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WATER SUPPLY

OF

ST. MARY AND MILK RIVERS

1898-1917

BY

B. E. JONES

United States Geijlogical Survey AND

R. J. BURLEY

Reclamation Service of Canada

Prepared under the direction of the

United States Geological Survey, United States Reclamation Service

and Reclamation Service of Canada

WASHINGTON

GOVERNMENT I>tlINTING OFFICE

1920

^

WATER SUPPLY /^^y

ST. MARY AND MILK RIVERS

1898-1917

BY

B. E. JONES

United States Geological Survey AND

R. J. BURLEY

Reclamation Service of Canada

Prepared under the direction of the . United States Geological Survey, United States Reclamation Service and Reclamation Service of Canada

WASHINGTON

GOVERNMENT PRINTING OFFICE

1920

\

a^

INTERNATIONAL JOINT COMMISSION

UNITED STATES Obadiah Gardner, Chairman Clarence D. Clark

William H. Smith, Secretary

CANADA Charles A. Magrath, Chairman Henry A. Powell, K. C. Sir William Hearst, K. C. M. G.

Lawrence J. Burpee, Secretary

LIBRARY OF CONGRESS

IVIAR9-1921 I

DOCUMENTS u,'.^3ION

'^ CONTENTS.

"^ Page.

*^ Letter of transmittal * 7

CIT" Authorization of work 9

Scope of report 9

Definition of terms.: 10

Explanation of data.. 11

Accuracy of stream -flow data, by N. C. Orover and J. C. Hoyt. . 12

Degree of accuracy required 12

Conditions affecting accuracy of records of daily discharge, ... 13

Accuracy of monthly or yearly means 18

St. Mary River basin •. 18

General features 18

Gaging station records. ,-., ,. 21

Stations on main stream. 21

St. Mary River near Babb, Mont 21

St. Mary River below Swiftcurrent Creek, at Babb, Mont 35

St. Mary River at Cook 's ranch, Alta. , near international boundary. 43

St. Mary River near Kimball, Alta., near international boundary . " 53

St. Mary River near Lethbridge, Alta 64

Stations on tributaries 72

Swiftcurrent Creek at Many Glacier, Mont 72

Swiftcurrent Creek below Sherburne Lake dam, Mont 77

Swiftcurrent Creek near Babb, Mont 82

Kennedy Creek near Babb, Mont 90

Boundarjt Creek at Fidler 's ranch, Alta 91

Rolph Creek near Taylorville, Alta 95

Rolph Creek near Kimball, Alta 96

Lee Creek at Layton 's ranch, Alta 102

Lee Creek at Cardston, Alta 107

Pinepound Creek near Spring Coulee, Alta 112

Pothole Creek near IVIagrath (upper station ) , Alta 116

Pothole Creek, near Magrath (lower station), Alta 120

Stations on canals 123

U. S. Reclamation Service St. Mary canal at Hudson Bay divide,

near Browning, Mont. 123

Fidler Brothers' ditch at Boundary Creek, Alta 124

Alberta Railway & Irrigation Co. 's canal at Kimball, Alta 125

Alberta Railway & Irrigation Co.'s canal near Kimball, Alta 129

Alberta Railway & Irrigation Co. 's canal at Spring Coulee, Alta . . . 134

Miscellaneous measurements 138

Milk River basin 140

General features 140

Gaging-station records 143

Stations on main stream 143

South Fork of Milk River near international boundary 143

South Fork of Milk River at Mackie's ranch, Alta 155

Milk River at Milk River, Alta ". 160

Milk River at Writing-on-Stone Police Dctadinient, Alia 169

Milk River at Peiidaut d'Oreille i'oiit^e Delachmiml . Ailu 176

Milk River at eastern crossing of international boundary, Mont. . . 183

3

4 CONTENTS. -

Milk River basin — Continued.

Gaging-station records — Continued.

Stations on main stream — Continued. . Page.

