Water-Supply and Irrigation Paper No. 187 Series M, General Hydrographic Investigations, 19 

DEPARTMENT OF THE INTERIOR

UNITED STATES GEOLOGICAL SURVEY

CHARLES D. WALCOTT, DIRECTOR

DETERMINATION OF STREAM FLOW 

DURING THE FROZEN

SEASON

BY

H. K. BARROWS AND ROBERT E. HORTON

WASHINGTON

GOVERNMENT PRINTING OFFICE

190T

CONTENTS.

Importance of winter records of stream flow.................................. 5

Methods of gaging streams during the open season............................. 6

General statement............'......................................... 6

Weir method ......................................................... 6

Velocity method ...................................................... 6

Slope method......................................................... 7

Conditions during the winter season.......................................... 7

Factors affecting ice formation .......................................... 7

Classification of winter conditions........................................ 8

Duration of ice season ................................................. 9

Change in thickness of ice.............................................. 10

Surface, anchor, and needle ice.......................................... 10

Range of winter gage heights ............................................ 13

Flow of streams under ice cover............................................. 14

General considerations................................................. 14

Friction due to air and ice.............................................. 14

Relative importance of air and ice friction................................ 15

Variation in slope due to freezing........................................ 17

Change in area of waterway required by freezing .......................... 18

Effect of thickness of ice on flow......................................... 19

Methods of obtaining winter records......................................... 21

Current-meter stations................................................. 21

Gage heights...................................................... 21

Current-meter discharge measurements................... ^........... 22

Stations at dams ...................................................... 25

Estimates from precipitation............................................ 25

Winter records............................................................ 26

Conditions at stations.................................................. 26

Catskill Creek at South Cairo, N. Y.................................. 26

Connecticut River at Orford, N. H .................................. 29

Esopus Creek at Kingston, N. Y .....................:.............. 30

Fish River at Wallagrass, Me....................................... 32

Kennebec River at North Anson, Me ................................ 33

Rondout Creek at Rosendale, N. Y.................................. 34

Wallkill River at Newpaltz, N. Y.................................... 35

Winooski River at Richmond, Vt.........................--------"..- 37

Gage heights and discharge measurements................................ 38

Station rating curves for ice cover -.............................--------. 43

General considerations ............................................. 43

Wallkill River at Newpaltz, N. Y.................................... 43

Kennebec River at North Anson, Me................................. 44

Connecticut River at Orford, N. H................-........--.----.-- 45
4 CONTENTS AND ILLUSTRATIONS.

Winter records Continued. Page. 

Station rating curves for ice cover Continued.

General form of rating curve for ice cover ............................ 46

Relation between discharge under ice cover and for open section ........ 46

Vertical velocity measurements" under ice cover ........................... 46

Details of vertical velocity curves.................................... 46

Summaries of vertical velocity curves ................................ 72

Form of vertical velocity curves..................................... 75

Relation of depth and velocity to form of curve....................... 77

Comparison of vertical velocity curves with and without ice cover....... 78

Position of threads of mean velocity................................. 79

Position of maximum velocity and relation to mean velocity............ 81

Relation of velocity at mid depth to mean velocity.................... 82

Relation of mean of velocities at 0.2 and 0.8*"depth to mean velocity..... 83

Percentage variation in observations at different depths................ 85

Slope determinations and values of n in Kutter's formula, under ice conditions.... 87

Data from other sources.................................................... 88

Conclusions............................................................... 89

Practicability of winter estimates of flow................................. 89

Recommendations as to methods........................................ 89

Index...:................................................................ 91

ILLUSTRATIONS.

PLATE I. A, Gaging station on Sandy River at Madison, Me., at dam of Madison

Electric Company; B, Gaging station on Winooski River at Richmond, Vt...... 24

FIG. 1. Cross sections of Chemung River at Chemung, N. Y , showing effect of

needle ice ..................................................... 12

2. Effect of freezing on a smooth section of a river terminated by rapids .. 17

3. Effect of change of stage on discharge under ice cover, with varying

thickness of ice ................................................ 20

4. Rating and velocity curves under ice cover, Wallkill River, New York.... 43

5. Rating curve under ice cover, Kennebec River, Maine.................. 44

6. Rating curve under ice cover, Connecticut River, New Hampshire ....... 45

7. Form of vertical velocity curves..................................... 75

8. Comparison of vertical velocity curves for streams with and without ice

cover .......................................................... 78

9. Vertical velocity curves under ice cover, Kennebec River, Maine......... 79

10. Vertical velocity curve under ice cover, Wallkill River, New York........ 80

11. Vertical velocity curves under ice cover, Connecticut River, New Hampshire ..--.......................-.-.-...--..--.-------.--.--.-.. 81

12. Vertical velocity curves under ice cover, Fish River, Maine.............. 82

13. Effect of depth on form of vertical velocity curves under ice ............ 83

14. Effect of very rough, broken, and tilted ice on form of vertical velocity

curves under ice cover ..........--..........-.....-----.-----.... 84
DETERMINATION OF STREAM FLOW 

DURING THE FROZEN SEASON.

By H. K. BARROWS and R. E. HORTON.

IMPORTANCE OF WINTER RECORDS OF STREAM FLOW.

Estimates of the flow of rivers are now being made by the United 

States Geological Survey in all parts of the country. To a great 

extent these are based on daily gage readings and numerous currentmeter measurements.

In the northern and central parts of the United States the streams 

may be closed by a more or less permanent ice cover for a considerable portion of the year. This- period varies from nearly five months 

in the extreme north to a few weeks or less in the Central and Atlantic 

States.

The methods in use for estimating flow under open-channel conditions have become well defined, and the limits of accuracy are known 

to be reasonable. On the other hand, the laws governing the flow 

of rivers that are frozen over have been but little investigated, and 

methods for estimating the flow under silch conditions have not been 

formulated. . Moreover, in winter the measurement of precipitation 

is more difficult, and available data of this kind are much less accurate 

than in summer. Finally, there is not even an approximate relation 

between the snowfall and the stream flow, so that the failure to obtain 

winter records of flow at a gaging station means a considerable percentage of uncertainty as to the total run-off as well as to its distribution.

In the Northern States droughts are apt to occur in the late summer or fall and during the winter. At times this condition of drought 

may be nearly or quite continuous between these two periods, with 

its culmination in January or February. If there is no melting of 

snow during the winter, the inflow to streams that freeze is chiefly 

derived from springs, ground water, and lake storage, and in a long, 

cold winter, especially if it succeeds a period of low water, the minimum flow for the year may be reached and continue for some time. 

Estimates of flow, therefore, to be of conclusive value on streams 

utilized for water power, must embrace these winter periods of low 

water.

5
6 STREAM FLOW DURING THE FROZEN SEASON.

METHODS OF GAGING STREAMS DURING TIIE OPEN

SEASON.

GENERAL STATEMENT.

The methods of stream gaging in common use by the United States 

Geological Survey contemplate especially the determination of discharge when streams are free from ice at or near the gaging stations. 

One object of the present paper is to determine what modifications 

of these methods are necessary to secure good results when the streams 

are ice covered. With this in view a brief description of open-water 

methods is given below.

In general a record of the fluctuations in stage is obtained by daily 

reading a gage or gages. Various methods are used to obtain a rating of the stream so that the discharge in second-feet can be determined 

from the gage readings. Three principal methods of rating are in 

use (1) the weir method, in which a weir or dam is used and the flow 

is computed for a given gage height; (2) the velocity method, in 

which a series of current-meter or float gagings are made at a given 

cross section and a discharge rating curve is obtained for that cross 

section; (3) the slope method, in which observations are made of the 

mean cross section and surface slope in a stretch of the river, and the 

velocity is computed by the Chezy-Kutter formula, V = Cv/RS, a 

suitable value being assumed for the coefficient C.

WEIR METHOD.

Weirs of standard type with sharp crest can be used on small 

streams only, on account of the cost of installation and liability to 

injury. Where practicable, they offer the best facilities for determining the flow. The flow at dam stations is usually divided part 

going over the dam, part through the wheels, and part through bychannels. A weir formula with modified coefficient is used to compute the flow over the dam. The- wheels are used as meters, a record 

being kept of gate openings, head, etc. Flow through by-channels 

which at many dams occurs only at intervals, is computed by the use 

of weirs, orifices, etc. The sum of these components is the total 

discharge of the river at the section. The general methods used at 

stations of this character are fully described in Water-Supply Paper 

No. 150.

VELOCITY METHOD.

The determination of the rate of flow past a certain section of a 

stream at a given time is termed a "discharge measurement." This 

rate is the product of two factors the mean velocity and the area of 

cross section. The mean velocity is a function of surface slope, 

wetted perimeter, roughness of bed, and the channel conditions at, 

above, and below the gage section. In this method it is assumed
WINTER CONDITIONS. 7

that the stream bed is constant in form and position and that the 

mean velocity at any given stage will always be the same. Therefore a rating curve may be obtained by plotting the results of a sufficient number of discharge measurements at different stages. In 

making the measurements an arbitrary number of points, known as 

"measuring points," are laid off on a line perpendicular to the thread 

of the stream, and the velocity and depth are observed. These 

points are usually at regular intervals from 2 to 20 feet apart, depending on the size and condition of the stream. The current meter is 

commonly used for obtaining velocities, althoughin a few cases rod or 

tube floats are utilized for this purpose. The area is thus divided 

into small sections in which the velocity is observed and the discharge 

computed, and the sum of the values for these sections gives the total 

area and discharge. If a sufficient. number of discharge measurements are made at different stages, a rating table can be constructed 

that will show the discharge at any stage of the stream. The methods 

used in selecting current-meter stations and in collecting data are 

fully described in Water-Supply Papers Nos. 94 and 95.

SLOPE METHOD.

The results obtained from the slope method are in general only 

roughly approximate, owing to the difficulty in obtaining accurate 

data and the uncertainty of the value to be used for n in Kutter's 

formula. f The most common use of this method is in estimating flood 

dischapge of streams when the only data available are the cross sections, the surface slope as shown by marks along the bank, and a 

knowledge of the general conditions.

Throughout this paper velocities are expressed in feet per second, 

gage heights in feet, and the volume of flow of streams in cubic feet 

per second, or second-feet.

CONDITIONS DURING THE WINTER SEASON. 

FACTORS AFFECTING ICE FORMATION.

Karely, if ever, in this country does a stream of any size freeze over 

throughout its whole length, there being usually short stretches that 

remain more or less open. Two important factors govern the formation of ice on streams (1) the climatic or general temperature conditions; (2) the size and character of the stream and the conditions 

affecting its flow.

In California, Washington, and Oregon, and south of latitude 37°, 

with the exception of perhaps a portion of northern New Mexico and 

Arizona in the Kocky Mountain district, the rivers do not in general 

freeze over sufficiently to affect records of flow or to occasion any 

change in methods from those of the open season.
8 STREAM FLOW DURING THE FROZEN SEASON.

In the most general sense, the character of the bed and banks of a 

stream depends 011 its slope and the materials over which it flows. 

A stream will not freeze over unless the water has a temperature as 

low as 32° F. and is comparatively still. If the water is greatly agitated, needle ice will be formed instead of an ice cover. This tendency to form needle ice always exists at rapids, particularly if the 

stream bed is very rough. If the cold is extreme and long continued 

even such places may eventually become frozen the freezing starting at the water's edge or around rocks and piers, where the velocity 

is lower, and extending toward the center of the stream. The result, 

however, is not in any case a smooth ice cover, but a piling up of very 

rough or " honeycombed " ice which maybe partly supported by rocks.

Where dams have been constructed there is usually above the dam 

more or less pondage and a great diminution in velocity, so that such 

portions of a river freeze over very readily. Below the dam quick 

water is frequently left, and conditions may be the same as at rapids.

Any special conditions tending to raise the temperature of the water 

may have a marked effect on the time or manner of freezing over of a 

portion of a stream. Near the outlets of lakes or in streams fed by 

springs or ground water there may be a sufficient inflow of water 

having a temperature considerably above 32° F. to prevent wholly or 

c,t least for some time the formation of an ice cover. Such conditions are also potent in assisting the rapid wearing away of the under 

surface of the ice and, in general, they result in very unstable conditions as regards ice cover. The temperature of springs is ordinarily 

about equal to the average annual temperature of the locality, which 

is for the Northern States 40° to 50° F.

CLASSIFICATION OF'wiNTER CONDITIONS.

It is evident that streams of any considerable length can not be 

classified as a whole with regard to ice formation or winter conditions, for the reason that very diverse conditions may occur at different parts of the same stream. The conditions on short stretches of 

streams, and particularly on such stretches as need to be considered 

in selecting current-meter stations, may be classified as fellows:

Classification ofvnnter conditions at current-meter stations.

(1) Smooth, permanent ice cover.

(2) Tendency for anchor or needle ice to accumulate underneath ice cover.

(3) Unstable ice cover, due to 

(o) Effect of warmer inflow from lakes or tributary streams. 

(&) Effect of inflow of ground water.

(c) Effect of warm currents due to artificial causes, such as factory waste, etc.

(d) Concentrated quick water and wearing away due to friction.

(e) Considerable fluctuation in stage occasioned by winter freshets.

(4) Rough ice cover and piling up of ice due to quick water and rough bed.
WINTER CONDITIONS. 9

(5) Tendency for ice jams to occur, with consequent backwater, etc.

(6) Streams that remain open altogether or freeze over thinly for short times, owing to 

(a) Extremes of conditions as noted under (3).

(b) High temperature, mainly in the southern portion of the area,, subject to 

ice conditions in winter.

The above classification is intended for the ordinary winter. The 

winter of 1904-5 was much colder than the average, and many 

streams remained frozen over in places where ordinarily there would 

not be permanent ice. On the other hand, the winter of 1905-6 

was remarkably mild, and ice was carried away by freshets at many 

points where this very rarely happens. A gaging station, then, can 

be only approximately fixed in any of the above classes.

The following tables summarize the winter conditions at 179 current-meter stations and 25 dam stations:

Summary of winter conditions at current meter stations.

Class.

(2) Tendency for anchor and needle ice to accumulate.

New England.

11

4 

10

7

1

5

38

New York 

and lower 

Michigan.

11-

5 

3

3

1

10

33

Atlantic 

States.

13

2 

21

6

8

7

57

Central 

States.

35

00 ^

(a\

(a)

7

51

" Not reported in detail.

Of the 179 stations considered 29 remain unfrozen thruout the 

winter, and at these stream flow can be estimated in the same manner 

as during the open season. Smooth, permanent ice cover is found at 

70 stations. The remaining 80 stations have miscellaneous conditions, 

all of which are probably unfavorable for estimating winter flow.

Summary ofiointer conditions at stations at dams.

Good conditions for estimates, crest unobstructed, ice cut away, or water mostly used 

by wheels................................................................ .13

Poor conditions for estimates, crest seriously obstructed........................... 12

DURATION OF ICE SEASON.

25

The following table gives the usual duration of ice cover in different 

areas where the streams freeze during the winter.

Duration of ice cover, by areas.

Locality. Date of closing in. Date of breaking up.

March 1-15...... .........

Time 

frozen.

Months. 3J-5

2 -3J

 li-3

3 -4

U-2J

1-21

34 di
10 STREAM FLOW DURING THE FROZEN SEASON.

A large amount of information relating to the duration of the ice 

season, especially with regard to lakes and navigable streams, was 

'published in the report of the United States Deep Waterways Commission. a A few of the results for rivers there given are compiled in 

the following table:

Duration of ice cover on northern streams.

River.

Do......... ...-:.........

Locality.

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

Do ....................... St. Louis, Mo ...................

Ohio......................... Cincinnati. Ohio....... ..........

Length 

of record.

Years. 

42 

12 

87 

53 

18 

25 

31. 

24 

15 

39

Average date of 

Closing.

Dec. 12 

Dec. 9 

Dec. 15 

Dec. 17 

Nov. 28 

Dec. 12 

Dec. 19 

Nov. 25 

Nov. 15 

Jan. 15

Opening.

Mar. 12 

Mar. 16 

Mar. 20 

Feb. 21 

Mar. 19 

Mar. 19 

Jan. 20 

Mar. 31 

Apr. 13 

Jan. 25

Time 

closed.

Days. 

90 

97 

95 

66 

111 

97 

32 

126 

151 

10

CHANGE IN THICKNESS OF ICE.

After a stream becomes frozen over, the thickness of the ice usually 

increases rapidly, reaching a maximum generally by midwinter and 

then remaining nearly constant until shortly before the open-water 

season begins. As a rule there is some melting and thinning of the ice 

before it goes out, but a heavy early spring freshet may carry out ice 

at its maximum thickness.

The following table shows the ice thickness at intervals through the 

winter at two fairly typical gaging stations.

Thickness of ice on Connecticut River at Orford, N. H., and, Esopus Creek at Kingston, N. Y.

Date.

March 30. ................................

Connecticut River at j Esopus Creek at KingsOrford, N. H. ton, N. Y.

1903-4.

Feet.

6

1.7 

1.85 

1.9

2.1

±2. 

0

1904-5.

Feet. 

0 

.3 

.7 

1.3 

1.5 

1.7 

2.1 

2.2 

2.1 

0

1905-6. | 1903-4.

Feet. 

0 

.1 

0 

0 

.7 

0 

1.05

t? 

0

Feet.

6 

0 

.5 

.95 

1.1 

1.25 

1.25 

.6 

aQ

1904-5.

Feet.

0 

.4 

.65 

.6 

1.25 

1.5 

1.6 

.7 

afl

1905-6.-

Feet.

0 

.1 

.4

.5 

.75 

.9 

.4 

.25 

afl

a March 31-.

SURFACE, ANCHOR, AND NEEDLE ICE.

The three following forms of ice occur in streams and each of them 

affects the flow in a different way: (1) Cake, border, or surface ice; 

(2) needle ice, or "frazil," so called from the French word signifying

a House Doc. 192, 54th Cong., 2d sess.
WINTER CONDITIONS. 11

"forge cinders," which are suggested by its dull, slushy appearance; 

(3) anchor ice, which closely resembles needle ice, but which is formed 

in a different manner.

Surface ice is formed when the temperature of a quiet body of water 

becomes 32° F. As the maximum density of water occurs at 39.1°, 

the temperature of a quiet body of water that is cooled from the surface will gradually increase from the surface downward after a general 

water temperature of 39.1° has been reached. Surface ice probably 

always begins to form at the shore or at the borders of solid objects 

and is extended by spicules shooting out and forming a network, the 

process being analogous to the growth of crystals in a saturated solution except that ice is formed at the surface only. The surface layer 

of ice gradually increases in thickness and continues to grow as long 

as the air temperature is below 32° F. The rate of such increase 

varies with the temperature and other atmospheric conditions affecting heat radiation. The thickness of the ice layer increases in nearly 

direct proportion to the square root of the time. Surface ice also forms 

over smooth-flowing water, but as the velocity and roughness of the 

current are increased a condition is soon reached where the projecting 

ice needles are broken off as fast as they are foremd.

It is obvious that the surface temperature of a stream passing over 

rapids where surface ice can not form would often fall below 32° F. 

if a portion of the water were not converted into ice in some manner 

and enough latent heat released to maintain the temperature constantly at 32°. It is well known that perfectly quiet water can be 

cooled below 32° F. without the formation of ice, apparently because 

the necessary nuclei and other conditions to start ice formation are 

not present. If, however, the slightest motion occurs, the water 

molecules are enabled to assume the arrangement necessary to crystallization and the water becomes filled with ice spicules.

Elaborate experiments by Prof. Howard T. Barnes by means of an 

electrical-resistance thermometer indicate that flowing water in a 

stream can not be cooled more than one one-hundredth of a degree 

below the freezing temperature without the formation of ice. The 

ice spicules that form in agitated water vary in character with the 

variations in the rate of their formation. Elongated needles, cubical 

crystals, and broad, thin plates have been observed under different 

conditions. Apparently the stream may be filled with needle ice 

formed in the manner described without the flow being affected in any 

considerable degree. If, however, the needle ice is carried underneath 

the layer of surface ice, it forms an effective obstruction.

Observations in St. Lawrence River indicate that masses of needle 

ice may travel under the surface ice for several miles. There is 

undoubtedly some flow through these masses, but the velocity is very
12 STEEAM FLOW DUEING THE FROZEN SEASON.

slight. It has not been found possible to measure the flow through such 

ice with the current meter. The existence of flow is, however, indicated by the presence of impurities in the ice. A striking illustration 

of this flow is also given in fig. 1, which shows two cross sections of 

Chemung River.^At the upper section the channel underneath the 

surface ice was almost completely blocked by needle ice, while at the 

lower section, 200 feet downstream, there was but little needle ice;

DISTANCE FROM INITIAL POINT 

3 100 IZO 14-0 160

.80 100 IZO 140

DISTANCE FROM INITIAL POINT

FIG. 1. Cross sections of Chemung River at Chemung, N. Y., showing effect of needle ice.

yet the observed velocities at the lower section were so great as to 

indicate that considerable flow through the masses of needle ice must 

have taken place./

Gage readings or attempts to estimate the winter flow of streams 

at cross sections affected by needle ice are apparently worthless. 

Although the general features of ice formation in a given locality will be 

the same from year to year, a consideration of the conditions of needle-
WINTER CONDITIONS. 18

ice formation shows that the differences will be sufficient to produce 

in effect a constantly changing regimen. The formation of needle ice, 

like that of surface or anchor ice, is due chiefly to radiation of heat 

from the water mass. Needle ice never forms underneath surface ice 

and is most frequently formed on cold, clear nights, when the heat 

lost by radiation is most greatly in excess of that received at the 

earth's surface. Professor Barnes states that the margin between the 

disintegration and the formation of the ice is exceedingly narrow, 

amounting to only a few thousandths of a degree change of temperature, the radiation and the absorption of the sun's rays by water being 

controlling factors.

Snow falling on the surface of a stream becomes water-logged and 

forms a slush resembling floating needle ice. Snow crystals probably 

often form the nucleus of masses of needle ice, but the presence of 

snow is not an essential or important condition for the occurrence of 

such ice, as is sometimes supposed.

Anchor ice is sometimes formed when stones or other objects in a 

stream are cooled by radiation to 32° F. It is a crystalline growth 

similar to needle ice and having the same density. It remains 

attached to the objects upon which it is formed as long as their surface temperature is below 32°. Like needle ice, it forms most readily 

when the difference between radiation and absorption is a maximum. 

Apparently it never forms underneath surface ice; but whenever the 

relative loss by radiation is decreased, as, for instance, on a cloudy 

day, it may become detached and rise to the surface, carrying with it 

stones or other objects. It affects the regimen of streams chiefly by 

forming obstructions in portions of the channels that do not freeze 

over, thereby causing back water, or by rising and floating underneath the surface ice, as needle ice often does. 'Anchor ice does not 

ordinarily form in streams with earth beds and apparently forms more 

extensively on dark-colored rocks, radiation from dark objects being 

greater than from light ones. °

RANGE OF WINTER GAGE HEIGHTS.

Data regarding extremes of winter gage heights are given in connection with station descriptions (pp. 26-38). In general, winter 

freshets are uncommon in the northern portion of the area, in which 

the streams freeze and the range in stage is small, but the liability of 

^ their occurrence increases rapidly to the south. They are, however, 

usually not of long duration, and are not serious factors in winter

a Kept. Commission oi Engineers on Floods, Montreal, 1890. Henshaw, Geo. H., Frazil ice: Trans. 

Canadian Soc. Civil Eng. vol. 1, pp.' 1-23. Barnes, Howard T , Formation and agglomeration oi frazil 

and anchor ice: Canadian Engineer, May, 1897, pp. 6-10; Formation of anchor ice and precise temperature measurements: Trans. Am. Soc. Mech. Eng., 1905, Ilorton, R. E., Anchor ice and frazi : Paper 

Trade Journal, December 24,1903,
14 STREAM FLOW CUBING THE FROZEN SEASON.

estimates unless they are of sufficient size to cause the ice to break up 

and go out more or less completely, when the conditions of flow may 

become entirely changed. As a rule the regimen of flow changes less 

in winter than during the open season.

FLOW OF STREAMS UNDER ICE COVER.

GENERAL CONSIDERATIONS.

Ill the Chezy formulas

V = Cv/ES

C is the coefficient dependent on the physical character of the 

stream bed and the hydraulic radius. The physical character enters 

into the determination of C in the form of a coefficient of roughness, 

n. The relation of n, R, and C, as deduced by Kutter, is as follows 

(for English units):

. _ 1.811 0.00281

i . 41 ftfl. 0- 00281 1+ 41.6Q 

It will be seen that for a given slope and hydraulic radius the mean 

velocity of a stream is nearly proportional to l-^-n; that is, the velocity 

is inversely proportional to the roughness of the stream bed. The 

Chezy and Kutter formulas are empirical and in their application 

values of n determined from previous experiments are selected by 

judgment.

FRICTION DUE TO AIR AND ICE.

If V, R, and S are given, the value of n may be calculated from the 

Kutter formula. In such calculations for open-channel conditions 

the hydraulic radius is taken as the ratio of area of cross section to the 

wetted perimeter, not including the surface in contact with the air. 

It is probably true, however, that the mean velocity of a stream is 

usually less than it would be if there was no friction between water 

and air.

If the air-contact surface is replaced by a film of ice, then, in making 

a calculation of C or of the velocity, the entire wetted perimeter, 

including that portion of the boundary of the stream section in contact with ice, would naturally be included in calculating the hydraulic 

radius.

If the value of n is derived by considering the wetted perimeter as 

including the air and ice contacts as well as those of bed and banks, 

and if the frictional resistance of the water-ice contact is greater than
STREAM FLOW UNDER ICE. 15

the frictional resistance of the water-air contact, then n will have a 

correspondingly greater value for conditions of ice cover than for 

those of open channel. In other words, the ice cover increases total 

friction by an amount representing the difference between air and ice 

resistance and not by an amount representing the total ice friction.

The ordinary friction of a stream bed may be considered as made 

up of two parts (1) skin friction and (2) internal motion.

In most instances a film of water adheres to the surface of solid 

objects over which the water flows, and the skin friction between the 

water and these objects is essentially the same as that between two 

fluid surfaces. It is measured by the viscosity of the liquid, the 

energy absorbed probably being for the most part converted into 

heat.

If the stream bed ia rough, the impact of the water creates swirls or 

eddies, in which a portion of the energy is converted into internal or 

vortex motion not useful in causing forward motion.

So far as known, no experiments have been made relative to the 

skirt friction of a smooth ice surface. It may be assumed, however, 

to be about the same as for a smooth glass or planed-wood surface, 

especially the latter. A layer of water adheres to such a surface or is 

entrapped by the capillaries, so that the friction surface is essentially 

a layer of liquid particles, the conditions thus closely resembling 

those where water at 32° F. is in contact with ice.

The value for glass or planed-wood surfaces of n in Kutter's formula 

is given by various authorities as about 0.009, or from one-fourth to 

one-third the resistance due to an ordinary stream bed. When the 

under ice surface is rough, broken, tilted, or honeycombed, its impact 

resistance may become of the same or even greater relative importance than that of an earth or rock surface. It is presumable that 

cases are rare where the under surface of the ice cover is so free from 

irregularities as to give a value of n as low as those applying to glass 

or planed wood.

Occasionally a layer of needle ice of varying thickness floats under 

or accumulates on the lower surface of the ice cover. Such ice not 

only obstructs the flow through the portion of the cross section 

occupied, but also greatly increases the friction as compared with 

that of a smooth ice surface.

RELATIVE IMPORTANCE OF AIR AND ICE FRICTION.

