CONTENTS.Page.Introduction7Factors that modify winter run-offClassificationClimatic factorsPrecipitation and temperatureBarometric pressureChinook windsGeologic factorsTopographic factorsNatural storageLocation, size, and trend of drainage basinsCharacter of streamsVegetational factors .Artificial controlFormation of ice General conditionsSurface iceMethod of formation .Length and severity of cold periodTemperature of affluents 'Velocity of water and. character of bedFluctuations in stageFrazilAnchor iceEffect of ice on relation of stage to dischargeThe control sectionSurface iceGeneral effects -Effect on distribution of velocities in the verticalGaging station studiesValue of workElk River near Big Lake, MinnCrow Wing River at Pillager, Minn -Red River near Grand Forks, N. DakSt. Mary River near Babb, MontRaquette River at Piercefield, N. YFrazilAnchor iceGeneral 03031313132323435373839404242Gaging station studies42Kootenai River at Libby, MontSchroon River at Riverbank, N. Y42483

4CONTENTS.PagftComputation of flow of frozen streams4fMethods available *First methodSecond methodThird methodEye method .Graphic method . -Application of graphic methodField methodsSelection of stationsPower-plant recordsGages -Climatologic recordsDischarge measurementsDetermination of sectionInstrumentsMethodsNumber and costPersonal equipment of the engineerIce notesOffice methodsGeneral featuresComputations -FormsAccuracyDischarge measurementsGage heights1Estimates of daily and monthly dischargeIndex 4F4?4 5]53525&5T5T59596162626364676869696970717272737375

ILLUSTRATIONS.Page.?LATE I. A and Bf Winter measurements on Rum River near Cambridge, MinnII. Winter measurements: A, Vermilion River below VermilionLake, Minn.; B, Bigfork River near Big Falls, MinnIII. Relation between open-water curve and ice measurements:Red River at Grand Forks, MinnIV. Diagrams showing relation between temperature, gageheights, and discharge: Kootenai River at Libby, MontV. Diagrams showing relation between temperature, gage heights,and discharge: Schroon River at Riverbank, N. YVI. Diagrams showing relation between gage heights, backwater,and temperature: Rainy River at International Falls, MinnVII. A, Ice chisel, measuring stick, and bag; B, Winter measurement on Shoal Pond Brook, New Hampshire .1. Diagram showing surface of ground-water table during theperiod from fall to spring2. Diagram comparing temperature and discharge: MississippiRiver above Crow Wing River, Minn3. Thermograph trace from Havre, Mont., January 22-26, 1907,showing increase in temperature caused by a chinook4. Map showing location of Bigfork, Littlefork, and Vermilionrivers, Minn5. Diagram showing relation between flow of Rainy River atInternational Falls and stage in Rainy Lake6. Diagram showing a Average ice period from winter 1876-77 towinter 1895-96 inclusive7. Diagram illustrating distribution of velocity under ice cover:Cannon River at Welch, Minn8. Typical cross section of ice-covered stream and rating curvefor same section9. Relation between open-water curve and ice measurements:- Elk River near Big Lake, Minn10. Relation between open-water curve and ice measurements:Crow Wing River at Pillager, Minn11. Relation between open-water curve and ice measurements:St. Mary River near Babb, Mont12. Relation between open-water curve and ice measurements:Raquette River at Piercefield, N. Y13. Cross section of Chemung River at Chemung, N. Y., showingeffect of frazil 14. Gaging station on Kootenai River at Libby, Mont15. Backwater curve and plotted fictitious discharge measurements for Rainy River at International Falls, Minn16. Diagrams showing relation between temperature, backwater,and discharge: Elk River near Big Lake, Minn17. Diagram showing factors used in making discharge measurements and new form proposed18. Proposed computation 546672