Milk River at Havre, Mont 193

Milk River at Chinook, Mont 211

Milk River at Malta, Mont 212

Milk River at Hinsdale, Mont 226

Milk River near Vandalia, Mont 231

Stations on tributaries '. '. 235

North Fork of Milk River near Browning, Mont 235

North Fork of Milk River near international boundary 237

North Fork of Milk River at Knight's ranch, Alta 246

North Fork of Milk River near Mackie's ranch, Alta 249

Deer Creek at Dickinson's ranch, Alta 252

Deer Creek at Deer Creek Cattle Co. 's ranch, Alta „ 254

Lodge Creek at Hartt's ranch, Alta 256

Lodge Creek at Hester's ranch, Alta 259

Lodge Creek at international boundary 261

Lodge Creek near Chinook, Mont 268

Thelma Creek at English's ranch near Thelma, Alta.* 270

Middle Creek at MacKinnon's ranch, Alta 274

Middle Creek at Ross's ranch, Sask 279

Middle Creek at Hammond 's ranch, Sask 286

Battle Creek at Tenmile Police Detachment, Sask 292

Battle Creek at Wilkes's ranch, Sask 300

Battle Creek at Stirling's ranch, Sask 307

Battle Creek at Nash 's ranch, Sask 308

Battle Creek at international boundary, Sask . . ^ 316

Battle Creek near Chinook, Mont 317

Sixmile Creek at Soderstrom's ranch, Sask 329

Sixmile Creek at Spangler's ranch, Sask 331

Tenmile Creek near Tenmile Police Detachment, Sask 337

Frenchman River near Belanger, Sask. 342

Frenchman River at Gordon's ranch, Sask 344

Frenchman River at Phillip 's ranch, Sask • ■. 345

Frenchman River at Eastend, Sask 351

Frenchman River at " 76 " ranch, Sask 358

Frenchman River at Huff's ranch, Sask 362

Frenchman River at Buzzard 's ranch, Sask 363

Frenchman River at Martin's ranch, Sask .' 366

Frenchman River at international boundary 368

Oxarart Creek at Wylie's ranch, Sask 370

Sucker Creek at Gilchrist's ranch, Sask. 378

Belanger Creek at Garrison's ranch, Sask 385

Belanger Creek at Oakes 's ranch, Sask 388

Lonepine Creek at Hewitt's ranch, Sask 393

Davis Creek at Drury 's ranch, Sask 399

Fairwell Creek at Drury 's ranch, Sask 405

Blacktail Creek at Garissere's ranch, Sask 412

North Branch of Frenchman River at Cross's ranch, Sask 414

Rose Creek at Dorrell, Sask 422

Mule Creek at Gunn's ranch, Sask. 426

Bate Creek at Bate's ranch, Sask 429

Denniel Creek near Val Marie, Sask 432

Bigbreed Creek near Buzzard's ranch, Sask 436

CONTENTS. 5

Milk River basin — Continued.

Gaging-station records — Continued.

Stations on tributaries — Continued Page.

