fork Flathead 

River near Columbia Falls and is not defined over 

as large a range in discharge. This is as would be 

expected because the reservoir flooded much of the 

land area that previously had contributed much of 

the base flow at the downstream station. The period 

of record prior to the construction of the reservoir 

covered a wider range in discharge conditions. The 

recession characteristics of the reservoir inflow 

were considered satisfactory for a preliminary 

evaluation of its utility as a forecasting parameter 

for the low-water season.

During the period of study, October 1964-April 

1967, a recession index was determined for the 

first day of each month from the water-budget

data. For other months during power years 1949- 

68, a recession index was developed from data for 

South Fork Flathead River at Spotted Bear Ranger 

Station near Hungry Horse and (or) above Twin 

Creek near Hungry Horse and for Sullivan Creek 

near Hungry Horse. These values are shown in table 

34.

INFLOW FORECASTS

The July-April flows for power year 1937 were 

assumed to be indicative of the minimum flows for 

natural (unregulated) conditions. As a means of 

comparing "assured" flows for the period of regulated flows with flows for power year 1937, an 

equivalent recession index for the, critical year was 

determined for the beginning of each month. It was 

assumed that the flows for each month resulted 

entirely from the recession index for that month.

TABLE 34. Recession index for the inflow to Hungry Horse Reservoir

year

1949 ---.........

1950 ............

1951 ----.....--.

1952 ---.-.-.....

1953 -----.-.....

1954 ............

1955 ---.---.....

1956 -----.-.....

1957 -------.....

1960 -----..----.

1961 ............

1962 ............

1963 ---.-.......

1964 .---.-.,....

1965 -----.-.....

1966 .------.....

1967 .--.-.......

1968 ...-.

1969 ............

Avg ........

Max ........

Min

July

9 79ft

... 16,900

... 7,800

... 4,400

o QoA

... 12,700

8,970

6,030

8,700

4,450

8,440

... 5,890

... 10,100

7,370

.-- 6,310

... 12,900

... 6,100

8,160

1 £ Qftft

O 7OA

August

1,040

O C1 A

2,500

1 or? A

9 ftOA

2,440

2,150

1,620

1,580

1,180

1,780

1,350

1 RRft

9 1 7ft

1 Q.flft

1,910

1,500

1,860

1,040

September

CQA

1 QQA

1,350

7Qf»

840

1 Q.Q.ft

800

930

1.260

QQA

740

QAA

710

1,250

1 Q.9ft

QfTA

n jtf\

1,040

1,020

1 Q9ft

CQft

October

560

550

fTQ A

1,510

490

600

1,070

690

2,360

C1 A

QQA

79A

CQA

1,340

560

C7A

960

O QQA

490

Recession 

(cfs)

November

500

1,030

n QfTA

1,900

450

470

1,440

1,420

3,730

1,140

1,240

490

1 QfTA

1,040

650

1,450

1 QAA

O fTQA

450

index

December

500

1,500

1 QQft

1,050

Q£A

CQA

i 9ftft

fTQ A

9 74ft

740

OCA

1,340

JQA

1,080

1.000

CQA

1,090

1 ftfift

2,740

QfiA

January

450

QQA

2,500

750

QQA

690

1,200

1,030

/ A A

CQA

1 99ft

490

1,680

7QA

79ft

690

QQA

2,500

QQA

Febrary

370

550

QQA

720

720

530

530

610

950

600

590

630

480

970

660

900

1,140

7ftft

1,140

Q.7ft

March

590

7Qfl

1,180

630

540

610

440

630

590

1,120

670

1,200

380

1,070

560

580

1,520

770

1,520

380

April

610

830

1,020

690

1,120

740

560

1,220

3,530

1,790

880

2,020

620

770

3,740

710

2.080

1,350

3,740

560
60 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

Thus, if the recession index for the flow during a 

regulated period was lower than the equivalent 1937 

index, then its assured flows would be less than 

flows for power year 1937. This equivalent index 

and the number of times that the recession indexes 

during the period of regulated flows were less than 

indexes for power year 1937 are shown in the following tabulation :

Equivalent Number of 

1937 index times less 

(cfs) than 1937

July ---. 3,800 1 

Aug ---- 1,200 2 

Sept .... 800 5 

Oct -... 680 9 

Nov .... 505 4

Equivalent Number of 

1937 index times less 

(cfs) than 1937

Feb -----

March 

April -.--

610 

355 

400 

700 

5,400

3 

0

1 

7 

17

TABLE 35. Monthly precipi

Power 

year

1948 -----------

1949 -----------

1950 -----------

1951 -----------

1952 -----------

1953 -----------

1954

1955 -----------

1956 -----------

1957 -----------

1958 -----------

1959 -----------

1960 -----.-.-..

1961 -----------

1962 -----------

1963 -----------

1964 ...........

1965 -----------

1966 ----.--....

1967 ------.....

1968 -----------

Max ------

Min -------

TABLE

July

0.49 

3.90 

1.53 

2.26 

1.68 

1.84 

.10 

2.81 

3.49 

1.90 

.77 

1.05 

.20 

.14 

1.47 

.29 

1.02 

3.29 

1.24 

1.57 

.22

1.49 

3.90 

.10

August

3.78 

1.24 

.79 

1.43 

2.97 

.94 

1.52 

5.21 

0 

3.31 

.98 

.73 

2.11 

3.74 

1.53 

2.04 

.87 

2.31 

4.31 

2.13 

.11

2.15 

5.21 

0

36. Accumulated

September

1.94 

.55 

1.95 

1.19 

3.79 

.49 

.97 

1.19 

3.67 

2.69 

.28 

4.47 

5.48 

1.10 

4.02 

2.15 

2.42 

3.48 

3.52 

.65 

.97

2.24 

5.48 

.28

monthly

October

4.04 

1.15 

2.96 

6.80 

6.56 

.29 

.56 

1.98 

6.30 

2.85 

3.74 

1.73 

4.54 

3.15 

3.17 

5.00 

1.98 

2.92 

.90 

3.35 

5.78

3.32 

6.80 

.29

This is an extreme test because concurrent weather 

conditions during each month had some modifying 

effect, particularly the fall rainstorms. Even with 

these severe restrictions, the recession index by itself indicates the probability that the flows for 

about two-thirds of the fall and winter months 

would equal or be greater than those for power 

year 1937.

