LIBRARY COPY

DEPARTMENT OF THE INTERIOR 

UNITED STATES GEOLOGICAL SURVEY

GEORGE OTI8 SMITH, DIKECTOK

WATER-SUPPLY PAPER 337

THE EFFECTS OF ICE ON STREAM FLOW

BY

WILLIAM GLENN HOYT

WASHINGTON

GOVERNMENT PRINTING OFFICE 

1913

CONTENTS.

Page.

Introduction____________________________________ 7

Factors that modify winter run-off_______________________ 9

Classification_________________________________ 9

Climatic factors_______________________________ 9

Precipitation and temperature____________________ 9

Barometric pressure__________________________ 17

Chinook winds________________________________ 18

Geologic factors________________________________ 19

Topographic factors______________________________ 20

Natural storage_____________________________ 20

Location, size, and trend of drainage basins____________ 22

Character of streams_________________________ 22

Vegetational factors_____________________________. 23

Artificial control _________________________________ 23

Formation of ice______________________________^____ 24

General conditions ________________________________ 24

Surface ice __ __ __ ___________________ 24

Method of formation____________________________. 24

Length and severity of cold period__________________ 25

Temperature of affluents________________________'__ 26

Velocity of water and. character of bed_______________ 27

Fluctuations in stage__________________________ 27

Frazil______________________________________ 28

Anchor ice_____________________ __________ 29

Effect of ice on relation of stage to discharge_________ ______ 30

The control section _____________________________ 30

Surface ice __ __ _ __ ___ 31

General effects__________________-____________ 31

Effect on distribution of velocities in the vertical__________ 31

Gaging station studies____________ _________ ___ 32

Value of work_____________________________ 32

Elk River near Big Lake, Minn_____ _ _ 34

Crow Wing River at Pillager, Minn__^____- ________ 35

Red River near Grand Forks, N. Dak________________ 37

St. Mary River near Babb, Mont_____________ 38

Raquette River at Piercefield, N. Y__ _ 39

Frazil____________ 40

Anchor ice 42

General effects 42

Gaging station studies 42

Kootenai River at Libby, Mont 42

Schroon River at Riverbank, N. Y 48

3
4 CONTENTS.

Pagft

Computation of flow of frozen streams____________________ 4f

Methods available____________________________*___ 4F

First method _________________________________ 4?

Second method________________________________ 4£

Third method___________________________________ 5]

Eye method ________________________________.. 53

Graphic method_______._______-_______________ 52

Application of graphic method____________________ 5&

Field methods ___________________________________ 5T

Selection of stations_____________________________ 5T

Power-plant records____________________________ 59

Gages_______________________-_______________ 59

Climatologic records______ ___ _ __ _ _ 61

Discharge measurements___________________________ 62

Determination of section___ ________ ________ 62

Instruments ____ _ 63

Methods____________________________________ 64

Number and cost___ 67

Personal equipment of the engineer__ ____ 68

Ice notes______________ ____ _ _ _ 69

Office methods_____________________________________ 69

General features _ 69

Computations______________ ___-_______________ 70

Forms____________________ _ _ 71

Accuracy___________ 72

Discharge measurements 72

Gage heights__________ __ 1 73

Estimates of daily and monthly discharge 73

Index___^______________ 75
ILLUSTRATIONS.

Page.

?LATE I. A and Bf Winter measurements on Rum River near Cambridge, Minn ______________________________ 10 

II. Winter measurements: A, Vermilion River below Vermilion

Lake, Minn.; B, Bigfork River near Big Falls, Minn____ 20

III. Relation between open-water curve and ice measurements:

Red River at Grand Forks, Minn_________________ 38

IV. Diagrams showing relation between temperature, gage

heights, and discharge: Kootenai River at Libby, Mont__ 46 

V. Diagrams showing relation between temperature, gage heights,

and discharge: Schroon River at Riverbank, N. Y______ 48 

VI. Diagrams showing relation between gage heights, backwater,

and temperature: Rainy River at International Falls, Minn_ 52 

VII. A, Ice chisel, measuring stick, and bag; B, Winter measurement on Shoal Pond Brook, New Hampshire_________. 64

1. Diagram showing surface of ground-water table during the

period from fall to spring__________ ______ __ 10

2. Diagram comparing temperature and discharge: Mississippi

River above Crow Wing River, Minn______________ 12

3. Thermograph trace from Havre, Mont., January 22-26, 1907,

showing increase in temperature caused by a chinook___ 18

4. Map showing location of Bigfork, Littlefork, and Vermilion

rivers, Minn _____________ _______________ 21

5. Diagram showing relation between flow of Rainy River at

International Falls and stage in Rainy Lake _____ 23

6. Diagram showing a Average ice period from winter 1876-77 to

winter 1895-96 inclusive_______________________ 27

7. Diagram illustrating distribution of velocity under ice cover:

Cannon River at Welch, Minn__________________ 32

8. Typical cross section of ice-covered stream and rating curve

for same section _ ____ _ 33

9. Relation between open-water curve and ice measurements: 

- Elk River near Big Lake, Minn__________________ 35

10. Relation between open-water curve and ice measurements:

Crow Wing River at Pillager, Minn______________ 37

11. Relation between open-water curve and ice measurements:

St. Mary River near Babb, Mont_________________ 39

12. Relation between open-water curve and ice measurements:

Raquette River at Piercefield, N. Y _____________ 40

13. Cross section of Chemung River at Chemung, N. Y., showing

effect of frazil____________________________- 41

14. Gaging station on Kootenai River at Libby, Mont 43

15. Backwater curve and plotted fictitious discharge measurements for Rainy River at International Falls, Minn 50

16. Diagrams showing relation between temperature, backwater,

and discharge: Elk River near Big Lake, Minn 54

17. Diagram showing factors used in making discharge measurements and new form proposed 66

18. Proposed computation sheet 72

5

TIE EFFECTS OF ICE ON STREAM FLOW.

By WILLIAM GLENN HOYT.

INTRODUCTION.

The design, installation, and operation of any plant that depends 

for its success upon flowing water demands from those concerned a 

knowledge of the total flow of the stream and its variation throughout the year, including not only the mean flow but also the maxknum 

and minimum flow and the periods of their duration.

Stream-flow records extending over considerable periods are now 

available for many streams in the United States, and additional 

records are being obtained. For open-water periods methods for 

collecting stream-flow records have been standardized, the accuracy 

of such records has been established, and the laws of stream flow have 

been determined. On the other hand, during the winter the presence 

of ice affects the flow so much that the laws of flow pertaining to o<pen 

channels are not entirely applicable, and no standard methods for 

collecting and interpreting data have been recognized. In many 

localities ice persists in the streams for periods ranging from a few 

days to several months, and, although the conditions resulting from 

ice are most pronounced in northern regions, they are prevalent over 

wide areas, and especially at high altitudes. As the minimum flow 

the flow that determines the success or failure of most hydraulic 

works is most likely to occur during periods when the streams are 

ice-covered and temperatures are low, accurate information concerning this flow is essential.

The flow of streams is ascertained primarily by means of the law 

of relation between stage and discharge. For most parts of the 

United States this relation remains so nearly constant during periods 

when the stream channels are unobstructed that it can be expressed 

in rating tables based on occasional discharge measurements, the 

mean daily flow being determined by applying to the table the 

records of mean daily stage. During the winter months low temperatures give rise to conditions that frequently disturb the openwater relation between stage and discharge and make the proper 

interpretation of winter records exceedingly difficult.

7
8 THE EFFECTS OF ICE ON STREAM FLOW.

A report on winter stream flow and its measurement,1 published by 

the Survey in 1907, brought together the information available at 

that time and formulated for the first time certain laws that relate to 

the distribution of velocity under ice and have been found to be applicable under practically all observed conditions. Knowledge of 

these laws has been of great value in making winter measurements 

of flow. The report dealt mainly with field operations in making 

discharge measurements, however, and contained little information 

in regard to the use of these measurements in estimating discharge 

from daily gage-height records and data concerning ice.

Recent studies have added much information in regard to the factors influencing stream flow when ice is present, and especially in regard to the collection and interpretation of winter records. With a 

view to standardizing, so far as practicable, the methods for ascertaining winter flow, this paper presents the available information on 

the subject, discussing the factors that influence the run-off during 

the periods of low temperature, the varieties of ice and their effect on 

the applicability of the laws of open-channel flow, and the collection 

and interpretation of necessary data. Some of the conclusions derived from the study of these factors differ from those previously 

reached because many of the earlier studies were local, both in scope 

and application, whereas effort is here made to deal broadly with 

conditions whose occurrence is coextensive with ice and low temperatures.

The report is based on the experience of the author in Minnesota 

during the winters of 1911-12 and 1912-13, supplemented by observations in Montana by B. E. Jones under the direction of W. A. 

Lamb, in New York and New England under the direction of C. C. 

Covert, and in Alberta, Canada, by Messrs. F. H. Peters and P. M. 

Sauder. Acknowledgment is also due to W. O. Hartwell, E. F. 

Chandler, S. B. Soule, and B. J. Peterson for assistance in the work. 

Of the various publications which have been reviewed in connection 

with the preparation of the paper 2 special mention should be made 

of the following:

Ice formation, with special reference to anchor ice and frazil, by Howard 

T. Barnes. John Wiley & Sons, New York, 1906.

The flow of streams and factors that modify it, with special reference to 

Wisconsin conditions, by Daniel W. Mead: University of Wisconsin Bull. 425, 

1911.

The determination of stream flow during the frozen season, by H. K. Barrows and Robert E. Horton: U. S. Geol. Survey Water-Supply Paper 187, 1907.

1 Barrows, H. K., and Horton, R. E., Determination of stream flow during the frozen 

season: U. S. Geol. Survey Water-Supply Paper 187, 1907.

2 Since this paper was prepared the Commission of Conservation of Canada has published a report on Long Sault Rapids, St. Lawrence River, by A. V. White, with an 

appendix (No. 25) by Prof. H. T. Barnes, discussing the formation of surface ice, frazil, 

and anchor ice with special reference to conditions in the St. Lawrence.
FACTORS THAT MODIFY WINTER RUN-OFF. 9 

FACTORS THAT MODIFY WINTER RUN-OFF. 

CLASSIFICATION.

The quantity and distribution of winter stream flow are the results of the combination of factors that may be classified as climatic, 

geologic, topographic, and vegetational. The climatic factors are 

precipitation, temperature, barometric pressure, and winds; the 

geologic factors include surface and underground rock structure and 

texture; the topographic factors include relief and slope, which determine the character and amount of natural storage, the location, 

size, and trend of the drainage basin, and the character of the 

streams and their tributaries; the vegetational factors comprise not 

only forestation but the effects of all plant growth and cultivation. 

A fifth factor is the result of the artificial control of the streams for 

water supply or power.

CLIMATIC FACTORS. 

PRECIPITATION AND TEMPERATURE.

The climatic conditions that influence stream flow are probably 

more important than any others, but the conditions are so interrelated 

that it is difficult to distinguish the effect of one from that of another.

Stream flow during the winter is supplied by precipitation directly, 

in the form of rain or snow, and indirectly, from melting snow and 

from ground water.

Precipitation in the form of snow does not add perceptibly to the 

rim-off of an area until the local temperature rises above the freezing 

point. Rain falling on frozen ground not covered with snow will 

run off quickly at a rate depending on the slope, for the frozen surface acts nearly as effectively as a rock stratum in preventing absorption by the ground. Rain falling on snow gradually increases the 

water equivalent of the snow to the point of saturation, when it will 

run off. Heavy snow on ground whose surface is not frozen may 

melt slowly from beneath, sink into the ground, and thus augment 

the supply of ground water. The amount of water held in snow 

cover naturally varies with variations in altitude and temperature.1

At the end of the growing season, generally about the 1st of 

October in the northern part of the United States, the ground water 

has generally been depleted by the needs of plant growth and by 

high evaporation, and conditions probably vary less from year to

methods of measuring amount of water held in snow storage are described in 

Weather Bureau Bull. 445, Circular E, 1910; also in article by J. Cecil Alter entitled 

" Snow surveys for predicting stream flow" : Eng. News, vol. 69, pp. 111Q-1113, May 29, 

1913.
10 THE EFFECTS OF ICE ON STREAM FLOW.

year than at any other season.1 From this time until a period whose 

beginning ranges from the middle of November to the 1st of December the time depending on the year and locality the groundwater table will tend to rise, since practically no water is needed for 

plant growth and loss from evaporation rapidly decreases as temperature decreases. After the ground becomes frozen to any considerable depth little water will be added to that stored in the ground 

until the spring breakup, as any surface water tends to run off (see 

fig. 1). The flow during the winter season therefore depends to a 

large extent on the amount of ground water present at the beginning of winter, and this amount in turn depends on the precipitation 

during the preceding period of replenishment.

The close relation between temperature and winter flow is revealed 

by a study of the precipitation. Temperature influences the winter

run-off (1) by its

I I \ I 1 - "^ "*" s Frozen ground <

effect on surface 

and ground water, 

and (2) by its effect on the character of the precipitation.

When the temperature falls below the freezing 

point a certain amount of surface water is changed to ice, and with 

continued low temperature this ice will gradually increase in thickness 

to a depth depending on the length and severity of the cold wave. The 

water so frozen will be held until it is released by temperatures under 

which the ice will melt. If such higher temperatures are delayed until 

spring, the water from the melting ice will join the run-off from 

melting snow and light rain to augment the spring floods. The 

amount of water held in storage as ice in stream channels and in 

shallow ponds may be considerable, particularly on streams so situated that the natural run-off per square mile is low. For example, 

the low-water flow of Rum River, in Minnesota (PI. I), during 

January or February is about 70 second-feet. The river above the 

gaging station is approximately 100 miles long, its average width is 

about 100 feet, and its gradient is small. Ice forms over its entire 

surface in thicknesses ranging from 1^ to 2 feet. If in two months 

a 2-foot ice cover is formed, approximately 80,000,000 cubic feet of 

water will be stored as ice, an amount equal to about 15 second-feet 

flow, or about 21 per cent of the low-water flow of the river at the 

gaging section for these two months.

1 Hoyt, John C., Comparison between rainfall and run-off in the northeastern United 

States: Am. Soc. Civil Eng. Trans., vol. 59, p. 43, May, 1907.

FIGUBE 1. Diagram showing position of ground-water 

table during period from fall to spring.
U, 6. GEOLOGICAL SURVEY WATER-SUPPLY PAPER 337 PLATE I

A.

WINTER MEASUREMENTS ON RUM RIVER NEAR CAMBRIDGE, MINN.

FACTOES THAT MODIFY WINTEE ETJN-OFF. 11

<

Hae -freezing of the water also temporarily affects stream flow by 

suddenly increasing friction and thus causing the flow at a given 

cross section to decrease until the winter regimen has been established. 

At the beginning of each cold period, therefore, stream flow will 

drop suddenly, but will increase to some extent later.

Low temperature affects the run-off derived from ground wat$£ 

by affecting the rate of movement above the freezing point, the rat® 

at which water at a temperature of 32° F. flows through sand being 

about 64 per cent of its rate at a temperature of 60° F.1 The depth 

to which the ground will freeze ranges from 1 to 5 feet or more, 

depending on the character of soil, the vegetal covering, and the 

length and seTerity of the cold period. Early snows may form a 

cover that will protect the ground from freezing even under the 

influence of later low temperatures, and the condition of the ground 

whether frozen or not should be considered in all studies of the 

problem. The water contained within this zone is held in storage 

until it is released by higher temperatures.

Whether freezing of the ground water or obstruction of the channel 

by ice is more effective in causing decrease in discharge at the beginning of a cold period depends largely on the character of the drainage basin. In steep, mountainous areas, where a thin soil rests on 

solid rock, extreme cold will freeze the ground nearly to the rock 

and will cause a large decrease in ground flow; but streams draining 

such areas have, as a rule, narrow channels and considerable fall, so 

that obstructions due to ice hold back a comparatively small amount 

of water. In a rolling country, where the surface deposits consist of 

heavy sand or soil and where a large amount of water is in storage 

below the frost line, freezing affects only a small proportion of the 

stored water; but the streams in such regions usually are characterized by small slope and large cross section, so that obstructions due 

to ice will form a considerable check to the flow and may hold back 

large quantities of water in storage. In very flat valleys both these 

causes are operative, for the zone of freezing may extend below the 

bed of the streams, stopping all underground supply, and most of the 

surface flow may be held back by the large amount of ice that forms 

on the sluggish streams draining these valleys. Streams draining 

comparatively large basins consisting of flat valleys up to 2,000 

square miles in extent may, under such conditions, cease to flow; 

whereas during the summer, even in periods of low precipitation, 

they would be fed by ground water.

As already stated, freezing temperatures indirectly affect ground 

water by converting the surface into an impervious stratum that 

prevents downward percolation of surface water.

' 'Slicbter, C. &., Field measurements of the rate of 'movement rof underground water: 

U. S. Geol. Survey Water-Supply Paper 140, p. 13, 1905. '
12 THE EFFECTS OF ICE ON STEEAM FLOW.

Rising temperatures tend to increase run-off even if the rise does 

not extend above 32° F., doubtless because it releases considerable 

ground water. Winter temperatures above 32° F. add to run-off by 

melting ice and snow.

The diagrams comparing daily flow and temperature for Mississippi Eiver above the mouth of Crow Wing Eiver (fig. 2) and 

Kootenai Eiver near Libby, Mont. (PI. IV, p. 46), graphically 

exhibit the relations.

The daily discharge of the Mississippi above the mouth of Crow Wing 

was determined by the Corps of Engineers, United States Army, from

30'

uT 20' 

a:

3,000

o 2,000 

o

ce 1,000

Nov.,1896 V Dec,l896

Mean te nperature o

V

c feet per a :con<j

JanJ897 ' Feb,l897

'basin averaged in five i lay periods

Nov.,1896 Dec,,l896 Jan.,1897 Feb.,1897

Mar,l897

Man, 1897

30?

'10'.

FIGURE 2. Diagram comparing dally flow and temperature : Mississippi River above mouth

of Crow Wing River, Minn.

discharge measurements made almost daily throughout the period. 

The temperature is the mean temperature for the basin, averaged in 

5-day periods. The slope of the main river and its tributaries is 

small and the many lakes and swamps above the stations tend to 

regulate the flow. These conditions are apparently less.favorable to 

close correspondence between run-off and temperature than they 

would be on a stream having less lake and swamp storage. Nevertheless, the diagram shows a decrease in flow, amounting to 1,800 

second-feet during the month of November, coincident with a drop 

in mean temperature from 31° F. to 5° F. Part of this flow was regained with the rise in temperature the early part of December, but
FACTORS THAT MODIFY WINTER RUN-OFF. 13

with the drop in temperature in the middle of December the run-off 

again decreased; increase accompanied the small temperature rise at 

the end of the month. The slight increase in temperature in the 

middle of January did not increase the flow, but it retarded the decrease that began with the first drop in temperature on January 1, 

and reached a minimum a short time after the minimum temperature. 

It will be noticed that the stream flow increased immediately with 

the increase in temperature in the latter part of January, even though 

the temperature was still below freezing. The minimum flow for the 

winter was reached soon after the date of minimum temperature in 

February.

Kootenai River above Libby, Mont., drains a mountainous area on 

the western slope of the Eocky Mountains in British Columbia. As 

the basin contains many heavily forested areas ground storage during 

the open season is large, and on the higher areas, where precipitation 

is heavy, is at its maximum. It would seem therefore that the flow 

during the closed season would depend more largely on temperature 

than on fluctuations in the annual precipitation.