Littlebreed Creek, near Buzzard's ranch, Sask 439

Beaver Creek near Malta, Mont 441

Beaver Creek near Saco, Mont 443

Beaver Creek overflow near Bowdoin, Mont 447

Rock Creek near Barnard, Mont 452

Rock Creek near Hinsdale, Mont '. 455

Horse Creek near Barnard, Mont 462

McEachran Creek at McCoy's ranch, Sask 465

East Branch of McEachran Creek at McCoy's ranch, Sask 467

Porcupine Creek at Nashua, Mont 468

Stations on canals 475

Fort Belknap canal near Chinook, Mont 475

Winter- Anderson canal near Chinook, Mont 484

Paradise Valley canal near Chinook, Mont 485

Harlem canal near Zurich, Mont 493

Agency ditch near Harlem, Mont 501

Deer Creek Cattle Co's west ditch, near St. Kilda, Alta 507

Deer Creek Cattle Co.'s east ditch near St. Kilda, Alta 508

Fornfeist ditch, near St. Kilda, Alta 510

H. T. Clark north ditch, near Eagle Butte, Alta 511

H. T. Clark south ditch, near Eagle Butte, Alta 511

English ditch near Thelma, Alta 512

Reser ditch near Chinook, Mont 514

West Fork ditch near Chinook, Mont 514

Lindner ditch near Battle Creek, Sask 516

Marshall & Gaff ditch near Tenmile Police Detachment, Sask . . . 520

J. A. Gaff ditch near Battle Creek, Sask 520

Henry ditch near Battle Creek, Sask 522

Wilson ditch near Battle Creek, Sask 523

Gilchrist ditch near Consul, Sask 523

Richardson ditch near Consul, Sask 524

Jas. McKinnon ditch near Consul, Sask 525

Stirling & Nash ditch near Consul, Sask 525

Cook canal near Chinook, Mont 527

Matheson canal near Chinook, Mont 534

Wood & Anderson south ditch from White Mud Coulee, Sask 540

Wood & Anderson ditch near Coulee, Sask 541

Spangler ditch near Battle Creek, Sask 541

Henry ditch from Halfway Coulee, Sask 544

Strong's ditch at Eastend, Sask 544

Morrison's ditch near Eastend , Sask 549

Maple Creek Cattle Co.'s ditch near Oxarat, Sask 551

F. Cross's ditch near Dorrell, Sask 551

Barroby ditch near Ravenscrag, Sask 554

A. M. Cross's ditch near Eastend, Sask * 554

Bolingbroke ditch near Eastend , Sask 555

Bowroy ditch near Barnard, Mont 55G

Rock Creek canal near Hinsdale, Mont 557

Floods in Milk River basin 55S

Miscellaneous measurements 559

List of gaging stations 579

Publications relating to water resources 58 1

Index 5S:5

ILLUSTKATIONS.

Page.

Plate I. Map of St. Mary and Milk River basins In pocket.

11.^ A, St. Mary River near Babb, Mont., looking upstream ; B, Gaging station on St. Mary River near Kimball, Alta., at international boundar)'- 21

III. Hydrographof St. Mary River at Cook's ranch, near international

boundary, 190.3-1912 In pocket.

IV. Hydrograph of St. Mary River near Kimball, Aita., at interna-

tional boundary, 1908-1917 In pocket.

V. Hydrograph of St. Mary River near Lethbridge, Alta., 1911-

1917 In pocket.

VI. A, Gaging station on Swiftcurrent Creek at outlet of McDermott Lake, Many Glacier, Mont.; B, Gaging station below Sherburne

dam on Swiftcurrent Creek, Mont 72

VII. United States Reclamation Service St. Mary canal: A, Siphon

crossing St. Mary River; B, Drop No. 2 123

VIII. Alberta Railway & Irrigation Co.'s canal: A, Intake and dam,

Kimball, Alta. ;B, Flume No. 2, main canal below Magrath, Alta. 125 IX. Alberta Railway & Irrigation Co.'s canal: A, Head gates on Spring

Coulee; B, Waste gates 134

X. A, Gaging station of Canadian Reclamation Service on Milk River, at Milk River, Alta.; jB, International gaging st-ation on Milk

River at eastern crossing . .• 160

XI. Hydrograph of Milk River at Milk River, Alta., 1909-1917 ... In pocket. XII. Hydrograph of Milk River at eastern crossing of international

boundary, 1909-1917 In pocket.

XIII-XIV. Hydrograph of Milk River at Havre, Mont., 1903-1917 In pocket.

XV. Dodson dam on Milk River near Dodson, Mont., between Havre and Malta: A, Before installation of movable crest gates; B,

Movable crest gates and service bridge in place 212"

XVI -XVII. Hydrograph of Milk River at Malta, Mont., 1903-1917 In pocket.

XVIII. Hydrograph of Milk River at Hinsdale, Mont., 1908-1914.. In pocket. XIX. Vandalia dam of the United States Reclamation Service, Vandalia,

Mont. : A, Pool above dam; B, Crest gates — two closed, one open. 231 XX. Hydrograph of Milk River near Vandalia, Mont., 1915-1917. . In pocket. XXI. A, International gaging station on North Fork of Milk River near international boundary; B, North Chinook Irrigation Co.'s

dam on Lodge Creek near Chinook, Mont 237

XXII. Hydrograph of Lodge Creek near international boundary, 1910-

1917 In pocket.

XXIII. Hydrograph of Battle Creek at Nash's ranch, Sask., 1910-

1917 - In pocket.

XXIV. A, Enright & Strong's dam on Frenchman River near Eastend,

Sask.; B, Fort Belknap Indian dam for Agency ditch, on

Milk River near Harlem, Mont 351

XXV. Hydrograph of Frenchman River at Eastend, Sask., 1909-

1917 In pocket.

XXVI. Hydrograph of Frenchman River at Martin's ranch, Sask., 1914-

1917 In pocket.

6

LETTER OF TRANSMITTAL.

Department of the Interior, Canada,

Reclamation Service,

Ottawa, May 19, 1919. International Joint Commission,

Washington, D. C, and Ottawa, Canada. Gentlemen : In accordance with the authorization of the Inter- national Joint Commission contained in its Order No. 157, made at New York City February 4, 1918, there are transmitted herewith records of flow of streams and canals in the St. Mary and Milk River basins, collected by the United States Geological Survey in cooper- ation with the United States Reclamation Service and by the Reclamation Service of Canada. Respectfully submitted.