As already pointed out, the actual increase in friction due to an ice 

cover is the difference between the ice friction and the air friction previous to the formation of the ice cover. Owing to the divergent 

opinions entertained as to the magnitude of air friction, it has been 

thought well to discuss the matter somewhat at length.
16 STREAM FLOW DUEIJTO THE FROZEN SEASON.

In the Chezy formula and in most other similar slope formulas it 

is assumed that all the resistance to the motion of the water proceeds 

from the stream bed. Humphreys and Abbot 0 found, however, 

that the position of the point of maximum velocity in vertical velocity 

curves on Mississippi River was controlled by the direction and velocity of the wind. They give the following expression:

d=(0.317+0.06/) D

In this formula D=depth in feet; d=depth of point of maximum 

velocity; /= relative wind velocity on a scale such that a calm=0 

and a hurricane =10.

- In deriving a formula for the mean velocity of streams in terms of 

the slope and hydraulic radius, Humphreys and Abbot assumed that 

the frictional resistance between the water and air contact surfaces 

was similar in nature and magnitude to the bed resistance. In their 

formula, accordingly, the hydraulic radius is expressed as follows:

R- A

PTW

In this formula A = area of cijfss section, P = wetted perimeter in 

earth, W= width of surface.

In discussing the results of Humphreys and Abbot's investigations, 

the late James B. Francis made the following clear statement as to the 

effect of air friction: b

When the air in contact with the surface of the water flowing in an open channel is moving 

in the same direction and with the same velocity as the surface of the water, it is clear that 

it can have no effect on the motion of the water; but such exact conformity in the motion of 

the air and water is uncommon; ordinarily the air has some motion relatively to that of the 

water and either retards or accelerates the velocity of the surface. That the air may produce a material effect on the scale of velocities is apparent from the following considerations.

Let us suppose the surface of the water to move, relatively to the air, with the same 

velocity that the water at the bottom moves relatively to the bed; also that the inequalities 

of the surface of the water caused by the action of the air and those in the bed of the stream 

are alike; and suppose, also, that a sheet of water of uniform thickness, in contact with the 

bed, is at rest; we shall then have the water near the bottom moving over a bed of water 

and the water at the surface moving under a bed of air, and as both beds have the same 

inequalities, they will cause the same retardation in the velocity of the water, except as 

these beds, from the nature of the substances of which they are composed, offer more or 

less resistance. These resistances will be of the same nature as is experienced by a body 

moving in a resisting medium. According to well-known principles, the retardation in 

this case is as the square of the velocity of the moving body relatively to that of the medium 

and as the density of the medium. The density of the air is about -g^ of that of water; a 

body moving through the air with the same velocity will therefore be retarded -gfa as 

much as if it moved through water.

The above conclusions are confirmed by a comparison of the coefficients that have been determined experimentally for use in computo Physics and Hydraulics of Mississippi River, p. 305. 

& Lowell Hydraulic Experiments, pp. 158-159,
STREAM FLOW UNDEK ICE. 17

ing loss of pressure occasioned by the flowing of air and water through 

pipes, the form of expression adopted by Weisbach being used :

'

.

In this formula p = loss of pressure in pounds per square inch; 1 = 

length of pipe in feet ; d = diameter of pipe in inches ; v = mean velocity in feet per second ; f= coefficient of resistance to flow.

Rough average values of the coefficient,/', according to Weisbach's 

experiments, may be taken as follows: For air, f= 0.000 160; for 

water, /= 0.1 04, the relative friction loss for water being 650 times 

that for air.

It seems probable, then, that with still air the frictional effect of air 

on water surface is but a small percentage of that due to stream bed, 

although with a strong wind upstream the retardation of the filaments 

of water near the surface may be considerable.

VARIATION IN SLOPE DUE TO FREEZING.

As an ordinary stream is made up of smooth-water reaches separated by more or less pronounced rapids, and as the swiftest portions of a stream freeze least readily, the freezing of a stream will

FIG. 2. Effect of freezing on a smooth section of a river terminated by rapids.

lead to the following conditions: (1) There will be an increase in the 

total friction due to replacing the water-air contact surface by waterice contact surface; (2) if the discharge remains the same, it follows 

that with increased friction either the slope or the cross-sectional area 

must increase.

In a long, uniform channel, frozen throughout, there can be but little 

or no increase in slope; but in short reaches separated by open water, 

such as those where gaging stations are commonly located, an appreciable local increase in slope due to freezing may easily occur, as 

shown in fig. 2. As a result of freezing of the smooth-water reach

IKK 187 07 2
18 STREAM FLOW DURING THE FROZEN SEASON.

M N there is a tendency for the stage to be raised, as shown by the 

dotted line, and the upper stretch of quick water above N may be 

partly submerged by backwater. If the discharge remains the same 

the depth of open water at M will not be increased unless there is 

backwater here due to ice cover below this point. If the depth at M 

is not increased, the fall of the water surface between N and M will 

have been increased. There is no actual increase in slope, except in 

the vicinity of M, and the ice surface adjusts itself parallel to the 

channel bed, as in the case of flow in an open channel, but the effective 

fall from N to M is of course increased.

CHANGE IN AREA OF WATERWAY REQUIRED BY FREEZING.

The conditions that occur when a broad river becomes covered 

with a uniform ice surface are illustrated by the following example: 

Consider a rectangular channel in which the width B D is many times 

the depth, so that the wetted perimeter may be taken as approximately equal to the width. Neglecting the air friction, call the coefficient of roughness applying to the channel %. Consider also that 

the cover E F may be brought just in contact with the stream surface, 

the coefficient of roughness for this ice cover being nz . The slope and 

discharge being assumed to remain constant, the effect of cover of 

varying roughness may be illustrated as follows: 

Let width B D - 500 feet, 

slopeS =0.0005, 

depth D =5 feet, 

area of section =2,500 square feet, 

wetted perimeter = 500 feet approximately, 

hydraulic radius = 5 feet approximately.

Then for n = 0.030, as in an ordinary river, the mean velocity 

would be 3.29 feet per second, and the discharge would be 8,225 

second-feet.

If, now, the stream is covered over, if % and nz equal 0.030 each, 

and if the discharge is the same as before, then the stream stage must 

evidently rise in such manner that the increase hi C, resulting from 

increased hydraulic radius, together with the increase in R and A, will 

counterbalance the increased friction. Owing to the complexity of 

the Kutter formula, the result can best be determined by successive 

approximations rather than by analysis. 

We will have, if D remains as before,

R = 2.5 V-2.01 Q = 5,025 

If D is increased 1 foot,

R = 3.0 V = 2.29 A = 3,000 Q = 6,870 

If D is increased 2 feet,

R = 3.5 V = 2.56 A = 3,500 Q = 8,960 

By interpolation between the last two values it appears that the
STREAM FLOW UNDER ICE. 19

stage must increase about 1.65 feet in order that the discharge shall bethe same as for open channel. If, on the other hand, the value of «2 for 

the covered surface was 0.010, then since the wetted perimeter for 

the bed and for the covered surface are approximately the same, the 

average coefficient of roughness for the entire stream section would be

0.010 + 0.030 nno ^ u.uz

With this value of n, in order to give the original discharge of 8,225, 

the stage would need to be raised about 0.2 foot.

In actual streams the wetted perimeter of the stream bed will 

usually be somewhat more than half of the total cross-sectional boundary; furthermore, as shown elsewhere (pp. 14-15), when the stream is 

covered, the effect is to replace air-surface friction by ice-surface friction; so that, all things considered, the presence of a thin, smooth ice 

cover will probably not necessitate any very great increase in stage in 

order to maintain the discharge undiminished.

As a river becomes nearly or quite frozen over and the thickness of 

ice increases, the diminution of area of water may be considerable. In 

the example previously quoted, for the given stage the area of 

waterway would be reduced as follows (if the ice is floating):

Effect of thickness of ice on area of waterway.

Thickness Reduction in area of 

of ice. I waterway.

Feet. I Sg. ft. Per cent.

0.5 I 230 9.2

1 '460 18.4

1.5 690 27.(> 

920 36.8

With ice 2 feet thick, then which is no.t uncommon there would 

be a reduction in area of about 37 per cent. In the example, above, a 

rise of stage of 0.2 foot was occasioned by thin ice cover. With 2 feet 

thickness of ice a further rise of about 1.84 feet, with no snow load 

upon the ice, would be required to insure the same discharge. The 

total necessary rise of stage would then be 2.04 feet.

EFFECT OF THICKNESS OF ICE ON FLOW.

It is evident that the discharge for a given gage height, taken to the 

water surface where there is a thick ice cover, may be diminished very 

materially as compared with that for open-water conditions.

By further considering the data on page 18, and also assuming a 

change in depth (or gage height) from 5 to 8 feet, we obtain the 

following:
20 STEEAM FLOW DUEING THE FEOZEN SEASON.

Relation of gage height to discharge. 

[8=0.0005; n = 0.030 for open water; n =0.020 for thin ice cover.]

Depth 

(or gage 

height).

 Feet.

5.0

6.0

7.0

8.0

Discharge 

(open section).

Second-feet.

8, 225

11,200

14,500

18,200

Discharge under ice cover. 

Ratio fHs~charge~for open seclioru

Thin ice.

0.91

.91

.92

.92

Ice 1 foot 

thick.

0.65

.70

.73

.74

Ice 2 feet 

thick.

0.42

.49

..55

.59

For the rectangular section as chosen this indicates that for a given 

stage the ratio of discharge under ice cover to that for open section 

diminishes LS the ice thickness increases; for thin ice cover it is

01 1

to

0.40 0.50 

RATIO

0.60 0.70 0.80

DISCHARGE UNDER ICE COVER

DISCHARGE FOR OPEN SECTION

0.90

FIG. 3. Effect of change in stage on discharge under ice cover, with varying thickness of ice.

approximately constant for ordinary stages, but as the ice thickens, 

the effect on the ratio is much greater at the lower gage heights. To 

further illustrate this tendency, fig. 3 has been prepared. The properties of the gaging cross section of the Connecticut River at Orford, 

N. H., are here used (at gage height 4.0; area = 1,280; width = 267; 

hydraulic radius =4.76; slope assumed as 0.00012; n = 0.035 for openwater conditions; and n =0.025 for channel frozen). Under these 

assumptions with thin ice, the relation between discharge under ice
OBTAINING WINTEE EECOEDS. 21

cover and that for open water is nearly constant for ordinary stages; 

for thick ice this relation may vary 25 or 30 per cent in this range of 

gage heights (which is about the usual winter range at this station), 

the tendency being for this ratio to increase as gage heights increase.

The effect of a thickening ice cover for given conditions of slope and 

roughness and for a given gage height is as follows: (1) To diminish 

the cross-sectional area; (2) to slightly diminish the wetted perimeter, 

by lessening the width; (3) to decrease the hydraulic radius as a result 

of the loss of area while,the wetted perimeter changes only slightly.

Changes of area and hydraulic radius both tend to diminish flow. 

It is evident that the relative effect of this diminution will become less 

and less as stage increases, for both area and hydraulic radius increase 

directly as the gage height, while tin loss of area and hydraulic radius 

for a given thickness of ice is approximately the same at any ordinary 

stage.

METHODS OF OBTAINING WINTER RECORDS.

CURRENT-METER STATIONS. 

GAGE HEIGHTS.

Previous to the winter of 1903-4 records of gage heights for the 

frozen season were not in general obtained, the exception being in the 

case of a few gaging stations on Catskill Mountain streams in the 

vicinity of New York City, where the attempt was made to procure 

continuous records from the time of their establishment in 1901. 

Since 1903 gage heights have been procured during the winter at a 

considerable number of stations in the Eastern and Central States. 

An effort has been made to obtain data bearing on both the stage of 

the river and ice conditions.

The observer is not expected to read the gage and obtain the attendant ice data oftener than once or twice a week unless unusual conditions prevail (such as high water, due to rains or melting snow), as the 

change in stage under ice cover is usually a slow and even one. The 

essentials in these observations are as follows: (1) A hole is cut in the 

ice at (or underneath) the gage, the gage is read to the water surface 

and to the top of the ice, and the thickness of the ice is measured; (2) 

any special conditions are noted, either in remarks or by sketch, such 

as areas of open water, backwater effect due to ice jams, etc. Observers are instructed to measure the thickness of ice occasionally at other 

places in the cross section at the gage and at points up and down 

stream. For these winter duties observers are furnished with an ice 

chisel and an ice-measurement stick, so arranged with an L end that 

the bottom of the ice can be definitely located and the thickness noted.

The transition periods from open channel to frozen conditions in the 

fall and the reverse in the spring are important. During the falltransition period, while the river is freezing, two methods have been
22 STREAM FLOW DURING THE FROZEN SEASON.

used for gage readings, as follows: (1) Daily gage readings to the top 

of the ice are made continuously, until the ice is strong enough to 

walk on, the date of first freezing having been noted. After the ice 

cover forms the usual winter observations begin, as previously 

described. (2) The ice is broken daily under the gage, a good-sized 

hole being made with a weight and rope provided for the purpose, and 

gage heights are read to the water surface, until the ice is strong 

enough to walk on, when the thickness can be noted and the usual 

method folio we'd.

In spring when the ice goes out daily gage readings begin with any 

considerable increase in stage and conditions as to ice time of ice 

going out and of river being clear from ice, etc. are noted. If at any 

time during the winter high water occurs or the ice goes out, daily gage 

readings are resumed until steady conditions once more prevail.

CURRENT-METER DISCHARGE MEASUREMENTS.

Holes are cut in the ice at points in the cross section where it is 

desired to obtain velocity determinations. These holes can be cut 

usually to best advantage with an ice chisel and are made only large 

enough to allow the ready lowering of the current meter through them. 

A rectangular hole 12 by 24 inches, with its length in the direction of 

the cross section and with vertical sides, has been found convenient 

for thick ice; lesser dimensions may be used where the ice is thin. In 

a few cases it has been necessary to cut a continuous channel between 

two or more adjacent holes, especially where the holes are close 

together, to prevent rapid vertical pulsations of water in the holes. 

Where a large number of holes are to be cut, a special auger cutting 

out a cylindrical core of ice has been used to advantage by United 

States Army engineers. The auger is driven by hand, by means of 

a suitable framework and gearing, similar to a carpenter's frame boring machine.

The cross section at which open-water discharge measurements are 

made is always used, when possible, as more direct comparisons can 

thus be made of the various features of flow under ice cover, with 

similar data for open channel. If, as sometimes happens, it is desirable that the measurements of flow under ice cover be made at a 

different or auxiliary section in order to obtain more favorable conditions, it is necessary to install an auxiliary gage or reference point, or, 

by sufficient soundings at the section used to keep control of the area, 

positions of ice surfaces, etc.

Soundings are always referred to the surface of the water in the 

holes, and, in addition, the distance from the water surface to the top 

and the bottom of the ice is noted. The depth 'of snow covering the 

ice, if any, is also noted and if possible a determination made of its
OBTAINING WINTER RECORDS. 23

water equivalent. The character of the ice and of its under surface 

is noted, especially with regard to smoothness.

Gage heights are taken to the water surface and the top of the ice 

in the same way as by the observer, but, in addition, especially if an 

auxiliary section is being used for the current meter, holes are cut in 

the gage cross section and a little distance up and down stream in 

sufficient number to get a good average determination of the thickness of the ice and its position relative to the water surface.

Velocity observations have been most generally made by the vertical velocity-curve method, or at least a sufficient number of curves 

have been obtained to give good control of any single or double 

point method. Vertical velocity curves have also been very frequently taken for the reason that data were thus obtained for study 

and for the devising of shorter methods of observation.

A double-point method giving good results was developed from 

data obtained in 1904 and was used in measurements for the next 

two seasons. This consists in making observations at 0.2 and 0.8 

of the total depth (below the bottom of the ice), the mean of these 

two velocities being very nearly the mean velocity of the vertical.

Single-point methods, in which the velocity is determined at 0.4, 

0.6, or mid depth, are sometimes used, it being necessary to have 

vertical velocity curves at the same points and taken under similar 

conditions in order to deduce the mean velocity from the observed 

velocity.

Vertical integration has been used to a limited extent, but it has 

not been found as convenient as the methods previously describedand it gives no data for the study of the vertical velocity curve. 

It is also objectionable owing to the difficulty of properly handling 

the current-meter cable, which becomes wet and covered with ice.

The horizontal distance between velocity observations should 

probably be about the same as for open water for the best results, 

but frequently it is advisable to extend it somewhat beyond that 

limit, in order to reduce the labor required for cutting holes in the ice.

The current meter is used either suspende4 by a cable in the 

ordinary manner or fastened to a wooden or metal rod. If a cable 

is used, it is marked at intervals of 0.5 or 1 foot by small lengths of 

cord wound and tied about it for use in sounding and placing the 

meter. It is mos't convenient to refer these to the center of the 

meter and add to soundings the distance from the center of the 

meter to the bottom of the weight. If a rod is used (this is of 

course limited to comparatively small depths and low velocities), 

it may be graduated from the center of the meter in a similar way. 

The rating of the small Price meter when it is fastened to a rod, 

but free to tip on its horizontal axis, is almost identical with that 

when the meter is suspended by a cable in the usual way.
24 STREAM FLOW DURING THE FROZEN SEASON.

The meter must be kept in the water continuously, or nearly so, 

if the temperature of the air is much below freezing, as ice will 

form very quickly on exposure and perhaps cause the meter wheel 

to stick. If the temperature is very low, trouble is also experienced 

from ice gathering on the cable or rod supporting the meter.

Measurements during inclement weather can often be most conveniently made under a shelter consisting of a framework of light 

boards or poles covered with canvas. A cross plank at a height of 

about 3 feet serves as a convenient support for instruments and 

stop watches, as well as a datum for lowering the meter in making 

vertical velocity curves.

In moving from station to station the meter is drawn up until 

it clears the ice and left suspended from the cross plank while the 

entire shelter is carried forward to the next point of measurement. 

By this method the necessity of handling the wet cable, often troublesome, even when rubber mittens are used, is generally avoided.

The additional cost of measurements on frozen streams over that 

for the open season is occasioned by the following conditions: (1) 

General difficulty of field work during cold weather, and consequently longer time required; (2) labor required to cut holes in ice 

and perhaps clear off snow; (3) longer methods required in gaging. 

The following table gives data regarding the cost of gaging under 

ice cover at certain stations during 1904-1906 as compared with the 

cost of gagings made under open-water conditions.

Cost of current-measurements under ice cover.

Locality.

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

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

Number 

of 

stations.

3

9

Year.

1904

1905

1906

Number 

of 

gagings.

4

7

19

15

Average

cost per

gaging, 

exclusive 

of travel 

to and

from

station.

$30. 52

16.67

14.18

18 24

Average 

total 

cost per 

gaging.

$34. 64

18.82

15. 65

22.13

Usual

total 

cost per 

gaging, 

river

open.

$10.00

8.57

10.42

10.32

The "usual total cost per gaging, river open," is based on a record 

of actual costs during 1904 and 1905 for New England and from 

July, 1904, to July, 1905, for New York stations. During the 

greater part of the 1906 winter gagings in New England only one 

hydrographer was in the field, laborers being employed for the 

work of cutting holes in the ice and assisting in gaging. Previous 

to that .time there were usually two hydrographers. All New York 

gagings have been made by two hydrographers.

The average cost per gaging for ice cover, exclusive of travel, is 

from one and one-half to three times that for open-water conditions.
U. S. GEOLOGICAL SURVEY

A GAGING STATION ON SANDY RIVER AT MADISON, ME., AT DAM OF MADISON 

ELECTRIC COMPANY.

B. GAGING STATION ON IWINOOSKI RIVER AT RICHMOND, VT.

OBTAINING WINTER RECORDS. 25 

STATIONS AT DAMS.

A considerable number of the gaging stations of the Survey are at 

water-power plants, and records are obtained by observing the -flow 

over the dam, the wheel-gate openings, etc., and the amount of water 

used by wheels.

During cold weather ice may form in large quantities on the crest of 

a dam and vitiate the computations made from gage heights of flow 

over the dam. PI. I, A, gives an excellent illustration of the manner 

in which ice may form upon a dam. This plate shows one of the regular stations of the Survey at Madison, Me. In some cases this difficulty can be obviated by keeping the ice cut away from the crest, as 

is frequently done at an electric-light and power plant; or where that 

is impracticable, a record jof ice conditions, with proper corrections, 

may serve to make approximate estimates.

The flow through turbines is as easily determined in winter as in 

summer. Frequently the greater part of the flow is taken through the 

wheels. Gaging stations at dams and mills usually afford better 

opportunities for securing winter records than exist at many currentmeter stations.

ESTIMATES FROM PRECIPITATION.

Methods of estimating stream flow from precipitation are so generally known as to require no detailed explanation. In most such estimates the run-off in any month is determined from the contemporaneous precipitation by the use of a ratio or reduction factor. In crude 

estimates it is assumed that a constant percentage of the precipitation will appear as run-off regardless of the amount of precipitation. 

In more exact work a sliding scale t)f coefficients is used, the values 

depending on the amount of precipitation and the month or season.

For precipitous and impervious basins the run-off will be nearly 

coincident with the precipitation. If, however, there are lakes, forests, extensive ground-water storage, or accumulated snow within the 

basin, the precipitation in one month may not appear as run-off for a 

considerable interval of time, and any attempt to estimate the run-off 

for any month from the contemporaneous precipitation will be valueless. This is especially true in basins where much of the winter precipitation is in the form of snow, which accumulates on the ground, 

especially in ravines and forests, so that water representing several 

inches depth on the drainage basin may be carried forward from 

month to month, or from one calendar year to another, without entering the stream.

A heavy precipitation in the form of snow may occur without any 

appreciable effect on the stream flow. On the other hand, whenever 

the temperature rises above 32° F., run-off from melting snow occurs,
26 STREAM FLOW DUKIJTO THE FKOZEN SEASON,

and often the entire winter's snow storage enters the stream in the 

course of a few days. During from one to three months of the 

spring freshet season northern streams generally show a run-off considerably in excess of the contemporaneous precipitation.

Data regarding the evaporation loss from snow-covered surfaces 

are very meager. If records of the snowfall, snow accumulation, and 

temperature are at hand it may be possible to form estimates of the 

total run-off of a stream for the winter season. It is obviously impossible at present to form reliable estimates of winter flow for shorter 

periods from precipitation data alone in any manner similar to that 

commonly used in estimating the flow from the rainfall during the 

summer months.

The minimum flow of a stream, either in summer or winter, ordinarily occurs at times when there is no direct surface run-off and when 

the permanent supply from ground water, lakes, or storage reservoirs 

is at a minimum.

The presence of snow with low temperature effectively cuts off 

direct surface inflow in winter, sometimes for a period of several 

months. Careful studies of the laws of supply to' a stream from 

ground water during either summer or winter droughts will be of value 

in estimating the winter regimen.

With present knowledge it is evident that actual measurements of 

flow from gagings are even more needful in winter for the determination of available water supply from streams than in summer, although 

in the existing data of stream flow the winter period is to a considerable extent neglected.

WINTER RECORDS.

Data on open-water and winter conditions and the discharge 

measurements made during the frozen season are here given for the 

following stations :

Catskill Creek at South Cairo, N. Y. 

Connecticut Kiver at Orford, N. H. 

Esopus Creek at Kingston; N. Y. 

Fish River at Wallagrass, Me. 

Kennebec River at North Anson, Me. 

Rondout Creek at Rosendale, N. Y. 

Wallkill River at Newpaltz, N. Y. 

Winooski River at Richmond, Vt.

CONDITIONS AT STATIONS. 

CATSKILL CREEK AT SOUTH CAIRO, N. Y.

This station was established July 4, 1901. It is located at the 

highway bridge in the village of South Cairo, about 1 mile north of the 

Catskill Mountain Railroad station for that place. The drainage area
WINTER EECOEDS. 27

is 263 square miles. Measurements are made from the downstream 

side of the bridge at ordinary and high stages, and by wading a short 

distance above the bridge at low stages.

The drainage basin of this stream receives the run-off from the 

north slope of the Catskill Range and lies for the most part in the timbered highlands of Greene County. The source of the creek is in a 

swamp at Franklinton, Schoharie County. It enters Hudson River 

at Catskill after traversing Greene County for nearly 25 miles. The 

stream flows over a rocky bed through the greater part of its course, having a total fall of 1,200 feet.' At the station the bed consists of gravel 

and rock, the main channel lying nearest the right-hand abutment of 

the bridge, which has a clear span of about 194 feet. About twothirds of the way across is a gravel bar covered with brush which 

affects the discharge to some extent in high water and at low-water 

stages rapids about 1,800 feet below the bridge tend to cause slack 

water at the regular section for gaging. Both banks are high and not 

subject to overflow. The left bank is wooded; the right is rocky and 

abrupt. Below the bridge the stream is fairly straight for about 

1,000 feet; it then curves to the left and flows over some rifts, which 

at ordinary stages narrow the stream from about 200 to about 30 feet. 

Above the bridge the course is straight for about 500 feet; there is 

then a slight turn and some rapids that narrow the channel down to 80 

or 90 feet, the width at the bridge being about 125 feet. A portion of 

the stream bed is permanent, the gravel bar 011 the left-hand side having a tendency to shift.

From Hudson River to the mouth of Kaaterskill Creek, about 2 

miles, there is practically no velocity. From Kaaterskill Creek" to 

Leeds, 3 miles farther up, Catskill Creek flows through a gorge of bluestone, in which it has a fall of about 180 feet. Two dams formerly 

utilized a portion of this head at Leeds. There is no interference at 

the station, however, as it is about 3 miles farther up. The extreme 

stages observed are as follows:

Extreme stages observed on Catskill Greek at South Cairo, N. Y.

Gage 

height.

Feet. 

11.7

2.25

9.45

Discharge.

Second-feet. 

18, 600

18

18,582

Catskill Creek in this vicinity usually freezes over about December 1, 

and the general breakup comes about March 1, the stream being 

partly free from ice for short periods in January or February durirg 

what is commonly known as the January thaw. The entire width is 

usually frozen from a point 500 feet above the station to a point about
28 STREAM FLOW DURING THE FROZEN SEASON.

1,500 feet below; the rapids seldom freeze except in the coldest 

weather. ISTeedle ice is produced in abundance in this stream, the 

observer reporting that the channel is obstructed by this kind of ice 

for the greater part of the winter.

Ice conditions on Catskill Gre-ek at South Cairo, N. Y. 

SEASON OF 1903-4.

November 29, ice 0.6 foot; practically tho same up to December 13.

December 17, ice at gage 0.88 foot.

December 19, ice at gage 1 foot.

December 20, rains; creek broken up.

December 27, ice at gage 0.25 foot.

December 31, ice at gage 0.6 foot.

January 1-22, ice averaged about 0.65 foot.

January 23-26, inclusive, ice broken up.

January 27 to February 8, ice from 0.1 to 0.6 foot thick.

February 0, heavy thaw; ice went out.

February 16 to March 3, ice from 0.2 to 1 foot thick.

March 8, heavy rains; ice went out.

SEASON OF 1904-r,.

November 27, ice 0.1 foot thick.

December 1-7, ice 0.2 foot thick, increasing to 1 foot by December 27.

December 28, creek broken up.

January 5, creek filled with anchor ire.

January 7, anchor ice broken up.

January 15, creek filled with anchor ice.

January 25-28, ice 0.5 foot thick; stream frozen across to about same thickness both 

above and below gage. Observer states that stream is filled with anchor ice attached to 

bottom, except in narrow strip along gage. Conditions continued the same for three weeks 

with exception that general ice thickness increased from 1.2 feet upstream to 1.5 feet downstream from gage.

February 18, stream frozen over except along light bank, where ice becomes honeycombed and is broken.