In order to evaluate the relative significance of 

the various factors that affect the reservoir inflow 

during the fall and winter periods, a linear stepregression analysis was made of the following basic 

relationship :

tation, Hungry Horse Dam

Monthly precipitation 

(inches)

Novem- December ber

3.00 

2.79 

2.71 

1.53 

1.41 

.72 

2.46 

2.43 

6.42 

1.17 

1.57 

6.56 

7.37 

5.94 

3.16 

4.74 

2.64 

4.92 

3.26 

5.46 

2.88

3.48 

7.37 

.72

precipitation

1.49 

1.79 

2.53 

3.41 

4.67 

1.45 

4.50 

1.81 

5.94 

3.44 

3.13 

4.89 

1.03 

2.22 

4.94 

2.40 

2.31 

8.21 

1.72 

4.30 

3.37

3.31 

8.21 

1.03

through

Jan- Febuary ruary March

2.03 

1.30 

7.02 

2.80 

2.06 

5.27 

6.94 

1.65 

3.71 

2.01 

3.08 

6.85 

2.88 

1.94 

1.53 

2.41 

3.19 

3.83 

3.44 

6.22 

3.13

3.44 

6.94 

.13

April,

2.86 

3.49 

2.07 

2.49 

.91 

2.07 

2.48 

3.50 

3.02 

3.64 

4.48 

2.60 

1.70 

5.11 

1.75 

3.22 

.97 

3.23 

1.69 

1.33 

3.21

2.66 

5.11 

.91

Hungry

1.98 

2.16 

2.82 

1.60 

1.12 

2.23 

2.33 

1.69 

2.03 

1.75 

1.20 

1.61 

2.58 

2.80 

2.98 

2.94 

2.74 

.36 

3.17 

2.12 

2.85

2.00 

3.17 

.36

Horse Dam

April

3.92 

1.50 

1.72 

.81 

.57 

2.17 

2.12 

2.02 

2.22 

1.79 

3.50 

2.38 

1.59 

5.16 

3.06 

2.38 

1.82 

3.76 

2.01 

1.18 

1.37

2.24 

5.16

.57

Accumulated monthly precipitation 

(inches)

Power 

year

1948 .------...

1949 ----..-...

1950 ----------

1951 ..-----...

1952 --..--....

1953 -.----....

1954 ..........

1955 ----------

1956 ---------

1957 ----------

1958 ----------

1959 ----------

1960 ----------

1961 ----------

1962 ----------

1963 ----------

1964 ----..-...

1965 ----------

1966 ..........

1967 -.-.----..

1968 ---.-.-...

Max --....

Min ......

JulyApril

25.53 

19.87 

26.10 

18.32 

25.74 

17.47 

23.98 

24.29 

36.80 

24.55 

22.73 

32.87 

29.48 

31.30 

27.61 

27.57 

19.96 

36.31 

25.26 

28.31 

23.89

26.09 

36.80 

17.47

SeptemAugust- berApril April

25.04 

15.97 

24.57 

16.06 

24.06 

15.63 

23.88 

21.48 

33.31 

22.65 

21.96 

31.82 

29.28 

31.16 

26.14 

27.28 

18.94 

33.02 

24.02 

26.74 

23.67

24.60 

33.31 

15.63

21.26 

14.73 

23.78 

14.63 

21.09 

14.69 

22.36 

16.27 

33.31 

19.34 

20.98 

31.09 

27.17 

27.42 

24.61 

25.24 

18.07 

30.71 

19.71 

24.61 

23.56

22.60 

33.31 

14.63

OctoberApril

19.32 

14.18 

21.83 

13.44 

17.30 

14.20 

21.39 

15.08 

29.64 

16.65 

20.70 

26.62 

21.69 

26.32 

20.59 

23.09 

15.65 

27.23 

16.19 

23.96 

22.59

20.36 

29.64 

13.44

NovemberApril

15.28 

13.03 

18.87 

12.64 

10.74 

13.91 

20.83 

13.10 

23.34 

13.80 

16.96 

24.89 

17.15 

23.17 

17.42 

18.09 

13.67 

24.31 

15.29 

20.61 

16.81

17.33 

24.31 

10.74

DecemberApril

12.28 

10.24 

16.16 

11.11 

9.33 

13.19 

18.37 

10.67 

16.92 

12.63 

15.39 

18.33 

9.78 

17.23 

14.26 

13.35 

11.03 

19.29 

12.03 

15.15 

13.93

13.85 

19.39 

9.33

JanuaryApril

10.79 

8.45 

13.63 

7.70 

4.66 

11.74 

13.87 

8.86 

10.98 

9.19 

12.26 

13.44 

8.75 

15.01 

9.32 

10.95 

8.72 

11.18 

10.31 

10.85 

10.56

10.53 

15.01 

4.66

FebruaryApril

8.76 

7.15 

6.61 

4.90 

2.60 

6.47 

6.93 

7.21 

7.27 

7.18 

9.18 

6.59 

5.87 

13.07 

7.79 

8.54 

5.53 

7.35 

6.87 

4.63 

7.43

7.04 

13.07 

2.60

MarchApril

5.90 

3.66 

4.54 

2.41 

1.12 

4.40 

4.45 

3.71 

4.25 

3.54 

4.70 

3.99 

4.17 

7.96 

6.04 

5.32 

4.56 

4.12 

5.18 

3.30 

4.22

4.36 

7.96 

1.12

April

3.92 

1.50 

1.72 

.81 

.67 

2.17 

2.12 

2.02 

2.22 

1.79 

3.50 

2.38 

1.59 

5.16 

3.06 

2.38 

1.82 

3.76 

2.01 

1.18 

1.37

2.24 

5.16 

.57
LOW-FLOW FORECASTS 61

X, = aX2 + bX3 + cX*+d, 

where Xl = reservoir inflow, in 1,000 cfs-days,

Xz =recession index for the first of each

month, in cubic feet per second, 

X3 =precipitation at Hungry Horse Dam, in

inches,

and A"4 =degree days (65°F.) at Hungry Horse 

Dam.