TIE EFFECTS OF ICE ON STREAM FLOW.By WILLIAM GLENN HOYT.INTRODUCTION.The design, installation, and operation of any plant that dependsfor its success upon flowing water demands from those concerned aknowledge of the total flow of the stream and its variation throughout the year, including not only the mean flow but also the maxknumand minimum flow and the periods of their duration.Stream-flow records extending over considerable periods are nowavailable for many streams in the United States, and additionalrecords are being obtained. For open-water periods methods forcollecting stream-flow records have been standardized, the accuracyof such records has been established, and the laws of stream flow havebeen determined. On the other hand, during the winter the presenceof ice affects the flow so much that the laws of flow pertaining to o penchannels are not entirely applicable, and no standard methods forcollecting and interpreting data have been recognized. In manylocalities ice persists in the streams for periods ranging from a fewdays to several months, and, although the conditions resulting fromice are most pronounced in northern regions, they are prevalent overwide areas, and especially at high altitudes. As the minimum flowthe flow that determines the success or failure of most hydraulicworks is most likely to occur during periods when the streams areice-covered and temperatures are low, accurate information concerning this flow is essential.The flow of streams is ascertained primarily by means of the lawof relation between stage and discharge. For most parts of theUnited States this relation remains so nearly constant during periodswhen the stream channels are unobstructed that it can be expressedin rating tables based on occasional discharge measurements, themean daily flow being determined by applying to the table therecords of mean daily stage. During the winter months low temperatures give rise to conditions that frequently disturb the openwater relation between stage and discharge and make the properinterpretation of winter records exceedingly difficult.7

8THE EFFECTS OF ICE ON STREAM FLOW.A report on winter stream flow and its measurement,1 published bythe Survey in 1907, brought together the information available atthat time and formulated for the first time certain laws that relate tothe distribution of velocity under ice and have been found to be applicable under practically all observed conditions. Knowledge ofthese laws has been of great value in making winter measurementsof flow. The report dealt mainly with field operations in makingdischarge measurements, however, and contained little informationin regard to the use of these measurements in estimating dischargefrom daily gage-height records and data concerning ice.Recent studies have added much information in regard to the factors influencing stream flow when ice is present, and especially in regard to the collection and interpretation of winter records. With aview to standardizing, so far as practicable, the methods for ascertaining winter flow, this paper presents the available information onthe subject, discussing the factors that influence the run-off duringthe periods of low temperature, the varieties of ice and their effect onthe applicability of the laws of open-channel flow, and the collectionand interpretation of necessary data. Some of the conclusions derived from the study of these factors differ from those previouslyreached because many of the earlier studies were local, both in scopeand application, whereas effort is here made to deal broadly withconditions whose occurrence is coextensive with ice and low temperatures.The report is based on the experience of the author in Minnesotaduring the winters of 1911-12 and 1912-13, supplemented by observations in Montana by B. E. Jones under the direction of W. A.Lamb, in New York and New England under the direction of C. C.Covert, and in Alberta, Canada, by Messrs. F. H. Peters and P. M.Sauder. Acknowledgment is also due to W. O. Hartwell, E. F.Chandler, S. B. Soule, and B. J. Peterson for assistance in the work.Of the various publications which have been reviewed in connectionwith the preparation of the paper 2 special mention should be madeof the following:Ice formation, with special reference to anchor ice and frazil, by HowardT. Barnes. John Wiley & Sons, New York, 1906.The flow of streams and factors that modify it, with special reference toWisconsin conditions, by Daniel W. Mead: University of Wisconsin Bull. 425,1911.The determination of stream flow during the frozen season, by H. K. Barrows and Robert E. Horton: U. S. Geol. Survey Water-Supply Paper 187, 1907.1 Barrows, H. K., and Horton, R. E., Determination of stream flow during the frozenseason: U. S. Geol. Survey Water-Supply Paper 187, 1907.2 Since this paper was prepared the Commission of Conservation of Canada has published a report on Long Sault Rapids, St. Lawrence River, by A. V. White, with anappendix (No. 25) by Prof. H. T. Barnes, discussing the formation of surface ice, frazil,and anchor ice with special reference to conditions in the St. Lawrence.