February 25, stream frozen across both above and below gage 1,08 to 1.25 feet thick. 

Observer states that ice is gradually melting, and shows channel near left bank below gage.

March 4, ice throughout 0.83 to 1 foot thick, but narrow channel on each side.

March 19, ice broken up.

SEASON OF 1905-6.

December, some ice about the middle of the month, but river not frozen solid.

Januaiy 8, ice about 0.17 foot thick.

January 9-11, ice 0.25 foot thick.

January 12-14, ice 0.33 foot thick.

January 15, ice 0.25 foot thick

January 24, ice broken up.

February 1, about 0.83 foot of ice both above arid below gage, also at gage.

February 22, ice broken up.

February 28, creek filled with anchor ice, both above and below gage.

March 5, ice went out about this date.
WINTER EECOEDS. 29

The range of winter gage heights and maximum thickness of ice 

observed are as follows:

Range of winter gage heights and maximum thickness of ice on Catskill, Creel: at South

Cairo. N. Y.

Date.

1901-2...........

1902-3......................... ....... ......

1903-4. ........... . .................................

1904-5................ . ..... . .... ..... ..... ..

1905-6.................. ............... . ... . .

Gage height to water surface.

Minimum.

feet. 

2.90 

3.08 

3.10 

2.80 

2. 70

Maximum.

Feet. 

4.82 

4.90 

4.55 

3.05 

5.15

Range.

Feet. 

1.92 

1.82 

1.45 

.25 

2.45

Maximum 

thickness 

of ice.

Feet. 

1.37 

.16 

.54 

.17 

.83

CONNECTICUT RIVER AT ORFORD, N. H.

This station was established August 6, 1900. It is located at the 

wooden highway bridge between Orford, N. H., and Fairlee, Vt. 

The drainage area at this point is 3,305 square miles. Measurements 

are made from the downstream side of the highway bridge.

The bed of the stream consists of gravel and is permanent. Both 

banks are high and do not overflow. At the bridge the channel is 

about 275 feet wide at ordinary stages and is broken by one pier. It 

is straight for 1,000 feet above the station and for a considerably 

longer distance below. The channel is about the same width both 

up and down stream, but at the bridge this width is cut down approximately 13 feet by the pier.

Several small streams enter the Connecticut near Orford, but the 

only stream of any considerable size is Waits River, about 5 or 6 miles 

above this point. The nearest dam is at Wilder, about 18 miles downstream. Backwater effect from this dam reaches probably within a 

few miles of Orford. Upstream the nearest dam is at East Ryegate, 

about 20 miles above Orford. There is considerable fall in the river 

in this 20-mile stretch, although it is somewhat concentrated at a few 

points. The extreme stages observed are as follows:

Extreme stages observed on Connecticut River at Orford, N. H.

hei|!t. 'Discharge.

High water. 

Low water.

Feet. Second-feet.

26.1 I 33,000

2.0 i 640

E xtreme range. 24.1 32,360
30 STEBAM FLOW DUEING THE FEOZEIST SEASON.

Connecticut Kiver in this vicinity usually freezes over about 

December 1 and remains frozen until the middle or last of March. 

Near the bridge ice first forms at the shores and around the pier, the 

left channel always freezing over first and the right channel somewhat later. This portion of the river from the dam at Wilder to 

quick water at or above Wells Kiver has usually a permanent ice 

cover during the winter months. Anchor or needle ice has never 

been found here in sufficient quantities to affect gage heights or interfere with gagings.

During the season of 1905-6 the river was completely frozen over 

at the Orford bridge only from about December 30 to January 24, 

when a rise in stage carried out the ice. It did not freeze entirely 

across again during the winter. An area about 1,000 feet long and 

150 feet wide, nearly in the middle of the river and extending downward from the bridge, remained open.

Ordinary winter conditions are good at this station, and the range 

of gage heights is small. Occasionally a winter freshet such as those 

of December, 1901, and January, 1906, occurs, but these usually last 

only a few days. The range of winter gage heights and maximum 

thickness of ice observed are as follows:

Range of winter gage heights and maximum thickness of ice on Connecticut River at Orford,

N. H.

Date.

1900-1. . ..... .............................

1901-2. ... ................................

1902-3.....................................

1903-4..................... ...............

1004 ^>.... .................................

190^ 0

i Gage height to water surface.

Minimum.

Feet. 

........... n.8

............i 3.8

............! 6.6

............! 4.0

............] 4.0

. .........J 5.5

Maximum.

Feet. 

9.0 

21.7 

8.8 

8.3 

4.5 

20.5

Range.

Feet. 

3.2 

17.9 

2. 2 

I 3 

0.5 

15.0

Maximum 

thickness 

of ice..

Feet.

2.2 

2. 2 

1.5

ESOPUS CREEK AT KINGSTON, N. Y.

This station was established July 5, 1901. It is located at the 

Washington Street Bridge, Kingston, N. Y., about 1 mile from the 

West Shore Kailroad station. The measurements are made from the 

upstream side of a two-span highway bridge. The main span is about 

117 feet wide. There is also a short span of about 19 feet on the lefthand end for extreme high water. The drainage area above this station is 324 square miles. The bed of the stream consists of-earth and 

loose rock and is permanent. At ordinary stages the channel is from 

90 to 110 feet wide at the bridge, but it is wider above and below. 

Upstream the channel is straight for about 300 feet. It then deflects 

slightly to the right. Downstream the channel is fairly straight for 

700 or 800 feet. Rapids about 300 feet below affect the low-water
WINTER RECORDS. 31

flow. Measurements can be made by wading above the Ulster and 

Delaware Railroad bridge, about 1 mile upstream. The right bank is 

of earth, of medium height and slightly wooded; it is not subject to 

overflow except at very high stages. The left bank is of ordinary 

height, slightly wooded, and subject to overflow in high water. The 

conditions are such that the overflow can be readily estimated.

Esopus Creek receives numerous small tributaries mostly small 

torrential streams which cause rapid fluctuations in the main 

streams. The stream channel is usually broad and shallow, the bed 

being covered with cobbles and small bowlders, until the vicinity of 

the gaging station is reached, when the slope is more gradual and the 

current less swift. At Olivebridge, about 20 miles above the station, 

there is a natural fall of about 22 feet that is increased to 28 feet by a 

timber dam on the crest of the ledge, and at Glenerie, where the West 

Shore Railroad crosses the Esopus, about 6 miles downstream, there 

is a cascade that has a fall of about 56 feet. The final descent to tidewater at Saugerties is made through a fall of 42 feet.

There are no dams in the vicinity of the gaging station, and the 

channel is unobstructed except by small rapids which affect the lowwater flow only. The extreme stages observed are as follows:

Extreme stages observed on Esopus Creek at Kingston, N. Y.

Extreme range ............................... . . ................

Gage 

height.

Feet. 

25.0

3.7

21.3

Discharge.

Second-feet. 

23,400

36

23,364

Esopus Creek in this vicinity usually freezes over about December 

1, though the entire stream is not closed up. Ice generally forms 

first along the shore below the bridge and gradually works upstream, 

the velocity being swifter on the upstream side. The stream here 

has a wide range during the frozen season, the gage heights ranging 

from about 5 feet to 17 or 18 feet. These freshets sometimes occur 

as often as twice a month, and occasionally clear the creek of ice, this 

'depending somewhat on the time of year and the thickness of the ice. 

The channel'below the bridge sometimes becomes jammed, and in the 

spring it frequently has to be cleared out with dynamite. There is 

more or less open channel during the greater part of the winter at 

this station. Several ice measurements have been made here, and 

invariably there was a portion of the stream open. There are no 

reports or indications of needle ice, though it may form at times.

During 1901, 1902, and 1903 there was comparatively little ice in 

this stream, but in the winter of 1904-5 the ice had a thickness of
32 STREAM FLOW DURING THE FROZEN SEASON.

about 1.5 feet for a period of about six weeks, ranging from 0.1 to 0.2 

feet at other times. The ice went out about March 18. The range 

of winter gage heights and maximum thickness of ice observed are as 

follows:

Range of winter gage heights and maximum thickness of ice on Esopus Creek at Kingston,

N. Y.

Date.

1901-2................................. ... ... ........

1902-3. .................................................

1903-4. .................................................

1904-5. .................................................

1905-6. .................................................

Gage height to water surface.

Minimum.

Feet. 

5.28 

6.10 

4.91 

4.74 

5.35

Maximum.

Feet. 

9.95 

9.82 

18.23 

12.90 

14.60

Range.

Feet. 

4.67 

3.72 

13.32 

8.16 

9.25

Maximum 

thicknes 

of ice.

Feet. 

0.3fi 

.43 

.80

1.42

FISH RIVER AT WALLAGRASS, ME.

This station was established July 29, 1903. It is located just 

below the outlet of Wallagrass Brook. The drainage area at this 

point is 910 square miles. Measurements of the flow are made from 

a cable located about 1,500 feet downstream from the gage, r.nd 

soundings are made on the line of the cable. The bed consists of 

gravel and is permanent. The banks are of medium height, but 

rarely overflow during high stages. The channel is straight for 500 

feet above and 300 feet below the cable and is about 100 feet wide, 

being fairly uniform in cross-section near the station. Wallagrass 

Brook is the only stream of any considerable size entering Fish 

River in this vicinity. The gaging station is about 8 miles above the 

entrance of Fish River into the St. John and about 2 miles upstream 

from an undeveloped fall of about 20 feet. There are no dams in this 

vicinity. The extreme stages observed are as follows:

Extreme stages observed on Fish Rirer at Wallagrass, Me.

Gage 

height.

Feet. 

13. fi

1.7

11.9

Discharge.

Second-feet. 

8,300

50

8,25t)

Fish River in this vicinity usually becomes frozen over about 

December 1 and remains so without interruption until about April 1. 

Ice forms first at the shores and gradually extends across the stream, 

with the exception that in the vicinity of the gage a small area 

remains open for a time. Occasionally during the winter the ice 

thins out, owing to the entrance of water from springs. Winter 

freshets are unusual in this vicinity. Winter conditions are very 

uniform, fluctuations in stage are usually slow, and the ice cover is
WINTER RECORDS. 33

smooth and permanent, so that in general this station is especially 

favorable for records. The range of winter gage heights and maximum thickness of ice observed are as follows:

Range of winter gage heights and maximum thickness of ice on Fish River at Wallagrass, Me.

Date.

1903-4. .................................................

1904-5. .................................................

1905-6. .................................................

Gage height to water surface.

Minimum.

Feet. 

2.8 

3.3 

2.0

Maximum.

Feet. 

5.0 

5.2 

5.2

Range.

Feet. 

2.2 

1.9 

3.2

Maximum 

thickness 

of ice.

Feet.

1.9 

1.5

KENNEBEC RIVER AT NORTH ANSON, ME.

This station was established October 18, 1901. It is located 1J 

miles east of North Anson village and a short distance above the 

mouth of Carrabassett River. The drainage area at this point is 

2,880 square miles. Measurements are ordinarily made from the 

covered wooden highway bridge, known locally as Patterson Bridge.

The bed of the stream is rocky, with stone and gravel in places, and 

is permanent. The right bank is high. The left bank is of medium 

height and is subject to overflow in times of highest water. At the 

bridge the channel is about 350 feet wide, broken by one pier. It is 

straight for about 100 feet upstream and 200 feet downstream from 

the bridge and is curved beyond these points. The channel widens 

out to about 500 feet a short distance up and down stream from the 

bridge.

Carrabassett River enters the Kennebec about 1 mile below Patterson Bridge, and at its mouth is a large island dividing the Kennebec 

into two narrow channels. The nearest dam is at Madison, 6 or 7 

miles downstream, and backwater from this dam extends about to the 

mouth of Carrabassett River. Upstream the nearest dam is at Solon, 

about 8 miles above; the slope of the river in this portion*at ordinary 

stages is in general about 4 feet to the mile, althougn it is concentrated 

somewhat at several points. At low water the velocity at the bridge 

becomes somewhat low and poorly distributed, and measurements 

have been made by means of a boat at a distance of about 1,000 feet 

downstream. The extreme stages observed are as follows:

Extreme stages observed on Kennebec River at North Anson, Me.

High water......................... ...... .. .... .....'.....

Gage 

height.

Feet. 

14.95

1.55

13.40

Discharge.

Second-feet. 

39,000

800

 38,200

IER 187 07-
34 STREAM FLOW DURING THE FROZEN SEASON.

Kennebec River in this vicinity usually becomes frozen over during 

the first week in De'cember and remains so without interruption until 

about March 15 or April 15. Near the bridge ice first forms at the 

shores and around the piers and gradually extends, the channel being 

completely frozen over in a week or so in ordinary seasons. During 

the winter of 1905-6, however, narrow channels remained open in 

each span until about January 1, and narrow areas of open water 

remained somewhat after, this date for short distances above and 

below the bridge.

In December there is probably considerable needle and anchor ice 

in the vicinity of the station, but after the ice becomes permanent no 

trouble has been occasioned from this source.

Ordinary winter conditions are good for recording gage heights at 

this station. The range of winter gage heights and maximum thickness of ice observed are as follows:

Range of winter gage heights and maximum thickness of ice on Kennebec River at North

Anson, Me.

Date.

903-4.................................................

904-5 ..................................................

905-6 ..................................................

Gage height to water surface.

Minimum.

Feet. 

2.3 

3.8 

3.4

Maximum.

Feet. 

4.8 

6.6 

5.8

Range.

Feet. 

2.5 

2.8 

2.4

Maximum 

thickness 

of ice.

Feet. 

2.8 

2.7 

2.0

RONDOUT CREEK AT ROSENDALE, N. Y.

This station was established July 6,1901. It is located at the highway bridge in Rosendale about one-half .mile downstream from the 

Wallkill Valley Railroad station. The drainage area above this point 

is 380 square miles. There is some diversion through the Delaware and 

Hudson Company's canal, which is parallel to the river and is operated during the summer months from High Falls to tide water in Hudson River at the mouth of Rondout Creek. This canal receives its 

supply from Rondout Creek at High Falls, 3 miles upstream from 

Rosendale, but a large percentage of this diversion returns before 

reaching the gaging station. Observations made at Creeklocks of 

the stage of water in the canal and a record of the number of lockages 

afford sufficient data to estimate the flow through the canal. As the 

canal is closed during the winter months, it has no effect on the 

winter's record.

At the gaging station the bed of the stream consists of rock and is 

permanent. The channel at the bridge ranges from 90 to 135 feet in 

width and widens out considerably both above and below the bridge. 

It is straight for several hundred feet each way from the bridge, and 

some rifts about 1,000 feet downstream cause slack water at low
WINTER KEGOKDS. 35

stages, when measurements are made at a ford about 1 mile below. 

Both banks are high and rocky and are not subject to overflow. 

Water passes under the bridge at all stages.

There is practically 75 feet fall from the diversion dam near High 

Falls, about 3 miles above the station, to the junction with Wallkill 

River, about 3 miles below. There are no streams of importance 

flowing into Rondout Creek in the neighborhood of Rosendale. The 

extreme stages observed are as follows:

Extreme stages observed on Rondout Creek at Rosendale, N. Y.

^

Gage 

height.

Feet. 

19.40

6.00

4 13. 40

Discharge.

Second-feet. 

18, 130

50

18,080

Rondout Creek usually freezes over about December 1 and the ice 

goes out about March 1. There are usually two or three freshets during this period that break the ice up and in most cases carry it out.

The record was discontinued November 7, 1903, but started again 

about December 1, 1905, by the city of New York. The 1905-6 records show that the river was not closed by ice until about February 3 

and that the ice went out February 22. The range of winter gage 

heights and maximum thickness of ice observed are as follows:

Range of winter gage heights and maximum thickness of ice on Rondout Creek at Rosendale,

. N. Y.

Date.

1901-2. .................................................

1902-3. . ...............................................

1905-6. . ................................................

Gage height to water surface.

Minimum.

Feet. 

6.95 

6.95 

5.04

Maximum.

Feet. 

9.35 

9.85 

5.60

Range.

Feet. 

2.40 

3.10 

.56

Maximum 

thickness 

of ice.

Feet. 

0.42 

.40 

.46

WALLKILL RIVER AT NEWPALTZ, N. Y.

This station was established July 7, 1901, and was discontinued 

November 19, 1903. It was located at the highway bridge in Newpaltz, near the Wallkill Valley Railroad. The drainage area above 

this point is 736 square miles. The measurements were made from 

the downstream side of the highway bridge at all times except during 

extreme high water, when the Wallkill Valley Railroad bridge about 

3 miles below was used. At low stages the water is rather slack and 

it is difficult to obtain a satisfactory measurement. The bed of the 

stream is composed of clay with large cobblestones and some bowlders,
36 STREAM FLOW DURING THE FROZEN SEASON.

and is permanent. Upstream the channel is straight for 400 or 500 

feet; it then bends rather sharply to the right; downstream it is 

straight for several hundred feet. The right bank is rather high and 

slightly wooded, and does not overflow. The left bank-is of medium 

height and is subject to overflow during high-water stages.

The principal tributary to the Wallkill in the vicinity of Newpaltz 

is the Shawangunk Kill, which enters near Gardiner, about 7 miles 

above, its total drainage area being 149 square miles. The dam 

nearest the station is at Walden, about 12 miles above. At low 

stages slight rapids about 300 feet below the bridge cause slack water 

in places and affect the discharge; at extreme high water a plain on 

the left side is overflowed, making it impossible to determine the 

flow at this point. The extreme stages observed were as follows:

Extreme stages observed on Wallkill River at Newpaltz, N. Y.

Gage 

height.

Feet. 

24.8

5.5

19.3

Discharge.

Second-feet. 

24,480

105

24,375

While Wallkill River freezes more or less in December, there are 

no records that show the stream to be completely closed before January, and then only for short periods. Several discharge measurements under ice cover have been made, some showing backwater 

from ice and others giving fairly good results. In general, however, 

the river is partially open during the entire winter season, except in 

parts of January and February. The ice usually goes out about 

March 5.

Ice records on Wallkill River at Newpaltz, N. Y.

1902.

January 12, ice 1.2 feet thick. 

January 19, ice 1.2 feet thick. 

January 26, ice 1.2 feet thick. 

February 2, ice 1.3 feet thick. 

March 1, high water.

1903.

December 11, 1902, to January 4, ice about 0.5 foot thick. 

January 4-17, ice 0.83 foot thick. 

January 18-24, ice 0.92 foot thick. 

January 25-31, ice 0.83 foot thick. 

February 1-26, ice 1 foot thick. 

February 28, ice went out under bridge. 

March 1-4, ice 200 feet above and 300 feet below bridge. 

March 5, river clear.
WINTER RECORDS. 37

* The range of winter gage heights and maximum thickness of ice 

observed are as follows:

Range of winter gage heights and maximum thickness of ice on WaWcttl River at Newpaltz,

N.Y.

Date.

1901-2 ..................................................

1902-3 ..................................................

Gage height to water surface.

Minimum.

Feet. 

7.20 

7.05

Maximum.

Feet. 

18.50 

16.55

Range.

Feet. 

11.30 

9.50

Maximum 

thickness 

of ice.

Feet. 

1.25 

.82

WINOOSKI RIVER AT RICHMOND, VT.

This station was established June 25, 1903. It is located at the 

steel highway bridge about one-fourth mile from Richmond railway 

station on the road to Huntington. The drainage area at this point 

is 885 square miles. The bed consists of sand and gravel and is fairly 

permanent. The banks are fairly high, but overflow at extreme high 

water. The channel is slightly curved upstream, but straight for 

1,000 feet or more downstream. It is about 175 feet wide at the 

bridge, and somewhat wider above and below. The nearest dam 

downstream is at Essex Junction, about 8 or 9 miles below the station, and there is a considerable amount of undeveloped fall between 

these two points. Upstream the nearest dam is at Bolton Falls, 

about 7 or 8 miles above the station. The extreme stages observed 

are as follows:

Extreme stages observed on WinoosK River at Richmond, Vt.

Gage 

height.

Feet. 

18.7

3.7

15.0

Discharge.

Second-feet. 

+ 19,000

139

4-18,861

Winooski River in this vicinity usually freezes during the first part 

of December and remains frozen until about March 15. That part 

adjacent to and below the bridge, where the velocity is medium, 

freezes first. About one-fourth mile upstream, where a stretch of 

quick water begins, freezing takes place considerably later, and during some winters a permanent ice cover does not form here.

The contraction in the channel at the bridge tends to cause ice 

jams, and low velocity just below favors the formation of thick ice. 

During the January freshet of 1906 a jam affected gage readings during the remainder of the winter season. PL I, B (p. 24), shows the conditions at the gaging section March 9, 1906. The ice is extremely
38 STREAM FI+OW DURING THE FROZEN SEASON.

rough, broken, and tilted, and the gage heights give no index whatever of the flow, which was confined to about one-third the ordinary 

width of channel. The range of winter gage heights and maximum 

thickness of ice observed are as follows:

Range of winter gage heights and maximum thickness of ice on WinoosTci River at .

Richmond, Vt.

Date.

1903-4.

1904-5.

1905-6.

Gage height to water surface.

Minimum.

Feet.

4.15 

4.95 

4.9

Maximum.

Feet.

6.7 

5.7 

14.7

Range.

Feet.

3.55 

.75 

9.8

Maximum 

thickness 

of ice.

Feet.

2.75 

3.05 

±2.5

Ordinary winter conditions are rather poor for estimates of flow at 

this station owing to the liability of unstable conditions. During 

low stages, which frequently occur in winter, the change in discharge 

is considerable for a slight difference in stage, and a slight change in 

the controlling ice conditions downstream may markedly affect the 

discharge:

GAGE HEIGHTS AND DISCHARGE MEASUREMENTS.

The following measurements have been made at the stations 

described above.

Stream measurements during frozen season. 

CATSKILL CREEK AT SOUTH CAIRO, N. Y.

Date.

1901

December 9......

1902

January 15 ......

1906

February 16 .....

a +*

T3 £

Feet.

«65

90

100

d

under rea 

 <

Sq.ft.

106

166

190

^

velocii ean 

S

Feet

per

sec.

1.03

.89

.33

ischarge.

P

Sec.-

feet.

110

148

62

Gage 

height 

o> 

o

cj "S

water Dsu

EH

.Feei.

3.30

3.50

2.82

d 

_g s

bottom (

EH

.Fee*.

2.93

2.84

2.22

d

o

"iH

tlickness o

EH

Jfee^.

0.37

.66

.70

icelow on

03

Feet.

Gage height 

to water 

surface.

O 0)

«> cj r^

ischarg open- w condition:

P

Sec.-

feet.

120

152

56

£88

o ° o 

OJ O " £

o

0.92

.97

1.11

Gage height 

to bottom 

of ice.

O a>

Ol <£ 

ischarg open- w conditions

P

Sec.-

feet.

66

53

17

ig§ "-1 o, 1

if°l

S.- ®s '3 o+'-o

SEs^g' §-«s=8

o

1.67

2.79

3.65

o Gaging made 70 yards below bridge.
GAGE HEIGHTS AND DISCHARGE MEASUREMENTS. 39

Stream measurements during frozen season Continued.

CONNECTICUT RIVER AT ORFORD, N. H.

Date.

1903. 

January 24 . .....

January 29 . .....

February 7

1904.

1905.

1906. 

February 8.. .... 

February 15 ..... 

February 17 ..... 

March 14 ........

Width.

Feet. 

276 

273 

273 

276 

278 

278

240 

241 

239 

236 

235 

235

235 

235 

235

327 

3?7 

327 

327 

327

Area under ice.

S<7- ft. 

1,760 

1,610 

1,620 

1,760 

1,810 

1,810

851 

847 

804 

804 

813 

805

775 

794 

794

1,920 

1,870 

1,790 

1,560 

1,440

Mean velocity.

Feet 

per 

sec. 

1.69 

1.63 

1.66 

1.69 

1.65 

J.67

1.00 

.99 

.93 

.95 

93 

95

.88 

.96 

.93

1.17 

1.20 

1.14 

1.08 

1.04

Discharge.

Secfeet. 

2,970 

2,620 

2,690 

2,980 

2,990 

3,030

850 

840 

750 

760 

700 

765

686 

766 

739

2, 250 

2,240 

2,040 

1,680 

1,490

Gage 

height 

surface. To water 

Feet. 

7.33 

6.71 

6.75 

7.30 

7.38 

7.40

4.20 

4.17 

4.03 

3.99 

4.03 

4.03

4.07 

4.26 

4.25

..84 

6.80 

6.56 

6.00 

5.59

To ofbottom ice.

Feet. 

6.00 

5.40 

5.50 

6.00 

6.05 

6.05

2.40 

2.37 

2.23 

2.19 

2.23 

2.23

2.30 

2.40 

2.39

5.51 

5.32 

5.06 

4.56 

4.15

Thickness ofice.

Feet.

2.03 

2.03 

2.03 

2.03 

2.03 

2.03

2.01 

2.09 

2.09

1.48 

1.48 

1.52 

1.55 

1.55

Snow ice. on 

Feet.

0.1 

.1 

.1

.2 

.9 

.9 

.1

, -1

Gage height 

to water 

surface.

Discharge for t n-w rope ae 

conditions.

Sec.- 

feet. 

4,925 

4,240 

4,285 

4,890 

4,980 

5,000

1,880 

1,860 

1,760 

1,735 

1,760 

1,760

1,790 

1,925 

1,918

4,380 

4.340 

4,080 

3,470 

3,060

for Coefficient re- ducing open-water toic

conditions.

t.6D 

.62 

.63 

.61 

.60 

.61

.45 

.45 

.43 

.44 

.43 

.43

.38 

.40 

.39

.51 

.52 

.50 

.48 

.49

Gage height 

to bottom 

of ice.

Disch'arge for open-water 

conditions.

Sec.- 

feet. 

3,470 

2,880 

2,975 

3,470 

3,520 

3,520

815 

801 

738 

720 

738 

738

770 

815 

810

2,980 

2,810 

2,570 

2,160 

1,840

for Coefficient re- ducing open-to icewatr 

conditions.

0.86 

.91 

.90 

.86 

.85 

.86

1.04 

1.05 

1.02 

1.05 

1.03 

1.04

.89 

.94 

.91

.76 

.80 

.79 

.78 

.81

ESOPUS CREEK AT KINGSTON, N. Y.

1901.

December 4......

1902.

January 9 a ......

February 28?'....

December 11.....

December 1 c

1903.

January 14 d .....

February 24 e ....

1906.

February 15 .....

86

100

116

90

116.6

101.6

104.6

90

280

419

706

404

1,170

413

443

287

0.84

1.25

2.39

1.18

2.96

1.03

1.47

.87

236

522

1,690

476

3,460

425

654

250

5.28

6.54

9.14

1.60

13

6.9

7.1

5.60

5.20

6.41

8.94

6.50

6.32

6.70

5.17

0.083

.13

.20

.10

.58

.40

.33

329

716

2,030

741

5,300

864

950

412

0.72

.73

.83

.64

.65

.49

.69

.61

309

669

1,900

700

638

782

302

0.76

.78

.89

.68

.67

.84

.83

FISH RIVER AT WALLAGRASS ME.

1906.

February 15 .....

Do .'.........

March 15 ........

Do..........

95'

95

115

115

205

205 .._

0.95

.9fi

312 1-21

319 1.22

195

196

378

390

3.91

3.91

4.99

5.08

2.66

2.66

3.83

3.92

1.25

1.25

1.20

1.20

0.65

.65

.9

.9

620

620

1,080

1,125

0.32

.32

.35

.35

225

225

580

620

0.87

.87

.65

.63

o Partly frozen over; stations 20-70 and 110-115 open.