The diagram forming Plate IV (p. 46) shows the curves of maximum and minimum temperature, for the winter of 1912-13, the 

observed gage heights both/ before and after being corrected for 

anchor and surface ice, and the discharge determined from the corrected gage heights. It clearly exhibits general close relation between run-off and temperature. The drop in temperature that began 

January 4 and reached a minimum January 7 was accompanied by 

decrease in run-off from 3,000 second-feet on the 5th to 2,100 secondfeet on the 7th. The succeeding rise in temperature caused the runoff to increase gradually to 3,000 second-feet on January 16. The 

fluctuation of run-off with changes in temperature during the month 

of February is also clearly shown. The minimum discharge, 2,080 

second-feet, occurred February 10, about two days after the minimum 

temperature. After that date the flow gradually increased with rise 

in temperature until it reached 4,140 second-feet on February 19, 

about three days after the date of maximum temperature. The subsequent drop in temperature was accompanied by decrease in run-off. 

Increase in flow is noticeable February 10, although the temperature 

did not reach 32° F. until the 12th. This increase was undoubtedly 

caused by the releasing of stored ground water as a result of the 

higher temperature.

The effect of temperature and precipitation on stream discharge is 

also shown by the following table, which gives the results of a study 

of Minnesota streams.
Relation between minimum run-off of Minnesota streams ancl precipitation in the drainage basins 

and 1912-13.

Hudson Bay drainage basin.

River.

Ottertail.. ...............

Do..................

Littlefork.... ...........

Station.

Littlefork ...................

Big Falls......... ...........

Drainage 

area, 

square 

miles.

1,310 

433 

805 

3,450 

5,320 

1,310 

1,720 

1,320 

507

Precipitation, April to July.

Normal.

13.70 

13.70 

13.25 

13.50 

13.08 

11.18 

14.35 

14.23 

14.70

1910

6.06 

6.06 

5.56 

5.50 

5.46 

5.43 

7.90 

7.49 

8.30

Difference.

- 7.64 

- 7.64 

- 7.69 

-8-00 

- 7.62 

- 5.75 

-6.45 

- 6.74 

- 6.40

Per

cent.

0.44 

.44 

.42 

.41 

.42 

.49 

.55 

.53 

.56

Discharge, 

1910, 

July 

or 

August.

32.6 

5.6 

21 

236 

293 

35.7 

88.4 

65.3

Precipitation

to Dece

Normal.

5.92 

5.92 

6.59 

6.50 

6.41 

5.53 

7.72 

6-38 

8.20

1911

6.28 

6.20 

5.32 

5.10 

5.05 

5.43 

4.84 

4.88 

7.30

Lake Superior drainage basin.

Cloquet..................

120

3,420

698

14.05 9.54 - 4.51 .68 549

295

7.53 7.54 
llississippl River drainage basin.

MississiDDi

Do..................

Do..................

Elk......................

Do..................

Do...................

St. Paul.....................

Big Lake....................

Welch.......................

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

4,510

17,100

35,700 

3,230

815

615

2,520

1,160

1,560

6,300

14,600

1,940

1,190

825

422

1,290

1,120

821

1,560

647

425

13.97

13.13

13.22 

13.97

13.02

13.98

12.85

13.98

12.79

13.05

13.51

13.51

13.93

14.50

14.04

14.06

14.61

15.44

15.44

15.43

7.94

7.15

7.15 

7.00

6.64

6.70

6.66

6.70

5.49

8.35

7.71

8.01

9.21

7.00

6.34

5.06

4.54

4.65

4.65

5.25

-6.03

- 5.98

- 6.07 

- 6.97

 6.38

- 7.28

- 6.19

- 7.28

- 7.30

- 4.70

- 5.80

- 5.50

- 4.72

- 7.50

- 7.70

- 9.00

-10.07

-10. 79

-10. 79

-10.18

.57

.54

.54 

.50

.51

.48

.52

.48

.43

.64

.56

.59

.66

.48

.45

.36

.31

.30

.30

.34

1,915

3,390 

3,850 

283

42.6

58. 5

84.2

16.5

72.5

253

12

9.3

71.1

37.5

124

157

322

134

49.5

7.20

6.28

6.27 

6.14

6.00

6.53

7.21

6.53

5.25

5.54

5.66

5.44

5.86

9.27

8.82

8.04

7.68

7.68

8.29

8.29

7.87

5.68

7.26

9.23 

7.05

7.99

8.89

11.04

8-89

9.67

9.94

10.56

8.69

12.63

10.09

10.50

14.65

15.32

15.32

15.88

15.88

15.84
16 THE EFFECTS OF ICE ON STREAM FLOW.

In the slimmer of 1910 most of the streams in Minnesota reached 

a stage that was probably nearly as low as the lowest open-water 

stage of 1864, which has local reputation as the minimum stage.1 

The cause of the low open-water flow of 1910 becomes evident when 

the normal precipitation for the four months preceding the period 

of low flow is compared with the actual precipitation during the 

same months in 1910. The table shows deficiency in precipitation 

ranging from 5.5 inches in the western and northwestern sections to 

more than 10 inches in the southern and southeastern parts of the 

State that is, precipitation ranging from 30 per cent to 60 per cent 

of normal.

In January and February, 1912,2 notwithstanding the fact that, 

except over the Red River basin, the precipitation for the preceding 

months from September to December was equal to or exceeded the 

normal, the same streams reached a stage which in general was below 

that of the open-season flow in 1910. The table shows the normal 

precipitation from September to December inclusive 3 the four 

months that would ordinarily supply the flow from ground water 

during the winter and the actual precipitation from September 

to December, 1911, the period of replenishment for the ground 

water supplying the low-water flow of January and February, 

1912. In general, the figures indicate precipitation considerably 

above normal. The explanation of the conditions is found by 

considering temperature records. The 50 days from December 25, 

1911, to February 12, 1912, were the coldest that have been 

recorded by the United States Weather Bureau for the State of 

Minnesota. At Crookston, in the northwestern part of the State, the 

temperature fell below zero for 49 days out of the 50, and on January 

11, 1912, reached 39° F. The maximum temperature was below 

zero for 21 days and the highest recorded during the period was 24°, 

on January 31 and February 12. At St. Paul, the temperature for 

the same period fell below zero 34 days, the minimum being 30° F. 

on January 12. The conditions at Crookston and St. Paul were 

typical of those prevailing throughout the State. Probably nowhere 

in the State was the maximum temperature much if any above freezing during the entire period. The low flow of 1912 was therefore 

due not to lack of precipitation, but to the length and severity of 

the cold wave, which stopped all run-off except from ground water 

and undoubtedly retarded to a considerable extent the flow of the 

ground water.

1 Follansbee, Robert, Variability of run-oft of Minnesota streams during the low-water 

flow of 1910: Eng. News, vol. 65, pp. 536-538, May 4, 1911.

a Hoyt, W. G., Gaging Minnesota streams in winter: Eng. News, vol. 68, pp. 499-502, 

Sept. 12, 1912.

s These limits do not apply exactly to all parts of the State, because of differences 

resulting from latitude.
FACTORS THAT MODIFY WINTER RUN-OFF. 17

The table gives also the run-off record for the winter of 1912-13, 

in which the low flow was about the same as in 1912, though probably 

due to different conditions. The precipitation from September to 

December, 1912, preceding the period of low flow in January and 

February, 1913, was considerably below the normal for that period. 

During the winter of 1912-13 temperatures were normal or somewhat above and the flow from the ground water was probably little 

affected by low temperature.

The table therefore comprises records for a period (in 1910) of 

low open-season flow caused by a lack of precipitation, a period (in

1912) of low winter flow caused by low temperatures following a 

season in which precipitation was above normal, and a period (in

1913) of low winter flow caused by a lack of autumn precipitation, 

the winter temperature being normal. None of the low flows recorded in the table should be accepted as the absolute minimum that 

may be expected, because the available records do not cover a period 

of extremely low temperature preceded by a period of deficient 

precipitation. Although the low flow in 1910 might have been lower 

than any open-water flow recorded between 1864 and 1910, it was 

not of necessity lower than any closed-season flow within that period, 

since careful stream-gaging work during the winters of 1911-12 and 

1912-13 gave results lower in general than were recorded during 

1910. The years from 1864 to 1910 probably included more than 

one period of low precipitation during the fall followed by prolonged low temperature, causing a lower rate of flow than any that 

has been recorded, but unfortunately no extensive winter measurements were made until 1911-12. The conditions on the Minnesota 

streams, illustrated by the table, are typical of those on streams 

whose winter flow is affected by ice.

BAROMETRIC PRESSURE.

Changes in barometric pressure cause changes in the position of 

the ground-water table and therefore a change in the amount of 

ground water that reaches the rivers. Observations made by 

Baldwin Latham 1 in 1881 in England, by Otto Lueger 2 in Germany, 

and by F. H. King 3 in America, show a variation in the flow of 

springs with changes in barometric pressure. In explanation of 

these changes Slichter 4 says:

The phenomenon is usually explained by the expansibility of the air confined 

in the porous medium in the neighborhood of the ground water and of the air

1 Brit. Assoc. Adv. Sci. reports, p. 614, 1881, p. 495, 1883.

2 Binfluss des Atmospharendrucks auf die Ergiebigkeit von Brunnen: Centralblatt d. 

Bauverw., p. 8, 1882.

8 U. S. Dept. Agr. Weather Bull. No. 5, p. 50, 1892.

* Slichter, C. S., The motions of underground waters: U. S. Geol. Survey Water-Supply 

Paper 67, p. 72, 1902.

17020° WSP 337 13 2
18 THE EFFECTS OF ICE ON STREAM FLOW.

dissolved in the ground water itself. Even the air in the soil above the water 

table meets more or less resistance to its escape when the barometer falls 

and consequently a differential pressure must exist over the surface of the 

water table and the surface exposed at the well or spring.

A change of an inch in the height of the barometer corresponds to a change 

in pressure of about 1 foot of water. It is evident that such a differential pressure exerted over the surface of the water table is sufficient to materially affect 

the flow into wells and springs.

The effect of barometric pressure on winter run-off has not beei 

investigated, but during periods of low temperature there is in general a high barometric pressure which doubtless tends to decrease 

run off.

CHINOOK WINDS.

In Alberta, Canada, and in portions of Montana and Wyoming, a 

wind called the " chinook " plays a very important part in the rate of 

winter run-off. Chinooks are more or less periodic and come from 

the west and southwest across the Rocky Mountains. As a rule, they

E 

°o

°o

TUR

1

MP

I

Jan.22 January 23

N9on

January 24 January 25

3. Thermograph trace from Havre, Mont, January 22-26, 1907, showing increase in temperature caused by a " chinook."

follow an area of low pressure across the Canadian Rockies and cause 

heavy rain or snow on the west side and dry, hot winds on the east 

side. During a chinook the temperature will rise 30° to 50° (fig. 3) 

in a few hours i and the snow will melt rapidly.

The resulting rapid increase in discharge, occurring when the 

streams are ice bound and not able to carry an added run-off, gives 

rise to serious complications in the methods of measuring. Besides 

the effect of such winds on the snow they may also tend to increase

1 Moore, Willis B., Descriptive meteorology, pp. 186-187, D. Appleton & Co., New York, 

1910.
FACTOES THAT MODIFY WINTER RUN-OFF. 19

the flow from springs as a result of the accompanying decrease in 

pressure.

The increase in temperature caused by chinook winds is shown by 

the following table, giving data for Bow Kiver at Banff for January. 

1912, contributed by Mr. G. H. Whyte, first assistant hydrographer 

in the office of the Commissioner of Irrigation, Calgary. In forwarding this record Mr. Whyte said that the most noticeable chinook of 

the period (Jan. 1-31) took place January 13, when the observer reported the weather cloudy, a drop in temperature of 26° in three 

hours in the afternoon and a rise of many degrees by 8 p. m. The 

chinook struck Calgary about 6 o'clock on the evening of the 14th.

Daily gage height and temperature of Bow River at Banff, Alberta, for 1912. 

[N. B. Sanson, observer: V. A. Newhall, hydrographer.]

Day.

1... .................................

2....................................

3....................................

4....................................

5....................................

6....................................

7....................................

8....................................

9

10....................................

11....................................

12. ...................................

13....................................

14....................................

15....................................

16....................................

17....................................

18....................................

19....................................

20....................................

21....................................

22....................................

23....................................

24....................................

25....................................

26....................................

27....................................

28....................................

29....................................

30....................................

31....................................

January.

Gage 

height 

(water).

Feet. 

1.72 

1.76 

2.31 

2.15 

1.75

1.95

1.96 

2.20 

2.42

2.20 

1.99 

2.00 

2.00

2.03

1.75 

2.12 

2.35 

2.12 

2.12

2.00

1.96 

1.94 

1.78 

1.71

2.02 

1.95 

1.75

1.55 

1.40 

1.34

Thickness of 

ice.

Feet. 

1.1 

.9

1 

1

1

1.1 

1.5

1.9 

1.2 

1.15

.8 

.8 

.8 

.9 

.95

.95 

.95 

1 

1

1

1

.97 

.97

Gage 

height 

(ice).

Feet. 

1.76 

1.75 

2.32 

2.30 

1.93

1.9

1.95 

2.1 

2.2

2.4 

2.3 

2.1

Open.

Open. 

2.26 

2.3 

2.37 

2.19

2.2 

1.98 

1.78

1.9

Open. 

2.13

Open. 

Open.

Discharge, estimated.

Sec.-ft. 

284 

285 

286 

282 

280

282 

283 

284 

286 

290

294 

292 

' 307 

313 

314

303 

312 

317 

309 

303

298 

295 

291 

286 

280

282 

280 

278 

273 

270 

270

Temperature.

Maximum.

7.7 

4.5 

10.4 

4.8 

5.0

- 1.0 

15.3 

15.2 

- 2.0

-18.8

12.2 

23.2 

35.8 

44.6 

45.0

37.0 

20.2 

14.1 

12.2 

22.6

35.0 

33.0 

28.0 

31.0 

39.4

37.2 

32.1 

31.8 

42.0 

38.4 

32.0

Minimum.

-n.'o

 25.2 

- 6.0 

- 8.2 

3.2

-31.6 

-18.4

- 8.8 

-23.6 

-28.8

-37.6 

7.2 

5.8 

1.4 

34.6

19.7 

- 4.7 

-16.0 

- 2.8 

1.1

18.5 

16.2 

11.3 

13.0 

28.1

11.8 

15.2 

12.5 

26.3 

30.7 

9.2

Measured.

Gage 

height.

Feet.

1.78

2.03

2.08

Discharge.

Sec.-ft. 

286

314.8

284

GEOLOGIC FACTORS.

The amount of water held in storage in the ground at the beginning of the winter depends largely on the character of the material 

at and beneath the surface. In areas in which rocks lie at or near 

the surface nearly all the precipitation quickly reaches the streams 

and the ground will hold little water to aid in maintaining the flow 

when the surface water is diminished or exhausted. Unconsolidated
20 THE EFFECTS OF ICE ON STEEAM FLOW.

materials collect and hold the water, the amount so held depending 

on the depth and nature of the surface material and the structure 

of the underlying rocks. Low temperature will congeal the water 

in the layers above the frost line so as to render them of little value 

as a source of supply during the winter. Other geologic conditions 

affect stream flow during the winter as in the summer.

TOPOGRAPHIC FACTORS.

NATURAL STORAGE.

The effect of topography on winter stream flow is of minor importance except as it influences the ground storage, a rolling or 

mountainous country affording a greater reservoir for ground water 

available for the streams than one which is so flat that the groundwater table lies in general below the level of the stream channels.

Other conditions being similar, the greater the extent of natural 

storage on a drainage basin the larger will be the winter flow.

The water stored in swamps and lakes may increase winter stream 

flow to a greater extent than it adds to the low flow of the open 

season, for evaporation from lakes and swamps during the autumn 

replenishing period is small and their water level rises, whereas during the summer loss from evaporation may exceed gain from precipitation, and their effect may be positively detrimental.

The effect of topography and natural storage on winter run-off is 

well illustrated by three streams in northern Minnesota Bigfork, 

Littlefork, and Vermilion rivers on which conditions have been 

studied. The position of these rivers is shown in figure 4.

Bigfork River rises in Itasca County and flows northward across 

Koochiching County to its junction with Rainy River.

The surface formation of the entire drainage basin is glacial drift 

so thick that rock outcrops are found only in a few places along the 

river. The basin is very flat and is so poorly drained that except in 

a comparatively narrow strip along the river it is swampy. Below 

the outlet of Lake Wabatwangang it contains practically no lakes; 

above that point about 15 per cent of the area is water surface. The

i -cj-u u A/wiAn/i highest elev. lowest elevA slope of the basin is 0.00102 ( slopes -^ . 

V V area / 

Littlefork River, which enters Rainy River a few miles east of the 

mouth of the Bigfork, meanders through a narrow, flat, wooded valley, in which there are few clearings. The surface formation is blue 

till and is underlain by crystalline rocks. There is less swamp land 

in this basin than in the basin of the Bigfork, and the mean slope is 

0.00152.

Vermilion River, which enters Rainy River through Little Vermilion Lake, is the outlet of Vermilion Lake, an extremely irregular

mean
U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER 337 PLATE II

A. VERMILION RIVER BELOW VERMILION LAKE, MINN B. BIGFORK RIVER NEAR BIG FALLS, MINN.

WINTER MEASUREMENTS.

FACTORS THAT MODIFY WINTEE RUN-OFF. 21

water body covering an area of 71 square miles. Tributary to Vermilion Lake and at a somewhat higher elevation is Trout Lake, which 

covers an area of 11 square miles. North of Vermilion Lake the 

basin embraces a region of light drift or bare rock and the topography is rugged; south of the lake is a much smoother region that 

is covered with glacial drift in which gravel predominates, and that 

gradually slopes to the Mesabi range. The mean slope of the basin 

is 0.0043.

FIGURE 4. Map showing location of Bigfork, Littlefork, and Vermilion rivers, Minn.

The rainfall and run-off from the three areas are compared in the 

following table:

Comparison of rainfall and run-off in basins drained by Bigfork, Littlefork, and

Vermilion rivers, Minn.

Run-off (second-feet per square mile), 1912:

Run-off (second-feet per square mile), 1913:

Bigfork.

4.84

.023

.023

.026

Littlefork.

4.88

.049

.044

.041

6.75

.048

.034

.049

Vermilion.

7.30

.250

.231

.188

5.91

.198

.198

.198
22 THE EFFECTS OF ICE ON" STREAM FLOW.

The table shows clearly the effect of lakes and swamps in aiding 

winter flow. From the Vermilion basin, having large lake storage, 

the flow was nearly five times as great as from the swampy areas 

drained by the Bigfork and the Littlefork. The Littlefork, with a 

slightly greater slope and less swamp area, had a low-water flow 

nearly twice as large as that of the Bigfork. This relation held not 

only in the winter of 1911-12, following a season in which precipitation on the basin of the Vermilion had been greater than that on 

the basins of the Bigfork and Littlefork but also in the winter of 

1913, which followed a replenishing period of relatively low precipitation on the Vermilion basin.

LOCATION, SIZE, AND TREND OF BASINS.

The altitude and latitude of drainage basins also affect the winter 

flow of the streams. Streams in California, Washington, Oregon, 

and in general south of about 37° latitude, except possibly those of 

northern New Mexico, Arizona, and the Rocky Mountain district, are 

not affected to any important extent by low temperatures except in 

the parts of the basins at high altitudes. Streams having their 

sources or parts of their basins in regions where low temperatures 

occur are so affected. Southward-flowing streams are less subject to 

floods caused by ice breakups than are streams flowing northward. 

On Red River of the North annual floods are caused by jamming of 

ice in the northern stretches as a result of the opening of the 

southern sections first. Chandler says: 1

The water held as ice or snow is released by the spring thaws in the warmer 

southern portion of the valley several days or weeks before the spring warmth 

reaches the northern portion of the valley. Thus the snow water from the faraway southern boundaries and from the near-by districts reaches the lower river 

almost on the same day, and the flow surpasses the capacity of the channel. If 

the same amount of water were released over the whole valley in a single day 

(as is the case if there is a heavy and widespread storm in summer), the water 

from the nearest portions of the valley would reach the mouth of the river 

many days before that from the upper valley and the rise would be less in 

height because extended through a longer time. Second, the spring flood usually 

arrives at each section of the river channel before the ice has entirely thawed 

there. It is partially dammed by the heavy ice still remaining from the February thickness of 2 or 3 feet and is forced to rise higher than would be the result 

if the same quantity of water should enter the river in late spring or summer 

when the channel is entirely clear.