John C. Hoyt, Chief, division of surface waters,

United States Geological Survey, E. F. Drake, Director, Reclamation Sei^vice of Canada.

7

WATER SUPPLY OF ST. MARY AND MILK RIVERS,

1898-1917.

By B. E. Jones and R. J. Burley.

AUTHORIZATION OF WORK.

On January 12, 1918, the Secretary of the Interior suggested to the International Joint Commission that the commission should arrange for the compilation and publication of all stream-flow data collected at both the international and national stations in the Milk and St. Mary River basins, the data to be agreed upon by the United States Geological Survey, represented by John C. Hoyt, hydrauhc engineer, and the Irrigation Branch [now the Reclamation Service] of the Department of the Interior, Canada, represented by E. F. Drake, superintendent of irrigation, and to be published in the regular reports of the commission.

The commission's favorable action on this suggestion was com- municated to the Secretary of the Interior under date of February 18, 1918, by Mr. Whitehead Kluttz, the secretary of the commission, who stated that a similar suggestion had been made by the Canadian superintendent of irrigation.

Under the authority thus conferred on Messrs. Hoyt and Drake, Mr. B. E. Jones, hydrauhc engineer of the United States Geological Survey, was directed to compile the records collected in the United States, and Mr. R. J. Burley, chief engineer, drainage division, of the Canadian Reclamation Service, was directed to compile the Canadian records.

SCOPE OF REPORT.

Hydrometric work in the area drained by St. Mary and Milk rivers

was begun in 1897, when the United States Geological Survey

established a station on Milk River at Chinook, Mont. In 1898 this

station was moved to Havre, Mont., about 20 miles upstream. In

Canada records were first collected at a station established by the

Alberta Railway & Irrigation Co. in 1905 on St. Mary River at

Kimball, Alta. Additional stations have been established from

time to time in both countries, and at the end of December, 1917,

recol'ds had been obtained at 79 gaging stations on the main streams

and their tributaries and at 4 1 stations on canals.

9

10 WATER SUPPLY OF ST. MARY AND MILK RIVERS, 1898-1917.

Most of the records here assem])ied appeal^ as originally published in the reports of the Reclamation Service of Canada ^ and the United States Geological Survey, but some have been revised to free them from errors indicated by later data. The most notable need for such revisions was m the older estimates of winter flow, many of which, for stations on Milk E-iver, were based on inadequate data and have therefore been omitted from the compilation. Tables of daily discharge not heretofore published have been taken from the original records.

DEFINITION OF TERMS.

The volume of water flowing in a stream — the '^run-off" or '^dis- charge"— is expressed in various terms, each of which has become associated with a certain class of work. These terms may be divided into two groups — (1) those that represent the rate of flow, as second- feet, gallons per minute, miner's inches, and discharge in second-feet per square mile, and (2) those that represent the actual quantity of water, as run-off in depth of inches, acre-feet, and millions of cubic feet. The principal terms used in this report are second-feet, second- feet per square mile, run-off in inches, and acre-feet. They may be defined as foUows:

'^ Second-feet" is an abbreviation for ''cubic feet per second." A second-foot is the rate of discharge of water flowing in a channel of rectangular cross section 1 foot wide and 1 foot deep at an average velocity of 1 foot per second. It is generally used as a fundamental unit from which others are computed by the use of the factors given in the tables of convenient equivalents.

'"Second-feet per square mile" is the average number of cubic feet of water flowing per second from each square mile of area drained, on the assumption that the run-off is distributed uniformly both as regards time and area.

"Eun-off (depth in inches)" is the depth to which an area would be covered if all the water flowing from it in a given period were uniformly distributed on the surface. It is used for comparing run-off with rainfall, which is. usually expressed in depth in inches.

An "acre-foot," equivalent to 43,560 cubic feet, is the quantity required to cover an acre to the depth of 1 foot. The term is com- monly used in connection with storage for irrigation.

The following terms not in common use are here defined :

"Stage-discharge relation," an abbreviation for the term "relation of gage height to discharge."

"Control," "controUing section," and "point of control," terms used to designate the section or sections of the stream below the gage which determine the stage-discharge relation at the gage. It should

1 Formerly Irrigation Branch, Department of the Interior, Canada.

WATER SUPPLY OF ST. MARY AND MILK RIVERS; 1898-1917. 11

be noted that the control may not be the same section or sections at all stages.