6 Partly frozen over; stations 0-25 and 110-116 open. , 

« River frozen over 150 feet below bridge and 200 feet aboye. Measurements taken at 0.6 depth. No 

ice at bridge.

<* Stations 15-40 river open. 

« Stations 12-40 river open; ice rough.

NOTE. February 8 and 17, river partly open for a short distance below bridge. March 14 and 15, 

river partly open for a short distance below bridge, but not as much as on February 17.
40 STREAM FLOW DURING THE FROZEN SEASON.

Stream measurements during frozen season Continued.

KENNEBEC RIVER AT NORTH ANSON, ME.

Date.

1904.

March 2.........

1905.

Do.:........

1906.

January 10 a. ....

March 3 .........

March 30........

Do..........

Do.&.. .......

Width.

Feet,. 

240 

240 

230 

230

458 

458

440 

440 

445 

445 

447 

447 

450 

450

ice. Area under 

Sq.ft. 

393 

398 

285 

285

1,390 

1,390

1,100 

1,030 

1,140 

1,050 

1,180 

1,200 

1,210 

1,240

velocity. Mean 

Feet 

per 

sec. 

1.90 

1.97 

1.86 

2.01

1.50 

1.54

1.17 

1.09 

1.40 

1.31 

1.36 

1.38 

1.37 

1.38

Discharge.

Secfeet. 

749 

786 

529 

572

2,080 

2,140

1,290 

1,120 

1,590 

1,380 

1,600 

1,660 

1,660 

1,710

Gage 

height 

To surface. water 

Feet. 

3.40 

3.40 

3.55 

3.65

5.27 

5.32

3.58 

3.40 

4.26 

4.08 

4.77 

4.80 

4.70 

4.70

bottom ofTice.

Feet. 

1.55 

1.55 

1.45 

1.55

3.27 

3.32

2. 38 

2.22 

2.43 

2.27 

2.67 

2.70 

2.80 

2.80

of Thickness ice.

Feet. 

1.8 

1.8 

'2.1 

2.1

2.10 

2.10

1.28 

1.30 

1.97 

1.98 

2.26 

2.26 

1.95 

1.95

Snow ice. on 

Feet. 

2.0 

2.0

1.0 

1.0

. 1 

.1 

.1 

.1 

.0 

.0 

±1.0 

±1.0

Gage height 

to water 

surface.

for arge water itions.

s|l

 O 0

p

Sec.- 

feet. 

3,170 

3,170 

3,450 

3,650

7,530 

7,680

3,520 

, 3,170 

4,980 

4,580 

6,220 

6,300 

6,050 

6,050

ggl

^ Q. 2°3S

Si? * § s s «-e

O o 4^*0

63°3g

g'dfsS 

O

0.24 

.25 

.15 

.16

.28 

.28

.37 

.35 

.32 

.30 

.26 

. 26 

.28 

' .28

Gage height 

to bottom 

of ice.

t- n -S®

0> oj «; "fi

5 cS

»Ea

K »0 

 ~< O 0

fi

Sec.- 

feet. 

±675 

±675 

±600 

±675

2,920 

3,020

1,550 

1,370 

1,630 

1,420 

1,950 

1,990 

2,140 

2,140

for entre-ng open-ice toer

tions.

<a <a+i"O 

6 3 * 8 

§ «£§ 

O

±1.11

±1.16

± .88 

± .85

.71 

.71

.83 

.82 

.98 

.97 

.82 

.83 

.79 

.80

RONDOUT CREEK AT ROSENDALE, N. Y.

1901.

December 0<".. .. .

1902.

January 14. .....

February 8 ......

February 26 .....

Do..........

1903.

February 25 .....

1906.

February 27. ....

104

105

102

80

100

115

117

479

479

732

489

517

474

555

0.46

.88

1.62

1.11

1.32

1.6

.35

222

4OQ *1ZO

732

543

684

676

194

6.80

7 00

8.81

8.13

8.43

7.9

f5. 15

C. ; 1

6.53

8.41

6.71

7.01

7.40

4 51

0.26

.47

.40

1.42

<*1.42

.50

.46

415

540

2,330

1,610

1,930

4,370

0.53

.78

.31

.34

.35

.15

253

247

1,900

359

549

885

0.88

1.71

.40

1.51

1.24

.76

WALLKILL RIVER AT NEWPALTZ, N. Y.

1901.

December 11 /. . .

1902.

January 21 ......

January 23 g .....

January 31 ft .....

February 10 .....

February 24.. ...

1903.

February 7. .....

February 10 }....

February 26.....

135

80

140

100

115

oeOO

140

142

130

1,310

423

1,880

679

496

000

ooo

1,070

999

757

2.32

.78

3.22

1.72

1.20

.74

2.14

2.03

1.24

3,040

332

6,060

1,170

597

OCQ ZOO .

2,290

2,030

945

11.50

7.24

17.33

9.07

7.78

7 °Ji /. OO

11.2

10.9

8.85

10. S

6.04

16.41

8.07

6.78

a C OC *O. j£O

10.45

9.73

7.89

0.70

1.20

.92

1.00

1.00

2.10

.75

1.17

.96

3,830

860

9,290

1,980

1,160

919

3,580

3,330

1,830

0.79

.39

.65

.59

.51

.31

.64

.61

.52

3,250

277

8,300

1,330

619

2,970

2,440

1,230

0.94

1.20

.73

.88

.97

.77

.83

.77

a Frozen except for narrow channels above and below bridge. , 

6 Frozen except for narrow channel near left bank.

c Ice varied from one-half inch to 5 inches from bank to bank at riff just below; ice extended one-third 

way across.

d Estimated from previous measurements, same date. 

e Subject to correction. 

/ Ice cover from stations 40-85. 

g Ice badly broken at station 20. 

Mce badly broken at station 110.

* Below rating table; water considerably above top of ice. 

/ Stations 135-142 open.
B J±, £

P CT HJ

P CD CD i_2

?-8 3 P^ 

§ P § ®

III B s3 ^(

C ed

B* ^

h* p 

C^ P

i-S GfQ

P p

& ^ 

P p 

TO _

o p.* 

2. CD

kS OQ

sr 02 o' o

P 3

CD 

O 

H-h 02

e+ pt

PP

^
Single discharge measurements on frozen streams, 1906

River and station.

Genesee, Jones Bridge, Mount Morris, N. ¥. '.. .

Do f... .....................................

Do. ft ........................................

Otter Creek, Middlebury, Vt. *..................

Do. i .........................................

West Canada Creek, Twin Rock Bridge, N. Y.n.

Date.

1906.

March 10.........

February 9-10....

Width.

Feet. 

225 

332 

565 

344 

118 

118 

127 

306 

360 

130 

236 

106 

174 

172.6 

172.5 

175

Area 

under 

ice.

Square 

feet. 

1,040 

2,772 

1,984 

501 

298 

290 

373 

1,710 

1,020 

576 

597 

352 

1,710 

1,540 

1,740 

527

Mean 

velocity.

Feet per 

second. 

0.65 

1.00 

1.13 

1.23 

1.52 

1.65 

1.40 

.43 

.88 

1.23 

.77 

3.30 

3.14 

3.07 

3.57 

.78

Discharge.

Secondfeet. 

674 

2,761 

2,260 

632 

452 

479 

525 

728 

894 

709 

458 

1,160 

5,370 

4,710 

6, 220. 

412

Gage he

To water 

surface.

Feet. 

2.85 

4.82 

2.45 

16.13 

5.75 

5.78 

6.00 

1.40 

1.53 

3.90 

3.34 

13.40 

10.31 

8.77 

9.73 

3.02

a Gravel bed' under ice surface smooth; considerable needle ice.

b Gravel bed; open 70 feet wide upstream for a long distance; same for about 1,000 feet downstream; then froz

"Gravel bed; ice rough.

d Coarse gravel.

« Gravel and sand bed.

/Measurements made about 250 feet downstream from regular station.

g Gravel bed.

ftElmwood Avenue Bridge (regular station); ice smooth on bottom; some needle ice running at stations 100-

* Considerable needle ice; gravel bed. 

i Gravel bed; ice rough.

* Sand and gravel bed; river open 500 feet below gage for about 800 feet to dam and arch bridge where gaging 

' Gravel bed; river open, stations 150-175. 

m River open, stations 0-35 and 130-175. 

n Gravel bed; under ice surface nearly smooth; a little needle ice.
WINTER RECORDS. 43

STATION RATING CURVES FOR ICE COVER. 

GENERAL CONSIDERATIONS.

At several stations sufficient data have been gathered to construct a rating curve for conditions of ice cover, applicable to average ice conditions within the range of winter gage heights, but the 

variation in form of curve with change in thickness of ice is still 

uncertain, and the proper rating curve or coefficient to apply for the 

time when the ice is thin has not been sufficiently verified by gagings. 

A station rating curve for conditions of ice cover must evidently be 

constructed on one of the following bases: (1) Gage heights to the 

surface of the water as determined from a hole cut in the ice, or 

2) gage heights to the bottom of the ice.

FIG. 4. Rating and velocity curves under ice cover, Wallkill River at Newpaltz, N. Y.

In figs. 4 to 6 are shown the results of such gagings as have been 

made under ice cover at three gaging stations, the gage heights being 

plotted in each of the above ways and the open-water rating curve 

being shown for comparison.

WALLKILL RIVER AT NEWPALTZ, N. Y.

So far as can be determined at present, the rating curve based on 

gage heights to the water surface seems to give the best results; 

that is, the points lie more nearly on a smooth curve (fig. 4). There is 

no great difference, however, except in the case of the lowest gaging, in which the thickness of the ice was perhaps only half of the
44 STREAM FLOW DURING THE FROZEN SEASON.

distance, 2.1 feet, from the water surface to the bottom of the ice, 

indicating that the water below the ice was under some pressure. 

It will be noticed^ that the range in ice thickness is not large.

92.00

9

1.90

02.10

O2.IO

O

I.85

O

H.83

 I.8I

1.20

II.IS

IOOO 2000 3000 4000 5000 6000

DISCHARGE CU. FT. PER SEC.

1904 DISCHARGE MEASUREMENTS = O

1905 " " =9

FIGURES DENOTE DISTANCE FROM WATER SURFACE TO BOTTOM 

FIG. 5. Rating curve under ice cover, Kennebee River at North Anson Me.

KENNEBEC RIVER AT NORTH ANSON, ME.

The effect of varying thickness of ice on discharge for a given gage 

height is clearly shown (fig. 5). No one curve can be drawn through the 

points plotted for the gage heights to the water surface, although a few
STATION RATING CURVES. 45

more gagings would, perhaps, enable a series of curves to be drawn 

for different distances from the water surface to the bottom of the 

ice. It is preferable to use these distances rather than thickness of 

the ice, for the position of the bottom of the ice with reference to 

the water surface is not only dependent on the ice thickness (in 

general being about 92 per cent of it), but will also vary with the

o

7 

iu6

UJ

u.

z 

l- 5

UJ

X

UJ

3- 

2

t,

<f

2.0<JL

//

/rS* "

/ "'I;?

a*/

"///

O|.8P \u / / 

U//

^ / /

V

1

_£

/

4

^1.33 

1 1.48 ^1-25

1 1.50 ''

 y$ / o

^J* ^ /

v

\ 33

^

V

/

Y

Y

} 1000 2000 3000 4000 5000 60<

DISCHARGE-CU. FT. PER SEC.

1903 DISCHARGE MEASUREMENTS = ©

1904 »' »' « O

1905 " " = O

1906 " " = 

FIGURES DENOTE DISTANCE FROM WATER SURFACE TO BOTTOM OF ICE

FIG. 6. Rating curve under ice cover, Connecticut River at Orford, N. H.

snow load and thus include its effect. If gage heights to the bottom of the ice are used a fairly consistent curve is obtained for this 

station.

CONNECTICUT RIVER AT ORFORD, N. H.

The same general results appear here as in the case of the Kennebec, although the range of ice thickness is less (fig. 6). The gagings of 

1903 and 1904 are open to some question, owing to the manner in
46 8TEEAM FLOW DUEING THE FEOZEN SEASON.

which they were made, and have been ,given little weight in drawing the curve as shown.

GENERAL FORM OF RATING CURVE FOR ICE COVER.

The curve, as constructed with gage heights to the bottom of the 

ice, in general lies to the left of the open-water rating curve, but 

tends to approach it in its lower portion and perhaps to cross it.

The degree of curvature of'the two curves is in general about the 

same in their lower parts and, like the open-water curve, the rating 

curve for ice cover is apparently a tangent in its upper part. In 

fact, it will be noticed in the case of the Wallkill and Connecticut 

that the ice-cover curve will be approximately the same as the openwater curve if the latter is swung around the intersection point of 

the two curves until the upper parts coincide.

With gage heights to the surface of the water, the indications are 

that the curve for ice cover (or rather the series of curves constructed for different thicknesses of ice) will be approximately parallel to the curve determined by gage heights to the bottom of the ice.

RELATION BETWEEN DISCHARGE UNDER ICE COVER AND FOR OPEN

SECTION.

If gage heights are taken to the bottom of the ice and the discharge compared with that for the same gage heights in open channel, it is found that as the stage increases this ratio decreases. In 

the case of the Wallkill, this ratio is greater than unity below about 

gage height 6.8, where the curves cross, and decreases from this point 

to a value of about 0.71 at gage height 18.0. With the Connecticut 

the range in this ratio is from 0.97 at gage height 2.0 to 0.78 at gage 

height 6.0. Evidently no mean .value of the ratio can be assumed 

that will give anything more than rough results. 

 It is not deemed wise in the light of existing data to advise the use 

of either one of the above-described methods for the construction pf 

rating curves to the exclusion of the other, although the indication 

seems to be that the use of gage heights to the bottom of the ice will 

prove most generally convenient. There will undoubtedly be cases, 

however, where this method must be used with caution, more especially in the lower part of the curve, as it would not take into account 

the effect of ice being held down by shores or piers, and the consequent pressure or head under which flow was taking place.

VERTICAL VELOCITY MEASUREMENTS UNDER ICE COVER. 

DETAILS OF VERTICAL VELOCITY CURVES.

The principal data for vertical velocity curves at 25 stations are 

given on the following pages. It will be noted that each curve can 

be replotted from the table, if desired. In general, mean results 

are given for each set of curves taken, but some sets are subdivided 

in order to separate different conditions.
Vertical velocity measurements. 

CATSKILL CREEK AT SOUTH CAIRO, N.

Date.

1906.

Gage height to water

surface.

Feet. 

2 82

Gage height to bottom ofice

Feet.

31 

'S

£.£ *** O

go.

5 

5

Feet. 

25 

55 

60 

65

Total depth.

.Fee*. 

4.0 

3.6 

3.6 

3.3

3.6

1 

_o

£1

a 

'S.

o

P

JVrf. 

3.1 

2.7

2.7 

2 4

2 7

.Thickness ofice.

Feet. 

1.00 

LOO 

1.00 

.95

.98

Velocity in feet per second from vertical velocity 

curves.

03

r..37 

.41 

.48 

.51

.44

0.5 depth.

0.43 

.47 

.53 

.56

0.2 depth.

0.50 

.60 

.52- 

.50

0.8 depth.

0.28 

.24 

.44 

.52

T:

OC

d 

d

L 

J

<N

0.39

.42 

.48 

.51

O

0.30 

.50 

.32 

.25

Bottom.

0.14 

.10 

.35

.48

Maximum.

0.51 

.60 

.55 

.55

CHEMUNG RIVER AT CHEMUNG, N. Y.&

1906.

2.85

2.85

3.27

3.38

29

on

50 

60 

80

90 

100 

110

120

130 

140 

150

9.2

in 9

10.6 

9.1 

6 5

6.5 

6 2 

5 9

8,0

5 1

4 0 

3.6 

3.7

4 1

8.8

9 8

10.2 

8.9 

6.3

6.2 

5 8 

5.6

7.7

4.8

3.6 

3.2 

3.2

3,7

0.50

cn

.45 

.30

QA

.40 

.45 

.45

.40

.50 

.50 

.60

0 39

.56

93 

1.06

SQ

.66 

:36 .»

.65

.34

SI

.80

.64

0.50

1.38 

1.86 

2.12

1.54 

1.26 

.73

.40

.74 

.90 

.95

0.43

.58 

1.26 

1.55

.70 

1.05 

.50

.36

.71 

.72 

.75

0.40

.45

1.42 

1.30 

1.70

.66 

.86 

.52

.34

.61 

.67

85

0.42

60

1.00 

1.2S

.68 

,96 

.51

.35

.66 

.70 

.80

0.20

0

0 

0 

0

0 

0 

0

.32

.60 

.35

.48

0.06

.61 

.40 

1.20

.45 

.26 

.18

.14

.49 

.45 

.74

0.50

.85

1.70 

1.86 

2.13

1.72 

1.28 

.74

.39

.75 

.90 

.94

a Gravel bed. & Coarse gravel bed. Need
Vertical velocity measurements Continued.

CHIPPEWA RIVER AT EAU CLAIRE, WIS.o

Date.

1906.

Gage height to water

surface.

Feet.

4.82

o

S*S 

'S S 

 °5

0}

a

o

Feet. 

3.92

Distance frominitial 

point.

Feet. 

130 

150 

170

Total depth.

Feet. 

14 3 

13.5 

12.6

13.5

Depth below ice.

Feet. 

13.2 

12.4 

11.5

12.4

Thickness ofice.

Feet. 

1.10 

1.10 

1.10

1.10

Velocity in feet per second from vertical velocity 

curves.

a

03 

OJ

S

0.52 

.76 

1.14

.81

0.5 depth.

0.72 

.90 

1 38

0.2 depth.

0.53 

.67 

1.10

0.8 depth.

0.47 

.83 

1 18

X ia 

T

?

CM

C

i,

IN

0.50 

.75 

1.14

d 

o

0.18 

39 

.40

Bottom.

0.13

.58 

.54

Maximum.

0.73 

.92

1.39

CONNECTICUT RIVER AT ORFORD, N. H.&

1903.

1904.

February 4 ..................

6.71

6.75

7.30

7 3S

7.30

7.38

4.15

3.95

4.17

4.03

5.40

5.50

6.00

6.00

2.45

2.25

2.37

2.22

150

340

QA

100

110

130

140

150 

250

260 

270 

280 

200

110

3.8

3.9

5.3

7.7

8.2 

8.1 

7.4 

5.0

4.8

6.6

9 8

6.2

7 7

6.3

7.2

7.3

2.0

2.1

3.5 

6.0

6.5 

6.4 

5.8 

3.0

3.3

2.00

2.00

2.00 

2.00

1.85 

1.95 

1.85 

2.25

1.70

1.92

1.94

1,85

1.58

1.73

1.76

.67

.40

1.23 

1.04

1.03 

1.11 

1.10 

.61

1.12

2.17

2.12

1.96

1 Q1

1.93

.72

.42

1 33 

1.10

1.13 

1.17 

1.20 

.66

1.20

2.23

2.15

1.92

1,92

1.94

.86

.60

1.48 

1.21

1.16 

1.20 

1.22

.78

1.32

1.65

1.82

1.86

1 62

1.53

1.60

.52

22

1.00 

.92

.92 

1.03 

.98 

.43

.92

1.94

1.98

1.89

1 ^Q

1.72

1.77

.69

.41

1.24 

1.06

1.04 

1.12 

1.10 

.60

1.12

1.22

1.13

1.22

,76

1.15

1.22

.50

.48

1.09 

.80

.74 

.93 

.85 

.55

1.13

1.08

1.32

1.58

.85

1.19

1.05

.33

.00

.70 

.61

.52 

.82 

.70 

.20

.68

2.27

2.21

1.97

1 Q1

2.00

2.04

.87

.61

1.48 

1.21

1.18 

1.22 

1.23

.78

1.32

Gravel bed. 
Vertical velocity measurements Continued. 

CONNECTICUT RIVER AT ORFORD, N. H. Continued.

Date.

1904.

1905.

Mean of 8 curves. ......

Gage height to water

surface.

Feet. 

4.03

4.07

4.26

Gage height to bottom ofice.

Feet. 

2.23

2.25

2.40

Distance from initial 

point.

Feet. 

90 

100 

340

100 

110 

120 

150 

170 

190 

240 

260 

280 

330

110 

160 

180 

200 

250 

270 

320 

340

Total depth.

Feet. 

5.2 

4.2 

5.3

K 7

4.2 

5.0 

5.5 

5.2 

5.5 

5.0 

5.8 

6.7 

6.7 

5.5

5.5

5.2 

5.7 

5.7

4.5 

7.3 

7.1 

5.5 

5.6

5.8

Depth below ice.

Feet. 

3.6 

2.4 

4.2

3.1 

3.5 

3.9 

3.5 

3.7 

3.2 

3.6 

4.7 

5.1 

3.9

3.8

3.6 

4.0

3

Q

2.2 

5.3 

5.2 

3.8 

4.8

4.1

Thickness of ice.

Feet. 

1.75 

1.95 

1.60

1 91

1.3 

1.8 

1.8 

1.9 

2.0 

2.1 

2.5 

2.3 

1.9 

2.0

1.8 

1.9

2

1

2.6 

2.3 

2.2 

1.8 

1.1

1.98

Velocity in feet per second from vertical velocity 

curves.

R

03 

01

a

0.93 

.96 

.85

.92

1.00 

.88 

1.24 

1.12 

1.15 

.93 

.69 

1.13 

1.19 

.92

1.02

1.08 

1.28

.76 

.94 

1.25 

1.14 

.92

1.0(5

+3

ft

 8

1C

d

1.03 

1.06 

1.02

1.13 

1.02 

1.32 

1.27 

1.23 

1.04 

.87 

1.28 

1.33 

1.13

1.25 

1.48

.83 

.96 

1.37 

1.32 

1.12

a

1 

 o 

«

0

1.05 

1.15 

.98

1.00 

1.02 

1.36 

1.34 

1.32 

1.10 

.71 

1.10 

1.25 

.97

1.23 

1.39

.80 

1.07 

1.32 

1.27 

1.04

4 & o

00

o

0.82

.78'

.77

.98 

.74 

1.14 

.89 

.99 

.77 

.-63 

1.16 

1.13 

.82

.88 

1.15 

97

.72 

.85 

1.18 

1.01

.78

! c

<x> 

d

(M

d

H

(M

0.94 

.96

.88

.99 

.88 

1.25 

1.12 

1.16 

.94 

.67 

1.13 

1.19 

.90

1.06 

1.27 

1.15

l! 

1.

76 

96 

25 

14 

91

&

H

0.92 

.90 

.83

.58 

.40 

1.00 

1.05 

.85 

.73 

.33 

.87 

.83 

.30

92 

1.00

.56 

.88 

1.00 

.93 

.61

fi

3 +^

om

0.34 

' .45 

.00

.80 

.40 

.93 

.57 

.75 

.40 

.38 

.60 

.85 

.60

.48 

.72 

.23

.56 

.72- 

.92 

.55 

.35

fi 

3

1

3

1.06 

1.15 

1.02

1.15 

1.07 

1.38 

1.37 

1.33 

1.11 

.88 

1.29 

1.35 

1.22

1.32 

1.53 

1.41

.83 

1.07 

1.38 

1.33 

1.13
Vertical velocity measurements Continued. 

CO NNECTICUT RIVER AT ORFORD, N. H Continued.

Date.

1906.

Mean of 7 curves. ......

Gage height to water 

surface.

Feet. 

6.84

6.80

6.56

Gage height to bottom ofice.

Feet. 

5.51

5.90

5.61

Distance from initial 

point.

Feet. 

60 

140 

180 

220 

260 

300 

340

60 

140 

180 

220 

260 

300 

340

60 

140 

180 

220 

260 

300 

340

Total depth.

Feet. 

5.9

7.7 

7.2 

7.2 

7.5 

8.9 

8.0

6.0 

7.6 

7.3 

7.2 

7.5 

8.8 

8.0

7.5

5.6 

7.2 

7.1 

7.0 

7.4 

8.7 

7.8

7.3

to 

"a!

fl

Feet. 

4.6 

5.6 

6.1 

6.0 

6.3 

7.3 

6.4

6.0

4.5 

5.3 

6.1 

5.8 

6.2 

7.1 

6.3

5.9

4.1 

5.0 

5.8 

5.6 

6.0 

7.0 

6.0

5.6

Thickness ofice.

Feet. 

1.45 

2.15 

1.20 

1.30 

1.30 

1.90 

1.80

1.59

1.40 

2.20 

1.20 

1.30 

1.30 

2.00 

1.70

1.73

1.60 

2.20 

1.30 

1.40 

1.45 

1.90 

1.85

1.67

Velocity in feet per second from vertical velocity 

curves.

03

0.95 

1.58 

1.67 

1.44 

1.37 

1.06 

.63

1.24

1.09 

1.60 

1.58 

1.44 

1.36 

1.12 

.62

1.26

1.09 

1.49 

1.57 

1.29 

1.34 

1.07 

.55

1.20

43

"ft

OJ

o

1.03 

1.89 

1.86 

1.63 

1.57 

1.14 

.73

1.32 

1.92 

1.80 

1.63 

1.48 

1.21 

.70

1.27 

1.81 

1.73 

1.55 

1.53 

1.18 

.63

43"ft

O

1.09 

1.42 

1.87 

1.65 

1.53 

1.07 

.66

1.09 

1.45 

1.80 

1.66 

1.48 

1.14 

.64

1.07 

1.32 

1.73 

1.62 

1.46 

1.12 

.59

43

ft

a.

00 

0

0.85 

1.62 

1.53 

1.23 

1.21 

1.08 

.61

1.03 

1.75 

1.34 

1.19 

1.27 

1.14 

.59

1.07 

1.53 

1.39 

.98 

1.19 

1.03 

.52

f

"e 

 §

00

o 

o'

0.97 

1.52 

1.70 

1.44 

1.37 

1.08 

.64

1.06 

1.60 

1.57 

1.42 

1.38 

1.14 

. 62

1.07 

1.42 

1.56 

1.30 

1.32 

1.08 

.56

ft

o

0.89 

1.00 

1.44 

1.32 

1.03 

.90 

.37

.57 

.92 

1.25 

1.38 

1.04 

.90 

.44

.87 

.95 

1.38 

1.12 

1.19 

.85 

.49

_o 

"o

pq

0.34 

1.14 

.80 

.66 

.67 

.63 

.37

.75 

.65 

.96 

.73 

.98 

.79 

.38

.70 

1.05 

1.03 

.45

.77 

.80 

.14

B 

a

B

03

1.10 

1.95 

1.92 

1.72

i.eo

1.15 

.73

1.34 

1.97 

1.86 

1.69 

1.54 

1.21 

.71

1.29 

1.84 

1.80 

1.70 

1.54 

1.20 

.63

D

&

0

1

l

a Ice rougn.
Vertical velocity measurements Continued. 

CONNECTICUT RIVER AT ORFORD, N. H. Continued.

Date.

1906. 

March 14 ». ..................

Gage height to water

surface.

Feet. 

6.00

5.59

Gage height to bottom ofice.

Feet. 

4.56

4.15

Distance from initial 

point.

Feet. 

60 

140 

180 

220 

260 

300 

340

60 

140 

180 

220 

260 

300 

340

Total depth.

Feet. 

4.9 

6.6 

6.2 

6.5 

6.7 

8.1 

7.0

6.6

4.6

6.2 

6.0

6.1 

6.5 

7.5

6.7 

6.2

Depth below ice.

Feet. 

3.5 

4.5 

4.9 

5.2 

5.3 

6.3 

5.1

4.9

3.2

4.2 

4.6

4.7 

5.1 

5.7

4.8 

4.6

Thickness ofice.

Feet. 