 It can also be noted that the rise of each flood, at any season, is commonly 

more rapid than its fall in height; this is a usual characteristic of other rivers.

CHARACTER OF STREAMS.

Streams whose gradients are steep flow so swiftly that surface ice 

will not form to any important extent, and a correspondingly small

1 Chandler, Elwyn F., The Red River of the North : Univ. North Dakota Quart. Jour., 

vol. 1, p. 236, April, 1911.
FACTORS THAT MODIFY WINTER RUN-OFF. 23

amount of water will be held in ice storage. On the other hand, 

streams of small slope may be so icebound that a considerable part 

of their flow is held as ice during the winter, a condition typified 

by Kum Kiver in Minnesota. (See p. 10.)

VEGETATIONAL FACTORS.

Heavy evergreen timber and underbrush, under which snow may 

collect, may have a detrimental effect on the winter flow because the 

snow will not receive the direct rays of the sun and will not thaw so 

rapidly as in the open. Such a vegetal cover, however, tends also to 

protect the ground from freezing, so that the augmented supply from 

ground water may offset the loss due to slow melting of the snow.

ARTIFICIAL CONTROL.

The artificial control of streams for power development, for 

navigation, for flood prevention, and for log driving presents a 

conflict of interests. Eeservoirs used for power development only 

will, if possible, be so regulated tha-t they will contain a large amount

4

5,000

4,000

Nov., 1911

-Stage in Rainy Lake

monthly flow of R? iny River 

at International Falls, Minnesota

Dec.,1911 Jan.,l9IZ Feb.,l9IZ Mar.,l9ia

FIGURE 5. Diagram showing relation between flow of Rainy River at International Falls

and stage in Rainy Lake.

of water at the beginning of the winter and will be empty at the 

beginning of the spring break up. Reservoirs used in the interests 

of navigation will, as a rule, be closed during the winter, only the 

normal low-water flow being released. During open winters reservoirs so regulated may have a detrimental effect on the winter 

flow. The same may be said of reservoirs for flood prevention only.
24 THE EFFECTS OF ICE ON STREAM FLOW.

Reservoirs used to store water for logging operations can, as a rule, 

be used to benefit winter flow if the log-driving season ends in time 

to allow the reservoirs to be filled. In general, the gates of logging 

dams are kept open during the winter, so that, even though they are 

not used for storage, the natural flow will pass through. In general^ 

therefore, the only reservoirs that will have a detrimental effect on 

winter flow are those at which not more than the normal low-water 

flow is released.

The effect of artificial control on winter run-off is illustrated by the 

diagram (fig. 5), showing the relation between stage in Rainy Lake 

and the flow of Rainy River at International Falls, Minn., from 

November 1, 1911, to March 31, 1912. The stage of water in Rainy 

Lake is controlled by a dam at International Falls. The area of 

Rainy Lake is approximately 310 square miles, which, with a range 

in stage of somewhat over 8 feet, provides for storing about 69 billion cubic feet. The storage is used entirely for power. It will be 

noticed that the elevation of the lake is kept as high as possible until 

the beginning of the winter, and is drawn on as soon as the natural 

flow of the river begins to decrease as a result of low. temperatures.

FORMATION OF ICE.

GENERAL CONDITIONS.

Water cooled to 32° F. tends to crystallize, but the formation of 

ice on flowing streams is attended by complications that make it impossible to formulate rules to determine the amount. These complications so greatly affect the character and extent of the ice formed 

that a study of the various factors is essential to a study of records 

of winter run-off. The manner in which ice is formed and the character of the ice depend on the method of heat transmission and on 

local conditions which determine its existence as (1) surface ice, (2) 

frazil and slush ice, or (3) anchor ice.

SURFACE ICE.

Metlwd of foi*mation. As a sheet of water is cooled by contact 

with the air the upper layer is first affected and becoming heavier 

than the water beneath it, sinks to the bottom, and is replaced by a 

warmer water from below. The cooler layers continue to sink until 

the water body is cooled to 39.1° F., at which temperature the water 

attains its maximum density. As the temperature of the water drops 

below this point, the surface layer becomes cooler until it reaches 32° 

F., when freezing starts and ice is formed. The ice begins to form on 

the shore or at the edge of bodies projecting above the water and 

gradually increases in extent and thickness. To the transmission of 

heat by convection is due the fact that ice generally spreads from the
FORMATION OF ICE. 25

sides to the center, as the warmer air currents rise from the water 

and cooler air comes in from the sides so that the water is in contact 

with cooler air along the edge than at the center.

Ice does not form so quickly nor to so great thickness on running as 

on quiet water, partly because the agitation of the water tends tobreak off the small crystals as fast as they are formed and also because there will be more or less vertical motion of the water, causing 

the warmer bottom layers to mix with the cooler layer lying directly 

under the ice, thereby raising its temperature somewhat. When 

surface ice has formed convection of air currents from water surface 

ceases and there is little radiation, especially if the ice is thick or is 

covered with snow. Heat is, however, conducted from the water 

beneath through the ice to the air above, thus causing the ice to 

thicken. As ice is a very poor conductor of heat the ice thickens 

from beneath very slowly, but thickness may be added by the gradual 

accumulation on the surface of frozen precipitation.

The following mathematical formula 1 for computing the rate of 

ice formation on still water, based on the formation by heat conduction only, has been advanced by Prof. Howard T. Barnes, of McGill 

University:

, t=L8E -m

where

t is the time in seconds for the ice sheet to attain a thickness

of E centimeters; 

L is the heat of fusion, 80 calories ;

5 is the density of ice, 0.9166;

K is the conductivity of ice, 0.0057 calorie per degree difference 

of temperature per square centimeter per second;

6 is the difference in temperature, centigrade, between the underside of the ice sheet, 0°, and the air temperature. (Equivalent 

simply to the air temperature.)

The amount of ice that will form on a given section of a flowingstream will be determined by (1) the length and severity of the cold 

period; (2) the relative amount of the discharge received from lakes, 

ground -water, factory waste, etc.; (3) the velocity of water and 

character of bed; and (4) fluctuations in stage, both natural and 

artificial.

Length and severity of cold period. The rate of growth of sheet 

ice formed on still water when the surface of the ice is free from 

snow is shown in the following table, which is based on the table 

prepared by Prof. Barnes. 2

1 Barnes, Howard T., Ice formation, p. 102.

2 Idem, p. 103.
26 THE EFFECTS OF ICE ON STREAM FLOW.

Rate of growth of sheet ice.

Thickness 

of ice sheet, 

inches.

1........ . .

6............

10............

12............

24............

36............

Temperature.

+14° F. -4*F.

4 days........

-22° F.

2idays.......

21 days.......

-40C F.

31 minutes. 

12 hours. 

1 day. 

2 days. 

7 days. 

16 days.

For ice covered with snow the above table would have to be changed 

by unknown amounts.

A report of the United States Deep Waterways Commission x 

gives the information in the following table and in figure 6 concerning the duration of ice on ice-bound streams of the United States:

Duration of ice at points in the United States.

Location.

Albany, N.Y. ............................

Cairo, 111. (Ohio)..........................

Grand Forks, N. Dak. . ...................

Morris, 111 .................................

Peoria, 111 .................................

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

Pittsburgh, Pa.. ..........................

St. Paul, Minn. ...........................

Sioux City, Iowa.........................

St. Charles, Mo.. ..........................

Whitehall, N. Y....... ........ ...

Latitude 

north.

42 39 

46 29 

37 00 

37 00 

38 21 

39 06 

41 30 

40 61 

42 30 

48 02 

45 46 

47 55 

41 45 

39 05 

40 22 

43 49 

44 08 

45 31 

46 52 

41 21 

40 40 

40 41 

44 24 

40 32 

43 08 

44 58 

42 29 

38 46 

43 34 

39 59

Longitude 

west.

73 45 

94 10 

89 10 

89 10 

81 35 

84 30 

90 38 

91 25 

90 44 

104 01 

107 48 

97 01 

72 39 

94 37 

91 26 

91 15 

94 00 

73 33 

96 44 

88 25 

95 51 

89 37 

100 17 

80 02 

77 42 

93 03 

96 24 

94 05 

73 24 

82 00

Altitude 

above 

sea level.

Feet. 

1.30 

1,150 

279 

279 

1,619 

431 

541 

500 

585 

1,855 

2,727 

784 

0 

716 

477 

628 

756 

23 

866 

480 

907 

432 

1,426 

699 

508 

683 

1,066 

416 

95 

678

Winter 1876-77 to winter 

1895-96, inclusive.

Average dates.

Closing.

Dec. 22 

Nov. 20 

Jan. 9 

Jan. 21 

Jan. 12 

Jan. 15 

Dec. 13 

Jan. 3 

Nov. 27 

Nov. 10 

Dec. 9 

Nov. 8 

Dec. 17 

Dec. 25 

Jan. 8 

Dec. 7 

Nov. 29 

Dec. 10 

Nov. 17 

Jan. 9 

Dec. 21 

Dec. 21 

Nov. 22 

Jan. 27 

Dec. 13 

Nov. 24 

Dec. 17 

Jan. 12 

Dec. 25 

Jan. 3

Opening.

Mar. 26 

Apr. 17 

Feb. 4 

Jan. 29 

Jan. 20 

Jan. 26 

Mar. 19 

Feb. 23 

Mar. 18 

Apr. 9 

Mar. 18 

Apr. 15 

Mar. 7 

Feb. 1 

Feb. 26 

Mar. 24 

Apr. 5 

Apr. 19 

Apr. 17 

Feb. 28 

Mar. 1 

Feb. 28 

Apr. 2 

Jan. 29 

Apr. 6 

Apr. 12 

Mar. 17 

Jan. 31 

Apr. 6 

Feb. 25

Number

of days 

closed.

94 

149 

26 

8 

8 

11 

96 

48 

111 

150 

99 

153 

80 

38 

49 

107 

127 

130 

150 

50 

70 

60 

131 

2 

114 

139 

90 

19 

102 

53

The report shows a maximum average duration of 158 days of ice 

on Eed River of the North at Grand Forks, 1ST. Dak., and a minimum 

average duration of 11 days on Ohio River at Cincinnati, Ohio. On 

still water, such as the Duluth-Superior Harbor, Lake Superior, ice 

begins to form about November 15, attains a maximum thickness in

1 Fifty-fourth Cons., 2d sess., H. Doc. No. 192.
FOBMATIOK OF ICE. 27

Average ice period from winter of 7876-77, to winter of 1895-96 inclusive

LOCATION \NW.\DBC. JAN. FEB. MAR. APR. MAY

MISSOURI RIVER

Fort Benton, Mont 

Buford, N.D 

Bismarck, N. D. 

Pierre, 3. D. 

Yank ton, S.D. 

Sioux City, Iowa 

Omaha, Neb. 

Nebraska City, Neb. 

St. Joseph, Mo. 

L eavenworth, Kan . 

Kansas City, Mo. 

Jefferson City, Mo. 

St.Charles,Mo.

mm

m

mmmm

mmmmmm

mmmmmm 

mmmmm

mmmm

mmmm

mmm 

mm

m

YELLOWSTONE RIVER

Fort Custer, Mont. ||

RED RIVER OF THE NORTH

Moorhead, Minn. 

St.V/ncent, Mirin. 

Winnipeg, Ont.

WIN

Mankato, Minn.

NESC TA RIVE *

 t 

.MISSISSIPPI RIVER

Bra/nerd, Minn. 

St. Paul, Minn. 

Lake Pepin. 

La Crosse, Wis. 

Dubuc/ue, Iowa. 

Davenport, Iowa 

Rock Island, III. 

DesMoines Rapids 

Keokuk,/otva 

Quincy, III. 

St.Lou!s,Mo. 

Cairo, lit.

mmmmm 

mmmmm

mmmm

fffgf

mmmm

mmmm

m

ST. CROIX RIVER

Hudson, Wis. i

 T 

ILLINOIS RIVER

Morris, III. 

Seneca, III. 

Hennepin.lll. 

Peoria.m. 

Meredosia, III. 

Pearl, III.

mm

mmm 

i

mmmm

mmmm

mmmmmm 

mmmmmm 

mmmmmm

mmmmm 

mmmmt

mmmmm 

mmmm 

P»

OHIO RIVER

Pittsburgh, Pa. 

Cincinnati, Ohio 

Cairo, III.

KANAWHA RIVER

Charleston, W.Va. 

Point Pleasant, W. I/a. mm

SUSQUEHANNA RIVER

Duboistown, Pa. 

Harrisburg, Pa.

mmmm

mmm

mmm

mm

CONNECTICUT RIVER

Turners -Falls, Mass. 

Hartford, Conn.

MERRIMAC RIVER

Amoskeag,N.H.. || ^mmmm^mmmmmmm

GENE&EE RIVER

Rochester, N.Y. ||

ruary, and disappears 

about April 10, making 

the average length of ice 

cover about 150 days. In 

unprotected parts of the 

harbor the average thickness is about 27 inches; in 

shallow bays a maximum 

thickness of 52 inches has 

been reported by the 

United States Weather 

Bureau. Assuming that 

the ice at Duluth reaches 

a maximum thickness the 

latter part of February, 

using the average temperature for the period 

from November 15 to 

February 20, and applying Prof. Bames's formula (p. 25), a probable 

thickness of 45 inches is 

obtained. Conditions 

other than those of heat 

conduction therefore appear to reduce the thickness of ice formed by 

nearly one-half.

Temperature of affluents. The amount of ice 

formed is, of course, affected by any condition 

that tends to raise the 

temperature of water. 

Water flowing from a 

lake or millponcl whose 

surface is ice covered may 

be at a temperature sufficiently high to prevent 

the formation of ice on 

the stream for a considerable distance below the 

outlet point.

At a depth of 30 or 40 feet below the surface the temperature of 

the ground remains practically constant throughout the year at very

FIGURE 6. Diagram showing average ice period from 

winter of 1876-77 to winter of 1895-96, inclusive. 

From report of the United States Deep Waterways 

Commission: Fifty-fourth Cong., 2d sess., H. Doc. 

No. 192.
28 THE EFFECTS OF ICE ON STREAM FLOW.

nearly the mean annual temperature of the air above in the northern section of the country 35° to 40°. Flow derived from deep-seated 

ground water and springs may therefore so increase the temperature 

of the stream water near the point of inflow the amount depending 

on the quantity of inflow that ice will not form. On rivers and 

lakes the influence of the ground water becomes apparent, either by 

the absence of ice or by the presence of "blowholes." The warm 

water from factory waste and from sewers has the same effect. The 

thinness or absence of ice along the banks of rivers and shores of 

lakes is often probably due to relatively warm ground water inflowing at these points.

The variation in the flow of springs and ground water from year 

to year is shown by the fact that under practically the same conditions of temperature a stream will be frozen over in places in one 

year but will remain open the following year.

Velocity of water and character of the T)ed. The formation of a 

cover of ice may be prevented by high velocity of water or by roughness of the stream bed, which causes agitation of the water. In general, these conditions favor the formation of frazil or of anchor ice.

Fluctuations in stage. When temperatures are about 32° F., the 

daily fluctuations in stage caused by the operation of a power plant 

will tend merely to retard the formation of a surface cover of ice on 

the stream below the dam; when temperatures are lower, however, a 

heavy ice cover may form which will not rise and fall with the water 

to any extent, but over which water will flow and freeze, thus giving 

an ice cover considerably thicker than that which would form at the 

same temperature with no fluctuation in discharge. On some streams 

ice has formed to a thickness of 3 or 4 feet as a result of fluctuations 

caused by the operation of power plants.

Fluctuations in stage caused by increase in flow may lift the ice 

and make it irregular in thickness. In places, also, the freezing of 

water flowing on the surface of the ice will leave alternate layers 

of flowing water between two ice surfaces.

In general, irregularity in the flow of a stream tends not only to 

decrease the thickness of the ice but also to make it irregular both in 

manner of formation and in physical appearance.

FRAZIL.

If the velocity of a stream is sufficient to prevent the formation of 

surface ice and the temperature of the water is 32° F., " frazil" (a 

French Canadian term for fine, spicular ice) will be formed. In 

the formation of this ice enough latent heat is released to keep the 

temperature of the water at 32° F. Experiments 1 made'by Prof.

1 Barnes, Howard T., Formation of anchor ice and precise temperature measurements: 

Am. Soc. Mec. Bug., Trans. vol. 26, p. 569, 1905.
FORMATION OF ICE. 29

Howard T. Barnes by means of an electrical resistance thermometer so 

constructed that it would measure a change in temperature of 0.001°, 

indicated that flowing water in a stream could not be cooled more 

than one-hundredth of a degree below 32° F. without the formation of ice crystals. Frazil consists of fine, elongated needles, cubical 

crystals, and plates, and is probably formed in maximum, quantities 

during clear windy nights when the temperature is low. It never 

forms under a cover of ice, but it is carried with the current both yertically and horizontally, and, as shown by observations made on the 

St. Lawrence and on other rivers, may be transported for long distances both in open water and under ice cover, where it may jam and 

become compact enough to support bodies of considerable weight.

During periods of intense cold enormous quantities of frazil will 

form on uncovered, agitated bodies of water, which, when large 

quantities are present has a very dirty appearance. Small quantities 

in the water can be detected only by close observation.

The amount of frazil formed probably depends more largely than 

surface ice on climatic conditions other than temperature. At any 

given temperature below 32° F. less frazil will form on a clear sunny 

day than on a cloudy windy one when the water will be agitated and 

there will be a considerable amount of radiation from the surface 

cooling it. On sunny days the heat absorbed by the water will to 

some extent conteract the effect of low temperature.

ANCHOR ICE.

Anchor ice is similar in many respects to frazil, but is formed in en 

entirely different manner. By people of the south of Scotland it is 

called " loppered " ice because of its resemblance to sour milk, and 

by the French " moutonnee" from its fancied resemblance to the 

backs of white sheep at rest. Since 1788 various theories have been 

advanced to account for its formation. The theory now generally 

accepted is that it is due to the transmission of heat by radiation.

Anchor ice forms in large quantities on the beds of rivers or on 

obstacles under the water surface, but is never found in place under 

i,ce cover or under bridges. It forms chiefly during the night, when 

radiation from the ground is at a maximum, and apparently rarely 

forms in the daytime when radiation is at a minimum. It forms 

most rapidly on dark colored rocks, from which radiation is greater 

than on rocks that are light colored, and to a greater extent in 

shallow water than in deep, being rarely found at depths greater 

than 30 feet. When the rays of the sun reach anchor ice it becomes detached from the bed of the river and rising, often brings 

with it to the surface small rocks and other objects. It may grow to 

a thickness of a foot in a single night, and it may become thicker than 

this by the addition of frazil that has lodged on and frozen to it.
30 THE EFFECTS OF ICE ON STREAM FLOW.

fir

The influence of the sun is especially noteworthy in connnection 

with the formation of frazil and anchor ice, for by warming the 

water it tends to prevent the formation of frazil and to detach 

anchor ice and bring it to the surface where it will float away.

EFFECT OF ICE ON RELATION OF STAGE TO DISCHARGE.

THE CONTROL SECTION.