The data for Xl and X2 are shown in tables 32-34. 

The data for X3 and A~4 are shown in tables 35-38.

The analysis was made for each month JulyApril and for each group of months ending in April 

(July-Apr, and Aug.-Apr. for example). The results of this analysis are shown in table 39. The 

best equation was selected on the basis of the lowest 

standard error of estimate. The significance level 

of each component was based on the t test.

The recession index appears to be the most useful 

variable of those tested. However, under some circumstances the addition of precipitation and (or)

TABLE 37. Monthly degree days (65° F), Hungry Horse Dam, Montana

[Values through November of 1954 are estimated] 

Monthly degree days

Power year

1949 ........

1950 ........

1951 ..--....

1952 --......

1953 ---.-...

1954 --------

1955 --------

1956 --------

1957 --------

1958 --.-..-.

1959 ........

1960 --------

1961 --------

1962 ---.....

1963 --------

1964 ........

1965 --------

1966 ........

1967 .--.....

1968 -.--. ...

1969 __ ....

Avg ....

Max

Min ..--

*

l-»

---. 160

.---. 125

.... 75

.... 95

.... 135

..... 70

.... 78

.... 142

..-- 65

--.. 33

.... 62

.... 79

.... 11

.... 8

.... 88

.... 67

-... 58

.... 37

.... 51

..-. 112

-..- 74

--.. 160

.... 8

1 

3

135

100

90

150

100

90

132

37

09

85

21

130

144

9

00

64 inn

102

96

4

159

96

180

4

P. 

$

320

360

335

470

280

250

346

362

267

241

O17

337

272

471

186

407

573

1K0

123

364

324

573

123

1

710

7Qn

640

765

570

560

736

622

667

782

CKft

691

ei K

718

fi JO

557

662

525

660

626

79Q

663

7QA

625

1

980

830

1,040

1,050

1,030

845

805

1,259

1 A99

999

984

1,209

963

1,113

89B

885

961

AAQ

Q74

952

965

Qfll

1 9ftO

805

1 

1

1,480

1,320

1,100

1,530 1 9l\n

1,036

1,111

1,295

1 149

989

1,127

1.196

1 998

1.285

1,015

1,257

1 491

1,089

1,070

1 260

1.416

1 91,4

1,530

aao

§

^S

1 Qon

1 QQE

1,430

1,500

QAA

1,347

1 1Q7

1 900

1 AQC

1,117

1,260

1,404

1,120

1.438 i eio

1,106

1 A7C

1,230

1 fkfio.

1,276

1,625

1,359

1 QOn

QAA

i

1,350

1,130

1,160

1 ftQft

QOfh

Q14

1,202

1,265

1,127

978

1,204

1,171

Q1Q

1 IftQ

Qftl

1,033

1,014

1.025

1,001

1,067

1,350

010

1

3

1,150

1,095

1,290

1,100

840

1 170

1 947

996

1,007

995

916

1,017

876

1,054

895

1,071

1 91Q

Q79

1,057

7QC

1,038

1,290

786

I

600

775

720

625

770

818

815

711

705

675

684

703

657

608

678

733

659

713

7 CO

741

708

818

600

>>

1

350

515

460

400

520

434

558

389

293

165

546

480

390

485

423

452

468

321

429

477

428

558

165

s9 *>

230

280

330

250

280

339

184

188

159

132

221

184

79

202

200

251

202

264

180

252

220

339

79

I

9,395

9.215

8,670

9,025

7,545

7,881

8,411

8,564

8,230

7,191

7,992

8,651

7,184

8,530

7,698

7,662

8.221

7,759

7,423

7,507

TABLE 38. Accumulated monthly degree days (65°F) through April, 

Hungry Horse Dam, Montana,

Accumulated monthly degree days

Power year

1949 .........

1950 --.... ...

1951 -.--...--

1952 ---------

1953 -.-. _ -.

1954 .........

1965 . ___ ...

1956 ---------

1957 .-...-.--

1958 ---..-..-

1959 .---.-.--

1960 .........

1961 ..----.-.

1962 ---......

1963 ---------

1964 -.-.-..-.

1965 .........

1966 ---.-..-.

1967 ---...-..

1968 .........

Max -....

Min ......

W"3 A ?«

__ .. 3,816

-.-.-. 8,420

...... 7,880

------ 8,376

------ 6,746

------ 7,108

------ 7,669

--..-. 8.946

----.. 7.778

-.--.. 6,894

------ 7,226

-.---. 7,987

------ 6,715

------ 7.843

--.... 7,075

------ 6.959

------ 7.551

-.---. 7,174

------ 6,764

------ 6,777

...--- 7,535

------ 8,946

------ 6,715

1!