1.50 

2.15 

1.40 

1.35 

1.50 

1.95 

2.00

1.69

1.50

2.10 

1.50

1.45 

1.50 

1.90

2.00 

1.71

Velocity in feet per second from vertical velocity 

curves.

a

03 

03

s

1.01 

1.38 

1.39 

1.18 

1.24 

1.02 

.56

1: 11

1.01

1.36 

1.36

1.12 

1.22 

.98

.51 

1.08

"ft

 8

m 

o

1.24 

1.60 

1.56 

1.34 

1.38 

1.18 

.62

1.20

1.52 

1.50

1.27 

1.37 

1.10

.58

"ft

03

(M

C

1.06 

1.45 

1.58 

1.43 

1.37 

1.10 

.60

1.17

1.43 

1.45

1.35 

1.35 

1.05

.55

00 

C

0.94 

1.24 

1.22 

.95 

1.08 

.95 

.52

.88

1.27 

1.23

.90 

1.08 

.90

.47

|

0

t 

oc

0

+

C

IH

1.00 

1.34 

1.40 

1.19 

1.22 

1.02 

.56

1.02

1.35 

1.34

1.12 

1. 22

ft 

o

0.91 

1.12 

1.05 

.99 

1.28 

.83 

.57

.90

1.05 

1.33

1.08 

1.12

.86

.51 .43

o

o

PQ

0.25 

.88 

.87 

.60 

.72 

.49 

.31

.17

1.02 

.80

.55

.77 

.55

.30

|

OS

S

1.25 

1.63 

1.66 

1.48 

J.41 

1.20 

.63

1.23

1.55 

1.50

1.38 

1.40 

1.13

.60

DES MOINES RIVER AT KEOSAUQUA, IOWA.&

1906.

2.45 2.10 50

350 

380 

410 

520

4.2

5.5 

5.6 

6.3 

4.5

5.2

3.7

5.0 

5.1 

5.8 

4.2

4.8

0.5

.5 

.5 

.5 

.3

.46

1.19

1.86 

1.82 

1.65 

1.38

1.58

1.32

2.35 

2.03 

1.87 

1.52

1.33

1.79 

1.98 

1.91 

1.41

1.07

1.87 

1.66 

1.39 

1.38

1.20

1.83 

1.82 

1.65 

1.38

1.08

.63 

1.25 

1.35 

1.15

0.60

.95 

1.30 

.92

.78

1.37

2.35 

2.09 

1.97 

1.52

alee rough. 6 Gravel b
Vertical velocity measurements Continued. 

ESOPUS CREEK AT KINGSTON, N. Y.a

Date.

1901.

December 4 ..................

Mean of 2 curves. ......

1902.

January 9 ...................

Mean of 4 curves. ......

December 11 .................

Mean of 8 curves. ......

1903.

Mean of 4 curves

; towater 

,ce.

_q<8

§|

O 1/1

A

8>03

o

Feet.

5.28

6.54

6.6

6.90

J.

o

£1

°i

+* *4-l

 S,°

.SPa 

2 S ^o

M

o

Feei.

"3 

!s

S^ O "tn

e fl.

* " O 

o °*

s

03

fi

Feet.

90

100

70

80

90

100

30

40

50

60

70

80

90

100

55 .._

a"ft

0)

T3

10

C_j ~

.Feet.

6.8

5.0

5.9

4 9 . jj

6.8

8.1

6.1

6.3

3.0

4.0

3.2

3.8

4 2

7.0

8.0

6.2

4.9

3.5

70 4.2

90

105

7.7

4.6

5.0

§ 

is

o

1

A"ft

0)

fi

Feet.

6.7

4.9

5.8

6.6

8.0

6.0

5.2

2.9

3.9

3.1

3.7

4.1

6.9

7.9

6.1

4.8

2.9

3.6

7.1

4.0

4.4

£

"8

oil

§

M 

o

3

e

Feet.

0.10

.10

.10

(b)

.20

.10

.10

.10

.10

.10

.10

.10

.10

.10

.10

.10

.10

.60

,60

.60

.60

.60

Velocity in feet per second from vertical velocity 

curves.

03

a

0.91

.98

.94

1 "W

1.39

1.15

1.20

1.25

.87

1.14

1.21

1.24

1.28

1.27

1.17

1.06

1.16

1.08

1.08

1.01

.90

1.02

,d

ft

s7

>o 

d

1.10

1.08

1.50

1.50

1.33

1.32

1.05

1.28

1.50

1.39

1.42

1.48

1.23

1.23

1.12

1.22

1.09

1.15

a 

ft

 S

d

0.88

1.03

1.43

1.50

1.38

1.28

1.10

1.37

1.60

1.50

1.55

1.53

1.43

1.24

1.31

1.30

1.19

1.00

#"ft

CD 

13

00

d

0.88

.93

1.13

1.33

.96

1.18

.82

.93

.83

1.05

.98

1.13

.91

.91

.97

.95

.88

.70

a"£

b

-8

00

d

d

(M

0.88 

.98

1

1.

1.

1.

l!

1.

1.

1

1.

1.

1.

1.

1.

1.

a Sand and gravel bed.

28

42

17

23

96

15

22

28

26

33

17

08

14

12

04

85

ft

£

0.60

.88

1.05

1.05

.90

.80

.25

.30

.50

.50

1.25

.50

1.00

.82

.80

.96

.94

.65

g

o

"o

0.20

.10

.40

.90

.30

.50

.20

.55

.00

.50

.60

.00

.10

.30

.40

.34

.15

.05

H 

S

3P

1

1.10

1.08

1.55

1.53

1.40

1.32

1.11

1.40

1.65

1.53

1 55

1.55

1.45

1.28

1.32

1.32

1.22

1.16

6 E
Vertical velocity measurements Continued. 

ESOPUS CREEK AT KINGSTON, N. Y Continued.

Date.

1903.

 _

1906.

 Mean Qf 4 cufveg

»

to water

36.

*" 5

ifOJ M 

,d

§0

Feei.

7.10

5.60

5.60

4

o

,0 

5 §

f ^

.SPpj

01 5

^ S

§>

Feet.

"s

£= 

jg

0^

2.S «M Q

s ft

§

Feet.

60

70

85

90

30

40

60

110

70

80

90

100

A

i o

0

C_j

Feet.

4.2

4.8

7.2

7.8

6.0

2.7

9 Q

2.5

3.9

5.6

5.2

5.6

o

0

£

p<

p

Feet.

3.8

4.4

6.8

7.4

5.6

1.8

2.2

2

E

2.0

3.5

5.2

4.8

5.1

4.6

1

jiess o

0

.a 

H

Feet.

0.40

.40

.40

.40

.40

.70

.62

.50

.60

60

.50

.48

.52

.58

Velocity in feet per second from vertical velocity 

curves.

3

*

1.40

1.54

1.60

1.50

1.51

.45

.83

.73

.50

.62

.99

1.09

.96

.88

.98

fi "P.

*&

1.75

1.80

1.78

1.80

.47

.93

.82

.78

1.24

1.22

1.10

1.02

fi 

"P.

 o

1.82

1.88

1.70

1.63

.56

.96

1.21

.78

1.30

1.15

1.18

1.10

5 

A

 o

00

1.00

1.28

1.42

1.38

.31

.75

.16

.22

.68

1.03

.75

.67

ja

&-3

00

+

<M

1

c*

46

1.58

1.56

1.50

.

44

86

RH

.50

.99

1.09

.

.

96

88

Po

1.00

1.12

1.40

1.22

.52

.70

.92

.55

1.08

.75

.86

.40

£

o

0.35

.60

1.00

.60

1 S

.58

no

no

.30

.55

.35

.25

I

H

1.90

1.96

1.82

1.73

Kfi

1.00

.82

1.30

1.22

1.20

1.14

FISH RIVER AT WALLAGRASS, ME."

1906. 

February 15. ................. 3.91 3.25 90 

110 

130 

150

3.2 

4.5 

4.8 

3.0

3.9

1.7 

3.3 

3.6 

1.3

2.5

1.5 

1.2 

1.2 

1.7

1.40

0.84 

1.17 

1.04 

.52

on

0.98 

1.30 

1.19

.56

0.93 

1.20 

1.20

.56

0.72 

1.11 

.89 

.49

0.82 

1.16 

1.04 

.52

0.83 

.98 

.87 

.50

0.49

.84 

.44 

.42

0.97 

1.30 

1.25 

.57

a. Gravel bed.
Vertical velocity measurements Continued. 

FISH RIVER AT WALLAGRASS, ME. Continued.

Date.

1906.

to water 

ce.

?&

fs

ft

O

Feet.

3.91

4.99

5.08

i

,0 

f§

X2 O

f!

0)

of

o

Feet.

3.25

3.83

3.92

>m initial 

t.

P. 5 "-1 O 

gft

ft

Feet.

90

110

130

150

90

110

130

150

90

110

130

150

fi

a 

 S

c3 

O

.Feet

3.2

4.5

'4.8

3.0

3.9

4.3

5.6

5.9

4.1

5.0

4.4

5.6

6.0

4.3

5.1

£ 

Is

o

£

X!

& 

P

Feet.

1.7

3.3

3.6

1.3

2.5

2.9

4.3

4.6

2.3

3.5

3.0

4.3

4.7

2.5

3.6

£

o

a> i 

fl

.2

Feet.

1.5

1.2

1.2

1.7

1.40

1.4

1.3

1.3

1.8

1.45

1.4

1.3

1.3

1.8

1.45

Velocity in feet per second from vertical velocity 

curves.

«

0)

a

0.87

1.18

1.03

.55

.91

1.22

1.50

1.39

.88

1.24

1.52

1.40

.87

1.26

T3

0.98

1.30

1.17

.58

1.45

1.74

1.70

.95

1.44

1.76

1.70

.95

ft

0.93

1.24

1.17

.60

1.28

1.42

1.53

1.01

1.33

1.46

156

1.04

X!

30

0.77

1.13

.93

.49

1.15

1.62

1.43

.78

1.17

1.62

1.42

.74

*

n

00

+

0

1.

1.

1.

1.

1.

1

1.

1.

e.

W

18

15

54

m

52

48

jO

25

54

49

89

E-f

0.83

1.03

.76

.57

.70

.73

.43

on

.70

.77

.44

.92

fi 4^

"o

0.62

.76

.50

.42

.74

1.06

.35

.45

.80

1.07

.34

.35

1

o3

a

0.97

1.30

1.20

.60

1.45

1.79

1.71

1.01

1.45

1.79

1.72

1.04

FLAMBEAU RIVER AT LADYSMITH, WIS.o

1906.

16.13 15.33 120 

140

4.0 

3.3

3.6

3.1 

2.3

2.7

0.9 

1.0

.95

1.68 

1.62

1.65

1.77 

1.71

1.90 

1.79

1.44 

1.46

1.67 

1.62

1.88 

1.78

1.05 

1.12

1.90 

1.79

» Coarse gravel bed.
Vertical velocity measurements Continued. 

GENESEE RIVER AT MOUNT MORRIS (JONES BRIDGE), 

Date.

1906.

Mean of 7 curves .......

Gage height to water

surface.

Feet.

5.78

6.00

5.75

5.78

Gage height to bottom ofice.

Feet.

'

Distance from initial 

point.

Feet. 

110 

120

130 

140 

110 

115 

130 

135 

140 

17 

27 

37 

47 

57 

67 

77 

87 

97 

107 

117

90 

100 

90 

95 

100 

105 

125

f~

o

EFeet. 

4.9 

5.7

5.3 

4.2 

5.1 

5.0 

5.5

4.5 

3.3 

3.0

3.1 

3.5

3.5 

3.6 

4.4

4.9 

4.7 

. 4.0

2.8 

8.6 

3.8

4 Q

3.9 

4.1 

4.6 

5.4 

5.1

4.5

Depth below ice

Feet. 

4.4 

4.7

4.9 

3.8 

4.6 

4.5 

5.2 

5.2

4.2 

2.8 

2.4

2.6 

3.0

2.9 

3.0 

3.8

4.4 

4.2 

3.4

2.2 

3.8 

2.4

3.6

2.8 

3.2 

4.2

5.0 

4.2

3.6

Thickness ofice.

Feet. 

0.50 

.40

.40 

.40 

.45 

.50 

.30 

.30

.35 

.55 

.60

.60 

.60

.60 

.60 

60

60

.80 

.80

.80 

.54 

.60

.60 

.30 

40

.40 

.30

.44

Velocity in feet per second from vertical velocity 

curves.

03 

02

a

2.23 

1.66

2.28 

1.20 

1.63 

2.47 

2.06

.88 

.64 

1.15

1.63 

1.92

1.99 

2.06

1.84

1.46 

1.04

.59 

1.62 

.98

1 QO

1.14 

1.62

2.18 

2.35

1.80

f 

<o 

13 

10

0

3.02 

2.34

2.56 

1.41 

2.07 

3.00 

2.29

1.22 

.68 

1.38

1.83 

2.22

2.19 

2.30

2.14

1.65 

1.11

.72

1.54

3.20

1.66 

2.26 

3.25

3.23 

3.06

,d

$

13

0

2.31 

1.08

2.87 

1.47 

2.12 

2.79 

2.74

1.10 

.64 

1.34

1.79 

2.18

2.34

2.34

2.02

1.71 

1.20

.76

1.22

1.14 

1.26

1.32

9 04

ft 

%

00

o

2.04 

2.04

1.68 

.93 

1.23 

2.16 

1.42 

1.25

.57 

.62 

.99

1.41 

1.71

1.66

1.79 

1.61

1.55

1.20 

.93

.47

1.46

2.64

1.48 

2.45 

2.95

2.58

9 40

f

4

r 

00 

O

o

3 

A

D

3

2.18 

1.56

2.28 

1.20 

1.68 

2.48 

2.08 

1.66

l'

1.

1

2

84 

63 

16

60 

94

00

2.06 

1.94

1

1.

1

1

i!

2

78

46 

06

62

34

4?,

98 

44

9fi

1.95 

2.60

ft 

o

e

0.63 

.00

2.48 

1.24 

1.13 

.34 

2.57

.94 

.55

.85

1.49 

1.56

1.90

1.89

.87 

.78

.74

.0

.0 

.0

.16

o

o

K

1.06 

.96

1.07 

.62 

.10 

1.61 

.63 

.58

.00

.56 

.72

.98 

1.20

1.22

1.40

1.11

.90

.78

.03

1.21

1.08 

2.26

1.62

g 

|

03

a

3.08 

2.48

2.92 

1.48 

2.26 

3.27 

2.74

1.23 

.68 

1.45

1.88 

2.34

2.34

2.37

2.17

1.78 

1.21

.76

1.56

3.23

1.67 

2.46 

3.36

3.25 

3.06

a C oarse gravel bed. 
Vertical velocity measurements Continued. 

GENESEE RIVER AT ELMWOOD AVENUE BRIDGE, ROCHES

Date.

1906.

Gage height to water

surface.

Feet.

Gage height to bottom ofice.

Feet.

Distance from initial 

point.

Feet. 

40 

50 

60 

70 

80 

90 

100 

110 

120 

140 

150 

160 

170 

180 

190 

200 

210 

220 

250

Total depth.

Feet. 

4.2 

4.3 

4.5

5.1 

3.7 

3.8

3.5 

4.3 

4.2

3.0

4.6

4.3 

4.5 

5.0 

5.0

4.3 

4.3 

3.3

4.4

Depth below ice.

Feet. 

3.9 

4.0 

4.2

4.8 

3.4 

3.5

3.0

3.8

2.5 

4.1

3.8 

4.0 

4.5 

4.5 

4.6

3.8 

3.8 

2.9

3.8

Thickness ofice. 

Feet. 

0.3 

.3 

.3

.3 

.3 

.3

.45 

.5

.5 

.5

.5 

.5 

.5 

.5 

.5

.5 

.5 

.5

.43

Velocity in feet per second from vertical velocity 

curves.

a 

08

3

0.92 

.89 

1.06

.92 

1.24 

1 00

1.23 

1.20

.83 

.88

.69 

.82 

.76 

.73

.70 

.68 

.50

.89

Pi

 8

o

1.04 

1.04 

1.18

1.17 

1.35 

1.30

1.40 

1.34 

1.05

1.00 

1.14

.76 

.86 

.80 

.76

.80 

.82 

.74

ft

 8

CN1

o

1.08 

1.08 

1.18

.20 

.28 

.33

.36 

.36

1.10 

1.08

.78 

.88 

.80 

.90 

.85

.86 

.82 

.50

"PI

CD

00 

O

0.76

.72 

.98

.60 

1.18 

.66

1.04 

1.03

.65

.55

.72

.66 

.75 

.64 

.52 

.81

.63 

.58 

.46

£ 

-*-

a

00

o

c-j

o

LI

IM

0.9?

.90 

1.08

.90 

1.23 

1 00

1.20 

1.20 

Q4

82 

90

72 

82 

72 

71

74 

70 

48

cL

e

1.05 

1.12

1.10 

1.04

1.25 

1.15

1.04 

.86

.68 

.74 

.82 

.75

.74

.68 

.12

6

o 

o

ffl

0.26

.10

.48

.00 

.95 

.00

.65 

.70 

.20

.10 

.00

.40 

.66 

.25 

.33

.66

.30 

.35 

.10

6

s

oS

1.10

1.10 

1.20

1.23 

1.35 

1.36

1.40 

1.40 

1.24

1.10 

1.15

.80 

.90 

.80 

.90 

92

.86 

.85 

.74

a Coarse gravel bed.
Vertical velocity measurements Continued. 

GENESEE RIVER ONE-FOURTH MILE ABOVE ELMWOOD AVENUE BRIDGE

Date.

1906.

Gage height to water 

surface.

Feet. 

1.42

Gage height to bottom offee.

Feet.

Distance from initial 

point.

Feet. 

40 

60 

80 

100 

120 

140 

160 

180 

200 

220 

240

Total depth.

Feet. 

7.9 

8.0 

7.1 

7.7 

7.7 

8.1 

7.4 

7.1 

6.4 

5.4

7.1

Depth below ice.

Feet. 

7.4 

7.5 

6.6 

7.3 

7.3 

7.7 

7.0 

6.7 

5.9 

4.9 

4.7

6.6

Thickness of ice.

Feet. 

0.50 

.50 

.45 

.40 

.40 

.40 

.40 

.40

.50

.45

Velocity in feet per second from vertical velocity 

curves.

S

0.40 

.43 

.46 

.42 

.52 

.46 

.49 

.46 

.42

.48

.45

ft

-8

0

0.46 

.52 

.52 

.45 

.58 

.50 

.58 

.56 

.52

.55

a 

a

<M

b

0.45 

.50 

.56 

.44 

.54 

.44 

.50 

.53 

.55

.48 

.45

00

b

0.36 

.46 

.34 

.42 

.50 

.45 

.48 

.47

.48

g

00

b

+ N

b

0.40 

.48 

.45 

.43 

.52 

.44 

.49 

.50

.48

ft 

H

0.34 

.36 

.28 

.40 

.32 

.23 

.25 

.36

.30 

.30

|

o

W

0.22 

.06 

.16 

.24 

.38 

.32 

.18 

.00 

.00

.25 

.00

g

3

s'x 

1

0.50 

.52 

.58 

.45 

.58 

.5! 

.58 

.56 

.55

.55 

.50

--

HOOSIC RIVER AT BUSKIRK, N. Y.&

1906.

3.90 60

70

80

90 

100

4.6

5.5,

6.9

8.1 

7.5 

6.6

6.6

4.2

5.1

6.4

7.6 

7.0 

6.2

f 1

0.35

.40

.45

.45 

.45

.38

0.90

1.80

1.81

1.54 

1.64 

.81

1.57

1.38

2.06

2.52

2.75 

2.68

1.03

1.58

2.15

2.25 

1.35 

2.06

1.40

2.15

2.30

2.10 

2.30

1.21

1.86

2.22

2.18 

1.82 

1.87

0.0

.0

.0

.0 

.0

1.35

2.15

1.95

1.10 

1.00 

1.12

1.40

2.15

2.53

2.75 

2.80

a Coarse gravel bed. & Gravel bed. More or less needle ice u
Vertical velocity measurements Continued. 

KENNEBEC RIVER AT NORTH ANSON, ME.a

Date.

1904.

1905.

Gage height to water 

surface.

Feet. 

3.55

3.40

5.27

Gage height to bottom ofice.

Feet. 

±1.45

1.55

3.27

Distance from initial 

point.

Feet. 

50

60 

70 

80 

90 

100 

110 

120 

130 

140 

150 

160 

170 

180 

190

100 

110 

120 

130

101

31 

.50 

71 i 

92

Total depth.

Feet.

3.2

3.8 

4.1 

5.2 

6.1

Depth below ice.

Feet. 

0.9 

1.1 

1.1 

1.6 

1.9 

2.2 

2.3 

2.2 

2.0 

1.8 

1.7 

1.4

1.5 

1.1

.9

1.6

2 5

2.7

3.0

2.7

2.7

1.3

1.8 

2.1 

3.2 

4.2

Thickness ofice.

Feet. 

1.9 

1.8 

2.0 

1.9 

2.0 

2.0 

2.1 

2.4 

2.4 

2.2 

2.3 

2.3

2.1

2.4

2.15

1.9

2.0 

2.0 

2.1 

2.0

Velocity in feet per second from vertical velocity 

curves.

03 

o

s

1.78 

1.84 

1.66 

1.77 

2.26 

2.29 

2.44 

2.25 

2.11

2.06 

1.92 

1.75

1.62 

1.25

1.13

1.87

2.18

2.22

2 3Q

2.38

2.27

1.06

1.36 

1.92 

2.00 

2.23

a 

"ft 

 §

IO 

0

1.97 

2.09 

1.89 

2.24 

2.76 

2.76 

2.93 

3.10 

2.62

2.64 

2.45 

2.16

1.98 

1.60

1.30

2.38

2.47

2.60

1.16

1.60

2.08 

2.27 

2.54

a"ft

-s

IM

0

1.95 

1.78 

1.84 

1.65 

2.30 

2.60 

2.60 

2.18 

2.20

2.11 

2.10 

1.70

1.55 

1.12

1.11

2.59

2.70

2 94

1.06

1.62 

2.23 

2.37 

2.44

a 

ft

T3 

00 

O

1.56 

1.89 

1.43 

1.78 

2.20 

1.98 

2.30 

2.42 

2.06

1.91 

1.85 

1.72

1.63

1.09

1.72

1.75

1.67

1.06

1.04 

1.63 

1.63 

1.96

,j

^

" 

00 

0

<N

0

3

ff 

N

1. 7o 

1.83 

1.63 

1.72 

2.25 

2.29 

2.45 

2.30 

2.13

2.01 

1.97 

1.71

1.59

1.10

9 15

2.^30

1.06

1.33 

1.93 

2.00 

2.20

&

EH

1.80 

1.32 

1.60 

l.ns 

1.76 

1.80 

1.36 

.20 

.82

.92 

1.14

.88

.80 

.56

.90

2.69

2. S3

.62

1.22 

1.65 

1.45 

1.60

i Mo

W

1.16 

1.40 

1.00 

1.08

liso

.98 

1.65 

1.04 

1.32

1.26 

.70 

1.30

1.20

.84

.84

1.00

1.03

.86

OK

g

3

'$, 1 

rt 

S

2.00 

2.10 

1.92 

2.24 

2.77 

2.84 

2.98 

3.10 

2.66

2.72 

2.46 

2.20

2.00 

1.62

1.30

2.72

2.94

2 02

.85

.57 

1.25 

.92 

1.45

1.17

1.67 

2.27 

2.41 

2.63

o Gravel bed.
Vertical velocity measurements Continued.

KENNEBEC RIVER AT NORTH ANSON, ME. Contin

Date.

1905.

1906.

Mean of 6 curves .......

Gage height to water 

surface.

Feet. 

5.27

5.32

3.40

Gage height to bottom ofice.

Feet. 

3.27

3.32

2.05

Distance from initial 

point.

Feet. 

112 

134 

U134-

173 

194 

216

10*

31

1125 

154 

194 

236 

279 

320 

361 

409 

448

90 

130 

290 

330 

370 

410

Total depth.

Feet. 

6.1 

6,1 

|_JU)

6.0 

6.0 

6.3

5.4

3.2

3.9 

5.2 

6.2 

6.0 

6.1 

7.0 

5.5 

4.4 

3.7 

4.5 

4.5

5.0

4.0 

5.0 

4.4 

3.1 

2.6

2.9 

3.7

Depth below ice.

Feet. 

4.2 

4.2 

4.0

4.0 

3.9 

4.1

3.4

1.3

1.9 

3.2 

4.2 

4.0 

3.9 

4.7 

3.3 

2.3 

1.6 

2.6 

2.5

3.0

2.8 

3.7 

3.2 

2.1 

1.5

1.8

2.5

Thickness ofice.

Feet. 

1.9 

1.9 

2.0

2.0 

2.0 

2.2

2.00

1.9

2.0 

2.1 

1.9 

2.0 

2.0 

2.1 

2.0 

2.1 

2.1 

1.9 

2.0

2.01

1.3 

1.4 

1.3 

1.1 

1.3

1.3 

1.28

Velocity in feet per second from vertical velocity 

curves.

ti

03 

1

2.36 

2.47 

2.32

2.18 

1.57 

.89

1.85

1.25

1.50 

2.02 

2.42 

2.33 

1.63 

1.37 

1.15 

.70 

.99 

.66 

.41

1.37

1.40 

1.55 

1.45 

1.23 

.74

.58 

1.16

 § 

d

2.74 

2.77 

2.57

2.50 

1.98 

1.04

1.48

1.62 

2.44 

2.72 

2^52 

1.87 

1.58 

1.48 

.85 

1.15 

.90 

.48

1.53 

1.69 

1.55 

1.31

.88

.68

 o 

d

2.62 

2.59 

2.58 

2.34 

1.44 

.86

1.34

1.67 

2.36 

2.74 

2.58 

1.64 

1.32 

.72 

.78 

1.28 

.57 

.43

1.58 

1.73 

1.62 

1.37 

.93

.66

A"ft 

te 

 X3

00

d

2.08 

2.29 

2.10 

~270(r 

1.74 

.87

1.07

1.31

1.58 

2.07 

2.10 

1.61 

1.38 

1.52 

.58 

.67 

.67 

.35

1.18 

1.34 

1.29 

1.07 

.52

.46

f.

\ 

^ 

<x 

d

IN

d

i<

2.35 

2.44 

2.34

1.58 

.88

1 ?0

1.48 

1.97 

2.41 

2.34 

1.62 

1.34 

1.12 

.68 

.98 

.62 

.39

1. 

1. 

1. 

1.

38 

54 

46 

22

7?

.56

ft 

o

1.60 

2.02 

1.00 

.757^

:45

.62

.00

1.35 

1.82 

1.95 

2.03 

1.08 

.94 

.10 

.61 

1.20 

.25 

.30

1.35 

1.42 

1.42 

1.27

.78

.53

ao

o

PH

1.40 

1.40 

1.72

OT4 

.60 

.45

.61

1.08 

.62 

1.35 

1.60 

1.00 

.85 

1.03 

.14 

.10 

.00 

.20

.85 

.95 

.97 

.81 

.19

.25

s 

a

1

2.80 

2.78 

2.69

L98 

1.04

1.50

1.72 

2.49 

2.80 

2 6

1.88 

1.60 

1.63 

.86 

1.30 

.96 

.5

1.60 

1.75 

1.6

1.37 

.95

.7
Vertical velocity measurements Continued. 

KENNEBEC RIVER AT NORTH ANSON, ME. Continu

Date.

1906.

March 2......................

March 3.. ....................

Mean of 9 curves .......

Gage height to water 

surface.

Feet. 