The elevation of the water surface of a stream flowing in an open 

channel is determined from point to point by a succession of controls that may conveniently be referred to as control sections. These 

control sections of the stream may be dams or weirs, crests of rapids 

or abrupt falls, bars extending across the river, or, where the slope 

is uniform throughout, long stretches of the river bed. The water 

surface above each control section is determined by the height of 

water at the control section. Computations of daily discharge during periods of open water are based on the hypothesis that so long 

as the character of the river at the control section remains unchanged 

the discharge will remain constant for the same stage and will vary 

with the stage according to some fixed law.1 The open-water rating 

curve is the graphic representation of the formula for the discharge 

over the control section of the gage. Any change in the control section will change the position or shape of the curve. In considering 

winter discharge it is assumed that the control section remains constant except for ice, and that the causes for changes in the discharge 

curve for any gaging station are due to ice alone. For most sections 

this is probably true, as, except for ice, on northern streams changes 

in the control sections are due mainly to the scouring action at high 

water or the growth of vegetation. During the winter season both 

conditions are practically eliminated.

The definition of the control section implies that the elevation of 

the water at all gaging stations is controlled by some section below 

the gage. Since at stations with permanent control the only important factor in the change of the relation between winter stage and 

discharge is ice at the control section, changes in the rating curve 

can as a rule be studied by considering the effect of dee in the immediate vicinity of the control section.

The different forms of ice affect the relation between stage and 

discharge in much the same way, and as they are often associated 

with each other the factors covered by each form can not be wholly 

distinguished. Their tendencies, however, can be partly discussed.

1 The importance of control sections in stream-gaging work was first brought to the 

attention of engineers by M. R. Hall, formerly district engineer for the United States 

Geological Survey in the Southeastern States.
EFFECT OF ICE ON BELATION OF STAGE TO DISCHAEGE. 31

SITE-FACE ICE.

GENERAL, EFFECTS.

Surface ice may appear at the control section as (1) complete cover 

in flotation; (2) complete cover bridged across, free from or partly 

supported by the water; (3) partial cover, usually in flotation; (4) 

jams due to piling1 up of ice; or (5) alternate layers of ice and water.

The first result of surface freezing is to displace air by ice. thereby 

increasing the total friction, as the friction of water flowing in contact with ice is greater than that of water in contact with air. The 

second result is to diminish the effective cross section of the stream 

by displacing a portion of the water. Therefore, with the formation of an ice cover and a constant flow, there will be either an, increase in slope or increase in cross section. As the slope can increase 

only slightly, the general.effect will be to increase the stage. In 

general, it may be said that ice on a stream tends to increase the 

stage for a given discharge, the amount of increase depending on 

the quantity of ice at the control section. Discharge measurements 

of ice-cove red streams will therefore always plot either on the curve 

or at the left; under no circumstances will they plot to the right of 

the open-water curve if the measurements truly represent the discharge at the time they were made; and the curve used represents 

the true flow over the control section, independent of the effect of ice.

As the specific gravity of ice is lower than that of water and its 

tensile strength is rather low, ice is generally in flotation, except on 

small streams where it may be bridged across. If the ice is bridged 

at the control in such a way that the surface of the ice is not in contact with the water the ice will not affect the flow at the gage.

Surface ice will therefore affect the gage heights by amounts dependent on its quantity at the control section. The exceptions to 

this rule occur when ice jams are formed either between the control 

section and the gage, or below the section to such an extent as to 

drown out the control section; in either case a new temporary control 

is formed by the ice jams.

EFFECT ON DISTRIBUTION OF VELOCITIES IN THE VERTICAL..

The effect of surface ice on the distribution of velocities in the 

cross section was discussed by Barrows and Horton in their report 

on the determination of stream flow during the frozen season.1 

Under the theories therein outlined and since confirmed, the approximate mean velocity in the vertical may be ascertained by taking 

the mean of the observed velocities at 0.2 and 0.8 depths beneath the 

ice. The average position of maximum velocity is at 0.37 depth 

below the ice. The average coefficient for determining the mean 

velocity from the velocity at mid-depth is found to be 0.878, but as

1 U. S. Geol. Survey Water-Supply Paper 187.
32 THE EFFECTS OF ICE ON STREAM FLOW.

this coefficient has been found to range from 0.70 to unity, it is advisable to make specific determinations for each section under consideration. The general distribution of velocity in the horizontal 

and vertical under complete ice cover is shown in figure 7.

Distances in feet

40 50

'CURVES OF EQUAL VELOCITY

VERTICAL VELOCITY CURVES

Note: Figures at top of curve&'indicate measuring points 

^ Figures at bottom of curves indicate mean velocity in the vertical

-- 2

S 5

Horizontal divisions represent I foot per second velocity

:FIGURE 7. Diagram showing distribution of horizontal and vertical velocities under complete ice cover: Cannon River at Welch, Minn.

GAGING-STATION STUDIES. 

VALUE OF WORK.

Of the tnree varieties of ice surface, frazil, and anchor surface 

ice is the most common and its effect is evident on the gages at r, 

larger number of stations than is the effect of the other two. The 

relative value of readings of gage heights to water surface and gage 

heights to the under surface of the ice as a basis for computation of 

winter discharge has been much discussed, but. owing to the difficulty 

in accurately determining both the mean gage height to the bottom 

of the ice and the position of the control section, it is doubtful if the 

available data are sufficient to settle the question.

In a study x of winter records made at 14 gaging stations to obtain 

a coefficient for computing the flow of an ice-covered stream from

1 Adams, C. R., Determination of stream flow during the frozen season: Eng. News, 

vol. 65, pp. 124-126, Feb. 2, 1911.
EFFECT OF ICE ON RELATION OP STAGE TO DISCHARGE. 33

its open-channel rating curve, C was used to represent the coefficient 

with gage heights to water surface and C' the coefficient with gage 

heights to bottom of ice. The application of the coefficients to computed discharges

- Surface of ice Water surface

pen^atepgage AeuihtTof 

same'cf isobar? x//

CROSS SECTION OF STREAM HAVING ICE 

COVER IN FLOTATION.

Open watsr "., 

discharge curve

Discharge

apparently showed 

that the range in 

the variation of C 

was less than the 

range in the variation in C1", but at 

5 stations the total 

range in Cf was 

less than that of 

C. No attempt 

was made to group 

stations at which 

average distance 

from water surface to bottom of 

ice was taken at 

the control.

The cross section 

odf an ice-covered 

stream (fig. 8) 

shows the position 

of the water surface in a hole cut 

in the ice and the 

approximate position the water 

surface would hold 

were there no ice at 

the control section; 

d is the distance 

through which 

the water surface is raised by the ice, flow being constant; and 

df is the distance from the water surface as it stands in a hole 

cut in the ice to the average under surface of the ice. The winter 

measurements are plotted with respect to the open-water rating 

curve: Q is the measured discharge, Q± the result obtained by applying to the open-water curve the gage height to the under surface of 

the ice, and Q* the result obtained with gage heights of the water surface through a hole cut in the ice. With an open control section Q 

will equal Q2 , and d will equal zero. In computing flow affected by 

surface ice the problem is to determine d, which will always equal 

zero or be a positive quantity. 

17020° WSP 337 13 3

MEASUREMENTS PLOTTED FOR THE 

ABOVE CONDITIONS

O Measurements plotted for gage height to water surface

© Measurements plotted for gage height to under surface of icft'

OQ-s-Qj.-l.00 or leas 

C=Qi-Q,-±I.OO 

For ideal station 

d=Q

c-1.00

FIGURE 8. Typical cross section of and rating curve for an 

ice-covered stream.
34 THE EFFECTS OF ICE ON STREAM FLOW.

As the only appreciable effect of ice results from its presence at 

the control section, data to determine the value of gage heights to 

bottom of ice, which may be useful for certain stations, should be 

collected at that section, but for most stations gage heights to the 

water surface are preferable for the following reasons:

1. The effect of ice at the control section on the readings of gage 

heights to water surface is always positive; that is, the ice backs 

the water up at the gage so that the readings are higher than they 

would be for the same discharge in open channels.

2. Gage heights to water surface are more easily and accurately 

determined than those to the under surface of the ice, as it is necessary to cut through the ice only at the gage. The gage height to the 

under surface of the ice is obtained by cutting a large number of holes 

and computing the average depth from the water surface to the bottom of the ice; the results, because of irregularity of the ice and fluctuation of water in the holes, are of necessity only approximate. 

: 3. The position of the control section is uncertain.

ELK RIVER NEAR BIG LAKE, MINN.

, The gage on Elk River near Big Lake is on a pile a few feet above 

the bridge. During the greater part of the winter ice does not form 

within a few feet of the gage, doubtless because of the effect of 

inflow from a spring. The control section is not well defined but 

it is probably about 200 feet below the gage. The current-meter 

measurements have been made at a section about 300 feet below the 

gage where conditions are more favorable than at either the gage or 

the control section. The results of winter measurements made in 

1911-12 and 1912-13 are given in the following table:

Discharge measurements. Elk River near Big Lake, Minn., during 1911-12 

and. 1912-13, and, relation C and C'.

Date.

1911. 

Nov. 28....... ...............

1912.

Mar.14....... ...............

Do......................

Dec. 22. .....................

Do......................

1913.

Do.......................

Feb. 25... ...... .............

Mar. 18o. ...................

Ice thickness.

Feet. 

0.36 

.55

.92 

.77 

.77 

.60 

.60

.89 

.89 

.68

Water 

surface 

to top 

of ice.

Feet. 

.0 

.0

.09 

.02 

.02 

.0 

.0

.05 

.05 

.0

Gage height

Water 

surface.

Feet. 

0.98 

1.08

.97 

1.34 

1.34 

.84 

.84

1.24 

1.24 

1.32 

1.85

Bottom 

of ice.

Feet. 

0.62 

.53

.14 

.59 

.59 

.24 

.24

.40 

.40 

.54

Measured 

discharge.

Sec.-ft. 

96 

106

39 

73 

72 

94 

95

55

57 

69 

198

Gage height to 

water surface.

Discharge.

Sec.-ft. 

195 

224

192 

305 

305 

158 

158

273 

273 

298

c. 

0.49 

.47

.20 

.24 

.24 

.59 

.59

.20 

.21 

.23

Gage height to 

bottom of ice.

Discharge.

Sec.-ft. 

106

85

16 

98 

98 

31 

31

58 

58 

87

C'.

0.92 

1.25

2.24 

.74 

.74 

3.00 

3.00

.95 

.99 

.79

o Made 1,000 feet above gage; 40 per cent ice cover at control; 35 per cent ice cover at measuring section.
EFFECT OF ICE ON RELATION OF STAGE TO DISCHARGE. 35

The thickness of ice and the distance from water surface to bottom 

of ice were determined at each measurement, so that the gage height 

to the under surface of the ice can be computed. The open-water 

discharge, as shown by the station rating curve, is given for the two 

gage heights and the coefficient C and 6". It will be noted that the

2.0

1.5

1.0

.5

1.5

1.0

.5

.0

O

0

Jan.27, 

1912

C Nov.28,1911

0 Jan. 27,

ir. 14,1912

Dec. 28,1911 £>.

Dec.28,1911 

1912

Feb 25,1913

D°

Jan. 2 3.1913

Dec.22,1

Feb. 25, 1913

1,1913 

Dec. 22,1912

Winter per od, I9IH9I2

Mar. 18,1913

Winter pe iod,l9l2-l9)3

100 ZOO 300 

DISCHARGE IN SECOND-FEET

400 500

LEGEND

© Gage height to water surface 

© Gage height to under surface of ice

FIGURE 9. Relation between open-water curve and ice measurements: Elk River near

Big Lake, Minn.

values of C are all less than unity, ranging from 0.20 to 0.59, while 

C' ranges from 0.74 to 3.00.

The data in the table are presented graphically in figure 9. The 

diagram shows an entire lack of conformity between the plotted 

points, whether gage heights are read to water or to the under surface of the ice. The measurements, although not made at the control
36 THE EFFECTS OF ICE ON STREAM FLOW.

section, were probably made as close to it as most ice measurements 

are made at stations now established, and no curve could be drawn 

through the plotted points to which might be applied the uncorrected gage heights, and the discharge thus determined.

CROW WING RIVER AT PILLAGER, MINN.

The gage on Crow Wing River is about 11 miles above the confluence of that stream with the Mississippi River. The natural slope 

and cross sections of the river were nearly uniform from the gage to 

the mouth, the slope being about 2.6 feet per mile, without decided 

breaks, but the uniformity has now been destroyed by a dam. Probably the control section for the station is a long stretch of the river 

bed below the gage. Except in stretches within the influence of 

occasional springs and of ground water coming in along the banks, 

the ice forms to a practically uniform thickness, both across and 

lengthwise the river, so that the average distance from the water 

surface to the under surface of the ice would be approximately the^ 

same at all points near the gage. The results of measurements made 

at this station during the winter periods of 1911-12 and 1912-13 

are given in the following table and are shown graphically by 

figure 10.

Discharge measurements, Crow Wing River at Pillager, Minn., during 1911-12 

and 1912-13, and relation C and C'.

Date.

1911. 

Dec. 15. .....................

1912.

Jan. 24............. .........

Dec. 18. .....................

1913. 

Jan. 24.... ..................

Feb. 19..... .................

Ice 

thickness.

Feet. 

0.80

1.14 

1.34

.74

1.10 

1.40

-Water 

surface 

to 

top of 

ice.

Feet.' 

0.75

1.06 

1.32

.74

1.07 

1.32

height 

to 

water 

surface.

Feet. 

6.22

6.22 

6.54 

6.14

6.22 

6.47

height 

bottom 

of ice.

Feet. 

5.47

5.16 

5.22 

5.40

5.15 

5.15

Measured 

discharge.

Sec.-ft. 

476

326

368 

440

358 

344

Gage height to 

water surface.

Discharge.

Sec.-ft. 

1,089

1,089 

1,342 

895

956 

1,140

C.

0.44

.30

.27 

.49

.37 

.30

Gage height to 

bottom of ice.

Discharge.

Sec.-ft. 

598

438 

467 

440

334 

334

C'.

0.80

.74 

.74 

1.00

1.07 

1.03
EFFECT OF ICE ON BELATION OF STAGE TO DISCHARGE. 37

The diagram shows 

lack of conformity between the points of 

discharge as plotted 

with the gage heights 

to the water surface, 

but the discharge 

points determined 

with the gage heights 

to the under surface 

of the ice fall nearly 

in line with the openwater curve, a result 

to be expected, as they 

represent measurements plotted to the 

average gage height of 

the under surface of 

the ice at the control 

section.

66

6.4.

6.2

6.0

5.8

5.6

5.4

5.2

5.0

Jan. 24

RED RIVER NEAR GRAND, 

FORKS, N. DAK.

The station on Red 

River is on the Northern Pacific Railroad 

bridge between Grand 

Forks, N. Dak., and 

East Grand Forks, 

Minn. The drainage 

area at this point is 

25,000 square miles. 

Winter measurements 

have been made at this 

station. The results of 

these measurements since 1905 are given in the following table and 

are also plotted in Plate III:

0FeL28,l9IZ 

O Feb.HU9l3

I9IZ 

O 0Jan. 24,1913 0Di:c.l5,l9ll

O Dec 18 I9IZ

200 300 400 500 600

DISCHARGE. IN SECOND-FEET

LEGEND

© Gage height.to water surface 

© Gage height to under surface of ice

FIGURE 10. Relation between open-water curve and ice 

measurements : Crow Wing River at Pillager, Minn.
38 THE EFFECTS OF ICE ON STREAM FLOW.

Discharge measurements of Red River at Grand Forks, N. Dak., in 1905, 1906, 

1907, 1908, 1909, 1910, 1911, 1912, and 1913, and relation C and C'.

Date.

1905. 

Dec. 22. ........................

1906.

Mar.5.. ........................

"War 9^1

Dec. 21. ........................

1907. 

Jan. 28. ........................

Mar. 4..... .....................

1908.

1909.

Feb. 15.. .......................

Nov.23. .......................

1910.

Feb. 28.... .....................

Dec.13. ........................

1911. 

Feb. 14.. .......................

Feb. 18.... .....................

Feb. 25... ......................

1912.

Feb. 12.. .......................

Dec. 12. ........................

1913. 

Jan. 25.. .......................

Mar.8...... ....................

height 

water 

surface.

Feet. 

9.05

9.45 

9.51 

10.24 

8.59

8.07 

8.18

6.76 

7.76

6.50 

. 6.15 

7.78

8.77 

7.67 

3.74

4.10 

4.11 

4.33

3.50 

3.00 

5.00

4.50 

3.90

Gage 

height 

bottom 

of ice.

feet. 

8.02

7.79 

7.01

7.82 

7.71

6.74 

6.68

5.57 

5.89

4.67 

4.39 

7.34

7.65 

5.88 

2.80

2.60 

2.48 

2.88

2.41 

1.64 

4.24

3.30 

2.48

Measured discharge.

Sec.-feet. 

1,840

1,771 

1,554 

1,881 

1,698

1,177 

1,216

912 

924

677 

592 

1,482

1,530 

983 

312

198 

177 

235

175 

115 

473

319 

196

Gage height to 

water surface.

Discharge.

Sec.-feet. 

2,660

2,890 

2,930 

3,370 

2,400

2.120 

2,180

1.490 

1,960

1,220 

1,270 

1,970

2,510 

1,910

575

665 

668 

724

515 

400 

915

770 

615

C.

0.69

.61 

.53 

.56 

.71

.56 

.56

.61 

.47

.55

.47 

.75

.61 

.51

.54

.30 

.26 

.33

.34

.29 

.52

.41 

.32

Gage height to 

bottom ice.

Discharge.

See.-feet. 

2,090

1,980 

1,840 

1,990 

1,940

1,480 

1,460

1,080 

1,190

818 

740 

1,760

1.900 

1,180 

356

312 

286 

374

272

700

469 

288

C'.

0.88

.90

.84 

.94 

.88

.80 

.83

.84

.78

.83 

.80 

.84

.81 

.84 

.88

.64

.62 

.62

.64

.68

.68 

.68

The channel shifts somewhat, so that a new rating curve has been 

prepared each year, but the curve presented fits the entire series of 

measurements closely. Although neither the points plotted with gage 

heights to the water surface nor those plotted with gage heights to 

the bottom-of the ice follow any well-defined curve for winter periods 

considered separately, the entire series falls generally on two curves 

parallel to the open-water rating curve.

ST. MARY RIVER NEAR BABB, MONT.

The upper station on St. Mary Kiver is near the dam site 1 mile 

below the outlet of lower St. Mary Lake and 1 mile above the mouth 

of Swiftcurrent Creek.

During the greater part of the winter the stream is frozen over at 

the gage and for a distance of about 100 yards below and 200 yards 

above, but the channel remains open at the outlet of the lake and at 

the control section below the gage throughout the winter. At times 

during periods of ice the channel in the center of the stream for 

about one-fourth of its width is open below the gage, but there is
U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER 337 PLATE III

1911

o d

G

1912 

0

1912

O

,9,1 0'913

0

,1911

1913

01910

^1913 

©

1911

ffi 1910 /

1911 ®X

1911 i

(tf ^

1912 ~7

^1912

\ /

I9I3/

Q

u-^l9!2- 

©l912

0

IQAQ 1909

1909

1909 jS

\^r

1908 

0 0

0 I908

1908© ©

©1908

.X

 ^y^

/

'

,9070

1910

1907 

©

1910 ^^

X^K

X

0 1907

1907

.X

^^

1906

1910

0

0.909 

©1910,

®I909 

190%

^^

^^

1906

0

1906

0

1906 '90.6

/|\ tj?

^^

Q 1906

n«905

^1905

^F?"

LEGEND

O Gage height to water surface 

© Gage height to bottom of ice

^^

10

h ui

UJ

u.

h

I

CD 

UJ

I

UJ

CD

200 400 600 800 1,000 1,200 ; 1,400 1,600 1,800 2,000 2,200

DISCHARGE IN SECOND -fEET

RELATION BETWEEN OPEN-WATER CURVE AND ICE MEASUREMENT$: RED RIVER AT GRAND FORKS, MINN.