8,655

0 9QK

7.805

0 90n

6,610

7 nqfi

7,591

fi QflA

7 71 o

6,861

7.163

7 QftQ

6,704

7.835

6.987

6,892

7,493

7

1O7

6,713

6,769

T jfiO

8.804

6,610

II

(2<

8,620

8.195

7,715

8,130

6,510

6,948

7,469

Q J JO

ft coi

6,776

7,142

7 770

6,560

7 090

 % QQQ

6,828 7010

7.035

6,617

ft rjete

7.354

8,520

6,510

||

83

8,200

7.836

7 aan

7 ccn

6,230

6,698

7,113

7 Q9A

n GftA

6,635

ft QOC

7 QQ1

ft OOQ

7,355

6,577

C 0JO

6,906

e ,ieo

6,459

et etAo

7 niQ

o oftfk

6.230

»!=f !*fe«

7,490

7.045

6,740

6,895

5,660

6.138

6,377

6,561

e CO7

R 7RQ

6,175

6,700

R fiRPQ

e 4*017

R Ooe

c AOR

6 244

R QO7

E 7QA

6,016

ft OOQ

7,490

5,660

Ss

8ft Q<

6,510

tt 91 R

R Tnn

R QJ f

4,630

5,293

K C7O

R OCC

5,674

4,754

R 1Q1

5,491

4,710

K KOA

5,107

5,200

K OQQ

5,029

A QOE

5,064

5,344

6,510

4,630

Sah ?<

5,030

4,895

4,600

4,315

3,430

4,257

4,461

o oca

4,525

3,765

4,064

A OQR

O J79

A OOQ

A. ftQ9

ft Q4ft

O QCO

3,940

3,755

3,804

4,1-U

5,030

3,430

I'S

Is

3,100

3,000

3,170

2,815

2,530

9 am

3,264

9 7AO

9 QOQ

2,648

a QAji

9 QQ1

9 OR9

9 QA1

2,474

9 QO7

9 QQC

9 71H

9 It'79

9 R9Q

9 7Q7

O OttA

2,352

%* 

^

1,750

1,870

2,010

1,725

1.610

1,997

2,062

1,707

1 719

1,670

1,600

1 79ft

1.533

1.662

1,573

1,804

1 Q79

1,685

i 77n

1,627

1,7^3

2.062

1,527

1

<

600

775

720

625

770

818

815

711

705

675

684

703

657

608

678

733

659

713

763

741

7AQ

818

600
62 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

TABLE 39. Summary of step-regression analysis, reservoir inflow 

versus recession index, precipitation, and degree days (65°F)

Period

July .-.--..-..

Sept ..........

Oct -----------

Nov ..---.----.

Feb .--..-..-.

Mar .---.-..--.

Feb Apr

Best expression for Xi

.---.. 0.017X2+9.76X3 2.7

.--..- 0.019X2+1.80X3 +1.1

.--..- 0.043X2+7.77X3 0.046X4 +16.9

.-.-.- 0.043X2+7.19X3 22.6

.----. 0.025X2+1.47X3-0.023X4 +23.0

.-.--- 0.028X2+4.77X3 0.020X4 +13.2

.-.--- 0.015X2 0.008X4 +21.7

.-.--. 0.027X2+5.50X3-0.029X4 +24.0

.---.. 0.025X2 -0.034X4 +46.8

..--.. 0.700X4+616.0

..---- 0.033X2 +0.103X4 530.6

...... 0.120X2+6.16X3+0.047X4 353.0

..--.. 0.189X2+6.78X3+0.089X4 645.2

..--.. 0.116X2+6.20X3+0.070X4 436.2

.--... 0.088X2+6.66X3+0.029X4 120.4

..--.. 0.078X2 +153.0

------ 0.067X2 +142.9

------ 0.082X2 +121.7

------ 0.090X4+310.4

Correlation 

coefficient

0.92 

.96 

.91 

.87 

.97 

.88 

.90 

.66 

.76 

.77 

.86 

.79 

.73 

.71 

.86 

.59 

.54 

.28 

.25

Standard 

error of 

estimate

26.9 

3.6 

8.9 

19.1 

6.6 

10.7 

4.1 

12.4 

9.6 

42.0 

93.3 

84.2 

102.5 

97.5 

54.7 

65.3 

56.7 

60.5 

57.7

Significance le 

( percent)

X2 X3

<1 ~15 

<1 ~1 

<1 <1 

<1 <1 

<1 ~30 

<1 <1 

<1 >50 

~10 <10 

<1 >50 

>50 >50 

<1 >50 

<1 10 

~5 ~20 

1 <20 

<1 ~20 

~1 >50 

~2 >50 

~30 >50 

~50 >50

ivel

X4

>50 

>50 

~20 

>50 

~20 

~30 

~5 

~20 

<10 

<1 

<1 

~10

*^"O _.o

~10 

<30 

>50 

>50 

>50 

~30

Reservoir inflow

Mean

148.1 

39.7 

32.4 

42.6 

38.8 

33.5 

23.7 

25.9 

30.3 

117.3 

522.5 

372.8 

353.0 

317.5 

274.9 

236.0 

202.6 

178.9 

153.0

Standard 

deviation

65.7 

12.7 

20.0 

35.6 

22.6 

20.1 

8.8 

14.8 

14.0 

61.9 

167.3 

120.7 

135.0 

124.2 

95.5 

78.7 

65.3 

60.9 

57.7

temperature variables can make significant improvement in the reliability of the regression equations. This analysis indicates that if the actual 

values of the variables recession index, precipitation, and temperature are known for each time 

period, then the reservoir inflows could be computed 

with a smaller standard error of estimate than the 

standard deviation of the original reservoir inflows.

It is assumed that sufficient current hydrologic 

data would be available so that the recession index 

could be determined at the beginning of each time 

period. Future values of precipitation and temperatures cannot, with our present knowledge, be 

reliably forecast for a month or more in advance. 

Thus the basic use of equations such as those shown 

previously is to evaluate the probable range of 

reservoir inflows that can occur with different levels 

of precipitation and temperature. If average values 

of precipitation and (or) temperature are inserted 

into one of the equations above, then the resulting 

inflows should have an average chance of occurring. 