3.56

4.26

4.08

o 

ft

0>

SP

o

Feet. 

2.21

2.43

2.27

Distance from initial 

point.

Feet. 

90 

130 

290 

330 

370 

410

70 

90 

130 

170 

210 

290 

330 

370 

410 

450

70 

130 

170 

210 

290 

330 

370 

410 

450

Total depth.

Feet. 

4.2 

5.1 

4.6 

3.3 

2.7

3.1 

3.8

3.3

4.9 

5.9 

5.5

4.7 

5.3 

4.1 

3.5

Q Q

3.3 

4.4

3.1 

5.7

5.3 

4.5

5.0

3.8 

3.2

3.6 

3.1

4.2

Depth below ice.

Feet. 

3.1 

3.7 

3.4 

2.2 

1.6

1.9 

2.6

1.8

3.3 

3.9 

3.7

3.0 

3.4 

2.3 

1.7 

1.9

1.5 

2.6

1.6 

3.7

 3.5 

2.8

3.1

2.1 

1.4

1.8 

1.4

2.4

Thickness ofice.

Feet. 

1.2 

1.5 

1.3 

1.2 

1.3

1.4 

1.32

1.6

1.7

2.0 

1.9

1.9 

2.0 

1.9 

2.0 

2.0

2.0 

1.90

1.7 

2.0

2.0 

1.9

2.0

1.8 

2.0

2.0 

1.9

1.92

Velocity in feet per second from vertical velocity 

curves.

p 

§

a

1.35

1.65 

1.45 

1.21

.78

.64 

1.18

1.48

1.67

1.94 

1.71

1.15 

1.58 

1.40 

1.05 

90

.68 

1.35

1.38 

1.86

1.68 

1.06

1,43

1.31 

97

.78 

.61

1.23

d

1.52 

1.74 

1.59 

1.31

.87

.70

1.72

1.85

2.15 

1.92

1.30 

1.73 

1.53 

1.19 

1.00

.74

1.55 

1.99

1.83 

1.23

1.57

1.42 

1.10

.88 

.67

,a 

1ft 

-S

d

1.51 

1.78 

1.60 

1.36

.85

.75

1.62

1.84

2.18 

1.97

1.34 

1.77 

1.58 

1.21 

1.07

.73

1.50 

2.09

1.89 

1.23

1.64

1.38 

1.06

.86 

.62

,a 

%0> 

00

d

1.13 

1.50 

1.29 

1.03 

.65

.52

1.34

1.56

1.70 

1.52

1.01 

1.43 

1.23

.87

7O

.65

1.23 

1.63

1.54 

.92

1.28

1.23

QC

.69 

.59

£ 

4-

a 

T:

00

d

C-l

o

*

1.32 

1.64 

1.44 

1.20 

.75

.64

1...48

1.70

1.94

1.74

1.18 

1.60 

1.40 

1.04

.69

1.36 

1.86

1.72 

1.08

1 16

1.30 

.96

.78 

.60

o

1.24 

1.50 

1.32 

1.22 

.73

.64

1.-33

1.42

1.97 

1.39

.75 

1.27 

1.15 

1.00

.68

1.14

1.78

.95

1.14 

.92

.75 

.52

o

ffl

0.77 

1.25 

.93

.71 

.51

.36

.40

.75

1.14 

.94

.66 

1.10 

.92 

.52

CA

-.30

.97 

1.30

.90 

.48

.95

1.00 

43

.40

.48

£

3

s

=3

1.59 

1.82 

1.64 

1.37 

.90

.77

1.72

1.92

2.20 

2.00

1.38 

1.79 

1.61

1.27 

1.07

.74

1.63 

2.10

1.90 

1.28

1.66

1.44 

1.12

.90

.67
Vertical velocity measurements Continued.

KENNEBEC RIVER AT NORTH ANSON, ME. Continue

Date.

1906. 

March 30 .....................

April 11......................

Gage height to water 

surface.

Feet.

4.77

4.70

Gage height to bottom ofice.

Feet.

2.80

Distance from initial 

point.

Feet. 

90 

130 

170 

210 

290 

330 

370 

410 

450

90 

130 

170 

210 

250 

290 

330 

370 

410 

450

Total depth.

Feet. 

5.5

6.3 

6.0 

5.1 

5.7 

4.6

4.0 

4.1 

4.0

5.0

5.4 

6.3 

5.9 

5.1 

5.6 

5.7 

4.5 

3.9 

4.2 

3.8

5.0

Depth below ice.

Feet. 

3.5

4.1 

3.9 

3.0 

3.4 

2.4

1.8 

1.9

1.8

2.9

3.6 

4.3 

3.9 

3.2 

3.2 

3.6 

2.5 

1.8 

2.1 

1.8

3.0

Thickness ofice.

Feet.

2.3 

2.3 

2,3 

2.5 

2 3

2.4 

2.4 

2.4

2.34

1.8 

2.0 

2.0 

1.9 

2.4 

2.1 

2.0 

2.1 

2.1 

2.0

Velocity in feet per second from vertical velocity 

curves.

03 

0,

a

2.00 

1.74 

1.21 

1.52

1.04 

.93 

.61

1.33

1.50 

1.90 

1.74 

1.25 

1.10 

1.47 

1.35 

1.14 

.98 

.82

i o

IO

o

1.78

2.23 

1.99 

1.36 

1.63 

1.49

1.19 

1.02 

.70

1.81 

2.14 

1.96 

1.42 

1.22 

1.60 

1.50 

1.25 

1.12 

.91

,q 

o

1.72

2.25 

1.98 

1.39 

1.72 

1.47

1.23 

1.03 

.69

1.50 

2.00 

1.92 

1.34 

1.19 

1.61 

1.45 

1.30 

1.16 

.86

g,

00 

0

1.36

1.76 

1.50 

1.12 

1.39 

1.30

.96 

.84 

.56

1.50 

1.84 

1.50 

1.15 

1.01 

1.35 

1.25 

.96 

.81 

.80

1

a 

T:

0

,

"i4

2.00 

1.74 

1.26 

1.56 

1 38

1.

1. 

1. 

1. 

1. 

1. 

1. 

1. 

1.

10

94

62

50 

92 

71 

24 

10 

48 

35 

13 

98 

83

g,

1.18

1.67 

1.55 

.69 

1.15

.59 

.89 

.48

.75 

1.30 

1.50 

1.00 

.90 

1.27 

1.35 

1.15 

.92 

.65

so 

ffi

0.80

1.26 

.88 

.85 

1.12 

.89

.53 

.60 

.36

.90 

1.22 

1.15 

.75 

.76 

1.00 

.90 

.72 

.34 

.65

i 

i

2.29 

2.06 

1.42

1.72 

1.50

1.25 

1.04 

.73

1.82 

2.16 

2.03 

1.45 

1.25 

1.65 

1.50 

1.32 

1.20 

.92
Vertical velocity measurements Continued. 

MAUMEE RIVER AT SHERWOOD, OHlO. a

Date.

1906. 

February 11 b ...............

Gage height to water 

surface.

Feet. 

3.34

Gage height to bottom ofice.

Feet.

2.79

Distance from initial 

point.

Feet. 

50 

70 

90 

110 

130 

160 

180 

200 

220 

240 

260

Total depth.

Feet.

Depth below ice.

Feet. 

2.6 

2.3

2.6

2.5

2.4

2.3

2.7 

2.6

2.7 

2.3

2.4

Thickness ofice.

Feet. 

0.7 

.6

.5

.5 

.6

.5

.6 

.6

.6

.5 

.58

Velocity in feet per second from vertical velocity 

curves.

CS

a

0.69 

.69

.68

.82 

.81

.93

.87

.78

.84 

.70

.82

.78

0.5 depth.

0.76-

.74

.71

.90

.83

.98

.91

.82

.90

.85

a 

"ft 

 o

e;

o

0.73 

.72

.71

.88 

.89

.93

.98 

.86

.92 

.68

.83

0.8 depth.

0.65 

.64

.68

.75 

.72

.92

.73 

.69

.73 

.68

.81

a 

"ft 

 C

OC

c:

ei

o

0.69 

.68

.70

.82 

.80

.92

.86

.78

.82 

.68

.82

i

0.61 

.63

.68

.76 

.90

.83

.97 

.82

.78 

.58

.73

Bottom.

0.51 

.50

.56

.48 

.62

.72

.57 

.58

.54 

.62

.75

Maximum.

0.76 

.75

.72

.91 

.90

.98

.99 

.86

.93 

.72

.85

MOHAWK RIVER AT SCHUYLER STREET BRIDGE, UTICA, 

1902.

16.4

16.0

20

30 

40 

50 

60

10

20 

30

11.0

11.6 

11.4 

11.0 

9.6

10.9

9.2

11.0 

11.8

10.5

11.1 

10.9 

10.5 

9.1

10.4

8.7

10.5 

11.3

0.50

.50 

.50 

.50 

.50

.50

.50

.50 

1.15

0.74

.90 

.88 

1.03 

.97

.90

.45

1.00 

.50

0.91

1.08 

1.10 

1.22 

1.20

.58

1.20 

1.38

0.60

.68 

.62

.88 

.90

.52

1.20 

1.10

0.80

1.00 

1.02 

1.10 

1.00

.38

.75 

1.10

0.70

.84 

.82 

.99 

.95

.45

.98 

1.10

0.55

.56 

.52

.74 

.10

.35

.62 

1.05

0.50

.73 

.68

.83 

.71

.28

.38 

.65

0.95

1.10 

1.15 

1.23 

1.20

60

1.28 

1.38

o Gravel bed. b Ice rough.
Vertical velocity measurements Continued. 

MOHAWK KIVEK AT SCHUYLEK STKEET BKIDGE, UTICA, N. Y

Date.

1902.

Gage height to water

surface.

Feei. 

16.0

|

+2«W 

+i

03 

O

Feet.

Distance from initial 

point.

Feet. 

40 

50 

60 

70 

80

Total depth.

Feet. 

11.4 

10.9 

10.1 

9.8 

9.3

10.4

Depth below ice.

Feet. 

10.9 

10.4 

9.6 

9.3 

8.8

9.9

Thickness ofice.

Feet. 

0.50 

.50 

.50 

.50 

.50

.50

Velocity in feet per second from vertical velocity 

curves.

03 

®

1.20 

1.40 

1.28 

1.05 

.92

1.06

 S

0

1.40 

1.48 

1.40 

1.32 

1.10

i13 

O

1.30 

1.42 

1.26 

1.12 

1.00

f

0,

13 

00 

O

1.04 

1.10 

1.12 

1.00

.75

c

 c

00

d 

d

,

<N

1.17 

1.26 

1.19 

1.06

.88

&

Ei

0.56 

1.05 

1.10 

.48 

.65

o 

1

0.65 

.70 

.75 

.50 

.20

s

3

S

03

1.45 

1.55 

1.40 

1.32 

1.10

OLENTANGY K IVEK AT COLtMBUS, CHIO.o

1906.

6.77 6.22 20

30 

40 

60

80

2.5

4.3 

 5.0 

4.6

4.4 

4.2

2.0

3.8 

4.5 

4.0

3.8 

3 6

0.5

.5 

.5 

.6

.6 

.54

0.16

.34 

.29 

.22

.15 

.23

0.19

.38 

.30 

.24

.18

0.22

.38 

.29 

.26

.17

0.10

.30

.28 

.17

.14

0.16

.34 

.28 

.22

. 16

0.17

.32 

.27 

.23

.10

0.00

.20 

.27 

.12

.10

0.22

.39 

.30

.27

.18

a Gravel and silt bed.
30 March ..................... 5 Mean ofcurves. ......

CO

~a

CO

ggggo

K-O £o £ £ 

co co M co os to 

OOCOOCO CO 

O CO tO CO OS CO 

CO O Cn O O O 

00

co co o; co co co 

M Cn l i tO Cn t*. 

OS 1 i CO CO 00 Cn 

4^ CO CO CO 4^- 

O M Cn CO tO 

00 rf^ ' 1 CO rf^ 

4^ CO CO CO CO 

rf^ Cn 1 h- O CO 

Cn Cn Cn 00 tO 

CO CO CO CO CO 

S

t^h-t to K* 

Cn O 00 00 

co coco coco 

00 rf^ tO ' K- Cn 

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a5$g££

4^ CO CO CO 4^- 

^SS^fe

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88KS8 S3 

Cn M M 00 00 

OS OS M O 00 

OOMOOMOS -1 

tO 4^- H^ 00 CO OS 

CnCnCnU^tO

to CO O to M 

29 March ..................... of 6Meancurves. ......

00

3

i§s§§s

o coo tooo o 

rf-osjnto^o 0= 

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Cr>0 ": " Cr>< "i: 0 

to CO to tO CO CO CO 

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CO CO CO CO CO CO 

4^ CO Oi tO OS Cn 

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O Cn Cn O Cn Cn 

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en co Oo qs 1 i co 

tOOO tO CnO O 

to co to to coco 

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co ooooo too 

J^ tO K* K* tO tO 

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tOM to en t^ 

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CO CO CO CO CO CO 

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tO rf^ OS OS Cn O 

Cn Cn OS CO M 00 <I 

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OSMOSOSOSOO

ssasas T »

CO CO CO CO CO Ol 

Cn CO Cn 00 tO tO 

of 6Meancurves .......

g

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$

' hw- _, 

^

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gggggga

' h- ' h- IO tO CO O 

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^*Sj

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CO COCOCO COCO CO 

^8Sg^^ S 

COCO COCOCO 

MM MOSCn 

tO rf^ CO O OS 

Ofo

?

water to height Gage 

surface.

bot- to height Gage 

ice. of tom 

initial from Distance 

point.

' depth. Total 

ice. below Depth 

ice. of Thickness 

Mean.

depth. 0.5 

3S

CO CO CO CO CO CO 

§ggfefegfe

tO CO tO CO CO 

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depth. 0.2 

depth. 0.8 f 

CO CO CO CO CO CO 

to co oco to co 

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£oi£o-8£ t £8££3£ £ kS£££ £ 

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5

B

, ~ 0.2+0.8 

th. tep

Top.

Bottom.

Maximum.

feet. In 

cent per In 

depth. of 

feet. In 

cent per In 

depth. of 

feet. In 

cent per In 

depth. of 

Maximum.

depth. 0.5 

0.2+0.8

2 

depth.

«* 

"g

Lower.

in feetsecond from vertical per Velocity velocity 

curves.

of threads Depth 

mean velocity.

Hi

Coefficients for

to mean reducing velocity.

< 

~

anx jsiosvas
VERTICAL VELOCITY CURVES. 65

Coefficient? for reducing to meanvelocity.

Depth of thread ofmaximum 

velocity.

of threads Dpth 

velocity. mean 

from Velocity in feetsecond vertical velocity per

curves.

Lower.

01

p. 

^

 q^dap 

Z

8'0+S'O

 q^dap g-Q

 nmni 

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 qjdap jo

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 30Bjans

I

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IRR 187 07-
Vertical velocity measurements Continued. 

WALLKILL RIVER AT NEWPALTZ, N. Y.o

Date.

1901.

Mean of 4 curves .......

1902.

Gage heightto water 

surfa.ce*

Feet. 

11.5

13.7

7.24

17.33

Gage heightto bottom ofice.

Feet.

Distance from initial 

point.

Feet. 

53 

64 

75

85

115 

95

85 

75

50

70 

80 

90 

100

' 110

30 

40 

50 

60 

70 

80

Total depth.

Feet. 

9.9 

10.7 

12.2 

12.3

11.3

18.0 

16.0 

15.6 

14.5

16.0

14.4 

15.4 

18.0 

16.0 

21.6 

22.2

Depth below ice.

Feet. 

9.2 

10.0 

11.5 

11.6

10.6

13.5 

16.0 

15.6 

13.5

14.6

3.4 

5.0

5.8

6.6

7.8

8.4

6.2

13.0 

14.0 

17.0 

15.2 

20.8 

21.5

Thickness ofice.

Feet. 

0.70 

'.70 

.70 

.70

.70

4.50 

.05 

.05 

1.00

1.40

cl.20

1.20

1.40 

1.40 

1.00 

.80 

.80 

.70

Velocity in feet per second from vertical velocity 

curves.

d 

oj 

d.

S

2.45 

2.17 

2.64 

2.60

2.46

2.44 

3.48 

3.40 

2.63

2.98

.81 

1.01 

1.01 

1.02 

1.08 

.39

.89

2.20 

3.13 

3.63 

4.10 

4.02 

3.96

f

01

 o

IO

6

2.75 

2.'65 

3.03 

2.98

2.97 

4.00 

3.94 

3.10

.88 

1.10 

1.17 

1.20 

1.25 

.50

2.58 

3.62 

4.00 

4.24 

4.38 

4.30

X3 

"P.

5T 0 

<M 

O

2.45 

2.98 

2.98 

2.96

2.24 

3.22 

3.13 

2.44

.90 

1.14 

1.07 

1.22 

1.18 

.43

1.96 

3.23 

3.70 

4.21 

4.19 

4.21

^ 

 H

& 

 o

°°

0

2.51 

1.22 

2.25 

2.25

2.70 

3.74 

3.60 

2.89

.70 

.85 

.94 

.88 

.96 

33

2.37 

3.13 

3.72 

4.02 

4.11 

3.88

£ 

^_

0.

 c

00

d 

+

<N

d

H 

(N

2.48 

2.10 

2.61 

2.60

2.47 

3.48 

3.36 

2.66

.80 

1.00 

1.00 

1.05 

1.07 

.38

2.16 

3.18 

3.71 

4.12 

4.15 

4.04

&

H

1.85 

2.24 

2.15 

2.25

.55 

2.35 

2.15 .

.85'

.68 

.96 

.66 

.45 

.70 

.22

1.58 

1.60 

1.45 

2.70 

2.10 

2.40

5 

o4^ 

 H 

O

«

1.80 

.20 

1.35 

1.20

1.04 

2.25 

2.20 

2.30

.10 

.36 

.55 

.50 

.50 

.14

1.40 

1.30 

1.60 

2.20 

1.60 

2.00

'«| 

03 

S

2.76 

3.25 

3.23 

3.13

3.00 

4.14 

3.96 

3.13

.95 

1.18 

1.19 

1.25 

1.27 

.52

2.65 

3.62 

4.00 

 4.28 

4.38 

4.32

o Clay and coarse gravel bed. *> Ice very rough and broken. "Mean. 
Vertical velocity measurements Continued. 

WALLKILL RIVER AT NEWPALTZ, N. Y.-Continued

Date.

1902.

Mean of 5 curves .......

Gage heightto water

surface.

Feet. 

17.33

9.07

7.78

7.35

Gage heightto bottom ofice.

Feet..

Distance from initial 

point.

Feet. 

90 

100 

110 

120

40 

50 

60 

70 

80 

90 

100

80 

90 

100 

110

40 

80 

90 

100 

110

Total depth.

Feet. 

22.2 

21.6 

23.2 

16.8

19 1

6.8 

6.2 

5.1 

8.8 

8.8 

10.0 

11.5

8.2

7.5 

8.5 

9.6 

10.1

8.9

5.7 

7.3 

8.0 

9.0 

9.3

7.9

Depth below ice.'

Feet. 

21.5 

20.8 

22.4 

16.0

10 O

5.8 

5.1 

4.1 

7.8 

7.8 

9.0 

10.3

7.1

6.5 

7.5 

8.6 

8.9

7.9

3.5 

5.3 

6.0 

7.0 

7.0

5.8

Thickness ofice.

Feet. 

0.70 

.80 

.80 

.80

Q9

1.00 

1.00 

1.00 

1.00 

1.00 

1,00 

1.20

1.03

1.00 

1.00 

1.00 

1.20

1.05

a2.20 

2.00 

2.00 

2.00 

2.30

2.10

Velocity in feet per second from vertical velocity 

curves.

1

s

3.93 

3.89 

3.73

2.77

3

K4

1.52 

1.86 

1.74 

2.08 

2.14 

2.09 

2.24

1.95

1.43 

1.43 

1.53

.78

1.29

.53 

.84 

.86 

.98 

.53

.75

JS

& 

o 

13 

IO

o

4.27 

4.20 

4.17 

3.22

1.70 

2.06 

2.06 

2.35 

2.35 

2.37 

2.48

1.61 

1.58 

1.80

.82

.63 

.98 

1.00 

1.12 

.61

f 

ft

Oj 

13

O

4.23 

3.90 

3.82 

3.20

1.60 

2.09 

2.09 

2.34 

2.38 

2.38 

2.28

1.54 

1.66 

1.56 

.50

.60 

.92 

1.02 

1.05

.58

S3 

+J 

fi. 

Oj 

13 

00 

0

3.63 

4.00 

3.80 

2.50

1.42 

1.62 

1.35 

1.83 

2.02 

1.83 

2.24

1.32 

1.22 

1.43 

.96

.45 

.84 

.72 

.84 

.44

£. 

*.

4

T

IN 

Q

*,

IN

3.93 

3.95 

3.81

2.85

1.51

1.85 

1.'72 

2.08 

2.20 

2.10 

2.26

1.43 

1.44 

1.50 

.73

.52 

.72 

.87 

.94 

.51

d

0

2.80 

2.00 

2.20 

1.60

1.20 

1.60 

1.48 

1.72 

1.28 

1.15 

1.62

.95 

.90 

1.12

.28

.25 

.65 

.60 

.69 

.42

S 

o 

 *-» +j

o

ca

2.00 

2.20 

2.00 

1.10

.92 

.96 

.46 

.95 

1.30 

1.15 

1.35

.88 

.90 

.90 

.61

.26 

.45 

.50 

.50 

.24

E.

B

5 "K

08

a

4.37 

4.20 

4.18 

3.45

1.73 

2.13 

2.15 

2.43 

2.45 

2.46 

2.48

1.68 

1.74 

1.81 

.98

.64 

1.02 

1.08 

I'.IS 

.63

Thickness of ice as given i-ncludes considerable water above i
Vertical velocity measurements Continued. 

WALLKILL RIVER AT NEWPALTZ, N. Y. Continued.

Date.

1903.

January 7. ...................

Mean of 4 curves. ......

February 10. ................

Mean of 5 curves .......

February 26 .................

Mean of 7 curves .......

; towater 

ce.

S *

§3

a ffl

o>

O

Feet.

11.2

10.8

8.85

"o 

S »

fl"3

'S a

 ^-2

s

b

Feet.

1

^.s *" o 

g ft

fl

oS

S

Feet.

60

80

90

110

25

40

60

80

110

25

40

60

80

100

110

120

^

ft

13

"3

O

Feet.

7.6

11.1

11 6

13.1

10.8

5.2

7.0

5.2

8 8

10.2

11.2

. 8.5

8.0

sJ

|

"3

ft

"ft

5?

Q

Fee*.

6.8

10.3

10.8

12.3

10.0

4.8

8.0

6.0

9.6

11.8

8.0

5.2

5.8

4.2

7.8

9.2

10.5

7.9

7.2

8

"8

GO

a

2

Feet.

0.80

.80

.80

.80

.80

1.33

1.00

1.00

1.00

1.00

1.06

1.20

1.20

1.00

1 00

1.00

.70

.60

.96

Velocity in feet per second from vertical velocity 

curves.

p

03

S

2.23

2.54

2.38

2.52

2.42

1.29

2.26

2.17

2.53

2.65

2.18

.59

1.20

1.12

1.43

1.41

1.87

.68

1.20

ft

'ft

13

d

2.51

2.74

2.57

2.82

1.42

2.44

2.59

2.78

3.00

.63

1.31

1.40

1 58

1.57

2.04

.80

.d

ft

c

13

d

2.77

2.91

2.68

2.63

1.38

2.20'

2.55

2.79

2.81

.72

1.40

1.42

1.58

1.60

1.80

.70

_jg

ft

5?

13

00

d

1.66

2.25

2.20

2.58

1.14

2.30

1.71

2.32

2.52

.52

1.15

.73

1.30

1.20

1.92

.68

f

g1

 §

GO

d

d

2.5

2.1

<M

2

)8

2.44

2.60

1.26

2.25

2.15

2.,

2.f

>6

>6

.62

1.28

l.(

1

)8

14

1.40

l.j

.(

*6

>9

ft

o 

E2.00

1.60

1.30

1.74

1.00

1.86

1.70

1.80

1.98

.42

1.00

.90

IMS

1.15

1.30

.28

P 

o

 p

o 

PQ

1.00

1.80

1.70

1.70

.82

1.95

.90

1.50

.80

.15

.00

.00

.65

.62

1.27

.20

as

a

oS

2.80

2.94

2.72

2^83

1 42

. 2. 43

2.65

2.89

3.02

.76

1.43

1.53

1.68

1.68

2.20

.80
Vertical velocity measurements Continued. 

WEST CANADA CREEK AT TWIN ROCK BRIDGE, N. 

Date.

1906.

1903.

Gage height to water

surface.

Feet. 

3.03

3.03

3.8

Gage height to bttom ofice.

Feet.

Distance from initial 

point.

Faet. 

25 

30 

40 

50 

60 

120 

130 

140

20 

25 

' 30 

35 

40 

45 

50 

55 

60

Total depth.

Feet. 

3.6 

3.8 

3.6 

5.9 

6.5 

5.0 

4.2 

4.2

5.2

3.8 

4.1 

4.2 

4.2 

4.2 

'4.0 

3.9 

3.8 

4.0

4.0

Depth below ice.

Feet. 

2.4 

2.6 

2.3 

4.7 

5.0 

3.4 

2.6 

2.6

2.3 

2.6 

2.7 

2.7 

2.7 

2.5 

2.2 

2.0 

2.5

2.5

Thickness of ice.

Feet. 

1.25 

1.30 

1.32 

1.34 

1.48 

1.58 

1.60 

1.75

1.5 

1.5 

1.5 

1.5 

1.5 

1.5 

1.75 

1.75 

1.5

1.56

Velocity in feet per second Irom vertical velocity 

curves.

§

01

a

1.58 

1.70 

2.12 

1.45 

.65 

1.10 

1.28 

.95

1.35

1.65 

1.57 

1.50 

1 65 

1.82 

1.83 

2.18 

2.22 

2.00

3.82

a

& 

 o

10

0

1.78 

1.77 

2.30 

2.03 

.72 

1.13 

1.32 

1.03

1.84 

1.70 

1.65 

1.84 

2.12 

2.04 

2.30 

2.31 

2.19

fi +1

a

o

 o

N

d

1.71

1.85 

2.35 

1.67 

.73 

1.16 

1.34 

.95

1.70 

1.79 

1.74 

1.80 

1.97 

2.17 

2.30 

2.38 

2.45

,d

& 

"O 

CO

d

1.48 

1.53 

1.89 

1.15 

.54 

1.02 

1.21 

.93

1.56 

1.26 

1.21 

1.51 

1.54 

1.40 

1.97 

1.99 

1.56

S

§

13 

00

d 

+C<J

d

c<»

1.60 

1.69 

2.12 

1.41 

.64 

1.09 

1.28 

.94

1.63 

1.52 

1.48 

1.66 

1.76 

1.78 

2.14 

2.18 

2.00

&

e

1.00 

1.86 

2.23 

.86 

.50 

1.16 

1.23 

.80

1.53 

1.61 

1.40 

1.46 

1.58 

1.74 

2.00 

2.32 

2.30

ec

i 

«

0.98 

1.23 

1.47 

.00 

.38 

.76 

1.12 

.84

.66 

.85 

.84 

.88 

.92 

.90 

1.69 

1.54 

.88

i

s

1.81 

1.86 

2.39 

2.06 

.76 

1.16 

1.35 

1.04

1.84 

1.82 

1.76 

1.86 

2.18 

2.24 

2.34 

2.38 

2.35

Coarse gravel bed. 6 Needle ice on unde
Vertical velocity "measurements Continued. 