, The '^ point of zero flow" for a given gaging station is that point on the gage — the gage height — to which the surface of the river would fall if there were no flow.

EXPLANATION OF DATA.

The base data collected at gaging stations consist of records of stage, measurements of discharge, and general information used to supplement the gage heights and discharge measurements in deter- mining the daily flow. The records of stage are obtained either from direct readings on a staff gage or from a water-stage recorder that, gives a continuous record of the fluctuations. Measurements of dis- charge are made with a current meter by the general methods out- lined in standard textbooks on the measurement of river discharge.

From the discharge measurements rating tables are prepared that give the discharge for any stage, and these rating tables, when ap- plied to the gage heights, give the discharge from which the daily, montlily, and jearlj mean discharge is determined.

The data presented for each gaging station in the area covered by this report comprise a description of the station, a table giving results of discharge measurements, a table shov/ing the daily discharge of the stream, and a table of monthly and yearly discharge and run-off.

If the base data are insufficient to determine the dail}" discharge, tables giving daily gage heights and results of discharge measure- ments are published.

The description of the station gives, in addition to statements re- garding location and equipment, information in regard to any con- ditions that may affect the constancy of the stage-discharge relation, covering such subjects as the occurrence of ice, the use of the or tr earn for log driving, shifting of channel, and the cause and effect of back- water; it gives also information as to diversions that decrease the flow at the gage, artificial regulation, maximum and minimum recorded stages, and the accuracy of the records.

The table of daily discharge in general gives the discharge in second-feet corresponding to the mean of the gage heights read each day. At stations on streams subject to sudden or rapid diurnal iTuc- tuation the discharge obtained from the rating table and the mean daily gage height may not be the true mean discharge for the day. If such stations are equipped with water-stage recorders tlio mean daily discharge may be obtained by weigliting discharge for parts of the day.

In the table of monthly discharge the coUimii hejicied "Maximum" gives the mean flow for tlie day when th(^ menu gage heiglit was highest. Ab the gage height is the mean for the day it does not

12 WATEK SUPPLY OF ST. MARY AND MILK ER^ES, 1898-1917.

indicate correctly the stage when the water surface was at crest height and the corresponding discharge was consequently larger than given in the maximum column. Likewise, in the column headed ^'Mini- mum" the quantity given is the mean flow for the day when the mean gage height was lowest. The column headed '^Mean" is the average, flow in cubic feet for each second during the month. On this average flow computations recorded in the remaining columns, which are defined on page 10, are based.

ACCURACY OF STREAM-FLOW DATA.^

By N. C. Grover and J. G. Hoyt. DEGHEE OF ACCURACY REQUIRED.

The laws relating to many natural phenomena have been reduced, to an exact science; those for many more are largely empirical and are based on experiments and assumptions that only approximate the truth. In the empirical class are included the laws of the science of hydrology and especially of that branch of hydrology which relates to the flow of water in open channels. It is possible, nevertheless^ by carefully considering the various factors, to reduce the incidental errors so that resulting records will be sufficiently accurate for tha purposes for which stream-flow data are required.

In most problems two degrees of accuracy must be considered- first, that which is practicable or possible to obtain, and, second, that which is desirable or necessary. The obtainable accuracy of stream- flow data depends largely on the amount of money available for their collection. The desirable accuracy depends on the proposed use of the data.

Stream-flow records have three principal uses — first, in predicting flow, generally in connection with the design of hydraulic works; second, in the immediate operation of hydraulic works; and, third, in studying conditions of past flow, usually in connection Vvdth the adjustment of water rights. For the second and third uses data as accurate as can be collected may be needed. In considering the first use, however, it should be remembered that both the total flow of a stream and its regimen change from year to year, and that the conditions existing at any particular time may never recur. For this use, therefore, reasonably accurate records that extend over a considerable period are much more valuable than extremely accurate data covering a short period.

Studies of the accuracy of stream -flow data serve to determine the methods to be followed in their collection so that the records may meet the requirements of the proposed uses. Notes on accuracy that accompany stream-flow records should give, first, information by

J Republished from Contributions to the hydrology of the United States, 1916: U. S. Geol. Survey Water-Supply Paper 400, pp. 53-59, 1916.