On the other hand, if the minimum values of precipitation and (or) temperature were used, then 

the resulting inflows would have a minimum chance 

of occurring. These two values could provide a 

measure of the potential range in reservoir inflows 

that could be used as a guide in reservoir operations.

There are indications based on the above summary that useful forecasting of reservoir inflow 

during the low-flow period may be developed. The 

examination of the low-flow forecasting technique 

outlined above is by no means complete. There are 

other combinations of time-period variables and 

internal relations that should be examined and 

evaluated. The prospects are encouraging for the 

development of a level of inflow forecasting during

the drawdown period that would greatly enhance 

the operation of Hungry Horse Reservoir.

PRECIPITATION

Precipitation on the surface of Hungry Horse 

Reservoir is another item of inflow. The amount 

of inflow from assumed precipitation during the 

forecast period would be added to the reservoir 

inflow from the land area. In these studies the 

precipitation at Hungry Horse Dam was assumed 

to be representative of the precipitation over the 

entire surface of the reservoir. Some inherent variation is known to exist, but there are not enough 

data to justify any refinements. For forecasting 

the reservoir inflow, the use of average or minimum 

amounts selected from tables 35 and 36 probably 

will supply the range in values needed as guides in 

reservoir operation.

One inch of precipitation represents about 1,000 

cfs-days when the reservoir is at full-pool elevation. 

For amounts other than 1 inch or reservoir areas 

other than those at a stage of 3,560 feet, inflow 

values can be obtained by simple ratios. Monthly 

precipitation values have ranged from 0 to 8.21 

inches; thus the range of inflow would be from 0 

to 8,210 cfs-days at full-pool level. If the 8.21 inches 

of precipitation had occurred when the area of the 

reservoir was 21,000 acres, then it would have resulted in (21,000/24,000) x 8,210, or 7,184 cfs-days. 

Likewise seasonal values for the period July-April 

could have ranged from 17,470 to 36,800 cfs-days.

EVAPORATION

Evaporation from the surface of Hungry Horse 

Reservoir is a loss as far as usable water for the 

project is concerned. Like precipitation, this is an 

unknown for each forecast period and its potential
LOW-FLOW FORECASTS 63

magnitude would have to be evaluated from past 

records.

Records for a class A evaporation pan have been 

collected since 1948. The normal evaporation period 

is considered to extend from May through October, 

with perhaps minor amounts occurring at other 

times. The data for periods not covered by observations were estimated and are included along with 

the observed readings in table 40. The energybudget study of evaporation made in connection 

with this study provided a measure of the actual 

evaporation from the surface of the reservoir. The 

energy-budget values are shown in table 16.

TABLE 40. Monthly and seasonal evaporation, class A pan, 

Hungry Horse Dam

Evaporation 

(inches)

Year

1948 --------

1949 .-.-_.--

1950 ---_-__.

1951 ------

1952 --------

1953 --------

1954 - ......

1955 -__.....

1956 --______

1957 --------

1958 _----___

1959 ........

1960 .--_____

1961 .......

1962 ___....-

1963 ........

1964 ........

1965 ________

1966 ___.....

1967 ........

1968 ...--_-_

Avg 

Max --.- 

Min -_..

May

3.72 

5.03 

4.86 

5.07 

4.59 

4.32

5.'03 

5.41 

5.51 

8.10 

4.21 

4.74 

4.98 

3.68 

5.37 

4.54 

4.62 

6.35 

4.78 

4.68

4.98 

8.10 

3.68

June

5.55 

6.73 

4.95 

4.88 

5.00 

4.68 

4.78 

7.38 

6.64 

5.65 

6.47 

5.96 

6.70 

7.62 

6.26 

4.99 

5.20 

6.24 

5.06 

6.13 

5.29

5.82 

7.62 

4.68

July

6.76 

7.27 

7.28 

7.36 

7.10 

8.99 

8.10

7!63 

9.61 

8.00 

8.90 

11.28 

8.60 

8.06 

7.62 

7.37 

7.75 

8.10 

9.90 

7.75

8.13 

11.28 

6.76

August September October

5.21 

7.54 

5.41 

5.89 

7.29 

6.71 

5.93 

10.35 

6.17 

6.74 

9.14 

7.17 

5.53 

7.74 

6.03 

7.06 

5.00 

5.24 

6.82 

9.39 

4.96

6.73 

10.35 

4.96

4.51 

3.72 

3.94 

1 2.5 

4.02 

4.49 

2.33 

4.03 

3.70 

4.17 

4.32 

2.86 

3.72 

2.90 

3.34 

3.40 

2.66 

1.97 

3.73 

5.29 

2.65

1.1 

1.0 

1.4 

4.0 

2.27 

1.7 

1.0 

1.06 

1.3

l!4 

1.2 

1.6 

1.8 

1.8 

1.35 

1.26 

1.68 

1.39 

2.06 

.98

3.54 1.53 

5.29 * 4.00

1.97 1 .7

Season 

total

26.85 

31.29 

27.84 

29.70 

30.27 

30.89 

27.14 

35.15 

30.85 

31.75 

37.43 

30.30 

33.57 

33.64 

29.17 

29.79 

26.03 

27.50 

31.45 

37.55 

26.31

30.69 

37.55 

26.03

1 Estimated or partially estimated.

A comparison was made of the energy-budget 

evaporation data and the class-A-pan data. Ratios 

of the energy-budget amounts to the class-A-pan 

amounts were calculated for the periods used in 

the energy-budget study and are shown graphically 

in figure 28.

Monthly coefficients were selected to be used to 

convert the class-A-pan data to equivalent energybudget data. These are shown in the following 

tabulation:

May 

June 

July

0.4 

.5 

.6

Aug. 

Sept. 

Oct. .

0.9 

1.3 

1.6

If the average amounts of evaporation from the 

class A pans were modified by these coefficients, 

the equivalent energy-budget evaporation amounts, 

in inches, would be the following:

May 

June 

July

1.99

2.91

4.88

Aug. 