WINOOSKI RIVER AT RICHMOND, VT.

Date.

1905.

March 3 «. ...................

Mean of 13 curves ......

March 4«. ....................

Mean of 13 curves. . . . . .

1

o 

S>H

'<s S

&>

o

Feet.

5.45

5.58

1

4^ ^

°5 g

+J

o

Feet.

2.70

2.83

3

'3

§ £

"s ^

g

1

S

Feet.

5

10

15

20

25

30

35

40

45

50

55

60

65

5«

10

15

20

25

30

35

40

45

50

.55

60

65

^3

ft

*O

3o EH

Feet.

3.3

4.0

3.9

3.6

3.6

3.5

3.4

3.4

3.4

3.3

3.0

2.8

2.2

Q Q

3.4

4.0

4.0

4.0

3.7

3.8

3.6

3.8

3.6

3.5

3.3

3.0

2.6

......1 3.6

S

0

3

&

S

Feet.

1.2

1.9

1.8

1.9

1.6

1.8

1.6

1.4

1.6

2.0

1.9

1.4

.8

1.6

1.3

1.8

2.0

2.0

1.7

2.0

1.6

1.6

1. 1

2.1

1.9

1.5

1.0

1.7

1

"S

o

aM 

o

3

Feet.

2.6

2.5

2.4

2.25

2.2

2.1

2.2

2.4

2.1

1.5

1.5

1.6

2.0

2.10

2.75

2.75

2.55

2.3

2.35

2.1

2.25

2.3

2.1

1.55

1.55

1.6

2.0

2.17

Velocity in feet per second from vertical velocity 

curves.

s(0

1.20

1.78

2.09

2.29

2.45

2.32

2.04

1.97

2.05

1.70

1.66

1.93

1.50

1 09

1.41

2.00

2.27

2.63

2. 60

2.25

2.58

2.36

2.54

2.50

2.65

2.39

1.83

2.31

,s

ft

 §

o

1.52

2.02

2.34

2.74

2.88

2.81

2.58

2.45

2.50

2.55

1.97

2.33

1.80

1.67

2.25

2.51

2.97

3.25

2.92

3.18

2.57

3.23

3.23

3.02

2.90

2.10

jj

ft

 §

IN

O

1.23

2.09

2.27

2.54

2.74

2.42

2.42

2.45

2.32

2.35

1.27

2.14

1.85

1.46

2.24

2.45

2.87

2.77

2.37

2.73

2.96

2.67

2.50

3.17

2.75

2.04

a

ft»

TS

00 

0

1.13

1.50

1.92

2.00

2.13

2.14

1.62

1.48

1.70

.69

1.93

1.55

1.25

1.25

1.74

2.03

2.39

2.23

2.01

2.18

1.87

2.23

2.30

2.17

1.85

1.62

4

4

t

00

O

IN

O

J_

^

w

18

L80

2. 10

2.27

2. 44

2.28

2.02

1.96

2. 01

1.52

1. 60

1.84

1.55

1.

1.

2.

2.

2.

2.

2.

2.

2.

2.

2.

2.

1.

36

99

24

63

50

19

46

42

45

40

67

30

83

ft

0

EH

0.70

1.20

1.72

1.55

1.50

1.25

.90

1.33

1.13

.62

.83

1.80

.56

1.25

1.65

2.15

2.33

1.72

1.00

2.13

1.58

1.50

.35

2.43

2.10

1.70

**

"o

pq

0.68

.88

1.02

.98

1.23

1.45

.80

.25

1.09

.00

1.20

.78

.30

.76

1.00

1.40

1.23

1.20

1.25

1.25

1.20

1.30

1.70

.75

1.00

.65

D

S

=3

1.52

2.15

2.36

2.76

2.95

2.83

2.80

2.53

2.65

2.94

2.22

2.33

1.79

1.67

2.32

2.53

3.03

3.24

2.95

3.20

2.97

3.27

3.53

3.18

2.98

2.13

a At section about one-half mile above bridge; gravel bed.
Vertical velocity measurements Continued. 

WINOOSKI RIVER AT RICHMOND, VT. Continued.

Date.

1906. 

March go. ....................

Gage height to water 

surface.

Feet. 

5.62

Gage height to bottom ofice.

Feet. 

3.42

Distance from initial 

point.

Feet. 

21 

30 

40 

50 

60 

60

Total depth.

Feet. 

11.5 

10.0

7.5 

7.3 

6.9 

7.0

8.6

Depth below ice.

Feet. 

9.0 

7.0 

4.8 

5.3 

4.9 

5.0

fi.2

Thickness ofice.

Feet. 

2.5 

3.0 

2.75 

2.0 

2.0 

2.0

2.45

Velocity in feet per second from vertical velocity 

curves.

§

0>

1.74 

2.10 

2.24 

2.02 

1.93 

1.80

1.99

a 

"ft 

 a

0

2.19 

2.82 

2.69 

2.86 

2.50 

2.50

ft 

o> a

IM

O

1.13 

2.44 

2.38 

2.03 

1.76 

1.41

13

00

d

2.27 

2.04 

1.96 

1.77 

2.04 

2.15

|

a 

T

00

d

<N

0

1.

2. 

2. 

1. 

1. 

1.

j,

IM

70 

24 

17 

90 

90 

78

o

EH

0.50 

.20 

2.02 

1.46 

.50 

.40

eo 

 p

o

n

1.28 

.30 

.94 

.56 

1.00 

.70

D

e

2.46 

'2.86 

2.70 

3.00 

2.52 

2.52

a At bridge; sand and gravel bed; ice cover very rough, broken, a
72 STREAM FLOW DURING THE FROZEN SEASON. 

SUMMARIES OF VERTICAL VELOCITY CURVES.

The mean results from the vertical velocity curves (pp. 47-71) 

have been arranged in three groups (1) 352 curves for smooth ice 

cover, (2) 51 curves for rough ice cover, (3) 13 curves for very rough 

ice cover.' It will be noted that in some cases where gage heights 

were approximately the same for different sets of curves they have 

been combined. There is little difference between the results of 

groups 1 and 2, but as rough ice cover was reported for group 2, it 

seemed best not to include it in the larger list.
Summary of vertical velocity curves under ice cover.

SMOOTH ICE COVER.

River.

Catskill...... ..........

Fish.......-------.....

Wallkill.. .............

Station.

South Cairo, N. Y .................

Orford, N. H.. ....................

Mount Morris (Jones Bridge), N.Y.

Utica, N. Y...... .................

*\

Number ofcurves.

4

18 

12 

6 

2 

8 

12 

8 

8 

8 

20 

11 

19 

4 

12 

15 

19 

10 

9 

23 

13 

17 

3 

11 

4 

14 

13 

10

Gage height to water 

surface.

Feet. 

2.82 

2.85 

4.16 

± 4.1 

5.6 

5.28 

5.60 

6.6 

7.0 

3.91 

5.00 

5.9 

1.42 

1.55 

.3.40 

3.48 

3.55 

4.17 

4.70 

4.77 

5.30 

616.2 

9.6 

5.15 

7.3 

7.78 

8.95 

11.2 

17.33

Depth under ice.

Feet. 

2.7 

3.7 

4.0 

4.1 

7.3 

5.8 

3.4 

4.9 

5.0 

2.5 

3.5 

3.8 

6.6 

3.8 

2.7 

2.6 

1.6 

2.5 

3.0 

2.9 

3.2 

10.1 

9.2 

6.7 

6.0 

7.9 

7.2 

9.5 

18.2

Ice thiknss.

Feet. 

0.98 

.51 

1.97 

1.91

.10 

.56 

.10 

.50 

1.40 

1.45 

.54 

.45 

.43

1.30 2.15' 

1.91 

2.04 

2.34 

2.00 

.50 

1.60 

.75 

±1.2 

1.05 

1.00 

.85 

.92

Mean velocity.

Ft. per 

sec. 

0.44 

.64 

1.04 

.92 

1.80 

.94 

.80 

1.19 

1.26 

.90 

1.25 

1.62 

.45 

.89 

2.27

1.17 

1.87 

1.30 

1.32 

1.33 

1.61 

1.00 

3.24 

.55 

.83 

1.29 

1.57 

2.35 

3.54

Depth of thre

velocity

§ 

«

6

n 

«

a p

0.06 

.16 

.11 

.07 

.12 

.10 

.03 

.07 

.08 

.07 

.14 

.07 

.09 

a. 01

.04 

.18 

.07 

.10 

.08 

.12 

.21 

.17

(C?11 

.22 

.10 

.11 

.16

«

33

«

M

1O 

^

0.70 

.79 

.69 

.63 

.73 

.74 

.63 

.69 

.67 

.70 

.77 

.67 

.72 

.70 

.63 

.66 

.77 

.69 

.71 

.70 

.70 

.78 

.74 

.65 

.70 

.76 

.70 

.71 

.79

o Upper thread of mean velocity at 4 curves only. & Below reference point. 
Summary of vertical velocity curves under ice cover Contin

SMOOTH ICE COVER Continued.

River.

West Canada Creek . . .

Mean of 352 curve 

Highest

Station.

Twin Rook Bridge, N. Y ..........

s

Number ofcurves.

9 

26

Gage height to water 

surface.

Feet. 

3.8 

5.5

Depth under ice.

Feet. 

2.5 

1.6

Ice thickness.

Feet. 

1.50 

2.10

Mean velocity.

Ft. per 

sec. 

1.82 

2.12

Depth of thre

velocity

Upper mean.

0.04 

.12 

.10 

.22 

.00

Lower mean.

o.t>6

.72 

.71 

.79 

.63

ROUGH ICE COVER.

Orford, N. H.. .................... 7

7 

21 

5

11

5.59

6.00 

6.70 

2.45

3.34

4.6

4.9 

5.8 

4.8

2.5

1.71

1.69 

.1.66 

.46

.58

1.08

1.11 

1.23 

1.58

.78

0.08

.09 

.14 

.13

.11

.14

.08

0.70

.70 

.74 

.73

.68

.71

.74

.68

VERY ROUGH ICE COVER, BROKEN AND TILTED

Wallkill . . . . . .......... Newpaltz, N. Y. ..................

4

4

4-70

13.7

5.62

5.3

14.6

6.2

8.7

0.45

1.40

 4-9 x,

1.45

0.74

2.98

1.99

1.90

0.27

.27

.22

.25.

+00.88

.88

.81

.86

No lower mean thread of velocity for 1 curve.
VERTICAL VELOCITY CURVES. 75 

FORM OF VERTICAL VELOCITY CURVE.

For an ideal cross section and length of river, the difference in 

velocity at different points in a vertical section is due to the difference in resistance to flow met with by the filaments of water at 

different depths. If no resistances of any kind existed, the vertical 

curve of velocity would be a straight line normal to the surface of 

the stream. If bed friction and the incidental losses due to it were 

the only resistances to flow, the vertical velocity curve would probably be curved in the lower part and straight in the upper part, the 

line being tangent to the curve at that point in the vertical where the 

effect of bed resistance is lost (fig. 7, a) ; or if the bed friction is of 

sufficient amount relatively to the depth the curve might be continuous to the surface (fig. 7, 6). Varying degrees between a and & 

would be met with, depending on the relation of depth to velocity, 

condition of bed, etc. If there is resistance at the surface due to air 

friction only, there would be a similar effect on the form of the curve

_ __ s Water surface __.

Stream bed

(a) (b) (c) (d) 

FIG. 7. Form of vertical velocity curves.

(e)

from the surface downward. If there were no bed friction, the form 

of curve would be as in fig. 7, c, or some modification of 'this, as 

explained above.

Resistance to flow occasioned by the roughness of the sides of a 

stream is also an important factor in determining the form of the vertical velocity curve, especially if the channel is narrow and deep. 

F. P. Stearns a has advanced the theory that there is an upward flow 

toward the center at the surface. He says:

Let us first suppose the case of a single obstacle projecting from the lining of a channel. 

The current approaching this obstacle loses some of its velocity just before reaching it, and 

thereby causes an excess of head in a small pyramid of water just above the projection.

This excess of head in turn causes a transverse flow of the water in all directions; but the 

strongest transverse flow will be in the direction of the least resistance, which is, as a rule, 

vertically toward the surface.

oTrans. Am. Soc. Civil Eng., vol. 12, 1883, pp. 331 et seq.
76 STEEAM FLOW DURING THE FROZEN SEASON.

The irregularities upon the surfaces of even the smoothest channel linings met within 

practice are very large in comparison with the size of the particles of water striking them, 

and they may be considered as obstacles present in all parts of the lining, each tending to 

produce an upward flow, as above indicated. * "" """-

Although the tendency to upward flow is general, yet since it can not occur without a 

corresponding downward flow to replace the water which rises it follows that it will take 

place only in thosje portions of the width of the channel where the obstacles producing it are 

the more frequeni and nearer the surface i. e., generally at or near the sides.

It is therefore Ijhe theory that there is at the sides of channels an upward flow, due to the 

cause already described, which carries with it the slow-moving water always found in the 

immediate vicinity of channel linings, and that this water, reaching the surface, flows 

toward the middl<b of the channel, retarding by its slower movement the velocity of the surface layers, thereby causing the maximum velocity to be, in most cases, below the surface.

It must not be jnferred from what has just been stated that the writer believes there is a 

continuous flow i^i the direction indicated, since it is well known that the motions of water 

are very irregular; particularly in channels with rough linings or variable sections, and that 

masses of water fi|nd their way from the bottom to the surface in the middle of the channel 

as well as elsewhere. The idea which he wishes to convey is that in most cases the resultants 

of these irregular movements are in the directions indicated.

The typicaljvertical velocity curve for open-water conditions (fig. 7, d) 

may be considered as due to a combination of these various resistances,but the! amount and direction of the wind may change greatly 

the retardation due to air friction, and consequently the form of the 

curve. The Relative effect of bed and surface friction will be in a 

measure shown by the difference in length of mn and or, or, in other 

words, the re' ation of surface and bottom velocities to the maximum 

velocity. If there is an ice cover the upper part of the vertical velocity curve wil be still more curved (fig. 7, e), and, as shown later (pp. 

78-79), may even be more pronounced in this way than the lower part.

The foregoing statements would apply to a straight stretch of river 

with the bed Approximately parallel to the water surface. The usual 

uneven conditions of bed and banks have a modifying influence and 

tend to obscure more or less the relative effect of be$l and surface 

friction. This relation of top and bottom velocity to the maximum 

will, however, serve to indicate something of the relative amount of 

resistance due to ice cover and to the stream bed, and will be briefly 

considered.

For open-water conditions the results from 78 vertical velocity 

curves under various conditions at gaging stations on New York 

streams are as follows: a i

Relation of top, maximum, and bottom velocity for open-water conditions.

Top........................................................................

Velocity in 

, terms of 

mean velocity =1.00

1.15

1.18

.50

Difference 

as regards 

maximum 

velocity.

O.,03

.68

a See Water-Sup, and Irr. Paper No. 76, U. S. Geol. Survey, 1903, p. 25, fig. 3.
VERTICAL VELOCITY CURVES. 77

The relation of air or water surface friction to that of bed friction 

is here $;£f, or 0.044. (Compare with Francis's ratio of ¥J¥ for still 

air, p. 16.)

For smooth ic$ cover, the comparative effect of bed and ice friction 

is shown for several cases in the following table. The average amount 

of resistance due?to ice cover is 0.58 of that due to roughness of bed, 

but there is considerable variation from this amount.

Comparative effect of bed and ice fnction on vertical velocity curves under smooth ice cover.

River and station.

Kennebec, North. Anson, Me. . . 

Connecticut, Orford, N. II.....

Wallkill, Newpaltz, N. Y ......

Gage 

height.

Feet. 

3.48 

4.17 

4.77 

4.15 

5.59 

6.00 

6.70 

3.91 

5.04

Number 

of curves

18 

-19 

9

18 

7 

7 

21 

8 

8 

26 

5

Average 

depth.

Feet. 

2.6 

2.5 

2.9 

4.0 

4.6 

4.9 

5.8 

2.5 

3.0 

1.6 

8.0

Average 

velocity.

Feet per 

second. 

1.17 

1.30 

1.33 

1.04 

1.08 

1.11 

1.23 

.90 

1.25 

2.12 

2.18

Difference as regards maximum 

velocity.

Top(l).

0.22 

.30 

.40 

.50 

.27 

.32 

.41 

.23 

.64 

.59 

.37

.39

Bottom

(2).

0.62 

.62

.57 

.66 

.72 

.72 

.65 

.51 

.74 

.77 

.65

.66

Ratio of 

Ito2.

0.35 

.48 

.70 

.76 

.38 

.44 

.63 

.45 

.86 

.77 

.57

.58

For very rough ice cover, the frictional effect of ice cover is the 

greater of the two, averaging 1.28 times that for roughness of bed.

Comparative effect of bed and ice friction an vertical velocity curves under very rough ice cover.

Eiver a<id. station.

i

Wallkill, Newpaltz; N. Y. ...............

Number 

of curves.

4 

4 

5

Average 

depth.

Feet. 

5.3 

14.6 

6.2

Average 

velocity.

Feet per 

second. 

0.74 

2.98 

1.99

Difference as regards maximum 

velocity.

Top (1).

1.02 

.81 

1.11

.98

Bottom

(2).

0.55 

.89 

1.05

.83

Ratio of 

Ito2.

1.86 

.91 

1.06

1.28

RELATION OF DEPTH AND VELOCITY TO FORM OF CURVE.

It is evident from the foregoing tables that for a given mean velocity the vertical velocity curve under ice cover becomes flatter as the 

depth increases, since" the curvature due to top and bottom resistances 

is distributed through a greater distance. (See fig. 13, p. 83.) For a 

given depth, as the mean velocity increases, the curvature will become greater, as both top and bottom resistances increase with 

velocity. 
78 STREAM FLOW DURING THE FROZEN SEASON.

For a given station the "change in curvature as the stage increases 

will depend on the relative increase of depth and velocity. In the 

case of Wallkill River (fig. 10) the depth increases considerably 

faster than the velocity, and it will be noted that the curve becomes 

flatter as the stage increases.

«»

COMPARISON OF VERTICAL VELOCITY CURVES, WITH AND WITHOUT

ICE COVER.

Fig. 8 affords a comparison of mean vertical velocity curves for 

conditions of open water and ice cover, at substantially the same 

stations. The essential difference between these curves is the greater

o.zo 0.40 0.60 0.80 1.00 

VELOCITY IN TERMS OF MEAN VELOCITY = 1.00

 Mean of 78 curves without ice cover 

~" Mean of 42 curves with ice cover

1.20

FIG. 8. Comparison of vertical velocity curves for streams with and without ice cover.

drawing back of the curve for ice cover in its upper portion, on account 

of the greater retarding effect of the ice over that of air. As a consequence of this there are two threads of mean velocity, viz, at 0.13 and 

0.71 of the depth, for ice cover, as compared to one mean thread at 

0.61 depth for the open section. The position of maximum velocity 

is lowered from about 0.14 depth in the case of open section to 0.36 

depth with ice cover, its relative value as regards mean^velocity being
VERTICAL VELOCITY CURVES. 79

slightly less in the case of ice cover. The bottoms of the two curves 

are at substantially the same position, as would be expected.

With very rough ice cover the difference between the two curves 

becomes still more pronounced, and the drawing back of the curve 

in its upper part may predominate over the curvature existing in 

the lower part due to roughness of bed.

POSITION OF THREADS OF MEAN VELOCITY.

The data in the table on pages 73-74 and figs. 8 to 14 serve as a 

basis for the following discussions, except where special reference 

is made to other material.

0.2

_J

O1-

u.

00.4

*.EOu

^0.6

0

Z

U>

t

lu

1.0 

^*<4^

"" ^

'/

y

//

///'

/ -t'' j4*

\

\

\

 T i

// ///

f

0.20 0.40 0.60 0.80 1.00 1.20

VELOCITY IN TERMS OF MEAN VELOCITY = 1.00

6AGE 

REI6HT

3.48

4.17

4.77

MO. OF 

CURVES

18

19

9

AVERAGE 

DEPTH

2.6

2.5

23

WERA&E 

VLLOCITl

1,17

1.30

133

_____ Jan. 10,1906 

* . ____ _ Mar 2,1906

-______ Mar. 30,1906 4.77

FIG. 9. Vertical velocity curves under ice cover, showing change in form of curve with change of stage, 

Kennebec River at North Anson, Me.

The average of 352 vertical velocity curves made under widely 

varying conditions (pp. 73-74) indicates that in general under ice cover 

two threads of mean velocity occur in the vertical, their average 

position being at 0.10 and 0.71 of the depth below the bottom of 

the ice.
80 STREAM FLOW DURING THE FROZEN SEASON.

The depths of threads of mean velocity being plotted as ordinates and the total depths as abscissas, it is seen that there is a 

general tendency for both threads to move toward the bottom of 

the curve as depth increases. A similar plat for depths of threads 

of mean velocity and for mean velocities indicates that as mean 

velocity increases both threads of mean velocity become lowered. 

An increase in stage for a given station means usually an increase 

of both depth and mean velocity; consequently it will be found

i.o

0.40 * 0.60 0.80 1.00

VELOCITY IN TERMS OF MEAN VELOCITY 1.00

. Jan. 21, 1902 

. Jan. 31, 1302 

. Jan. 23,I90Z

HEIGHT

7.24

9.07

17.33

OtPTH

6.7

9.0

21.3

VELOCITY

1.04

2.16

3.93

FIG. 10. Vertical velocity curves under ice cover; average of curves at stations 80, 90,100 for different 

stages, WaUMll River at Newpaltz, N. Y.

that both threads of mean velocity tend to move downward as the 

stage increases. (See figs. 9 to 11.)

The range in position of mean threads seems to be about-the 

same for both upper and lower threads, being about 0.18 depth 

(with a few exceptions). Moreover, the change in position of the 

two threads is about the same in amount, the average difference 

being 0.60 of the depth. With very rough ice cover the tendency 

is toward greater depression of both mean threads, but it will be
VEETICAL VELOCITY CUKVES. 81

noted that they still preserve about the same distance apart, viz, 

0.60 depth. (See table on pp. 73-74, and fig. 14, p. 84).

POSITION OF MAXIMUM VELOCITY AND RELATION TO MEAN VELOCITY.

The average position of maximum velocity is at 0.37 depth below 

the ice, varying from 0.19 to 0.52 depth. In general, it becomes

0.20 0.40 0.60 0.90 1.00 

VELOCITY IN TERMS OF MEAN VELOCITY = 1.00

i.ao

6A6E 

HEI6HT

415

6.70

6.00,

J.S9

HO OF 

CURVES

10

21

7

7

AVERAGE 

DEPTH

4.0

5.8

4.9

4.6

AVERAGE. 

VELOCITY

1.04

1.23

I. II

1.06

______ Feb. 1905

_ ______ Feb. J906 

__ ___ Mar. 1906 

---._____ Mar. 1906

FIG. 11. Vertical velocity curves under ice cover, showing change in form of curve with change of 

stage, Connecticut River at Orford, N. H.

lower as the depth and velocity increase and hence as the stage 

increases. Rough ice cover tends also to lower the depth of the 

maximum thread, and when the ice becomes broken and tilted or 

when needle ice accumulates near its under surface the thread may 

be considerably below mid depth, indicating a greater effect due to 

ice friction than to that of the stream bed; in other words, the 

curve is a complete reversal of the ordinary open-water vertical 

velocity curve.

IEE 187 07 6
82 STREAM FLOW DUELNG THE FEOZEN SEASON.

The average coefficient to apply for obtaining maximum from 

mean velocity is 0.839, the variation being from 0.76 to 0.90. This 

coefficient becomes less as the velocity increases, but greater as the 

depth increases, consequently its variation from the mean is not 

large for smooth ice. For rough ice it is considerably diminished 

and may reach a value of 0.75.

RELATION OF VELOCITY AT MID DEPTH TO MEAN VELOCITY.

The average coefficient for obtaining mean velocity from that at 

mid depth is 0.878, the range being from 0.82 to 0.92. The range

0.20

0.40

0.60

f- 0.80

1.00

0.40 0.60 0.90 1.00 

VELOCITY IN TERMS OF MEAN VELOCITY

I.ZO

1.00

Feb. 1906

GAGE 

HtlOHT

3.91

504

NO OF 

CURVES

9

0

AVERAGE 

DEPTH

2.5

3.6

IVE.RAGE 

VtVOCITV

0.90

 _ Mar. I90G I.ZS

FIG. 12. Vertical velocity curves under ice cover, Fish. River at Wallagrass, Me.

in values for this coefficient, like that for maximum velocity, is 

small, as the tendency is for it to increase directly with the depth 

and inversely with the velocity; consequently for a given station 

little variation occurs as the stage changes. Nearly this same average relation was found on the upper Mississippi by A. O. Powell, 

assistant engineer, under the direction of Col. Charles J. Alien, Corps 

of Engineers, U. S. Army, in 1882 and 1890,a the variation being

o Ann. Kept. Chief of Engineers, U. S. A., 1890, pt. 3, p. 2104.
VERTICAL VELOCITY CURVES. 83

between 0.87+ and 0.88+ . No data are given, however, as to conditions of depth, velocity, or bed of stream. The coefficient for 

obtaining mean velocity from that at mid depth becomes less for 

very rough ice, just as in the case for maximum velocity, the average value for the 13 curves being 0.82, with a range ef from 0.76 

to 0.85.

RELATION OF MEAN OF VELOCITIES AT 0.2 AND 0.8 DEPTH TO MEAN

VELOCITY.

The average coefficient for obtaining mean velocity from the mean 

of the velocities at 0.2 and 0.8 depth is 1.002, the range being from

020 0.40 0.60 080 1.00 

VELOCITY IN TERMS OF MEAN VELOCITY =

1.40

1.00

. Winooski River, af Richmond, Vt.

BtD

Gravel

Ctaf&CobblK

NO OF CURVES

26

S

AVERAGE 

DEPTH

1.6

8.0

AVERMiE 

VELOCITY

2.12

_____ Wall kill River af Mivpaltz NY 2-16

FIG. 13. Effect of depth on form of vertical velocity curves under ice cover.

0.98 to 1.04, there being, however, but one set of curves with a 

greater value than 1.02. This relation is shown graphically by connecting the 0.2 and 0.8 depth points of the mean vertical velocity 

curves and noting where this line crosses the horizontal at 0.5 depth. 

(See figs. 8 to 13.) '

In general, this coefficient seems to decrease slightly as gage 

heights increase. (See figs. 8 to 11, and table on pp. 73-74.) For very 

rough ice cover the mean value is 1.002, the range being from 1.00.
84 STREAM FLOW DURING THE FROZEN SEASON.

to 1.04, indicating that rough ice tends to increase this coefficient 

slightly.

The typical vertical velocity curve for open-water conditions corresponds approximately in form with an ordinary parabola drawn 

through top, bottom, and mid-depth points of the curve and with 

axis horizontal. The mean ordinate to this parabola is a mean of 

the ordinates at 0.22 and 0.79 of the depth, and it is evident that 

the mean of the ordinates at 0.2 and 0.8 depth would always be 

less than the true mean ordinate, so that if the vertical velocity

00.60

0. 0.80 

uJ

0.20 0.40 0.60 080 1.00 

VELOCITY IN TERMS OF MEAN VE.LOC1TY = 1.00

1.20 1.40

Rondout Creek af Rosendtxle, N. Y. 

Wall kill River at Netvpaltz, N.Y. 

Winooski River af Richmond, Vt.