•WATEE SUPPLY OF ST. MAEY AND MILK EIVERS, 1898-1917. 13

which the technical man may study the records and judge their ac- curacy, and, second, information by which both the general and the technical user may judge the reliability of the records without mak- ing a study. These two uses should be kept in mind in preparing the data as well as the notes. Consideration of the accuracy of records to be collected at any station should begin with the reconnaisance for the site and continue through the selection, establishment, mainte- nance, and operation of the station, the computation and interpreta- tion of the data, and the preparation of the records for publication. In other words, records should be collected with the desired degree of accuracy in view instead of leaving it to be determined after the field data are collected and estimates have been made.

In this discussion of accuracy it has been assumed that personal or instrumental errors, both in field and office, are reduced to a negli- gible amount. In order that this assumption may be true, however, all operations connected with the work must be carefully conducted and instruments must be kept in proper working order.

The conditions affecting accuracy may introduce errors that may be consistently compensating, consistently cumulative, or alternately compensating and cumulative. Therefore care must be taken to de- termine the way in which the incidental errors affect the results.

CONDITIONS AFFECTING ACCURACY OF BECORDS OF DAILY

DISCHARGE.

The obtainable accuracy of records of daily discharge of a stream depends on the following factors, information in regard to which will determine the methods of operation and give a basis for evaluat- ing the records after they are collected:

1. Permanence of the stage-discharge relation.

2. Precision with which the discharge rating curve is defined.

3. Refinement of gage readings.

4. Frequency of gage readings.

5. Methods of applying the daily gage heights to the rating table to obtain the daily discharge.

Permanence of the stage-discharge relation. — The permanence of the relation of discharge to stage as determined by the control is a fundamental factor in the collection of records of daily discharge of a stream. It may be disturbed either by a cliange in the control itself or by conditions that counteract the effect of the control, such as backwater from log or ice jams or floods in tributary streams below the station. The general character of the control and the con- ditions that may affect it are determined by inspection. The effec- tiveness of the control, however, can be finally determined only by plotting the results of discharge measurements. If sucli })lotting does not define a smooth curve the inconsistenc}'^ is duo to poor

14 WATEE SUPPLY OF ST. MARY AI?fD MILK RIMERS, 1898-1917.

current-meter measurements of discharge, to instability of the con- trol, or to disturbing influences. If the control is unstable the ac- curacy of the record will depend on the number of the discharge measurements and their distribution as to time and stage.

Errors due to lack of permanence of the stage-discharge relation may be either compensating or cumulative, according to the physical conditions affecting the nature and stability of the control.

Precision of the disch<irge rating curve. — The precision with which the discharge ratmg curve is defined depends on the accuracy of the discharge measurements, their distribution in range, and the per- manence of the control. If the relation of the (discharge to stage were permanent and truly defined by the rating curve and the dis- charge measurements were absolutely accurate a series of measure- ments for a station would plot on a smooth curve. Unfortunately, such ideal conditions do not exist; therefore, a series of measure- ments for a station will plot somewhat discordantly, and the rating curve should be drawn among them in such a way as to represent aver- age conditions. For permanent conditions of control combined with a good measuring section the variations of individual measurements from the mean curve should be compaTatively small and as likely to be plus as minus. The probable error of a rating cm?ve may be computed by the method of least squares and will be a factor in determining the probable error of the estimates of daily discharge.

Errors in determinations of daily discharge resulting from errors in the position of the rating curve will be cumulative for any stage, but may be partly compensating if the curve used lies first on one side and then on the other side of the true curve.

Refinement of gage readings.— RGG.n&DAent of gage readings affects the accuracy of stream-flow data to a degree dependent on the sensitiveness of the station, which in turn is determined by the size and shape of the channel at the control in relation to the quantity of discharge. The sensitiveness is indicated b}^ the magnitude of the change in stage accompanying a given change in discharge. The limiting requirements as to sensitiveness should be a change in stage, that is readable on the gage used for a change of 1 per cent iii dis- charge. In general the more sensitive the station the more accurate the records that can be collected by ordinary methods and the less refinement necessary in the gage readings.

Errors due to lack of refinement in reading will generally be com- pensating, but they may be cumulative when the stage shows only small fluctuations during a considerable period or when they are due to systematic personal errors of the observer.

The degree of refinement in record of stage necessary to give a sufliiciently accurate determination of discharge will vai*y inversely

WATER SUPPLY OF ST. MARY AND MILK RTVERS, 1898-1917. 15

with, the stage and is determined by the sensitiveness of the station * as disclosed by a study of the discharge rating curve.

Gages are usually read to hundredths, quarter-tenths, half -tenths, or tenths. The resulting absolute errors of observations in individual readings are shown by the following table :

Absolute errors for individual gage readings.