Sept 

Oct. .

6.06

4.60

2.45

MAY JUNE JULY AUG SEPT OCT

FIGURE 28. Ratio of evaporation amounts calculated by energy budget and by class A pan, 

Hungry Horse Reservoir, 1965 and 1966.

The loss for these amounts would be 1,000 cfs-days 

per inch at full reservoir pool.

The evaporation during July-October is of prime 

concern in this study. The amounts of evaporation 

and precipitation are in opposite directions, and 

the average values of each are compared below:

Evaporation 

(inches)

Precipitation 

(inches)

Net precipitation 

(inches)

July ------

August - - - 

September 

October -.

4.88

6.06

4.60

2.45

1.49

2.15

2.24

3.32

-3.4

-3.9

-2.4 

+.9

Thus evaporation losses are, on the average, greater 

than gains from precipitation during July, August, 

and September.

STORAGE CHANGES

The total storage change is composed of that 

within the topographic limits of the reservoir and 

that within aquifers adjacent to the reservoir. Each 

of these must be evaluated in order to compute the 

amount of water available for project use. The 

stage record at Hungry Horse Dam and the capacity 

table can be used to evaluate the changes in reservoir storage. The model solution 0.8 (Af2 +0.4M4 ) 

can be used to evaluate ground-water storage 

changes occurring in response to changes in stage 

of the reservoir.

WATER AVAILABLE

The water available at Hungry Horse Reservoir 

can be evaluated by considering each of the following components: Inflow from the land area ( + ), 

precipitation on reservoir area ( + ), evaporation 

from reservoir surface (-), changes in reservoir
64 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

storage (±), and changes in ground-water storage 

(±).

Of these, the inflow from the land area and 

changes in reservoir storage are the largest. But 

each of the other three components is large enough 

to be considered in project operations.

SUMMARY AND CONCLUSIONS

The Hungry Horse Project is a major element 

in the Federal Columbia River Power System. It 

furnishes important at-site and downstream power 

benefits and local and downstream flood control. 

Certain operating problems have been intensified 

because of an apparent imbalance between inflows 

and outflows. The multipurpose operation of Hungry 

Horse Reservoir can be enhanced by resolving this 

difference. The basic objective of this study was 

to determine more accurately the water available 

for project use, including bank storage, and to improve the methods of forecasting the inflows to the 

reservoir during the low-flow period. In its simplest 

form, the water available for project use can be 

expressed as follows:

Outflow=inflow ± changes in storage.

Each of these items is composed of many factors, 

often interrelated. The accurate measurement or 

evaluation of each of the various components of 

outflow, inflow, and changes in storage is essential 

to the solution of this problem.

The least known or understood factor in this 

study is the ground-water storage in the aquifers 

adjacent to the reservoir. This bank-storage effect 

has received emphasis in the first phase of this 

study. The alluvium adjacent to Hungry Horse 

Reservoir has been evaluated as a ground-water reservoir, its hydraulic characteristics have been inferred, and a mathematical model has been developed for computing gains to and losses from 

the reservoir in response to changes of stage of 

Hungry Horse Reservoir.

Two approaches were used: (1) a comprehensive 

water budget based on field data collected over a 

31-month period and (2) a theoretical model of the 

response of the aquifer to changes in stage of 

Hungry Horse Reservoir. Residuals in the water 

budget represent ground-water storage changes 

which are masked by the accumulation of all the 

errors in field measurements. The mathematical 

model is poorly defined because rigid assumptions 

may not truly represent the field prototype and 

because the hydrologic properties of the aquifer 

material lack definition. However, by using the two

methods jointly, improved water-budget balances 

were obtained and a "best fit" set of hydrologic 

constants was derived for the model. The model 

was studied relative to possible errors and a final 

set of constants selected. This solution is probably 

within ±25 percent of the true solution of the 

gains to and losses from ground-water storage in 

response to changes in the stage of Hungry Horse 

Reservoir.

The recommended solution is a combination of 

two applications of the mathematical model. Each 

part is computed by equations 5 and 6, or by use of 

the simplified equations 5a, 5b, 6a, 6b, and 6c. 

In the model where hydrologic constants are designated by 0.8 (M2 + 0.4M4 ), segment M2 is calculated using a=851 feet, S=0.15, and T/a?S= 

0.003 per day. The second segment, M4 , is 0.4 times 

the calculation using a=851 feet, S=0.20, and 

T/a?S= 0.0256 per day. The sum of the two segments is then multiplied by 0.8.

From the model, the inactive and dead groundwater storage below an elevation of 3,336 feet is 

calculated as 48,100 cfs-days and probably lies between the limiting curve values of 36,000 and 

60,000 cfs-days.

Ground-water storage capacity between elevations of 3,336 and 3,560 feet is computed as 108,300 

cfs-days, with probable limits of 81,200 and 135,400 

cfs-days. All this storage would be available for 

use only if the stage of Hungry Horse Reservoir 

were lowered to an elevation of 3,336 feet and held 

at that level for approximately 1 year.

The release of water from the aquifer in response to stage changes of Hungry Horse Reservoir 

forms a loop curve over each seasonal cycle of drawdown and fill. The volume of water to be gained 

by Hungry Horse Reservoir during a drawdown 

period is controlled by the aquifer characteristics, 

the rate of change of stage, the antecedent changes 

in stage, the time since they occurred, and the time 

sequence during draft. Because of the time-lag and 

loop effects, a simple relation of yield per foot of 

draft, or a percentage of the capacity table, cannot 

be expected to produce valid estimates.

Calculations of potential ground-water storage 

the maximum to be expected if Hungry Horse Reservoir were held full for a long time (1 year), 

were drafted and then were held at that level for 

about a year are shown below for the three drawdown periods. Also shown are the ground-water 

storage releases for these periods derived from the 

model.
SUMMARY AND CONCLUSIONS 65

Draft

season

1964-65 .---.