FACTORS THAT MODIFY WINTER RUN-OFF.9FACTORS THAT MODIFY WINTER RUN-OFF.CLASSIFICATION.The quantity and distribution of winter stream flow are the results of the combination of factors that may be classified as climatic,geologic, topographic, and vegetational. The climatic factors areprecipitation, temperature, barometric pressure, and winds; thegeologic factors include surface and underground rock structure andtexture; the topographic factors include relief and slope, which determine the character and amount of natural storage, the location,size, and trend of the drainage basin, and the character of thestreams and their tributaries; the vegetational factors comprise notonly forestation but the effects of all plant growth and cultivation.A fifth factor is the result of the artificial control of the streams forwater supply or power.CLIMATIC FACTORS.PRECIPITATION AND TEMPERATURE.The climatic conditions that influence stream flow are probablymore important than any others, but the conditions are so interrelatedthat it is difficult to distinguish the effect of one from that of another.Stream flow during the winter is supplied by precipitation directly,in the form of rain or snow, and indirectly, from melting snow andfrom ground water.Precipitation in the form of snow does not add perceptibly to therim-off of an area until the local temperature rises above the freezingpoint. Rain falling on frozen ground not covered with snow willrun off quickly at a rate depending on the slope, for the frozen surface acts nearly as effectively as a rock stratum in preventing absorption by the ground. Rain falling on snow gradually increases thewater equivalent of the snow to the point of saturation, when it willrun off. Heavy snow on ground whose surface is not frozen maymelt slowly from beneath, sink into the ground, and thus augmentthe supply of ground water. The amount of water held in snowcover naturally varies with variations in altitude and temperature.1At the end of the growing season, generally about the 1st ofOctober in the northern part of the United States, the ground waterhas generally been depleted by the needs of plant growth and byhigh evaporation, and conditions probably vary less from year tomethods of measuring amount of water held in snow storage are described inWeather Bureau Bull. 445, Circular E, 1910; also in article by J. Cecil Alter entitled" Snow surveys for predicting stream flow" : Eng. News, vol. 69, pp. 111Q-1113, May 29,1913.

10THE EFFECTS OF ICE ON STREAM FLOW.year than at any other season.1 From this time until a period whosebeginning ranges from the middle of November to the 1st of December the time depending on the year and locality the groundwater table will tend to rise, since practically no water is needed forplant growth and loss from evaporation rapidly decreases as temperature decreases. After the ground becomes frozen to any considerable depth little water will be added to that stored in the grounduntil the spring breakup, as any surface water tends to run off (seefig. 1). The flow during the winter season therefore depends to alarge extent on the amount of ground water present at the beginning of winter, and this amount in turn depends on the precipitationduring the preceding period of replenishment.The close relation between temperature and winter flow is revealedby a study of the precipitation. Temperature influences the winterrun-off (1) by itseffect on surfaceand ground water," "*" s Frozen ground and (2) by its effect on the character of the precipitation.When the temFIGUBE 1. Diagram showing position of ground-waterperature falls betable during period from fall to spring.low the freezingpoint a certain amount of surface water is changed to ice, and withcontinued low temperature this ice will gradually increase in thicknessto a depth depending on the length and severity of the cold wave. Thewater so frozen will be held until it is released by temperatures underwhich the ice will melt. If such higher temperatures are delayed untilspring, the water from the melting ice will join the run-off frommelting snow and light rain to augment the spring floods. Theamount of water held in storage as ice in stream channels and inshallow ponds may be considerable, particularly on streams so situated that the natural run-off per square mile is low. For example,the low-water flow of Rum River, in Minnesota (PI. I), duringJanuary or February is about 70 second-feet. The river above thegaging station is approximately 100 miles long, its average width isabout 100 feet, and its gradient is small. Ice forms over its entiresurface in thicknesses ranging from 1 to 2 feet. If in two monthsa 2-foot ice cover is formed, approximately 80,000,000 cubic feet ofwater will be stored as ice, an amount equal to about 15 second-feetflow, or about 21 per cent of the low-water flow of the river at thegaging section for these two months.III1\-1 Hoyt, John C., Comparison between rainfall and run-off in the northeastern UnitedStates: Am. Soc. Civil Eng. Trans., vol. 59, p. 43, May, 1907.