EFFECT OF ICE ON RELATION OF STAGE TO DISCHARGE. 39

always heavy ice on the banks of the river. The channel opposite the 

gage is comparatively deep and sluggish. Four measurements made 

when ice was present below the gage gave the following results:

Winter discharge measurements on St. Mary River near Babb, Mont.

Date.

March 14, 1911 «............'.........................

December 8, 1911 «. ..................................

March 16, 1912 *> ......................................

March 30, 1913«.. ....................................

Width.

Feet. 

86

62

50

76

Area of 

section.

Sq.ft. 

69

82

33

66

Mean 

velocity.

Ft.per sec. 

1.13

1.05

1.48

1.30

Gage 

height.

Feet. 

0.93

1.00

.68

1.00

Discharge.

Sec.-ft. 

79

86

4Q

86

a, Incomplete ice cover at gage. 

6 Ice cover complete.

The relation between the open-water discharge curve and ice 

measurements is shown graphically in figure 11. The measurements 

apparently indicate that the ice 

has little, if any, 

effect on the rating curve so long 

as the lower control section is 

open and ice below the control 

section causes no 

backwater.

1.10

J.OO

,30

u. 

2

I .80 

(9

UJ

5. 

tu

.70

.60

.50

Mar. If ,1912

RAQUETTE RIVER 

AT PIERCEFIELD, 

N. Y.

The gage on the 

Raquette at 

Piercefield is located one-half 

mile downstream 

from the plant of 

the International 

Paper Co. and 

about threefourths mile 

below Black 

Rapids. Between 

the dam and the 

head of the rapids the river freezes over annually to a depth of 1 to 2 

feet. Ice rarely forms on the rapids, the crest of which is the control 

section for the gage. The open-water curve for this station, with the

Dec.8,191

Mar. 30,191

i Mar 14,1911

f&' / O,

20 40 60 80 100

DISCHARGE IN SECOND-FEET

FIGURE 11. Relation between open-water discharge curve and 

ice measurements: St. Mary River near Babb, Mont.
40 THE EFFECTS OF ICE ON STEEAM FLOW.

following discharge measurements plotted with the gage height to 

the water surface, is shown in figure 12.

Winter discharge measurements on Raquette River at Piercefield, N. T.

Date.

February 23, 1911 «. .................................

January 31, 1912«. ...................................

Width.

Feet. 

258

268

270

Area of 

section.

Sq.ft. 

796

1,180

1 

' 054

Mean 

velocity.

Ft. per sec. 

1.12

.87

.43

Gage 

height.

Feet. 

5.10

5.38

4.00

Discharge.

Sec.-ft.

QQQ

i nsn

AZA

a River completely open at control except for a little ice on rocks near shore. 

6 Control free from ice.

It will be noticed that the measurements of February 23, 1911, and 

January 31, 1912, plot practically on the open-water curve, and that

of February 20, 1913. 

plots within 6 per 

cent of the curve, so 

that the 

rating

5.5

5.0

4.0 ('Feb. 20, 

1912

G/Feb.2:t, 

7 1911

Jan.31, 

I9IZ

The presence of 

frazil in a stream 

makes the determination of discharge 

exceptionally difficult. 

Whether floating 

throughout the cross 

section of the stream 

in small quantities, 

compacted in large 

quantities either 

under ice or in the 

open, or lodged in connection with anchor

{QQ it tends to decrease 

,, n> ,- the enective cross section of discharge and to raise the stage by an amount depending 

on its quantity. When carried with the current in small quantities

open - water 

curve may be 

safely used to determine the winter discharge even for periods when ice may be 

present between the 

gage and control.

FRAZIL.

400 600 800 I,OOO 1,200 

DISCHARGE IN SECOND-FEET

FIGURE 12. Relation between open-water curve and ice 

measurements: Raquette River at Piercefleld, N. Y.
EFFECT OF ICE ON RELATION OF STAGE TO DISCHARGE. 41

30

DISTANCE IN FEET FROM INITIAL POINT 

60 90 120 150 180 210 240

10

SECTION AT BRIDGE

SECTION ABOUT ZOO FEET BELOW BRIDGE

30 60 90 120 150 180 

DISTANCE IN FEET FROM INITIAL POINT

ZIO

FIGURE 13. Cross section of Chemung River at Chemung, N. Y., showing effect of needle

ice or frazil.
42 THE EFFECTS OF ICE ON STREAM FLOW.

its effect on the stage is probably so slight that it can be ignored, 

though it may temporarily raise the stage at the control section. 

When, however, it is present in sufficient quantities to completely fill 

the channel it forms temporary jams that raise the water until the 

ice is overflowed or until the increased pressure pushes the frazil 

forward. The nucleus of these jams is probably anchor ice.

Because of the great difficulty in making discharge measurements 

when frazil is present, few examples are available. The general 

effect of frazil on cross sectional areas and velocities is, however, 

shown in the accompanying diagram 1 (fig. 13).

At the upper section the channel underneath the surface ice was 

almost completely blocked by frazil or needle ice; at the lower section, 200 feet downstream, there was but little frazil, yet the observed 

velocities (shown by the figures) at the lower section were so great 

as to indicate considerable flow through the masses of frazil. The 

mean of the measured velocities is shown by the contours.

ANCHOR ICE. 

GENERAL EFFECTS.

When attached to the bed of a river, anchor ice tends to raise the 

stage of the water in the stretch of channel above the point of its 

formation, and this backing up effect is increased when frazil becomes 

jammed in with the anchor ice. At a gage located above a decided 

ripple or rapid which in general remains open, the formation of 

anchor ice at the control section may have the same general effect 

as would the building of a submerged weir. In the absence of surface ice the effect of anchor ice on the gage heights can be closely 

determined by means of temperature records and frequent gage readings, as it is detached from the bed of the stream under the first 

warming influence of the sun.

The effect of anchor ice on stage and its relation to temperature is 

shown in studies of the records of Kootenai River near Libby, Mont., 

and of Schroon River near Riverbank, N. Y.

GAGING-STATION STUDIES. 

KOOTENAI RIVER AT LIBBY, MONT.

The gaging station at Libby, Mont., was established by the Forest 

Service, in cooperation with the United States Geological Survey, 

October 13, 1910. A sketch of river in vicinity of the gages is given 

in figure 14.

1 From Barrows and Horton, Determination of stream flow during the frozen season : 

U. S. Geol. Survey Water-Supply Paper 187, p. 12, 1907.
EFFECT OF ICE ON RELATION OF STAGE TO DISCHARGE.
44 THE EFFECTS OF ICE ON STBEAM ^FLOW.

Measurements at this station were made from a car suspended from 

a ferry cable until 1912, when a bridge was built about 100 feet below the station and the ferry cable was removed. A good low-water 

rating curve has been developed for the station.

During the winter of 1912-13 measurements were made from a boat 

attached to a rope stretched across the river at the old cable section. 

Distances were marked off on a tag line stretched across the river 

just above the rope. At this section there was in the winter of 1912- 

13 an open channel 240 feet wide, and an ice-covered channel 80 feet 

wide on the right bank. The section contains a few large bowlders, 

but on the whole is good. The open section carried about 95 per cent 

of the discharge. There was considerable slush ice, and the temperature was sometimes below zero at the time of the measurements; but 

after placing the meter in the water it was not removed until the 

boat reached the opposite side of the river, where all the ice was 

located, so that the bearings and cups of the meter were not affected 

by ice. Except as affected by the small amount of water flowing under the ice, the measurements are probably as accurate as those commonly made in open channels, and an error as great as 10 per cent 

in the discharge under the ice-covered area would make an error of 

only one-half of 1 per cent in the total discharge.

The control section for the station is a riffle or rapid about 500 feet 

below the gage, and for some distance below the control seption the 

stream is open throughout the winter. About 1| miles above the station the 'channel is divided by an island. During low water practically the entire flow is in the channel on the left side of the island, 

where rapids occur. This channel remains open throughout the 

winter, as does also the greater portion of the channel between the 

island and the station. In the winter of 1912-13 the stream was 

frozen over for a distance of 10 miles above the island.

Discharge measurements were made daily from February 3 to 

February 20, and thereafter on alternate days up to March 13. A 

plot of the measurements from February 3 to 16 indicated that no 

definite relation existed between the temperature and the relation of 

gage height to discharge, though backwater at the gage, caused by 

anchor ice formed above the rapids at the control, apparently varied 

in a general way with the temperature.

An examination of the riffle at the control below the regular gage 

indicated that the stream was not greatly affected by anchor ice and 

that gage heights taken at a lower point might be more reliable. 

Therefore, on February 17, a secondary gage, called gage No. 2 (see 

fig. 14), was installed on the right bank at a point about 1,000 feet 

below the bridge. The new gage consisted of an iron pin graduated 

to tenths and driven into the gravel about 300 feet below the head of 

the rapids that form the control for the regular gage. At this point,
EFFECT OF ICE ON RELATION OF STAGE TO DISCHARGE. 45

and for a considerable distance below, the river is open the year round 

except for a little ice along the banks. The possibility that gage No. 2 

might be affected by ice on the riffle just above, which might divert 

the water to one side or the other, led to the installation of a third 

gage (No. 3 on fig. 14), similar to No. 2, on the right bank about 200 

feet farther downstream. This gage served only as a check on gage 

No. 2.

The cold wave during the latter part of February caused anchor 

ice, which on February 25 affected the stage at the regular gage by 

0.49 foot. On the same date gage No. 2 fell 0.13 foot between morning and night, showing that it also was affected by ice to some extent.

The following are the readings of the two gages for the day:

Comparative readings of gages.

Gage No. 1.

Time.

9.00a.m.

11.00a.m.

12. 00 noon

1. 05 p. m.

2.10p.m.

4.50p.m.

Feet.

3.01

3.00

2.95

2.82

2.55

2.52

Gage No. 2.

Time.

9. 10 a. m.

11.45a.m.

1. 15 p. m.

2. 25 p. m.

4.30p.m.

Feet.

2.93

2.93

2.90

2.81

2.80

A similar change was observed every day when anchor ice was seen 

in the river that is, a large variation between the morning and 

afternoon readings of gage No. 1, and little, if any, variation in 

readings of gage No. 2.

Attempts to find a place along the open section where anchor ice 

would not affect the gage readings were unsuccessful, but it was observed that no anchor ice formed under surface ice, even though the 

ice might be thin and the water sluggish. Therefore, on February 

27 a fourth gage was installed about 2 miles above the bridge, where 

the river was completely frozen over, the ice extending for a distance 

of about 10 miles upstream. The stream at this point is deep and 

sluggish but there are rapids about one-fourth mile below the gage. 

Gage No. 4 was a pine staff driven into the bed of the stream through 

a hole in the ice 20 feet from the left bank and in about 5 feet of 

water. The ice was about 2 feet thick. The readings are affected 

not only by the surface ice at the gage but by surface ice that forms 

at the riffle below and blocks one channel (see fig. 14) ; they are not 

affected by anchor ice. The gage heights at No. 4 are slightly 

affected by the temperature, most of the variation being between 

morning and afternoon readings. A rise in stage appeared between 

morning and night and a fall during the night.

At temperatures as low as 13° below zero no anchor ice formed 

at the open-water section at the riffle below gage No. 4, probably 

because the water coming from the stream under ice cover was at a 

slightly higher temperature.
46 THE EFFECTS OF ICE ON STKEAM FLOW.

In order to study the fluctuations of the water surface at gage No. 

4 and at the riffle below still another gage, No. 5, was installed on 

the left bank on March 2 a short distance below the ice-covered section and about 1| miles above the regular gaging station. The channel at this point is divided by an island, but at low stages during the 

winter practically the entire flow of the stream is in the channel to 

the left of the island, where gage No. 5 was located. Libby Creek 

enters the Kootenai below gages Nos. 4 and 5 but above the station 

gage (No. 1) and gage No. 2. The variation in flow of Libby Creek, 

however, during the winter season is not more than 50 second-feet, 

so that it was disregarded (see fig. 14).

The closed-season readings of gage No. 5 differed from those of the 

open season because of conditions in the channel to the right of the 

island. During the winter this channel is practically closed by ice 

and most of the flow passes gage No. 5; but when the ice goes out 

the discharge is divided between the two channels, and the stage at 

gage No. 5 is decreased. A similar effect was noticed on gage No. 4, 

at which the stage was controlled by ice at the head of the riffle. 

Eeadings on gage No. 5 were less affected, however, than those on 

No. 4, the total shift amounting to about 0.4 foot at No. 5, as against 

1.2 feet at No. 4. Readings on gage No. 2 were not affected by surface ice and were affected by anchor ice at a temperature of 9° F. 

by only about 0.13 foot, or 7 per cent. Eeadings on gage No. 3 were 

affected in the same way as those on gage No. 2, and the gage was 

not so well located. After it was found, therefore, that the gage 

heights at No. 2 were unaffected by surface ice gage No. 3 was discontinued.

Records kept during the period covered by the measurements indicate that temperature was the controlling factor affecting the gage 

heights, which were characterized by large and rapid fluctuations. 

The measurements made during February show that as a rule the discharge of the river changes slowly during the coldest weather. The 

sudden fluctuations in stage are due, first, to ice that forms at the 

control section, increases the height of water at the gage, and then 

goes out suddenly, causing a fall; and, second, to anchor ice which 

may cover the whole bottom of the river near the control section. 

The anchor ice forms during the night, and if the day following its 

formation is clear and the temperature is sufficiently high it will 

rise to the surface, causing great differences between morning and 

afternoon readings. When the weather is cloudy the anchor ice may 

remain at the bottom for one or more days and cause continued 

high gage heights.

On February 7 two measurements were made. At the beginning 

of the first measurement, in the morning, the gage reading was 0.7 

foot and the discharge was found to be 2,160 second-feet. At the
U. & GEOLOGICAL SURVEY WATER-SUPPLY PAPER 337 PLATE IV

Gag e heights correcte J for 

anciorand

DIAGRAM SHOWING RELATION BETWEEN TEMPERATURE, GAGE HEIGHTS, AND DISCHARGE: KOOTENAI RIVER AT LIBBY, MONT.

EFFECT OF ICE ON RELATION OF STAGE TO DISCHARGE. 47

end of the second measurement, in the afternoon, the gage read 0.09 

foot and the discharge was found to be 2,180 second-feet. Thus 

during the day the gage height fell 0.61 foot, though the discharge 

remained practically constant.

The relation of daily discharge to gage height and temperature 

from November 1,1912, to March 30,1913, is illustrated on Plate IV, 

which shows a large daily fluctuation in the gage heights that corresponds very closely with the variations in temperature. The rise 

in the gage heights was caused by the formation of anchor ice; 

the fall was the result of its detachment and floating away. . The 

anchor ice would form during the night at temperatures below 14° 

above zero and would cause a rise of as much as 0.6 or 0.7 foot on 

the gage; its going out, which usually began about noon, would 

cause a corresponding fall in stage; within a few hours it would 

nearly all disappear.

When a fall in gage height appeared while a discharge measurement was being made the gage height at the end of the measurement 

was adopted instead of the mean between beginning and end. The 

gage heights during the period when anchor ice existed were very 

unreliable, as conditions changed daily and in an irregular manner, 

whereas the gage heights observed after the anchor ice was out were 

affected only by the permanent backwater from surface ice.

The daily discharge for the period from December 1, 1912, to February 3, 1913, when no discharge measurements were made, was computed from the minimum gage heights as shown in outline on the 

gage-height diagram (PL IV), which doubtless represents approximately what would have been the gage heights if there had been no 

anchor ice.

The effect of backwater at the gage, aside from that caused by 

anchor ice, was estimated from the plotting of the measurements with 

reference to the open-water rating curve after February 3, 1913, and 

from December 1, 1912, to February 3, 1913, from observations of 

temperature and the amount of backwater on February 3, with the 

following results:

Foot.

Dec. 1 to 5______________ 0.05 

Dec. 6 to 15_____________ .1 

Dec. 16 to 23_____________ . 15 

Dec. 24 to Jan. 7__________ . 2

Foot.

Feb. 4 to 16______________ 0.5 

Feb. 17 to Mar. 5__________ . 3 

Mar. 6 to 12 _____________ . 2 

Mar. 13 to 28 _____________ . 1

Jan. 8 to Feb. 3___________ .3

By subtracting these amounts from the gage heights shown by the 

dotted line on the gage-height diagram (PI. IV) the curve of effective 

gage height was obtained, to which the open-channel rating table was 

applied.

The gage-height curve apparently indicates that anchor ice did not 

form to such an extent in the early part of the winter as it did after
48 THE EFFECTS OF ICE ON STREAM FLOW.

February 1, and that most of the fluctuations were caused by ice that 

formed on the control during short periods and then went out suddenly.

SCHROON RIVER AT RIVERBANK, N». Y.

The station on Schroon River near Riverbank, N. Y., was established September 2, 1907, by the United States Geological Survey in 

cooperation with the New York State Water Supply Commission, 

The records of maximum and minimum temperature, precipitation, 

original and corrected gage heights, and discharge at this station are 

compared in Plate V.

The discharge of Schroon River does not conform to all-changes in 

temperature, because the river has a large amount of natural storage 

in Schroon Lake. The records show that anchor ice generally formed 

whenever the minimum temperature fell below 10° F. and that it 

usually left the river during the afternoon. The increase in backwater indicated during the period from February 5 to 17 was probably caused by .surface ice. The gradual decrease in the flow as the 

winter advances is natural.

COMPUTATION OF FLOW OF FROZEN STREAMS.

METHODS AVAILABLE.

The complex manner in which ice may form and the varying conditions presented by streams preclude the formulation of any method 

that can be universally employed to determine winter flow. In general the following methods may be used:

1. The readings of gage heights to the water surface may be directly 

applied to the open-water rating curve.

2. The observed gage heights may be applied directly to a special 

rating curve based on winter discharge measurements and gageheights to water surface.

3. Discharge measurements may be used in connection with gage 

heights and with data showing climatic conditions and the occurrence of ice. This method may be applied (a) by the eye that is, 

by inspecting the records of temperature, precipitation, and gage 

heights, estimating the daily discharge for the period between times 

of measurements, and adjusting the determinations by comparing 

with results obtained at near-by stations; or (&) graphically by plotting the records of temperature, precipitation, and gage heights to 

water surface and determining the correction to the gage heights 

necessary to insure the applicability of the open-channel rating 

curve.

FIRST METHOD.

The use of the first method to determine the daily discharge of r 

frozen stream the application of water-surface gage readings to
DISCHARGE IN SECOND-FEET GAGE HEIGHT IN FEET TEMPERATURE, FAHRENHEIT

COMPUTATION OF PLOW OF FROZEN STREAMS. 49

the open-water rating curve is advisable only when the stream is 

open at the control section and no backwater exists at the gage.

If the control section is entirely free from ice the relation between 

slope, stage, and discharge will not be appreciably changed even by 

complete ice cover between the control section and the gage. Attention was first directed to this fact in an article by C. R. Adams,1 who 

offered the following explanation:

Let it be assumed that a gage has been installed above the weir and a rating 

table obtained for open-channel conditions. A moment's reflection will show 

that this rating table is not affected by floating logs or other material in the 

pond above the weir; the reason being that gage heights are determined only 

by the height of water required at the weir to pass the discharge over this 

weir. If this floating material is ice it has no effect upon gage heights, so we 

can lay down the rule that under such conditions the open-water rating table 

will apply equally well where there is ice cover.

Unfortunately conditions favorable to the use of this method are 

rare, but it is used at several stations, notably at Raquette Kiver at 

Piercefield, N. Y. (see p. 39 and fig. 12), and at St. Mary River near 

Babb, Mont. (p. 38 and fig. 11). Considerable ice is present at both 

stations, but as a rule the control section remains clear throughout 

the winter.