1965-66 .....

1966-67 .--..

Draft

(feet)

----- 100

----- 59

----- 119

Potential storage

(1,000 cfs-days)

56.0

35.0

65.2

Storage release

(1,000 cfs-days)

34.0

19.9

43.0

Ratio of

released

storage to

potential

storage

0.61

.57

.66

Antecedent conditions were more favorable for filling the ground-water reservoir in 1964-65 when 

pool level was held constant for 6 months in contrast 

to 2 months in 1966-67. This condition was more 

than offset by the earlier and longer draft period 

of 8 months in 1966-67 compared to 4 months in 

1964-65. Thus, even though there was greater aquifer storage in the first year, the yield to the reservoir was proportionally less, because the time for 

drainage was small compared to the 1966-67 season.

The second phase of this study was devoted to 

improving the methods of forecasting the reservoir 

inflow during the low-flow periods, July-April. In 

the period of natural flow prior to September 1951, 

forecasts of "assured" flows were based on the data 

and characteristics for the outflow gaging station 

South Fork Flathead River near Columbia Falls.

In the period of regulated flows subsequent to 

September 1951, the inflow to the reservoir was 

not measured directly but was indirectly computed. 

Prior to the present study this was done by adjusting the measured outflow for changes in reservoir contents. Forecasts of reservoir inflow were 

made by the technique developed for natural conditions. This proved to be unsatisfactory because of 

the erratic nature of the computed inflow. The index equation for computing reservoir inflow developed in the 1959 studies was not considered 

adequate for present use.

During the period of this study the reservoir 

inflow, except for precipitation, was in effect a 

measured quantity. Index equations were developed 

from these data which could be used to evaluate 

the inflow to the reservoir for other periods of 

time. The water-budget data for the inflow to 

Hungry Horse Reservoir were analyzed by stepregression analysis, and an index of reservoir inflow, 

except for precipitation, was developed. This equation is

X1 = I.ISX2 + 4A7X3 + 1,246,

where Xl = monthly reservoir inflow except precipitation, in cfs-days,

X2 =monthly runoff, South Fork Flathead 

River above Twin Creek near Hungry 

Horse, in cfs-days,

and Xs = monthly runoff, Sullivan Creek near 

Hungry Horse, in cfs-days.

This equation has a correlation coefficient of 0.9999, 

a standard error of estimate of 2,230 cfs-days, and 

an average deviation of 1,470 cfs-days. This equation was used for computation of reservoir inflows 

after April 1967.

A similar index for use prior to October 1964 

was developed. It is

Xl = 1.20X2 + 6.94^3 - 777, 

where Xl = monthly reservoir inflow except precipitation, in cfs-days,

X2 = monthly runoff, South Fork Flathead 

River at Spotted Bear Ranger Station 

near Hungry Horse, in cfs-days, 

and X3 = monthly runoff, Sullivan Creek near 

Hungry Horse, in cfs-days.

The correlation coefficient is 0.9994, standard error 

of estimate is 4,747 cfs-days, and average deviation 

is 2,830 cfs-days.

These two index equations and the water-budget 

data were used to estimate the inflow to Hungry 

Horse Reservoir except for precipitation for power 

years 1949-68 where data were available.

The recession characteristics of the reservoir inflow were analyzed and recession indexes were computed for periods when data were available. The 

"assured" flows from these indexes are larger than 

those from an equivalent index for the period 1936- 

37 in more than two-thirds of the fall and winter 

months.

A preliminary step-regression analysis of the 

monthly reservoir inflow versus the recession index, 

precipitation, and degree days (65°F) indicated 

that the recession index was the most significant 

factor in forecasting reservoir inflows during the 

period July-April. Further study of other time 

periods and meteorological data for stations other 

than Hungry Horse Dam are needed to fully develop the potential indicated by the above analysis.

Forecasts of water available for project use must 

include reservoir inflow ( + ), precipitation on the 

reservoir ( + ), evaporation from surface of reservoir (-), changes in reservoir storage (±), and 

changes in ground-water storage adjacent to the 

reservoir (±). The reservoir inflow and changes 

in reservoir storage are the largest components, but 

precipitation, evaporation, and changes in groundwater storage should be evaluated in order to enhance the efficient operation of Hungry Horse Reservoir.
66 HYDROLOGY OF HUNGRY HORSE RESERVOIR, NORTHWESTERN MONTANA

REFERENCES

Anderson, E. R., 1954, Energy-budget studies, in Water-loss 

investigations Lake Hefner studies, technical report: 

U.S. Geol. Survey Prof. Paper 269, p. 71-119.

Carslaw, H. S., and Jaeger, J. C., 1959, Conduction of heat 

in solids: London, Oxford University Press, 510 p.

Hantush, Mahdi S., 1961, Discussion of paper by P. P. Rowe, 

"An equation for estimating transmissibility and coefficient of storage from river-level fluctuations": Jour. 

Geophys. Research, v. 66, no. 4, p. 1310-1311.

Koberg, G. E., 1958, Energy-budget studies, in Water-loss 

investigations Lake Mead studies: U.S. Geol. Survey 

Prof. Paper 298, p. 20-29.

Rorabaugh, M. I., 1964, Estimating changes in bank storage 

and ground-water contribution to streamflow, in Symposium Surface waters: Internat. Assoc. Sci. Hydrology 

Pub. 63, p. 432-441.

Ross, C. P., 1959, Geology of Glacier National Park and the 

Flathead region, northwestern Montana: U.S. Geol. Survey Prof. Paper 296, 125 p.

Sachs, M. S., 1957, Methods and procedures used in forecasting dependable inflow to Grand Coulee Project, 

Washington: Washington State Coll. Hydraulics Conf.; 

Am. Geophys. Union, Pacific Northwest Branch, 4th Ann. 