FACTOES THAT MODIFY WINTEE ETJN-OFF. 11Hae -freezing of the water also temporarily affects stream flow bysuddenly increasing friction and thus causing the flow at a givencross section to decrease until the winter regimen has been established.At the beginning of each cold period, therefore, stream flow willdrop suddenly, but will increase to some extent later.Low temperature affects the run-off derived from ground wat by affecting the rate of movement above the freezing point, the rat at which water at a temperature of 32 F. flows through sand beingabout 64 per cent of its rate at a temperature of 60 F.1 The depthto which the ground will freeze ranges from 1 to 5 feet or more,depending on the character of soil, the vegetal covering, and thelength and seTerity of the cold period. Early snows may form acover that will protect the ground from freezing even under theinfluence of later low temperatures, and the condition of the groundwhether frozen or not should be considered in all studies of theproblem. The water contained within this zone is held in storageuntil it is released by higher temperatures.Whether freezing of the ground water or obstruction of the channelby ice is more effective in causing decrease in discharge at the beginning of a cold period depends largely on the character of the drainage basin. In steep, mountainous areas, where a thin soil rests onsolid rock, extreme cold will freeze the ground nearly to the rockand will cause a large decrease in ground flow; but streams drainingsuch areas have, as a rule, narrow channels and considerable fall, sothat obstructions due to ice hold back a comparatively small amountof water. In a rolling country, where the surface deposits consist ofheavy sand or soil and where a large amount of water is in storagebelow the frost line, freezing affects only a small proportion of thestored water; but the streams in such regions usually are characterized by small slope and large cross section, so that obstructions dueto ice will form a considerable check to the flow and may hold backlarge quantities of water in storage. In very flat valleys both thesecauses are operative, for the zone of freezing may extend below thebed of the streams, stopping all underground supply, and most of thesurface flow may be held back by the large amount of ice that formson the sluggish streams draining these valleys. Streams drainingcomparatively large basins consisting of flat valleys up to 2,000square miles in extent may, under such conditions, cease to flow;whereas during the summer, even in periods of low precipitation,they would be fed by ground water.As already stated, freezing temperatures indirectly affect groundwater by converting the surface into an impervious stratum thatprevents downward percolation of surface water.' 'Slicbter, C. &., Field measurements of the rate of 'movement rof underground water:U. S. Geol. Survey Water-Supply Paper 140, p. 13, 1905.'

12THE EFFECTS OF ICE ON STEEAM FLOW.Rising temperatures tend to increase run-off even if the rise doesnot extend above 32 F., doubtless because it releases considerableground water. Winter temperatures above 32 F. add to run-off bymelting ice and snow.The diagrams comparing daily flow and temperature for Mississippi Eiver above the mouth of Crow Wing Eiver (fig. 2) andKootenai Eiver near Libby, Mont. (PI. IV, p. 46), graphicallyexhibit the relations.The daily discharge of the Mississippi above the mouth of Crow Wingwas determined by the Corps of Engineers, United States Army, 0?Mean te nperature o 'basin averaged in five i lay periodsuTa:20'V3,000c feet per a :con j'10'.o 2,000oce 1,000Nov.,1896Dec,,l896Jan.,1897Feb.,1897Man, 1897FIGURE 2. Diagram comparing dally flow and temperature : Mississippi River above mouthof Crow Wing River, Minn.discharge measurements made almost daily throughout the period.The temperature is the mean temperature for the basin, averaged in5-day periods. The slope of the main river and its tributaries issmall and the many lakes and swamps above the stations tend toregulate the flow. These conditions are apparently less.favorable toclose correspondence between run-off and temperature than theywould be on a stream having less lake and swamp storage. Nevertheless, the diagram shows a decrease in flow, amounting to 1,800second-feet during the month of November, coincident with a dropin mean temperature from 31 F. to 5 F. Part of this flow was regained with the rise in temperature the early part of December, but

FACTORS THAT MODIFY WINTER RUN-OFF.13with the drop in temperature in the middle of December the run-offagain decreased; increase accompanied the small temperature rise atthe end of the month. The slight increase in temperature in themiddle of January did not increase the flow, but it retarded the decrease that began with the first drop in temperature on January 1,and reached a minimum a short time after the minimum temperature.It will be noticed that the stream flow increased immediately withthe increase in temperature in the latter part of January, even thoughthe temperature was still below freezing. The minimum flow for thewinter was reached soon after the date of minimum temperature inFebruary.Kootenai River above Libby, Mont., drains a mountainous area onthe western slope of the Eocky Mountains in British Columbia. Asthe basin contains many heavily forested areas ground storage duringthe open season is large, and on the higher areas, where precipitationis heavy, is at its maximum. It would seem therefore that the flowduring the closed season would depend more largely on temperaturethan on fluctuations in the annual precipitation.The diagram forming Plate IV (p. 46) shows the curves of maximum and minimum temperature, for the winter of 1912-13, theobserved gage heights both/ before and after being corrected foranchor and surface ice, and the discharge determined from the corrected gage heights. It clearly exhibits general close relation between run-off and temperature. The drop in temperature that beganJanuary 4 and reached a minimum January 7 was accompanied bydecrease in run-off from 3,000 second-feet on the 5th to 2,100 secondfeet on the 7th. The succeeding rise in temperature caused the runoff to increase gradually to 3,000 second-feet on January 16. Thefluctuation of run-off with changes in temperature during the monthof February is also clearly shown. The minimum discharge, 2,080second-feet, occurred February 10, about two days after the minimumtemperature. After that date the flow gradually increased with risein temperature until it reached 4,140 second-feet on February 19,about three days after the date of maximum temperature. The subsequent drop in temperature was accompanied by decrease in run-off.Increase in flow is noticeable February 10, although the temperaturedid not reach 32 F. until the 12th. This increase was undoubtedlycaused by the releasing of stored ground water as a result of thehigher temperature.The effect of temperature and precipitation on stream discharge isalso shown by the following table, which gives the results of a studyof Minnesota streams.