Readings to hundredths

Readings to quarter-tenths .

Readings to half-tenths

Readings to tenths

Maximtun	Average
error.
Foot.	Foot.
0.005	0. 0025
.012	.006
.025	.012
.05	.025

Fractional

part of a

tenth of a

foot.

T5

For staff and chain gages 2 per cent has been selected, more or less arbitrarily, as the limit of allowable average error in a determination of daily discharge due to errors in the determination of mean daily gage height. The table indicates that the maximum error for any ono day is twice the average error, so that the maximum error for any one day may be 4 por cent. According to the law of probabilities the average error in the determination of a monthly mean discharge for fluctuating stages resulting from a 2 per cent average error in the determination of mean daily discharge is about one-third of 1 per cent.

The refinement to which the records of mean daily gage height must be used — whether to hundredths, half-tenths, or tenths — in order to obtain this limit of accuracy in determinations of discharge at any given stage will depend on the percentage of difference in dis- charge for such least differences in gage readings at that stage, as shown by the rating table.

In determining this refinement the engineer should proceed as follows and enter the results in a table of the form given below, in which the Potomac at Point of Rocks, which is read once daily to hundredths, is used as an example.

Limits of accuracy in the use of gage readings.

	Present readings.	Mini- mum height.	Mjni- nuim' dis- cliarge.	Error in discharge duo to error of 0. 1 fool in the gage at niini- ninm disdiarge.	ITse gage heights to—
Station.	Num- ber per day.	To—	Hun- dredths below—	Ihilf- tenths be- tween—	Tenths above—
Potomac River at Point of Jtooks, Md	1	Font. O.Oi	Feet. 0.40	Sec.-ff.	Per coil. 36	Feet. 1.0	Feet. 1.0-2.0	Feet. 2.0

16 WATER SUPPLY OF ST. MARY AND MILK RIVERS, 1898-1917.

The discharge rating table shows that the minimum discharge is 580 second-feet and occurs at gage height 0.4 foot. The difference per tenth between gage heights 0.4 and 0.5 foot is 210 second-feet, or 36.2 per cent of the minimum discharge.

The hmits of stage between which it is necessary to use mean daily gage heights to hundredths, half-tenths, and tenths, respectively, in order not to introduce an average error of over 2 per cent in the determination of daily discharge are shown in the last three columns and are determined by trial by testing values from the discharge rating table at selected haK-foot intervals, as follows:

In testing at the 2-foot gage height for gage records to tenths the difference between the discharge at 2.0 feet and that at 2.1 feet is found to be 360 second-feet. The average error of a mean daily rec- ord to tenths is one-fourth tenth. Therefore at gage height 2.0 feet the average error for such record, expressed in second-feet, is -2^ = 90 second-feet, which is 1.8 per cent of 5,020 second-feet, the discharge at the 2-foot stage. Therefore it is not necessary to use gage-height records closer than 0.1 foot- above the 2-foot stage, as above this stage the average error is less than 2 per cent, which is the allowable error.

A continuation of this analysis shows that in order to keep the error in the determination of discharge resulting from lack of refine- ment in gage readings below 2 per cent, the gage at Point of Eocks should be used to hundredths below the 1-foot stage, to haK-tenths between 1.0 foot and 2.0 feet, and to tenths above 2.0 feet.

For a record obtained with a water-stage recorder the same pro- cedure is f ollov/ed except that the allowable error should be 1 per cent.

For stations T^'ith shifting control the methods of analysis above described can be used only in a general way.

In practice the limits of use of gage heights can be readily deter- mined by the following rules:

Find the stage at which the difference in discharge per tenth is 8 per cent of the discharge at that stage. Gage heights above this stage should be used to tenths.

Find the stage at which the difference in discharge per tenth is 16 per cent of the discharge at that stage. Gage heights below this stage should be used to hundredths.

Gage heights between the two stages thus found should be used to half-tenths.

Frequency of gage readings. — The frequency of gage readings is an important factor in the accuracy of records of streams that are subject to considerable daily fluctuation in stage. To obtain a gage record so accurate that its use with the fating table wiU give the true mean discharge for the day the number of readings should vary, according to the nature of the fluctuations, from one or two daily to a continuous record obtained by some form of water-stage recorder.