BED

Rook

Clays cobbles

Samfsgravet

NO. or

4

4

5

AVERAGE

S.3

14.6

6.2

AVERAbE

0.74

2.99

1.59

FIG. 14. Effect of very rough, broken, and tilted ice on form of vertical velocity curves under ice cover.

curve were truly parabolic the coefficient for this method would 

always be slightly greater than 1.00. Usually the parabola passes 

wholly to one side of the actual curve above 'mid depth and on the 

opposite side below mid depth, the resulting effect being that the 

mean of the velocities at 0.2 and 0.8 depth ordinarily gives closely 

the mean velocity for the vertical.

For ice cover the vertical velocity curve diverges markedly from 

a parabola drawn as described above. The results of the table on 

pages 73-74 seem to indicate, however, that this relation holds almost
VEETICAL VELOCITY CUEVES. 85

as well for curves under ice cover as with open section, and the 

0.2 and 0.8 method, as it is called, seems to have much promise as 

a two-point method, being both reasonably accurate and convenient 

for use.

The range of variation in the reduction of coefficients is as follows:

Range of coefficient to reduce to mean velocity.

0.14 

.10

Maximum.............................................................

Mid depth ......._..._._.....-.._.._..__.__....___..__....,_..__._.._..

0.2 and 0.8 deptb.......................................................... .06

The accuracy of the method being assumed to be proportional to 

the square root of the number of observations, and either of the singlepoint methods being adopted as a basis, the computed probable range 

of error for the two-point method would be 

Range for single point 72 '

or, as compared with maximum point, the range would be 0.099; with 

mid-depth point, the range would be 0.071. The actual range of 

variation for the two-point method is considerably smaller, indicating 

that it has a greater accuracy as compared with single-point methods 

than can be attributed to the use of two observations instead of one.

PERCENTAGE VARIATION IN OBSERVATIONS AT DIFFERENT DEPTHS.

In general the top and bottom of the vertical velocity curve is most 

poorly determined, because greater variations occur in velocity in 

these portions of the curve. The 0.5 depth method has the advantage 

of utilizing a depth of observation at which variations in velocity are 

least apt to occur.

As bearing on the variations between successive observations at 0.2 

and 0.8 depth, the following table gives results-from two sets of curves 

where independent observations were made at these depths just after 

the curves were completed:

Variation in observations at 0.2 and 0.8 depth, Connecticut River at Orford, N. H., meter

suspended from cable. 

MARCH 14, 1906, GAGE HEIGHT, 6.00.

Highest ..............................

Observed velocity.

Ratio: Velocity from

curve.

0.2 

depth.

0.993

1.07

.94

0.8 

depth.

0.995

1.05

.95

Ratio of velocity

determined by

the 0.2 and 0.8

method to the 

mean velocity.

Actual 

observation. «

1.013

1.04

.98

From 

curve. 6

1.004

1.02

.99

Depth 

under

Feet.

5.0

6.3

3.5

Mean 

velooitv.

Feet ver

second.

1.10

1.39

.56

a Mean from 0.2 and 0.8 velocity as observed.

6 Mean from 0.2 and 0.8 velocity taken from vertical velocity curve.
86 STREAM FLOW DURING THE FROZEN SEASON.

Variation in observations at 0.2 and 0.8 depth, Connecticut Ewer at Orford, N. H., meter 

suspended from cable Continued.

MARCH 15, igoe, GAGE HEIGHT 5.59.

Highest. ..................

Observed velocity

Ratio: Velocity from

curve.

0.2 

depth.

1.006

1.04

.95

0.8 

depth.

0.974

1.13

.90

Ratio of velocity

determined by

the 0.2 ahd 0.8

method to the 

mean velocity.

Actual 

observation.

1.011

1.05

.97

From 

curve.

1.003

1.01

.99

Depth 

under

Feet.

4.6

5.7

3.2

Mean 

velocity.

Feet per

second.

1.08

1.36

.51

As would be expected, the actual observations at 0.2 and 0.8 depth, 

when used to obtain mean velocity, give a larger percentage variation in coefficient than do the curve values at these depths, but the 

average variation is small and far within the degree of accuracy 

required.

A further index of the amount of variation in observations at 0.2 

and 0.8 depth is afforded by two successive gagings made February 

15, 1906, on Fish River at Wallagrass, Me., under ice cover, when the 

gage heights height remained the same.

Comparison of velocities for two separate gagings on Fish River at Wallagrass, Me., gage 

height 3.91, meter fastened to rod.

FEBRUARY 15, 1906, GAGE HEIGHT 3.91.

Average of 4 stations, observations at 0.2 and 0.8

Highest ............................................

Ratio of velocities obtained 

in first and second gagings.

0.2 

depth.

1.002 

1.06 

.93

0.8 ' 

depth.

' 0.972 

1.08 

.91

Mean

0.990 

1.05 

.94 

0.978 

1.01 

.95

Depth.

Feet. 

2.6 

4.1 

.9 

2.5 

3.6 

1.3

Mean 

velocity.

Feet per 

second. 

0.88 

1.10 

.62 

.90 

1.18 

.86

Other details of these gagings are given on page 53. It will be noted 

that the depths are small and that in order to get 0.2 and 0.8 depth 

the meter had to be held within a range of 0.2 to 0.8 feet from the 

bottom of the ice and the bed of the river. The average variation in 

the results of these two sets of velocities at 0.2 and 0.8 depth is small 

and, in fact, is less than in the case of the vertical curves.
STREAM FLOW DURING FROZEN SEASON.

SLOPE DETERMINATIONS AND VALUES OF n IN KUTTER'S FORMULA, UNDER ICE CONDITIONS.

In 1906 two sets of slope determinations and measurements of the 

other hydraulic properties were made on Connecticut River at 

Orford, N. H.

February 17, 1906. River in general frozen. A strip of open 

water, beginning at bridge, extended about 1,000 feet downstream. 

This was about 100 feet wide and approximately in the middle of the 

channel. The ice was rough in places and numerous ice cakes were 

frozen in, owing to high water and a partial going out of the ice during 

January. There were about 11 inches of snow on the ice.

Bench marks, consisting in most cases of spikes in trees, were 

established along each bank by a double-rodded line of levels. 

Soundings for determination of cross section were made at 100 feet, 

250 feet, and 516 feet upstream from the gage. The level was set on 

the ice in the middle of the river, and water-surface elevations were 

determined on both banks at each section at holes cut in the ice. The 

following table gives results of the best set of observations:

Slope determinations and value of'n" on Connecticut River at Orford, N. H., February 17,

1906.

[Gage height to water surface, 6.65 feet; gage height to bottom of ice, 5.15 feet; gage height to top of ice 

6.67 feet; discharge, 2,070 second-feet.]

Distance 

of section 

from

gage.

Feet.

516

250

100

Width 

below 

ice.

Feet.

302

340

329

Area 

below 

ice.

Sq. ft.

2,110

1,890

1,730

Velocity.

Ft.per

sec.

0.98

1.10

1.20

Wetted 

Perimeter.

Feet.

605

685

659

Hydraulic 

Radius.

Feet.

3.49

2.76

2.63

Distance 

between 

sections.

Feet.

266

| 150

Difference in elevation of 

water

surface.

Feet.

0.026

.043

Slope.

0.000098

.000287

Average 

Hydraulic 

radius.

Feet.

3.12

2.70

Average velocity.

Ft. per

sec.

1.04

1.15

n.

0.030

.042

March 15, 1906. The conditions were about the same as during 

February, but the strips of open water were considerably shorter and 

narrower. There was no snow on the ice. Iron rods 4 or 5 feet long 

were driven into the bank to within about 6 inches of the water surface in holes cut in the ice. These were located on each bank at sections 100 feet, 296 feet, and 516 feet upstream from the gage and the 

elevation of the tops was determined by several series of levels. 

Measurements were then made from these points to the water surface 

with a 2-foot rule. Independent observations were made at each 

point by two men, each man's set being averaged separately and the 

mean of the two sets being finally used. The results were as follows:
88 STREAM FLOW DURING THE FROZEN SEASON.

Slope determinations and value of'n" on Connecticut River at Orford, N. H., March 15,1906.

[Gage height to water surface, 5.62 feet; gage height to bottom of ice, 4.18 feet; gage height to top of ice 

6.67 feet; discharge, 2,070 second-feet.]

i»

M oS

 Sg

® 2 oi; fl *.l

5

Feet.

516

296

100

8

"3

a

!2

^

JYei.

295

330

319

.§

|

OJ

oS

£

Sq.ft.

1,800

. 1,530

1,440

 |

.2

>

Ft, per

sec.

0.83

.98

1.04

J5

OJ

S.

10) £

.Fm.

592

662

640

a

 3

aS

.0

aS^

p», w

Fe^.

3.04

2.31

2.25

a

QJ

Ira

.sg

§0

aS EJQ

m

5

Feet.

I 220

1

I 196

1

0

2

II

£ ^

0)

< '

Feet.

2.67

2.28

£

1'Si 

SD '

oj t*

>

^

F< per

sec

0.90

1.01

t

'E

M

1

2 

3

1

2

3

|fc

H &

aj 1© .

03 2 ^

i2J 'al %

s>§

Q

Feet.

0.020

.020 

.024

.030

.031

.030

Slope.

0.000091

.000091 

.000109

.000153

.000158

.000153

n.

0.030

.030 

.033

.030

.031

.030

Conclusions. The mean value of n for the February ob'sevations is 

0.036, and for the March observations is 0.031. The March series are 

much the more reliable of the two.

DATA FROM OTHER SOURCES.

Up to the present time very little information has been published 

on the flow of streams under ice cover, other than that gathered by 

the United States Geological Survey. a

Raucourt made experiments on the Neva 6 at a point where it is 900 

feet wide and of regular section, the maximum depth being 63 feet. 

When the river was frozen over the maximum velocity (2 feet 7 

inches per second) was found a little below the middle of the deepest 

vertical. It was somewhat less than double the velocity at the surface and bottom, which were nearly equal to each other.

The United States Engineer Corps 0 recently made some currentmeter measurements of flow under ice cover on St. Marys River.

No details of the observations are given, but the general results 

were as follows: (1) The location of the threads of mean velocity was 

found to be at 0.067 and 0.753 depth. (2) The maximum velocity 

was found to be at approximately 0.4 depth. (3) The friction caused 

by the ice was found to be 0.309 of that caused by the bottom.

Further measurements under ice cover on St. Marys River were 

made during 1905, but have not yet been reported for publication.

Considerable data on conditions in the frozen period, duration of 

the frozen season, etc., may be found in the proceedings of the International Meteorological Congress, Chicago, 1893.d

a Water-Sup, and Irr. Papers Nos. 76 (1903) and 95 (1904).

& Humphreys and Abbot, Physics and Hydraulics of Mississippi River, p. 190.

c Kept. Chief of Engineers for 1897, p. 4092.

<*The four great rivers of Siberia: Bull. U. S. Weather Bureau No. 11, 1893.
STREAM FLOW DURING THE FROZEN SEASON. 89

CONCLUSIONS. 

PRACTICABILITY OF WINTER ESTIMATES OF FLOW.

The classification of current-meter gaging stations on page 9 indicates that about one-sixth of them remain open during the winter 

and permit about the same degree of accuracy for winter estimates 

as for those of the summer; they can, therefore, be classed with stations south of the area subject to ice cover. About one-third of these 

stations usually have a smooth, permanent ice cover, and it is probably fair to assume that this is about the proportion at which winter 

estimates that will be fairly reliable can be made without too great 

cost. Undoubtedly there is a further number of stations where good 

estimates can be made if sufficient attention is given by the hydrographer, and particularly if an intelligent gage reader, with ability to 

note and sketch conditions affecting flow, is available.

Stations at dams, in general, give less trouble during the winter 

than current-meter stations, and this should be kept in mind where 

there is any question as to which form of station is preferable.

RECOMMENDATIONS AS TO METHODS.

The study of the flow of streams under ice cover is but just started, 

and in order to systematize the accumulation of data and to provide 

the material in convenient form for future use it is desirable that 

certain general methods be followed.

The methods of obtaining gage heights used should be as described 

on pages 21-23, and the observer should be especially encouraged to 

note any unusual conditions affecting flow, furnishing sketches where 

desirable. It should be kept in mind that what is desired is the 

average thickness of ice, distance from bottom of ice to water surface, 

etc., for the portion of the river near the gage, and that the hole cut 

in the ice should be so located as to give average results; preferably, 

several holes should be cut from time to time. The cost of currentmeter measurements under ice cover can be kept within reasonable 

limits by employing laborers when necessary to cut holes in the ice, 

so as to utilize to better advantage the time of the hydrographer, and 

by using the two-point method of observations at 0.2 and 0.8 depth, 

with a few vertical velocity curves, if possible, for purposes of study. 

In case time is short a single observation at 0.5 depth will give fairly 

good results, the coefficient 0.88 being applied, or if a few vertical 

curves have been taken a closer value of the coefficient can be determined from them.

By following the above suggestions the total time required for a 

gaging will not be usually more than half a day, and the cost will be 

but little greater than that for a gaging under open-water conditions.
90 STREAM FLOW DURING THE FROZEN SEASON.

For depths less than 5 feet it is desirable to use the current meter 

fastened to a rod for convenience in handling and in order that 0.8 

depth may be reached; in fact, this method is generally preferable to 

the use of a cable where depths and velocities are not too great.

Vertical velocity curves should be taken at typical points in the 

cross section when time permits just as for open water. These should 

always be taken just before or after the two or one point observations 

at the point in question to give further information as to the field 

accuracy of these methods, the observations by the point method not 

being incorporated in the vertical velocity curve.

Rating curves should be constructed in each of the two ways 

described on pages 43-46, and the method which seems to give the best 

results should be used. Special efforts should be made to obtain 

gagings for thin ice cover for the purpose of better defining the rating 

curve or coefficient to use under such conditions.

It is believed that the methods previously indicated for discharge 

measurements (pp. 22-24) will give results well within the degree of 

accuracy consistent with .winter estimates of flow, and that less time 

need be spent hereafter on individual gagings. This will make it possible to give more attention to the study and completion of station ratting curves the direction in which the most effort should be expended 

in the immediate future.
INDEX.

Page. 

Air, friction of........................... 15-17,77

Anchor ice, character of.................... 13

See also Ice. 

Barnes, H. T., on formation of ice.......... 11,13

Bed, friction of, comparison of ice friction

and.............................. 77

Buskirk, N. Y., gaging station at, conditions at......................... 42

velocity curves at, for ice cover........". 57

Catskill Creek, gaging station on, conditions at...................... 26-29,38

velocity curves on, for ice cover........ 47,73

Catskill Mountains, streams in, measurements of........................ 21

Chemung, N. Y., gaging station at, conditions at......................... 42

needle ice at, figure showing............ 12

velocity curves at, for ice cover......... 47,73

Chemung River, gaging station on, conditions at......................... 42

needle ice in, figure showing............ 12

velocity curves on, for ice cover........ 47,73

Chippewa, Wis., gaging station at, conditions at......................... 42

Chippewa River, velocity curves on, for ice 

cover...........................

Climate, effect of, on ice formation......... 7

Columbus, Ohio, velocity curves at, for ice

cover........................... 63

Connecticut River, discharge of, relation between ice cover and open flow in. ^6 

gaging station on, conditions at..... 29-30,39

ice on, thickness of..................... 10

slope determinations on................ 87-88

rating curve for ice cover on ........... 45-46

figure showing...................... 45

velocity of, variations in............... 85-86

velocity curves on, for ice cover. 48-51,73,74,77 

figure showing...................... 81

Cost of measurements under ice cover, discussion of....................... 24

Current meter, measurements by, cost of... 24 

measurements by, methods of.......... 22-24

use of................................... 90

Current-meter stations, ice conditions at. 9,26-38

See also Gaging stations. 

Dams, effect of, on ice formation........... 8

gaging stations at, conditions at....... 9

figure showing...................... 24

measurements at................... 25

Des Moines River, gaging station on, conditions at......................... 42

velocity curves on, for ice cover........ 51,74

Page. 

Discharge measurements, accuracy of...... 89,90

effect of freezing on..................... 19-21

figure showing...................... 20

See also Flow; Velocity, etc. 

Droughts, periods of....................... 5

Eau Claire River, gaging station on, conditions at......................... 42

velocity curves on, for ice cover........ 48

Esopus Creek, gaging station on, conditions at...................... 30-32,39

ice on, thickness of..................... 10

velocity curves on, for ice cover...... 52-53,73

Fish River, gaging station on, conditions

at............................ 32-33,39

velocity of, variations in............... 86

velocity curves on, for ice cover... 53-54,73,77 

figure showing...................... 82

Flambeau River, gaging station on, conditions at......................... 42

velocity curves on, for ice cover........ 54

Flow under ice, friction and, relations of. 14-17,

19-21,77

friction and, relations of, figures showing.............................. 20,84

measurements of, accuracy of.......... 89

methods for........................ 89-90

See also Velocity; Discharge. 

Francis, James B., on air friction.......... 16

Freezing, effect of, on slope................. 17-18

effect of, on slope, figure showing....... 17

Freshets, winter, occurrence and character

of............................... 13-14

Friction. See Air, friction of; Ice, friction

of; Bed, friction of. 

Gaging, cost of............................. 24,89

methods of, in closed season...... 21-22,23,89

in open season...................... 6-7

Gaging stations, conditions at............. 26-38

discharge under ice cover at, relations

between open section and...... 46

rating curves for ice cover at........... 43-46

Genesee River, gaging stations on, conditions at......................... 42

velocity curves on, for ice cover...... 55-57,73

Hoosic River, gaging station on, conditions

at............................... 42

 velocity curves on, for ice cover........ 57

Ice, character of............................. 10-13

discharge under, relation between open

flow and........................ 46

flow under.............................. 14-21

measurements of, accuracy of...... 89

formation of, factors affecting..'........ 7-8

91
INDEX.

Page 

Ice, friction of............................ 14-17,77

comparison of bed friction and..... 77

prevalence of............................ 5

roughness of, effect of, figure showing.. 84 

season of, duration of.................. 9-10

thickness of, change in................. 10

effect of, on flow.................... 19-21

figure showing.................. 20

Kennebec River, gaging station on, conditions at...................... 33-34,40

rating curve for ice cover at............ 44-45

figure showing...................... 44

velocity curves on, for ice cover... 58-61,73,77 

figure showing...................... 79

KeosaqB&v Iowa, gaging station at, conditions at......................... 42

velocity curves at, for ice cover......... 54

Kingston, N. Y., gaging station at, conditions at...................... 30-32,39

ice at, thickness of...................... 10

velocity curves at, for ice cover......... 52-53

Kutler's formula, value of'' n " in, under ice

conditions...................... 87-88

Ladysmith, Wis., gaging station at, conditions at......................... 42

velocity curves at, for ice cover......... 54

Madison, Me., gaging station at, view of.... 24

Massena Springs, N. Y., gaging stations at,

conditions at................... 42

 velocity curves at, for ice cover......... 64,73

Maumee River, gaging station on, conditions at......................... 42

velocity curves on, for ice cover........ 62,74

Middlebury, Vt., gaging station at, conditions at......................... 42

Minimum flow, period of................... 5

Mohawk River, velocity curves on, for ice

cover. ........................ 62-63,73

Mount Morris, N. Y., gaging stations at,

conditions at................... 42

velocity curves at, for ice cover......... 55,73

Needle ice, character of..................... 10-11

. effect of, on flow measurements........ 12

formation of............................ 8

conditions of....................... 11

movement in........................... 11-12

See also Ice. 

Neva River, velocity of, under ice.......... 88

Newpaltz, N. Y., gaging station at, conditions at...................... 35-37,40

rating curve for ice coVer at............ 43-44 -

figure showing...................... 43

velocity curves at, for ice cover... 66-68,73,77 

figures showing..................... 43,80

North Anson, Me., gaging station at, conditions at...................... 33-34,40

rating curve for ice cover at............ 44-45

figure showing...................... 45

velocity curves at, for ice cover... 58-61,73,77 

figure showing...................... 79

Olentangy River, velocity curves on, for ice

cover........................... 63

Orford, N. H., gaging station at, conditions

at............................ 29-30,39

ice at, thickness of...................... 10

Orford,N.H.,slope determinations at..... 87-88

rating curve for ice cover at............ 45-46

figure showing...................... 45

velocity at, variations in............... 85-86

velocity curves at, for ice cover... 48-51,73,77 

figure showing...................... 81

Otter Creek, gaging station on, conditions

at............................... 42

Precipitation, flow estimates from......... 25-26

Raquette River, gaging stations on, conditions at......................... 42

velocity curves on, for ice cover........ 64,73

Rating curves, construction of............. 90

details of............................... 4£-46

Raucourt, , velocity measurements by.. 88 

Richmond, Vt., gaging station at, conditions at...................... 37-38, il

gaging station at, view of.............. 24

velocity curves at, for ice cover... 70-71,74,77 

Rochester, N. Y., gaging stations at, conditions at......................... 42

velocity curves at, for ice cover...... 56-57,73

Rondout Creek, gaging station on, conditions at...................... 34-35,40

velocity curves on, for ice cover .. 65,73,74,77 

Rosendale, N. Y., gaging ttation at,

conditions at................ 34-35,40

velocity curves at, for ice cover...... 65,73,77

St. Marys River, velocity of, under ice...... 88

Sandy River, gaging station at, view of.... 24

Sherwood, Ohio, gaging station at, conditions at......................... 42

velocity curves at, for ice cover......... 62

Slope, determination of, under ice conditions

............................17-18, 87-88

measurement of stream flow by........ 7

variation in, due to freezing............ 17-18

diagram showing................... 17

Snow, effect of, on formation of ice......... 13

effect of, on stream flow.............. 5,25-26

evaporation of.......................... 26

South Cairo, gaging station at, conditions

at............................ 26-29,38

velocity curves at, for ice cover......... 47,73

Springs, temperature of..................... 8

Stearns, F. P., on form of vertical velocity

curves.......................... 75-76

Streams, character of, effect of, on ice formation ........................... 7,8

flow of. Sec Flow; Disharge: Velocity;

etc. 

Surface ice, character of.................... 11

See also Ice. 

Twin Rock Bridge, N. Y., gaging station at,

conditions at................... 42

velocity curves at, for ice cover......... 69,74

Utica, N. Y., velocity curves at, for ice

cover........................ 62-63,73

Velocities, mean and 0.2 and 0.8 depth, relations of ...................*.... 83-85

Velocities, mid depth and mean, relations of .82-83

Velocity, measurement of stream flow by.. 6-7

position of maximum thread of......... 81-82

position of mean thread of.............. 79-81

observations on, accuracy of........... 89

variation in, at different depths......
INDEX. 93

Page. 

Vertical velocity curves for ice cover, change

of, with change of stage........ 80

change of, figures showing.............. 79,81

comparison of curves without ice cover

and ............................. 78-79

figure showing...................... 78

depth and relations of, figure showing... 83 

details of................................ 46-71

form of................................. 75-77

figures showing... 75,78,79,80,81,82,83,84 

relation of depth and velocity to... 

rough ice, and relations of, figure

showing......................... 84

summaries of........................... 72-74

Wallagrass, Me., gaging station at, conditions at.......................32-33,39

velocity at, variations in............... 86

velocity curves at, for ice cover.... 53-54,73,77

figure showing...................... 82

Wallkill River, discharge of, relation between ice cover and open water 

at............................... 46

gaging station on, conditions at.... 35-37,40

rating curve for ice cover at........ 43-44

Wallkill River, gaging station on, rating

curve for ice cover at, figure showing. 43 

velocity curves on, for ice cover.........66-68,

73,74,77,78 

figures showing..................... 43,80

Waterway, area of, change in, due to freezing.............................. 18

Weirs, measurement of stream flow by.... 6

West Canada Creek, gaging station on, conditions at....................... 42

velocity curves on, for ice cover........ 69,74

Winooski River, gaging station on, conditions at...................... 37-38,41

gaging station on, view of.............. 24

velocity curves on, for ice cover,. 70-71,74,77 

Winter, conditions during.................. 7-14

conditions during, classification of. .... 8-9

observations during, accuracy of....... 89

See also Ice. 

Winter records, accuracy of................ 89

discussion of............................ 26-87

importance of.......................... 5

methods of obtaining................... 21-26

See also Gaging.

CLASSIFICATION OF THE PUBLICATIONS OF THE UNITED STATES GEOLOGICAL

SURVEY.

[Water-Supply Paper No. 187.]

The serial publications of the United States Geological Survey consist of (1) Annual 

Reports, (2) Monographs, (3) Professional Papers, (4) Bulletins, (5) Mineral 

Resources, (6) Water-Supply and Irrigation Papers, (7) Topographic Atlas of United 

States folios and separate sheets thereof, (8) Geologic Atlas of the United States 

folios thereof. The classes numbered 2, 7, and 8 are sold at cost of publication; the 

others are distributed free. A circular giving complete lists can be had on application.

Most of the above publications can be obtained or consulted in the following ways:

1. A limited number are delivered to the Director of the Survey, from whom they 

can be obtained, free of charge (except classes 2, 7, and 8), on application.

2. A certain number are delivered to Senators and Representatives in Congress 

for distribution.

3. Other copies are deposited with the Superintendent of Documents, Washington, 

D. C., from whom they can be had at prices slightly above cost.

4. Copies of all Government publications are furnished to the principal public 

libraries in the large cities throughout the United States, where they can be consulted by those interested.

The Professional Papers, Bulletins, and Water-Supply Papers treat of a variety of 

subjects, and the total number issued is large. They have therefore been classified 

into the following series: A, Economic geology; B, Descriptive geology; C, Systematic geology and paleontology; D, Petrography and mineralogy; E, Chemistry and 

physics; F, Geography; G, Miscellaneous; H, Forestry; I, Irrigation; J, Water storage; K, Pumping water; L, Quality of water; M, General hydrographic investigations; N, Water power; 0, Underground waters; P, Hydrographic progress reports. 

This paper is the nineteenth in Series M, the complete list of which follows 

(WS=Water-Supply Paper):

SERIES M GENERAL HYDROGRAPHIC INVESTIGATIONS.

WS 56. Methods of stream measurement. 1901. 51 pp., 12 pis.

WS 64. Accuracy of stream measurements, by E. C. Murphy. 1902. 99 pp., 4 pis.

WS 76. Observations on the flow of rivers in the vicinity of New York City, by H. A. Pressey. 1902.

108 pp., 13 pis.

WS 80. The relation of rainfall to run-off, by G. W. Rafter. 1903. 104 pp. 

WS 81. California hydrography, by J. B. Lippincott. 1903. 488 pp., 1 pi. 

WS 88. The Passaic flood of 1902, by G. B. Hollister and M. O. Leighton. 1903. 56 pp., 15 pis. 

WS 91. Natural features and economic development of the Sandusky, Maumee, Muskingum, and

Miami drainage areas in Ohio, by B. H. Flynn and M. S. Flynn. 1904. 130 pp. 

WS 92. The Passaic flood of 1903, by M. O. Leighton. 1904. 48 pp., 7 pis. 

WS 94. Hydrographic manual of the United States Geological Survey, prepared by E. C. Murphy,

 "J.C.Hoyt, and G.B. Hollister. 1904. 76pp., 3 pis.

WS 95. Accuracy of stream measurements Cseconct edition), by E. C. Murphy. 1904. 169 pp., 6 pis. 

WS 96. Destructive floods in the United States in 1903, by E. C. Murphy. 1904. 81 pp., 13 pis. 

WS 106. Water resources of the Philadelphia district, by Florence Bascom. 1904. 75 pp., 4 pis. 

WS 109. Hydrograpfiy of tne Susquehanna River drainage basin, by J.C. Hoyt and R. H. Anderson.

1904. 215 pp., 28 pis.