In using 'this method the engineer should closely inspect the gageheight records and compare them with temperature records to detect 

the presence of backwater. If discharge measurements made in 

several winters have shown that ice rarely occurs at the control section and that the regular open-water curve is applicable fewer measurements are needed with this method than with any other. An opencontrol section, however, with ice above, implies as a rule that the 

control section is at rapids at which anchor ice is likely to form. In 

order to detect the presence of anchor ice during extremely cold 

periods the gage should be read twice a day. Readings higher in 

the morning than in the afternoon indicate the presence of anchor ice, 

and care must be taken to read the gage soon after the point of maximum daily temperature, when the control section is likely to be clear.

SECOND METHOD.

The conditions favorable to the use of the second method in which 

observed gage heights are applied directly to a special rating curve 

based on winter discharge measurements and gage heights to the 

water surface are most likely to be found on the larger rivers, 

where the slope and cross section may be fairly uniform for long 

stretches. In general, however, this method should be used with 

great care and the period of applicability of the curve should be

1 Determination of stream flow during the frozen season: Eng. News, vol. 65, p. 126, 

February 2, 1911.

17020° WSP 337 13 4
3,000 4,000

DISCHARGE IN SECOND-FEET 1

5,000 6,000 7,000 '8/)00 N , 9,000" 10,000

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o t* 4

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November, 1912

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December-,1912 -| January.1913 February,l9

PJ 02 FIGURE 15. Backwater curve and plotted fictitious discharge measurements : Rainy 

§

^ S rt £"* ^ H- ^ O r^ m" ^ S ^ 

_ ^ ^ ,y ..,_.., ^ OQ ^ £ § ^ f ^ £ |p,^ g g t> S- 0 
COMPUTATION" OP PLOW OF FEOZEK STREAMS. 51

It will also not represent conditions if between the times of measurement the character of the ice cover has changed greatly as a result 

of changes in temperature.

If backwater is caused by a combination of anchor and surface ice, 

discharge measurements made at certain times might give a smooth 

curve that would in reality not apply except on the days of measurement. An illustration is furnished by observations on Rainy River 

at International Falls (fig. 15). It is assumed that measurements 

were made on December 2,17, January 5, 17, and March 14.

The diagram gives the actual backwater curve; the points plotted 

on the ice curves are deduced from the plotted points showing the 

actual discharge and backwater on the days when the measurements 

were made. It appears, therefore, that even a smooth curve derived 

from measurements may be deceptive, and that the continued use of 

such a curve as that shown on the diagram would lead to large errors.

This method should be used only when many discharge measurements have been found to plot on a smooth curve and when conditions of temperature and ice are stable for long periods. See, for 

example, the open-water curves and plotted ice measurements of Red 

River at Grand Forks, N. Dak. (PI. Ill, p. 38), Elk River near Big 

Lake, Minn. (fig. 9, p. 35), and Crow Wing River at Pillager, Minn. 

(fig. 10, p. 37), which exhibit lack of relation between the measurements made from year to year.

THIRD METHOD. 

EYE METHOD.

The method most commonly employed at the present time to determine the flow of streams either partly or completely covered with 

ice is that which utilizes the discharge measurements and data regarding climatic conditions and the occurrence of ice in connection with 

observed gage heights by means of eye-inspection of records of temperature, precipitation, and'gage heights, estimating the daily discharge for the period between times of measurement, and adjusting 

the determinations by comparing with results obtained at near-by 

stations. The monthly mean of such determinations is also compared 

with monthly means at adjacent stations in order that any large 

error may be detected.

The accuracy of this method depends largely on the uniformity 

of stream flow between times of measurements, the number of measurements, and the engineer's knowledge of general conditions. Care 

must be taken that the discharge, as estimated, is not greater than 

would be given by the application of gage heights to the open-water 

rating curve. In general this method should give more accurate 

results than method No. 2, because it considers the time and temperature factors.
52 THE EFFECTS OF ICE ON STREAM FLOW.

The method will give good results at stations in localities where 

temperatures are fairly constant over long periods of time and whe^e 

the flow is affected by surface rather than by anchor ice. Under su",h 

conditions fewer measurements and gage readings are required than 

at stations situated where climatic conditions are irregular. Temperature records from the nearest Weather Bureau station are generally sufficient.

The disadvantage of this method is that it is impossible to che?k 

its results, as no record is left of steps employed.

GRAPHIC METHOD.

The method that gives the best results^ taking into consideration 

as it does all conditions tending to destroy the open-water relation 

between stage and discharge, and that can be used at all stations 

whose control section is modified by ice, is the graphic method. In 

applying it the records of temperature, precipitation, and wate^*- 

surface gage heights are plotted on cross-section paper, and the correction that must be applied to the daily gage heights to insure the 

applicability of the open-water curve is determined, the variation in 

this correction between times of measurements being estimated by 

comparing the variations in gage height with those of temperatur0, 

precipitation, and ice. This method has the obvious advantage of 

enabling the engineer to compare directly the variation of discharge 

with temperature which has been shown to be the great factor in 

affecting winter stream flow. The method was first suggested by the 

author about a year ago.1 Later studies have resulted in minor 

changes in the mode of procedure but have confirmed the opinion 

that the method will give, especially for stations at which the flow is 

affected by anchor ice or a combination of anchor and surface ice, 

fairly accurate determination of the effective gage height.

The use of the method is illustrated by the studies of Rainy Eiver 

at International Falls, Minn., at a gaging station just below the plant 

of the Minnesota & Ontario Power Co. The flow at the plant is determined by the Canadian department of public works by means of 

wheel ratings; the flow at the gaging station is computed by tl e 

engineers of the United States Geological Survey from current-meter 

measurements. The mean monthly discharge,' as determined independently by the two methods during times when there is no back- 

.water at the Survey gage, is well within 5 per cent of the true mean. 

Although the slope between the dam and a point some miles below 

the gage is small, ice rarely forms on the river, apparently because

iThe graphic method of determining stream flow was proposed by the author at a conference of district engineers of the water-resources branch held in Washington, January, 

1913, when the relation between temperature, backwater, and stream flow was first shovn 

graphically. A brief outline of the method was published in Eng. News, vol. 69, po. 

725-727, Apr. 10, 1913.
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COMPUTATION OF PLOW OF FROZEN STREAMS. 53

the water coming from ice-covered Rainy Lake (having an area of 

over 300 square miles) is at a temperature high enough to prevent

*he formation of ice for a considerable distance, even though the 

mean temperature for six months is below freezing. The mean temperature (in degrees Fahrenheit) for November is 23°, for December 

0.7°, for January 5.4°, for February 5.7°, and for March 18.9°. As

*he temperature of the water slowly changes after leaving the lake, 

surface ice forms along the edges of the river, and at Manitou Rapids, 

about 31 miles below the gage, there is probably a combination of 

anchor and surface ice. Having the actual daily discharge as de-

*ermined by the water-wheel ratings, the gage heights at the Survey 

gage, and a well-defined rating curve for that gage, it has been possible to determine the actual backwater daily throughout the winter. 

The relation between the backwater and the mean temperature, as 

diagrammatically shown in Plate VI, is fairly well defined. The 

daily effect at the station of anchor ice at Manitou Rapids is diminished by the pondage in the river between the gage and the rapids. 

The average slope of the river between the gage and the rapids is 

approximately 0.22 foot per mile, and the amount of backwater 

ranges from zero to more than 2 feet. On Plate VI the backwater curve has been drawn separately from the gage height curve in 

order to show the relation between them. In practice it has been 

found that this extra step is not necessary and possibly is not advisable, as on an uncontrolled stream it is possible to vary the curve 

of effective gage height with the mean temperature. This method 

follows somewhat the Stout method 1 of determining the flow in 

shifting channels in using a single rating curve and correcting the 

observed gage heights to apply to the curve. In the Stout method 

^he correction is based almost entirely on discharge measurements; 

: n this ice method time and temperature are factors, as well as dis- 

"harge measurements.

The application of the method to the determination of flow of a 

stream completely covered with ice is illustrated in figure 16. In

*his diagram the line of effective gage height has been corrected 

somewhat to conform to the temperature.

The diagrams forming Plate IV (p. 46) illustrate the use of this 

'nethod to determine the flow of the Kootenai at Libby, Mont., whore 

'^tage is affected by both anchor and surface ice. The plate shows 

lhat anchor ice leaves the river with rise in temperature and exhibits 

also the close relation between temperature and effective gage height.

In order to develop this method and to determine the effect of the 

different varieties of ice on backwater and the relation between temoerature and stream flow, it is essential that detailed stream gaging

1 Hoyt, J. C., and Grover, N. C., River discharge, pp. 103-104, 106-107, John Wiley & 

'^ons, New York.
FAHRENHEIT T.EMPERATURE, SECOND-FEET IN DISCHARGE 

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i

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0

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FEET IN HEIGHT GAGE 

SIOHMJHE aoi KO 
COMPUTATION OF FLOW OF FROZEN STREAMS. 55

be carried on throughout the winter and that studies be made of 

maximum and minimum temperature, gage height, and discharge 

at stations at which stage is affected by ice.

APPLICATION OF GRAPHIC METHOD.

Many streams in the northern and western States are not completely covered with ice throughout the winter months. At many 

places the ice on a stream may extend but a short distance from the 

banks, leaving an open channel in the center; at others the current 

may be so swift that the channel remains entirely open throughout 

the winter. Such conditions are common in hilly or mountainous 

regions, where stream gradients change rapidly, and may exist in 

the vicinity of gaging stations to such an extent as to make it impossible to estimate discharge by methods that are applied to streams 

that are completely ice covered. For example, the channel may be 

open at the gage or at the control below, but the stage may be materially affected by the presence of anchor ice; or, if complete ice cover 

exists below the natural control section, ice jams may form, creating 

a temporary ice control which produces backwater at the gage. If 

the stream is frozen along the banks at the gage and at the control 

below, but is open in the center, the gage readings are affected by ice 

jams at the control and by changes in the conditions along the banks.

If a stream is deep and sluggish and under complete ice cover 

for a considerable distance above a gage located at a riffle, the gage 

readings may not be affected by ice because the water coming from 

beneath the ice is at a temperature sufficiently high to prevent the 

formation of ice at the control section.

The extent of these effects depends on the natural condition of the 

channel and on the general condition of the ice, the latter depending 

largely on temperature. Each station where such conditions exist, 

singly or in combination, presents a problem that can be solved only 

after a careful study of all the factors.

At a station located in a comparatively sluggish stretch of a stream 

where the channel is partly open throughout the winter and the 

control is a riffle the gage heights will be materially affected by 

anchor ice, which will form at temperatures of zero and below. The 

amount of anchor ice will depend on the roughness of the channel 

and the velocity of the current and will tend to increase as the temperature falls and decrease as the temperature rises, disappearing 

entirely as the temperature approaches 32°. As the variation in daily 

temperature may have an important effect on the amount of anchor 

ice formed, and therefore on the fluctuations in stage at the station, 

a record of the maximum and minimum temperatures is necessary 

to arrive at a proper interpretation of variation in the gage heights
56 THE EFFECTS OF ICE ON STEEAM FLOW.

caused by anchor ice. It is also necessary to have a more complete 

record of the gage heights at stations of this character than at stations where complete ice cover is formed. At least two readings 

should be made each day as nearly as possible at the time of maximum 

and minimum temperatures. Careful observations should be made 

to determine the maximum temperature at which anchor ice forms 

and at which it may be expected to disappear, and the relation between the increase of the anchor ice and the decrease in temperature. 

On days when the temperature rises above .this maximum, if other 

conditions are normal, it may be assumed that no anchor ice exists 

and that the gage heights at or immediately following the time of 

maximum temperature are reliable. With this information available 

it is possible to determine the corrections to be made to the gage 

heights in order that they may be applied to the open-channel rating 

curve. As a check on the gage corrections a number of discharge 

measurements should, if possible, be made at different temperatures.

On a stream with small slope the formation of anchor ice may 

create a reservoir in which a considerable part of the flow may for 

a time be stored. Discharge measurements made during that time 

will indicate a flow less than the natural flow of the river; but 

measurements made while the anchor ice is going out, or after it has 

gone out and before the river has returned to its normal stage, will 

indicate a flow greater than the normal flow of the river, because of 

the release of the water that had been held in storage by the anchor 

ice. It is doubtful whether any corrections can be determined^ and 

applied to discharge measurements made under such conditions, 

which will recur whenever anchor ice forms at the gaging station 

or at points above. The measurements should if possible be made 

when the stage is normal.

The relation between the temperature, gage heights, and discharge 

can be best studied by plotting the data on cross-section paper, using 

the horizontal ordinate for the time and the vertical ordinate for 

temperature, gage heights, and discharge. Care must be exercised 

in applying this method of correcting gage heights, especially when 

there is a great and sudden change in temperature which may change 

the general conditions at the station.

The effect of shore ice must also be considered. A large range in 

temperature doubtless affects the conditions along the banks of a 

stream, but to a less extent than it affects anchor ice in the open 

channel.

When the maximum temperature is at or above that at which it 

forms, anchor ice will rise to the surface and float away. If other 

conditions are normal, gage heights observed after the anchor ice 

has disappeared will be an index of the discharge and will represent 

the minimum gage heights for the day. By plotting the tempera-
FIELD METHODS. 57

ture and gage heights on cross-section paper and sketching in a curve 

following the minimum gage heights, when they occur at a temperature above that at which anchor ice forms, an estimate can be made 

of the effect of anchor ice on gage heights during the intervening 

days.

If tbere is in the vicinity of the station a section in which the current is swift and the channel remains open all winter, a gage should 

be installed, as at many stations gage readings in open sections with 

high velocity will indicate the discharge during periods of extreme 

low temperature in which the regular gage will be affected by ice.' 

The flow at such stations should be computed from the observations 

at the temporary gage, but the station gage should be read regularlv 

to obtain a record for comparison.

Whenever possible stations for winter records should be established 

at the outlets of lakes or in the vicinity of large springs. The water 

at such places is usually at a relatively high temperature, and if 

rapids are present a site can usually be found at which the channel 

remains open throughout the winter, even during periods of extremely 

low temperature.

FIELD METHODS.

SELECTION OF STATIONS.

The location and number of stations at which winter records will 

be maintained, as determined in connection with the work of the 

water-resources branch of the Geological Survey, depend on conditions that vary considerably in different districts, but the most important condition is common to all districts and is the amount of 

money available. The lack of winter records has not been entirely 

due to the difficulty in obtaining them, but rather to the fact that 

underestimation of their importance has led to an unequal distribution of funds. Comparison of the number of stations that have been 

discontinued on account of ice with the number that are maintained 

throughout the year shows that the greater part of the available 

funds has been expended on open-water records. As records of 

winter discharge are of great importance, funds should be so allotted 

that certain stations can be maintained throughout the entire year, 

even though the adoption of such a course may necessitate the 

abandonment of some stations at which open-water records have 

heretofore been collected. Other factors determining to some extent 

the number of stations to be maintained are (1) distribution of 

stations in the drainage basin, (2) action of ice at the control section, 

and (3) ease of operation.

The almost entire lack of close uniformity or agreement in the 

open-season flow of any two streams has been proved by many observations. Consideration of the factors that influence the winter
58 THE EFFECTS OF ICE ON STREAM FLOW.

run-off factors as varied and probably as influential as those affecting 

open-water flow shows that the flow at different stations is comparable only within a very small area, and even in such areas conditions 

may vary so widely that estimates of flow derived by comparing 

records would be subject to large errors. If comparison of the 

records at stations located in close proximity on a stream shows close 

agreement in the open-water flow, a close agreement in winter flow 

is probable, but it is doubtful if the comparative method should ever 

be used to estimate the flew of streams in adjacent drainage basins. 

! At least one station for winter records should therefore be maintained 

at or near a regular open-water station in each main river basin or 

subdivision.

The station selected for maintenance should, if choice is possible, be 

that whose control section is least affected by ice. If previous studies 

have shown that the control section is, as a rule, entirely free from ice, 

the station can be carried on in the same manner as an open-water 

station. The study of the station records known to be unaffected by 

ice will help greatly in determining the flow at stations at which ice 

is present, and the greater the number and distribution of such stations the greater will be the accuracy of the winter records throughout the entire district. Only occasionally can the records be used directly to estimate the flow at other stations, but they may serve to 

detect changes in uniformity of flow, and, if climatologic data are 

available, to determine the relative discharge.

The ease with which a gaging station may be operated will depend 

not only on the amount of ice present and the fluctuations in stage, 

but also on its proximity to headquarters. Stations maintained in 

groups or circuits are more economically conducted and in general 

will give more accurate records than isolated stations, as tendencies of 

flow can be closely compared. The ice on an uncontrolled stream will 

probably seldom be in such condition that measurements can not be 

made. On a stream controlled by power plants the ice may form 

layers with water between or standing on the surface, and measurements may be impossible. As a rule stations should not be maintained at localities where diurnal fluctuations in quantity of discharge 

occur in combination with fluctuations in stage caused by ice. It is 

doubtful if even a recording gage would afford a reliable basis for 

estimates of flow under such conditions; if the wheels can not be 

rated and records must be obtained, notes should be made regarding 

the daily operation of the plant.

The number of stations that will be carried through the year will 

depend to some extent on the number of stations maintained in cooperation with 'States, commissions, or private parties. As a rule, 

stations located at power plants or maintained largely by private
FIELD METHODS. 59

cooperation should, if possible, be operated throughout the year, 

especially if conditions are such that they afford fairly accurate 

records.

POWER-PLANT RECORDS.

At modern power plants large enough to utilize the mean annual 

run-off of a stream the greater part of the water during the winter 

passes through the wheels and very little escapes over the spillway. 

The necessity for determining the flow over spillways, flashboards. 

and through sluices is thus avoided, and one of the larger sources of 

errors is eliminated from estimates of the daily and monthly flow 

based on power-house records. The records of flow computed at most 

modern plants are nearly always available for use, and their accuracy 

can, as a rule, be checked. At plants so operated that all the water 

passes through the wheels, the wheels can be rated and the discharge 

can be estimated from records of gate openings and head. Eecords 

from power plants in any part of a drainage basin may assist greatly 

in the discovery of tendencies of flow at gaging stations within that 

basin.

At regular gaging stations located at dams care must be taken 

to. make allowance for the effect of apparent increase of head caused 

by ice on the crest. If the ice forms only in the pond and the crest 

is clear, the effect of backwater at the gage will be inappreciable.

Power plants that include storage systems will, in general, be so 

operated that the reservoirs will be filled to maximum capacity at 

the beginning of the period of ice and will be empty at the end. The 

records of water released from such reservoirs, either in terms of 

rate of flow or in terms of volume, are exceptionally valuable if 

gaging stations are located below them, as the measured flow can be 

corrected from the storage flow arid the revised figures showing 

natural discharge can be compared with records of discharge at other 

stations.

GAGES.

The presence of ice at the control section has heretofore had little 

consideration in determining the location of gaging stations. In 

collecting winter records at a station already established it will be 

necessary therefore either to use the gage as installed and make 

allowances for the effect of ice or to install a supplementary gage 

to be used during the winter months. In establishing new stations 

and installing auxiliary gages care should be taken to select sites 

with control sections as free from ice as possible throughout the 

winter. As the availability of an observer has determined the location of many of the gages, it may not be possible to find better sites 

than those now in use. On some rivers, however, it may be desirable 

to relocate the gages in stretches free from ice and to develop a new 

winter rating curve, either by comparison of the records with open-
60 THE EFFECTS OF ICE ON STREAM FLOW.

season records of discharge or by current-meter measurements. In 

sections of the country similar to Minnesota, where winter temperatures are low and stream gradients are small, many of the rivers 

have no open sections and the use of the present equipment must be 

continued.

Of the three types of gages chain, staff, and recording the chain 

gage is probably the most easily maintained during the wintei. 