Mtg., Proc., p. 119-137.

Simons, W. D., 1968, Hydrology of Hungry Horse Reservoir, 

Montana, basic data supplement; U.S. Geol. Survey 

open-file report, 154 p.

INDEX

Page 

Acknowledgments ----------------------- 11

Aquifer characteristics -------------- 24, 34

Aquifer storage -----------.....--13, S3, 63

Aurora Creek ----.-_-.._________-__12, 18, 31

Bank storage, analysis --------------.-25, 34

curve ---------_--_-._______.______._ 54

definition and computation ------..14, 37

effect on calculations --------------- 8

relation to geology ----.--..------.. 24

reservoir stage --------------------- 14

Belt Supergroup -----------_._..---..___ 23

Bibliography ---_--_______._____,___.____ 65

Canyon Creek ------___.______________.._ 39

Channel storage ------------------------ 31

Class A pans, evaporation data -------- 31

Columbia Falls ---------_-....__-.-.____ 4

Columbia River basin ...................1, 7

Columbia River Water Management 

Group -----_____.__.____._......_...-- 3

Conclusions ----------__-____...._____.__ 64

Constants ---------.....25, 36, 88, 41, 46, S3

Data analysis .-----.---.--.-..-.----..25, 84

Data collection .-------.-.....--12, IS, 38, 40

Deep Creek ...........................27, 39

Devils Elbow -----_.._.__.__________.___ 2

Discharge records --------------.6, 26, 48, 51

Drainage area .--------.--.......--....11, 18

Dry Park Creek --------------------- 18, 23

Energy budget .................... 12, 31, 63

Evaporation ---.------.-._______...____ 4

as outflow ----------.--------. 31, 56, 68

class A pans ------------------------ 31

data collection -_-___.__.____-----_-- SO

Federal Columbia River Power System -. 3

Flathead Range ---..----_-._--__.------_ 4

Flathead River .......................... 4

Forests ................................. 4

Franklin D. Roosevelt Lake ------------- 3

Gaging station network ------ 5, 8, 11, IS, 56

data collection -------_______________ 12

ungaged areas ..---______.__._____ 89, 44

use in water budget -------...--.--_ 86

[Italic page numbers indicate major references]

Page 

Geology --------------------------------- S3

Grinnel Limestone, Ravalli Group -------- 23

Ground-water, backwater ------------ 14, 40

inflow equations -------------------- 36

storage --------------------------- 53, 64

well data ------------------------ 83, 38

Hungry Horse Creek -------------------- 18

Hungry Horse Project ------------------ 8

Hydraulic conductivity ------------ 14, 25, 40

Hydraulic gradient -------------------- 14, 36

Hydrologic constants ------------- 25, 36, 38

computation ------------------------ 41

selection for model ---------------- 46, S3

Hydrology ------------------------------ 5

Index of reservoir inflow, regression

analysis ------------------------ 56, 61, 65

Inflow ................................ 8, 11

data collection ---------------------- IS

data for water budget --.---.-_---.-- 26 

equations ------------------ 57, 58, 61, 65

forecasts of low flows -------- 55, 59, 65

natural conditions ------------------ 55

procedure for estimating ------------ 13

recession characteristics ------------ 58

recession index ............... 56, 61, 65

regulated conditions ----------------- 56

Introduction ---------------------------- 1

Kalispell ------------------------------ 2, 4

Logging -------------------------------- 4

Lower Twin Creek ---------------------- 27

Mclnernie Creek ------------------------ 23

Mass transfer, evaporation computations - 31 

Mathematical model ------------------ 34, 64

comparison with water budget ---- 15, 41

development of equations ----------- 84

inadequacy of single solution -... 47, 49 

sensitivity of solutions -------------- S3

significance of components ---------- 48

solutions having two sets of constants 48 

use _----..--.----------------------- 54

Meteorology --------------------------- 4, 23

Missoula Group ------------------------ 23

Page 

Outflow -------------------------------- 12

data collection ---------------------- 18

water budget -------- ------------- SO

Outwash, hydrologic constants ---------- 38

Piegan Group, Siyeh Limestone -------- 23

Power, Hungry Horse Project ---------- 3

Precipitation .__------------_--_-------- 4

as inflow -------------- 12, SO, 56, 61, 68

data collection -------------------- 4, 23

Previous investigations ------------------ 8

Purpose and scope ---------------------- 1

Ravalli Group, Grinnel Limestone -------- 23

Reservoir, change in contents -------- SO, S3

change in storage ---------------- IS, 63

stage ------------------------- 14, 48, 47

Riverside Creek ------------------------- 23

Siyeh Limestone, Piegan Group -------- 23

South Fork Flathead River, discharge 

regimen .--------.-----------------.- 6

South Fork Flathead River basin ..-- 2, 4, 18 

Stage _-_--_-.------------.------- 14, 48, 47

Storage ------------ 8, 13, 84, 31, 34, 53, 63

Storage coefficient .. 25, 36, 39, 41, 47, 49, 53 

Summary ------------------------------- 64

Swan Range ---------------------------- 4

Temperature ---------------------------- 4

Theoretical considerations --------------- 11

Thermal surveys ------------------------ 20

Transmissivity -------------------------- 36

Twin Creek ---------------------------- 3

Underground backwater -------------- 14, 40

Water available ------------------------ 98

Water budget ------------------------ SB, 64

change in reservoir contents -------- 88

comparison with theoretical solutions - 41

inflow ------------------------------ S6

modifications ------------------ 48, 46, 51

need for further study -------------- S3

outflow ----------------------------- SO

possible errors ---------------------- 47

residual __-_-__.---------.-.-------- 88

Water Management Subcommittee ------- 10

Water temperatures -------------------- 20

West Glacier -- .--.---------------------- 4

U.S. GOVERNMENT PRINTING OFFICE: 1971 0 410-120