WATER SUPPLY OP ST. MARY AND MILK RIVERS^ 1898-1917. 17

To ascertain the frequency required it is necessary to compare the daily discharge obtained from one gage reading daily or the mean of two readings daily with that obtained from the mean of hourly gage heights or by a discharge integrator.

Errors due to insufficient gage readings may be cumulative or com- pensating, or alternately one and the other, according to the nature of the fluctuations in stage.

Methods of applying the daily gage heights to the rating table, — The method of applying daily gage heights to the rating table to ascertain mean daily discharge is determined by the curvature of the rating curve.

Theoretically, the mean daily discharge of a stream is the mean of the discharge for every second during the day. In ordinary compu- tation of daily flow, it is assumed that the rate of discharge through- out the day varies so little or with such regularity that the daily dis- charge may be determined by entering a rating table with a mean daily gage height obtained either from a few observations or from a continuous record made by a water-stage recorder. As discharge is in general an increasing curvilinear function of gage height, the use of a mean daily gage height with a rating table gives a result that is always too small. The magnitude of this error, which wiU vary with the curvature of the rating curve and with the daily range in stage, will determine whether the daily discharge can be ascertained directly by finding a mean daily gage height or indirectly by averag- ing the discharge corresponding to gage heights for shorter inter- vals. Hourly discharge is frequently used. As an ultimate limit the absolute mean discharge for the day may be ascertained by a dis- charge integrator, which operates much as a planimeter operates and contains as an essential element the rating curve of the station. Such an integrator has been devised by E. S. Fuller, formerly assistant engineer, United States Geological Survey.

It is necessary, therefore, to study each gaging station, in order to determine the length of the period that should be used in applying the gage heights to the rating table. In such an investigation a maximum allowable error of 1 per cent is assumed. The amount of daily range in stage allowable for a given mean daily stage,^ in order that errors due to curvature of the rating curve shall not exceed 1 per cent, can be found graphically by constructing a chord to the rating curve such that the horizontal distance, measured by the clischarge scale, from its middle point to the curve equals 1 per cent of the dis- charge at the gage height of the middle poitit. Tlio difference in gage height at the ends of the chord will be the allowable daily range.

123G78''— 20 2

18 WATER SUPPLY OF ST. MARY AND MILK RI^^RS, 1898-1917.

A table of such limits covering the range of stage, used with tables of mean daily stage and range in stage, will indicate the days for which the mean daily discharge can be found directly from the mean daily gage height and those for which more frequent intervals are necessary.

The errors resulting from the application of the gage height to the rating table will in general be cumulative, and their magnitude will vary with the method used in making the computations.

ACCTJIIACY OF MONTHLY OR YEARLY MEANS.

The foregoing discussion of accuracy relates only to determina- tions of daily discharge. For many uses the mean flow for longer periods may be sufficient. The monthly mean is in general use for hydraulic studies. If errors resulting from all causes in the esti- mates of daily discharge are compensating, the probable error in the determination of mean monthly discharge will be much less than the probable error of the individual determinations of daily dis- charge. A careful analysis of the estimates of daily discharge and monthly means computed from them shows that large errors m the dady estimates may be so compensated that the errors in the monthly means are small.

ST. MARY RIVER BASIN. GENERAL FEATURES.

St. Mary River rises in northwestern Montana, on the eastern slope of the Continental Divide (PL I), in a region of perpetual snow and ice. The stream flows out of the Blackfeet Glacier, probably the largest in the Rocky Mountains within the United States, and is joined by at least a dozen lesser streams that unite within a short distance of their sources. The combined waters flow into a lake which is hemmed in by lofty mountains and is known as Upper St. Mary Lake. A short stream through a narrow strip of land connects this lake with Lower St. Mary Lake, the total length of the two being 22 miles.

The river and all its tributaries except Boundary Creek on the west side and Rolph (Willow), Pinepound, and Pothole creeks on the east side rise in the main range of the Rocky Mountains, where the mean annual precipitation amounts to about 60 inches, and occurs in greater part as snow. Although comparatively small, this moun- tainous part of the basin furnishes practically all the water. The stream is subject to great fluctuation during the summer, furnishes water throughout the irrigation season, and maintains fairly constant though low flow during the winter.

WATER SUPPLY OF ST. MARY AND MILK RIVERS^ 1898-1917. 19

Altitudes in the drainage basin in the United States range from 4,000 to 10,000 feet above sea level, and the fall of the river is com- paratively rapid throughout its course, especially between the St. Mary Lakes and the Alberta Railway & Irrigation Co.'s intake. The elevation of the water level of