Staff gages, both vertical and inclined, unless extremely well fastened and protected, are likely to be changed in datum or wrenched 

loose from their supports by the pressure or motion of the ice. On 

wooden gages the numbers are effaced, making it necessary to install 

new gages each spring. An inclined gage is difficult to read, as the 

'ice pushes up over it and must be chopped with a chisel, the use of 

which may injure the gage itself. The same statement applies, 

although less forcibly, to the vertical staff gage. Vertical gages 

fastened to piers in the center of the river may at times during 

ice-forming periods and thaws be dangerously inaccessible to the 

observer.

Recording gages are serviceable for winter records only when 

intakes and wells are so constructed and protected that they will 

not freeze. The effect of freezing in the well can be reduced to 

some extent by the addition of oil, by burning an oil lamp, or by 

installing an electric light with the bulb near the surface of the 

water.

A chain gage can as a rule be maintained as satisfactorily and 

with as little care during the winter as during the summer. Its 

datum, especially when the gage is attached to a bridge, is no more 

likely to change in winter than in summer, its scale board is not 

subject to injury by ice, and thin ice can be broken by dropping 

the weight. If a recording gage is not used, the observer will lessen 

his labor by covering the gage hole with brush, which will to some 

extent prevent freezing.

The number of gage readings required will depend largely on the 

character of the ice at the station and the regularity of flow of the 

stream and, like the type of gage, must be determined experimentally. On ice-covered streams whose flow is uncontrolled by storage 

and is regulated largely by temperature, gage-height observations 

varying from three a week to one a day should be sufficient.

The determination of flow of streams solidly covered with ice and 

controlled by storage presents difficulties that can hardly be overcome with any number of gage readings, although possibly better 

results will be obtained with a recording gage than with any other 

type. If fluctuations in stage at any station are caused principally 

by anchor ice, the gage, if not of the recording type, should be read 

at least twice a day once in the morning and once shortly after
FIELD METHODS. 61

the period of highest temperature. On an uncontrolled stream whose 

winter flow is affected by anchor ice alone the lowest of two readings 

a day will probably give nearly as good results as the record of an 

automatic gage.

The engineers of the Geological Survey consider the use of a 

recording gage undesirable at stations where much ice forms, but 

favor its use at stations where the effect of ice is small and the 

flow is controlled. For certain stations at which the stage is affected 

by anchor ice, as, for example, on Kootenai Eiver, near Libby, Mont, 

(see PI. IV, p. 46), the use of a recording gage is advisable. At 

recording gage stations on streams that vary slightly in flow economy may be gained by discontinuing the automatic gage record during the winter and depending on twice-daily gage readings. On 

streams in the Great Basin, which show sudden fluctuations caused 

by changes in temperature, recording gages are advisable even 

though they are not in operation during periods of low tempera- 1 

ture. As the degree of accuracy of winter gage heights need not be 

greater than the accuracy with which the effective gage height can 

be determined, the necessity for recording gages during the winter 

is doubtful.

CLIMATOLOGIC RECORDS.

The climatologic data necessary for a proper interpretation of 

records of winter stream flow consist in general of records of temperature and precipitation. At many places, and especially when 

only surface ice is present, the records of the Weather Bureau may 

answer all requirements if arrangements can be made for receiving 

them,'but as a rule each winter station should be equipped with a 

reliable thermometer, and the temperature should be recorded on 

the cards in connection with the gage heights. The required outlay 

is small and will be more than compensated by the value of the 

records in making computations and the interest added to the work 

of the observer. Eeadings taken early in the morning and about 

noon will give data from which the mean temperature can be closely 

determined and fix the limits at which anchor ice forms and disappears.

The effect of precipitation on daily run-off during the winter is 

less than that of temperature, and the records are not so important 

in the computations. The weekly " ice bulletin " of the United States 

Weather Bureau probably furnishes all necessary data regarding 

snowfall, so that the gage reader need report only the occurrence o'f 

rain.

When anchor ice or frazil is present notes regarding the clearness 

of the sky an important factor in their formation may also be of 

value.
62 THE EFFECTS OF ICE OK STEEAM FLOW. 

DISCHARGE MEASUREMENTS. 

DETERMINATION OF SECTION.

If the regular section at a gaging station is open or only partly 

frozen, it may be used for winter measurements by working from 

the ordinary equipment over the open part and from the ice on the 

same section along the edges where ice cover may have formed. 

When the streams are entirely frozen and measurements have to be 

made through the ice a knowledge of the character of the section 

during open water is essential.

At stations on streams that freeze each year sections for making 

winter measurements should be selected during the open season and 

so marked in some way, either by posts or by distances from some 

permanent objects, that their position can be readily determined after 

the stream is frozen. These sections should have the same general 

characteristics as good open-water sections; that is, depth and velocity 

should be fairly uniform, the bottom should be smooth, and there 

should be no cross currents. The previous selection of the section 

insures more accurate determination of the flow under the ice than 

would otherwise be possible, as the character of the flow beneath the 

ice will be nearly the same as in the open section. If the approximate 

cross section of the stream is known, the holes can be so spaced that 

the amount of water measured at each point will be in proportion 

to the total discharge, as in open-water measurements. A knowledge 

of the cross section may also save labor in cutting holes to determine 

the position of the edge of the water.

If the presence of frazil or of floating anchor ice at a section affects 

more than about 10 per cent of the total cross section, the measurements 

should, if possible, be made at another section where such conditions 

do not exist; for example, at rapids, where velocities are high enough 

to carry away the ice quickly. Although such sections may not be 

so desirable, in view of the depth and distribution of velocity, as 

the regular sections, the measurement will probably be more accurate 

than that obtained in a section which is partly clogged with frazil.

When the section for winter measurements has not been selected 

previous to the formation of ice cover and the engineer has no knowledge of conditions the measurement should be made at the regular 

open-water section, if it is equipped with a cable. If the open-water 

section is at a bridge, however, it is generally wiser to go upstream, 

in order to avoid the disturbing influence of the piers on the current. 

Ordinarily the ice in the open will also be safer than that under a 

bridge, and safety of the ice should be one of the first conditions 

investigated in making winter measurements.
FIELD METHODS. 63 

INSTRUMENTS.

The instruments necessary in making winter discharge measurements are a current meter, weight, cable, telephone attachment, and 

regular equipment; standard rods, 5 to 7 feet long, an ice chisel, and 

an ice measuring stick.

The meter and all its connections should be carefully examined 

to see that they are in good working order before the instruments 

are taken to the section to be measured. The meter itself should 

be lubricated with oil of the best grade, but sparingly, for if large 

quantities of oil are used it is likely to congeal and increase the friction of the meter.

Where the depths are so great that rods can not be used, the 

regular cable attached to the stem of the meter can be more easily 

handled than the smaller wire generally used for that part of the 

cable that goes into the water. Markers on the meter cable, 1 foot 

apart, measuring from the center of the meter, will be convenient 

in measuring the depth of the water and in placing the meter. 

Where depths under the ice are 5 feet or less, a rod to the end of 

which the meter is fastened will be most satisfactory. For depths 

over 5 feet rods made in 3 or 5 foot sections may be employed, as a 

rod made up of more than 5 standard 1-foot sections is too flexible. Bods on which the meter can be placed at the required depth, 

and which are constructed with the foot piece to rest on the ground, are 

not suitable for use when the temperature is below 32°, as the 

meter may freeze during the time required to set it; and if it could 

be kept from freezing, the operation would be difficult, as the meter 

rod is likely to coat with ice. Either a meter should be used w;th the 

rod fastened to the yoke or the regulation old-style meter with the 

end of the rod in the slot.

For the recording device one wire may be used, the rod being employed for the second connection; but two wires, one running from 

the meter and the other fastened to the lower section of the rod and 

connected to a standard plug will generally be more satisfactory, as 

ice that forms in the joints of the rod seems to cause resistance to 

the electric current. The twisted wire can be carried up alongside 

the meter rod and secured at frequent intervals with tire tape. When 

the measurement is completed this wire can be wound around the 

lower section of the rod, to which one end of it is already fastened.

Another method* is to run a wire down inside the rods. The 

ordinary meter cable serves very well. Then two holes are bored 

near the bottom of the lower section and the two strands of cable 

brought out through these. One strand is permanently connected

1 Successfully used by the engineers of the United States Geological Survey working in 

the Montana district.
64 THE EFFECTS OF ICE ON STREAM FLOW.

with the rod, and a standard connecting plug is attached to the upper 

end of the cable, so that in setting up the meter only one connection 

is necessary. In taking down the rod the sections are unscrewed 

and slipped along on the cable, leaving sufficient space between, so 

that they may be folded up into a bundle no larger than one section.

A useful article that may be packed in the meter box is a Marble 

safety ax, with either a wooden or steel handle. With this implement sufficient wood can be cut to supply a small fire by which, if 

necessary, the meter may be thawed.

A satisfactory ice chisel * is illustrated in Plate VII, A. The 

blade of this chisel is narrow and is not notched, and it is made of 

rather soft steel so that it can be easily sharpened with the hand 

file that should form part of the equipment. The handle is solid 

steel, and the complete chisel weighs about 14 pounds. A chisel 

lighter than this is of little value, as its jar when the ice is struck 

tires the hands very quickly.

A number of ice augers for cutting holes in the ice are on the 

market, but unless a large number of measurements are to be made at 

a station their size precludes their use in general routine work. The 

United States Army engineers, whose measurements are made almost 

daily at one location, often use an auger rather than an ice chisel.

The measuring stick shown in Plate VII, A, is made of 1-inch 

by 1-inch material to one end of which a 3-inch angle is fastened. 

The sticy is graduated in feet and tenths by means of double pointed 

tacks, the zero being at the angle iron.

METHODS.

Winter measurements made from a cable or bridge in a section without ice cover are made in the same manner as open-water measurements, except that the meter should not be taken from the water unless 

absolutely necessary until the measurement is completed. The soundings can be taken by lowering the weight until it touches the bottom 

and then raising it until the head of the meter is just under the surface of the water, adding to this depth the distance from the top of 

the meter to the bottom of the weight. If it is necessary to remove 

the meter temporarily from the water, on its return it should be 

permitted to run for a period before the revolutions are recorded, 

as the warmer river water will tend to thaw out any slight congealing 

in the meter. If the meter is out of the water until it becomes practically rigid it should be thawed and thoroughly dried near a fire, 

care being taken that it does not become so hot as to melt the rubber 

connections or the solder on the cups.

1 This chisel is made by Gifford Wood Co. and, except for the jointed handle, is a regular 

stock pattern.
U. S. GEOLOG'CAL SURVEY

Jointy*

siaangle

A. ICE CHISEL, ICE MEASURING STICK, AND BAG.

B. WINTER MEASUREMENT ON SHOAL POND BROOK, NEW HAMPSHIRE.

FIELD METHODS. 65

The first operation in measurements under ice cover is the cutting 

of the holes through the ice. The holes should be spaced 5 to 10 

feet apart, the interval depending on the width of the stream. (Se6 

PI. I, A and B, p. 10; PI. II, A and #, p. 20; and PI. VII, B, p. 64.) 

On small streams, where measurements of velocities are desired at 

many points close together, an entire section may be cut out, thus 

preventing the greater part of the vertical pulsations of the water. 

The position of the holes need not be accurately determined before 

cutting; they should, however, be placed in a straight line and as near 

as possible at right angles with the current. Eound or oblong holes 

are easier to cut than square holes, and the larger diameter should 

be parallel to the current. They should be large enough to permit 

the meter to be easily raised and lowered. A shovel will be found 

almost essential in clearing away snow from the ice in the vicinity of 

the holes and removing the chopped ice from the holes. The first 

3 or 4 inches of the ice can be cut more quickly with a sharp ax than 

with the ice chisel, but with the chisel illustrated (PI. VII, A) 

an ax is not necessary. The ice should be cut only at the circumference of the circle, as large cakes can be taken out with less shoveling than the small ones that are made when the entire cross section 

of the hole is chopped. Care should also be taken not to cut through 

the ice into the water until a few rapid blows of the chisel will 

clear the entire section. By working carefully holes can be chopped 

through ice 1 to 3 feet thick with very little splash; if, however, 

water is standing or flowing on the ice to depths of 1 or 2 inches it 

is almost impossible to chop holes without getting wet.

Where depths under the ice are greater than 4 or 5 feet a small cord 

should be tied to the ice chisel to prevent it from slipping into the 

water if it penetrates the ice unexpectedly.

As a rule it is advisable to chop one hole through the ice in the 

center of the section in order to detect the presence of frazil or 

floating anchor ice. If the hole so cut can not be kept clear from the 

finer particles of frazil, the measurement will probably give inaccurate results, and the engineer should endeavor to find a better section.

When the holes are cut and cleared of the chopped ice the distances 

between them should be measured with a steel tape and recorded inthe1 notebook, leaving sufficient space between the recorded measure-! 

meats for the record of velocities in the vertical. As the winter flow 

is likely to be fairly uniform, the soundings may be taken independently from the measurements of velocity. The gage height to the 

water surface should then be read and the soundings taken either 

with the rod or with the weight and cable. At each hble should be 

recorded (a) the thickness of the ice, (b) the distance from under 

surface of ice to water surface, and (c) the total depth of the

17020° WSP 837 13 5
66 THE EFFECTS OF ICE ON STBEAM FLOW.

 0 .2 depth 

 " ~

water. From these data can be computed the depth at which the 

meter must be placed in each hole in order that it may be at the 

0.2, 0.8, or 0.5 position beneath the ice. Thus 

0.2 depth= (c b) X0.2+b 

0.5 depths (c b) X0.5+b 

0.8 depths (c b) X0.8-f-b

The notation and a form for recording the data are illustrated in

figure 17.

The information collected regarding the total thickness of the ice

need not enter into the measurement.

When holes are cut through the ice a vertical pulsation, which may

amount to nearly half a foot, is often noticed in the water. In measuring the depth of the 

water care should be 

taken to determine 

the mean. If the 

depths beneath the 

ice are greater than 

2.5 feet, the measurement should be 

made by the 0.2 and 

0.8 point method; 

for depths between 

1.5 feet and 2.5 feet 

velocities should be 

observed at 0.2 and 

0.8 and 0.5 depth; 

for depths less than 

about 1.5 feet the 

mid-depth method 

should be used.

When the depth 

at which the meter 

must be held in each 

hole to record the 

mean velocity has 

been computed the 

meter can be assembled, care being exFIGCRB 17. Diagram showing factors used in making dis- erClSed that all COncharge measurements and new form proposed. ,. ,

nections are thoroughly made before it is placed in the water. The gage heights to the 

water surface should then be read again and the measurement begun. 

The meter should be so held in the hole that the head is as far 

upstream as possible to avoid the effect of the vertical pulsations.

O .5 depth

= (c-b)x.5 + b

O .8 depth

= (c-b)x.8 + b

Distance 

from

initial

point

0

IO .

IS

Thickness 

of ice

Water surface

to 

bottom of ice

a

&

OBSERV

Total depth 

of water

Effective

water depth

C

c-T>

AT10NS

Depth of"1

water surface

c-b)x.2+b

c-b)x.5+b

c-b)x.8i-b

Time

seconds

1 "*
FIELD METHODS. 67

If a rod is used, the meter can be kept in position by holding the 

rod against the upstream side of the hole; if a cable, the meter can 

be held at one position more easily by standing on the cable than 

by holding it in the hand. The number of revolutions and the time 

are recorded as in open-water measurements. After the complete 

data for each observation have been recorded while the meter is still 

in the water, the meter can be carried quickly to the next hole and the 

observations continued. In this way, if no frazil is present, the 

entire measurement may be completed without having the meter in 

the air long enough for the water on it to congeal.

When it is necessary to make observations at mid-depth, a coefficient should if possible be determined for reducing the velocity to 

the mean. If the river is not deep enough to obtain satisfactory 

vertical velocity curves, a coefficient may be obtained by observing 

the velocities at 0.2 and 0.8 and mid-depth at a number of sections 

and comparing the average of the velocities at 0.2 and 0.8 depth 

with that observed at mid-depth.

When the gage heights fluctuate to any extent while a measurement is in progress, they should be read frequently, and corrections 

should be made to the recorded observations of depth and computed 

positions.

NUMBER AND COST.

The number of current-meter measurements necessary to determine the winter flow of a stream depends so largely on local conditions that no definite rule can be given, but the axiom applicable to 

open-water measurements the greater the number the greater the 

accuracy applies with equal force to measurements made when ice 

is present. If the control section of a station is always clear of 

ice or if the flow is affected only by anchor ice, no more measurements are necessary than are necessary to determine the openwater flow at the same station. If surface ice is present at stations 

on streams uncontrolled by storage, the number of discharge measurements will depend almost entirely on the temperature; when conditions of temperature and run-off are uniform one measurement a 

month may be sufficient to insure good records; when thaws are 

frequent the number increases rapidly, and during certain periods 

in the winter it may be necessary to make measurements almost daily.

The cost of winter measurements is slightly greater than that of 

open-water measurements because of the additional time required to 

make each measurement, the possibility of poor transportation facilities, and the extra help necessary to prepare the section. The extra 

help can at times be obtained near the station, but for measurements 

at isolated stations it may be necessary to take an extra man from 

the office. The average cost of 91 discharge measurements made
68 THE EFFECTS OF ICE ON STREAM FLOW.

under complete ice cover in the State of Minnesota during the winter 

of 1911-12 was approximately $12, which covered all expenses and 

is but little greater than the average cost of making open-water 

measurements.

PERSONAL EQUIPMENT OF THE ENGINEER.

The accuracy of discharge measurements made during the winter 

depends largely on the personal comfort of the engineer making the 

measurement. The question of clothing should therefore be given 

considerable attention.

Woolen underwear, much heavier than that worn in the office, is 

most satisfactory, and if necessary two suits can be worn. A sheepskin-lined coat, either half or three quarter length, is preferable for 

use in Maine, northern New York, Wisconsin, Minnesota, North and 

South Dakota, and Montana; in regions farther south a heavy inackinaw, of a good material, will probably be sufficient. Leather or rubber boots are not as a rule suitable for wear where measurements 

are to be made through the ice. The standard 8 or 10 inch hunting 

boots, with rubber feet and leather uppers are waterproof up to 4 

or 5 inches, and when worn with German socks, inside which a lighter 

woolen sock may be worn, will give excellent service under all conditions. The boots should be large enough not to pinch the feet. 

With this combination the trousers can be tucked inside the socks. 

An outfit of this type is worn throughout the winter by lumbermen, 

laborers, and others whose work takes them into snow and water.

When the water stands on top of the ice an extra pair of trousers, 

which can be slipped on over those regularly worn, will be beneficial, 

as in cutting holes through the ice more or less water is splashed, 

which freezes to the clothing.

If the stations are some distance from hotels, two or three pairs of 

leather mittens without fingers and a pair of knitted finger gloves 

are also desirable. The heavy leather mittens, which should be worn 

in cutting the holes with the ice chisel, will probably be so wet and 

frozen by the time holes are cut as to be of little further use until 

thorpughly dried. In making the discharge measurement a second 

large pair of mitten gloves can be worn over the knitted finger 

gloves; the outside gloves can be pulled off so that the notes can be 

made without exposing the hand. The woolen gloves will also be 

serviceable when setting up and repairing the meter. A third pair 

of gloves will be necessary for use when driving back to the hotel, as 

it is practically impossible to keep the mittens dry while cutting holes 

or making discharge measurements.

To one not accustomed to making discharge measurements in the 

winter, the foregoing details concerning clothing may seem unneces-
OFFICE METHODS. 69

sary, but it is believed that the accuracy of many measurements has 

been much impaired by hurried work resulting from the personal discomfort of the person making the measurement.

ICE NOTES.

Many of the notes regarding the thickness of ice at the gage, 

thickness of ice across the river, and distance from the water surface to the top of the ice required of the gage readers are not used 

in computing the discharge and therefore are unnecessary. As a 

rule, the gage reader is not qualified to determine the mean thickness 

of ice at the control section information that might enable the 

engineer to make a fairly accurate estimate of the discharge and 

data regarding the distance from the water surface to the top of the 

ice, which are collected particularly to show whether the ice is in 

flotation, do not at present enter into the computations. The gage 

reader should, however, be required to report the first appearance of 

ice in the river below the gage and the date of its disappearance. 

The average observer, if carefully instructed, can be so impressed 

with the importance of his part in the work of collecting streamflow records that he will furnish information other than the routine 

data called for.

OFFICE METHODS.

GENERAL FEATURES.

The winter is most emphatically the time of the year when a dailydischarge record should be kept constantly up to date, so far as 

possible, for all stations maintained, for one of the important points 

in connection with records of winter flow is the determination of 

the time when discharge measurements will be most valuable.

The form of ice and the manner in which the stations are operated tend to separate them in general into three groups: (1) stations at which the control section is open or nearly always open; 

(2) stations at which the stage is affected by anchor ice and. a small 

amount of surface ice; and (3) stations at which the flow is affected 

by surface ice only. Each group requires a different manner of 

treatment.

For stations of the first group the gage heights should be transferred at once from the weekly, report cards to the proper form, and 

the daily discharge should be determined by applying the gage 

heights to the open-water curve. When discharge as computed seems 

to be increasing and the temperature records do not indicate a thaw, 

the station should be visited and a current-meter measurement should 

be made; if the gage reader has already reported ice that may have 

gone out by the time the card has been received, the temperature
70 THE EFFECTS OF ICE ON STREAM FLOW.

record should be used to correct the discharge. When the control 

section is near the gage, the gage reader can note on the card the presence of the ice, or he may be able to infer backwater from increased 

gage heights and note it on the card.

For stations at which the flow is affected only by surface ice the 

same general method can be followed. As a rule, when surface 

ice has begun to form measurements should be made whenever 

the daily discharge as computed from the minimum gage height 

appears, on comparison with the temperature records, to be too large.

For stations at which the flow is affected only by surface ice the 

best results can probably be obtained by grouping them geographically, according to the results of experience both with the openseason and winter discharge, so that records for a week can be consistently compared. By means of this daily work and constant comparison the engineer can, as a rule, determine when the estimates at 

a given station are becoming unreliable and when a measurement 

should be made; knowing the true discharge for the day of measurement, and thus the gage-height correction, he can then correct the 

back records for that station and for other stations at which the 

flow is comparable.

By keeping the office work up to date it is, as one of the former 

engineers 1 of the Survey has said, " much easier to make discharge 

measurements at the right time than to make measurements which 

you trust and pray may be taken at the right time, and then, two or 

three months later, to wish you had other measurements in place of 

those you have and still others in place of those that you never took 

at all."

COMPUTATIONS.

The computations of winter flow have been more uncertain than 

any other work in connection with the determination of stream 

flow chiefly because the field men have failed to collect sufficient data 

to allow the estimates to be based on fact rather than on fancy. 

In all computations of open-season flow the various steps leading to 

the final results are recorded so that they may be checked at any 

time. No reason is apparent why similar records should not be made 

of the computations of winter flow. Any estimate has more weight 

if all the base data are available for inspection. It is therefore suggested that, regardless of the method used to determine the mean 

monthly discharge and the probable monthly variation in flow, the 

complete base data be kept in such shape that they can be inspected 

and the final results checked. Estimates derived from base data 

which can not be shown should not be published.

Experience has shown that the winter estimates can, as a rule, be 

made more quickly and more accurately by the engineer who has had

i B. H. Bolster.
OFFICE METHODS. 71

charge of the collection of the data and is familiar with the local 

conditions during the observations.

FORMS.

In order that only such base data as are fundamental will be collected and that these data may be grouped for study in such shape 

that any method that has yet been proposed can be used, the accompanying form for reporting the daily gage readings has been 

devised:

OBSERVATIONS OP RIVER HEIGHT, TEMPERATURE, ETC., DURING THE SEASON OP ICE. 

Station...........................................................................................

Month. ....... ......191...

Day of 

week. Date.

Time.

Reading.

Time.

Reading.

Time.

Reading.

Water height 

on gage.

A.M. P.M.

Temperature.

Low. High.

Weather.

4

Condition of ice below 

gage and at riffle.

See instructions in gage-height book.

Observer.

The card may call for more data than will be required at many 

stations, but only under exceptional circumstances will more data be 

required from the gage reader. The amount of data reported from 

each station will depend on the character of the stream and of the 

ice.

The gage-height books should contain the data recorded on the 

weekly card. The instructions for the observer have been made rather 

complete in the book but should be supplemented from time to time 

with circular letters. Temperature and weather should be noted each 

day. The temperature columns are marked " high " and " low," for 

it is unlikely that the observers will be able to record the absolute 

maximum and minimum; if they are careful, however, they will be 

able to so take the observations that the mean will approach the absolute mean.

To facilitate the study of the base data a form (fig. 18) has been 

devised on which the data furnished by the gage reader and field men 

are transcribed. This form, either alone or in connection with a
72 THE EFFECTS OF ICE ON STREAM PLOW.

graphic plot, such as-the plots shown for Kootenai, Schroon, and Elk 

rivers (Pis. IV and V, and fig. 16) will suffice for computations of 

winter flow under any conditions and with practically any method. 

The results of observations can be copied on this sheet as soon as the 

cards are received from the observers and the computations can be 

kept up to date by an office engineer.

UNITED STATES GEOLOGICAL. SURVEY

DAY

1

2

3

4

S

6

7

a

9

10

_/£_

Observed

Water height at gage

Morning

Time

 -_

Height

_ '

Afternoon

Time Height

~^~^

Mean 

height

"

Temperature

High Low Mean

^ 

Weather

tee 

at 

control

Results 

of 

discharge 

measure 

merits

Computed

effective 

gage 

height

'"" - 

Estimated 

discharge, 

second-feet

'

 -11 " "

24

25

26

27

28

29

30

31

^ <*

\

Mean discharge

___ __to_____

_____ .Maximum, _ 

-__ Minimum _

r -^___^ -^

Sec. ft.

/ 

Compis 

Checke

FIGURE 18. Proposed computation sheet. /

A sheet should be required for each month during which ice is 

present at a station for which estimates are being made.

ACCUBACY.

DISCHARGE MEASUREMENTS.

The number and distribution of the discharge measurements made 

during the winter determine the accuracy of the final computations. 

In general the individual winter measurement is less accurate than a 

measurement made in the summer for the following causes:

1. The presence of ice in the river, either covering the surface, 

attached to the bottom or banks in the form of anchor ice, or floating 

throughout the cross section as frazil or slush ice. When ice is float-
OFFICE METHODS. 73

ing throughout the cross section the meter soon becomes clogged and 

gives results that are too low. The meter must be then taken from 

ithe water to clean it, and when temperatures are near zero it will 

quickly freeze.

2. The freezing of the meter while the observer is passing it from 

measuring point to measuring point or making necessary repairs.

3. Hurry in the work, due to the physical discomfort of tjie engineer while making the measurement.

4. The inability of the engineer to detect under surface ice eddies or 

other conditions that disturb the distribution of flow, and his tendency to measure velocities at too few points.

5. The impossibility of measuring the effective cross section as 

accurately under ice cover as in open water.

GAGE HEIGHTS.

The gage-height records used to determine winter discharge are 

probably quite as accurate as those employed to determine open-season discharge. The accuracy of the observer's work varies little 

throughout the year except during periods in which, owing to dangerous condition of the ice, the gage can not be closely approached.

The accuracy of automatic gage records may possibly be impaired 

by ice which may form either in the intake or in the well.

ESTIMATES OF DAILY AND MONTHLY DISCHARGE.

In general the accuracy of the estimates of daily and monthly 

discharge will depend on the number of discharge measurements, 

which in turn will depend on the amount of money available for 

winter work. The error of daily estimates for days on which no 

discharge measurements are made is likely to be great. The accuracy of the monthly mean, however, should approach the accuracy 

with which the mean can be used either in designing or in operating 

hydraulic plants, which is about 10 per cent, and it is probably not 

advisable to spend money in trying to obtain winter records much 

closer than 10 per cent. At stations whose control section remains 

open throughout the winter or at which the stage Is affected by 

anchor ice only, the accuracy of the record should approach that of 

the open-channel record. For stations on streams uncontrolled by 

storage and at which flow is affected by surface ice or by frazil, 

the records can not approach nearer than 10 per cent of absolute 

accuracy and may fall below 25 per cent.1 Records at stations on 

streams which have a considerable diurnal fluctuation are far less

1 In the scale of accuracy adopted by the United States Geological Survey, A = within 

5 per cent, B = within 10 per cent, C = within 15 per cent, and D = within 25 per cent.
74 THE EFFECTS OF ICE ON STREAM FLOW.

accurate, for the effect of the fluctuations can not generally be determined with an automatic gage, as they can when the streams are 

open.

The absolute maximum discharge can be determined only by daily 

measurements. The absolute limits of maximum discharge may be 

obtained by applying the maximum gage height to the open-water 

curve, but the necessary correction is always uncertain, so that the 

maximum discharge as a rule is undeterminable.

If a careful watch is kept of temperature the absolute minimum 

during the winter should be obtained with almost the same degree 

of accuracy as during the rest of the year. On uncontrolled streams 

having little natural storage the minimum flow can generally be 

determined by measurements made soon after the longest cold period. 

For streams having a large amount of lake storage the minimum discharge will generally occur almost at the end of the winter, just 

before the added inflow caused by the spring breakup.
INDEX.

A. 

Accuracy, degree of.......................... 72-74

Acknowledgments to those aiding........... 8

Adams, C. R., on flow in ice-obstructed

streams......................... 49

Affluents, effect of, on ice formation......... 27-28

Altitude, effect of........................... 22

Anchor ice, effects of............... 42-48,60-61,62

effects of, gage studies of........... 42-48,55-^57

formation of............................. 29-30

Artificial control, effects of................... 23-24

effects of, figures showing................ 23,52

B. 

Babb, Mont., gage studies near.............. 38-39

gage studies near, figure showing........ 39

Bames, H. T., experiments of............... 28-29

ice formula of............................ 25

Barometric pressure, effect of................ 17-18

Bibliography................................ 8

Big Falls, Minn., winter measurements near,

view of.......................... 20

Bigfork River, Minn., rainfall and run-off on. 20-22

winter measurements on, view of........ 20

Big Lake, Minn., gage studies near.......... 34-35

gage studies near, figure showing........ 35

Bow River, Alberta, gage height and temperatureon.......................... 19

Brush, use of, to prevent freezing............ 60

C. 

Cambridge, Minn., winter measurements at,

view of......................... 10

Cannonball River, Minn., distribution of velocities on, beneath ice, figure 

showing........................ 32

Chain gages, use of.......................... 60

Chandler, E. F., on Red River of the North.. 22 

Channels, forms of, effect of, on ice formation. 28 

Chemung River, N. ¥., effect of frazil on flow

of, figure showing............... 41

Chinook winds, effect of..................... 18-19

effect of, figure showing................. 18

Climatic factors, descriptio ' of............... 9-19

See also Precipitation; Temperature;

Wind; Barometric pressure. 

Climatologic records, character of............ 61

Clothing, character needed for winter measurements. ....................... 68-69

Computations, making of.................... 70-71

Connecticut River, ice period on............. 27

Control, artificial. See Artificial control.

Control sections, classification of............. 69

nature of................................ 30,62

relation of, to surface ice........ 31,33-34,49,62

figure showing....................... 33

selection of.............................. 59

Covert, C. C., work of....................... 8

Crow Wing River, Minn., gage studies on.... 36-37

gage studies on, figure showing.......... 37

Curves, rating. See Rating tables.

D.

Dams, ice on, errors due to.................. 59

Discharge, daily and monthly, estimates of,

accuracy in...................... 73-74

Discharge, temperature, and gage heights,

relations of...................... 7

relations of, plate showing............... 46,48

Discharge under ice, computation of...... 30,48-57

measurements of, accuracy of............ 72-73

instruments for...................... 63-64

methods of.......................... 64-67

number and cost of.................. 67-68

section for, determination of......... 62

timing of............................ 70

E.

East Grand Forks, Minn. See Grand Forks,

N. Dak. 

Elk River, Minn., gage studies on........... 34-35

gage studies on, figure showing.......... 35

Engineers, equipment 6f.................... 68-69

Evaporation, effects of...................... 70

Eye method of computing discharge......... 51-52

F.

Field methods, description of................ 57-69

Forms, figure showing....................... 72

use of................................... 71-72

Frazil, detection of.......................... 65

effects of............................. 40-42,62

figure showing....................... 41

formation of............................. 28-29

Frozen ground. See Ground, frozen.

G.

Gage heights, on ice-obstructed streams, computation from................... 48-57

on ice-obstructed streams, determination

of............................... 34

determination of, accuracy of........ 73

Gage heights, temperature, and discharge,

relation of, plate showing..... 46,48,52

Gaging stations, selection of................. 57-59

studies at, details of............... 34-40,42-48

value of............................. 32-34

Gages, types of, description of............... 60-61

Genesee River, ice period on.../............. 27

Geologic factors, effect of.................... 19-20

Gradients, effects of......................... 22-23

Grand Forks, N. Dak., gage studies near.... 37-38

open-water and under-ice flow near, relation of, plate showing........... 38

75
76 INDEX.

Graphic computation of discharge, description of.......................... 52-55

use of................................... 55-57

figure showing...................... 46,54

Ground, frozen, effect of................... 9,10,11

normal depth of......................... 11

Ground water, amount of, effect of topography

on.............................. 20-22

amount of, relation of, to winter now.... 20

fluctuation of, with seasons.............. 9-10

figure showing....................... 10

release of................................ 12

H.

Havre, Mont., temperature rise at, figure

showing......................... 18

Hudson Bay, drainage in Minnesota, relation

of flow and temperature on...... 14

I. 

Ice,effect of................................. 11

formation of............................. 24-30

inaccuracy due to....................... 72-73

maximum thickness of.................. 27

measurements under. See Discharge,

measurements of.

See also Surface ice; Frazil; Anchor ice. 

Ice chisel, plate showing.................... 64

use of................................... 64

Ice holes, cutting and spacing of............. 65

Ice jams, effects of........................... 31

Ice notes, character of....................... 69

Illinois River, ice period on.................. 27

Inclined gages, disadvantages of............. 59

Instruments for measurements under ice,

nature of........................ 63-64

International Falls, Minn. See Rainy River.

J.

Jones, B. E., work of.

K.

Kanawha River, ice period on............... 27

Kootenai River, Mont., gage studies at. 13,42-48,53 

gage studies at, figure showing.......... 43,46

L. 

Lakes, effects of............................. 20-22

flow from, effect of, on ice............... 27

Lake Superior drainage in Minnesota, relation of flow and temperature on . 14 

Lamb, W. A., work of....................... 8

Latitude, effect of........................... 7,22

Laws of flow under ice...................... 8

Libby, Mont., gage studies at......... 13,42-48,53

gage studies at, figures showing.......... 43,46

Litflefork River, rainfall and run-off on...... 20-22

M.

Measuring stick, plate showing.............. 64

use of.................................... 64

Merrimac River, N. H., ice period on........ 27

Minimum flow, season of.................... 7

Minnesota, minimum flow in................ 16-17

minimum temperature in................ 16

relation of topography and storage in.... 20-22

figure showing....................... 21

Minnesota River, Minn., ice period on....... 27

Page.

Minnesota streams, relation of flow and temperatures on..................... 13-17

Mississippi River, ice period on.............. 27

relations of flow and temperature on..... 12-13 

figure showing....................... 12

Mississippi River drainage in Minnesota, relation of flow and temperature on. 15 

Missouri River,ice period on................ 27

Mountain streams, effect of freezing on .... 11

N.

Needle ice. See Frazil.

O. 

Office methods, computations, use in........ 70-71

forms used in............................ 71-72

figure showing....................... 71

nature of................................ 69-70

Ohio River, ice period on.................... 27

Open-season flow, lack of uniformity in...... 57-58

P.

Percolation, prevention of, by freezing...... 10,11

Peters, F. H., work of....................... 8

Piercefield, N. Y., gage studies at............ 39-40

gage studies at, figure showing.......... 40

Pillager, Minn., gage studies at.............. 36-37

gage studies at, figure showing.......... .37

Power-plant records, value of................ 50-60

Precipitation, effect of.................. 9-10,16-17

Publications, lists of......................... 8

R. 

Rainy River, Minn., artificial control of...... 24

artificial control of, figure showing...... 23,52

discharge curves for..................... 51

figure showing....................... 50

discharge of, computation of............. 52-53

figure showing....................... 46

gage studies on, plate showing........... 52

Raquette River, N. Y., gage studies on...... 39-40

gage studies on, figure showing........... 40

Rating curves. See Rating tables. 

Rating tables, open-water, applicability of.. 7 

changes in, by ice....................... 30,31

figure showing....................... 33

computation by, on ice-obstructed

streams.......................... 48-49

relation of, to ice rating tables, plate showing.............................. 38

Rating tables, special, on ice-obstructed

streams, figure showing.......... 50

on ice-obstructed streams, use of......... 49-51

Recording gages, use of...................... 60-61

Records, winter, factors in................... 8

interpretation of........................ 8

importance of........................... 7

Red River of the North, floods on........... 22

gage studies on.......................... 37-38

ice period on............................ 27

open-water and under-ice flow on, relation of, plate showing............ 38

Reservoirs, effect of......................... 23-24

records of................................ 59-60

Riverbank, N. Y., gage studies at............ 48

gage studies at, plate showing........... 48

Rum River, Minn., ice storage on........... 10

winter measurements on, view of........ 10
INDEX. 77

____ s.

St. Croix River, Wis., ice period on.......... 27

St. Mary River, Mont., gage studies on...... 38-39

gage studies on, figure showing.......... 39

Sauder, P. M., workof...................... 8

Schroon River, N. Y., gage studies at....'.... 48

gage studies at, plate showing........... 48

Shoal Pond Brook, N. H., winter measurements on, view of............... 64

Slichter, C. S., on barometric pressure....... 17-18

Slush ice. See Frazil.

Snow, effect of.............................. 9,11

Springs, eifect of, on ice..................... 28

Staff gages, use of........................... 60

Stage and discharge, relations of........... 7,30,31

Stream flow, effects of ice on, computation

of............................... 48-57

fluctuations of, effect of, on ice formation. 28 

records of, importance of................ 7

velocity of, effect of, on ice formation.... 28

See also Winter-flow records; Discharge. 

Surface ice, affluents and, relations of........ 27-28

bridging by, effect of.................... 31

discharge under, graphic computation of. 52-53 

figures showing...................... 54

duration of.............................. 25-27

effects of.............. i.............. 31-40,60

gaging-station studies on ............ 32-40

fluctuations and, relations of............ 28

friction of............................... 31

formation of............................. 24-25

stream bed and, relations of............. 28

Page.

Surface ice, velocity of water and, relations of. 28 

Susquehanna River, Pa., ice period on...... 27

T.

Temperature, effect of....................... 10-17

effect of, plates showing.............. 46,48,52

figure showing........................... 12

Topographic factors, effect of................ 20-23

V.

Valley streams, effect of freezing on. .^........ 11

Vegetational factors, effect of................ 23

Velocities under ice, distribution of.......... 31-32

distribution of, figure showing........... 32

laws of.................................. 8

Vermilion River, Minn., rainfall and run-off

on.............................. 20-22

winter measurements on, view of........ 20

W. 

Winds, warm, effects of..............r ...... 18-19

effects of, figure showing................. 18

Winter-flow factors, classification of.......... 9

description of............................ 9-24

See also Climatic factors; Geologic factors; 

Topographic factors; Vegetational factors; Artificial factors. 

Winter-flow records, importance of.......... 57

stations for.............................. 57-59

Y.

Yellowstone River, ice period on............ 27

o