Station.Cloquet.Littlefork. . Littlefork .Big Falls. .Do.Ottertail. ,420698- 7.64 0.44- 7.64 .44- 7.69 .42-8-00 .41- 7.62 .42- 5.75 .49-6.45 .55- 6.74 .53- 6.40 5.537.726-388.209.54 - 4.51.685492957.53Lake Superior drainage basin. 0.36 1.06 .28 1.05-1.27 .81-1.40 .78-1.36 .79- .10 .98-2.88 .63-1.50 .77- .90 .897.54 on, SeptemberDrain- Precipitation, April to July. Disto - Permiles. Nor- 1910 Differ- Per August.mal. 1911 ence. cent.mal.ence. cent.Hudson Bay drainage basin.7 1.23- -97 .49-2.296.766.756.875.91.651.22.881.08.72 0.60 1.10 .65 1.11 .01 1.00- .30 .956.526.576.606.20-2-67334140 4.86702342825703095Flow.3301561Dp.Natural.Do.9 Controlled.85 Natural.120 Controlled.Natural.58Do.Do.Do.10077Dis- Precipitation, Sep- Discharge tember to De- chargecember.1912,1913,JanuJanuary orary orDiffer- Per FebFebruary. 1912 ence. cent. ruary.Relation between minimum run-off of Minnesota streams ancl precipitation in the drainage basins in the summer of 1910 and the winters of 191J-12and 1912-13.OBQ

00Do.1,9401,190825422Welch. Do.Do. St. Paul. 5.98- 6.07- 6.976.38- 7.28- 6.19- 7.28- 7.30- 4.70- 5.80- 5.50- 4.72- 7.50- 7.70- 7.718. -10. 794.65 -10. 795.25 415.4332213449.558. ppl River drainage 4-1.52 .98 2.96 .91 1.99 2.36 3.83 2.36 4.42 4.40 4.90 3.25 6.77 .82 1.68 6.61 7.64 7.64 7.59 7.59 -2.58-1.86-1.86-1.17-1.17- 5441,9102,3303ffiH. QDo.Do.Do.Natural.Do.Do.Do.CHag 2ggDo.Do.Do.Do.Do,DqlDo.

16THE EFFECTS OF ICE ON STREAM FLOW.In the slimmer of 1910 most of the streams in Minnesota reacheda stage that was probably nearly as low as the lowest open-waterstage of 1864, which has local reputation as the minimum stage.1The cause of the low open-water flow of 1910 becomes evident whenthe normal precipitation for the four months preceding the periodof low flow is compared with the actual precipitation during thesame months in 1910. The table shows deficiency in precipitationranging from 5.5 inches in the western and northwestern sections tomore than 10 inches in the southern and southeastern parts of theState that is, precipitation ranging from 30 per cent to 60 per centof normal.In January and February, 1912,2 notwithstanding the fact that,except over the Red River basin, the precipitation for the precedingmonths from September to December was equal to or exceeded thenormal, the same streams reached a stage which in general was belowthat of the open-season flow in 1910. The table shows the normalprecipitation from September to December inclusive 3 the fourmonths that would ordinarily supply the flow from ground waterduring the winter and the actual precipitation from Septemberto December, 1911, the period of replenishment for the groundwater supplying the low-water flow of January and February,1912. In general, the figures indicate precipitation considerablyabove normal. The explanation of the conditions is found byconsidering temperature records. The 50 days from December 25,1911, to February 12, 1912, were the coldest that have beenrecorded by the United States Weather Bureau for the State ofMinnesota. At Crookston, in the northwestern part of the State, thetemperature fell below zero for 49 days out of the 50, and on January11, 1912, reached 39 F. The maximum temperature was belowzero for 21 days and the highest recorded during the period was 24 ,on January 31 and February 12. At St. Paul, the temperature forthe same period fell below zero 34 days, the minimum being 30 F.on January 12. The conditions at Crookston and St. Paul weretypical of those prevailing throughout the State. Probably nowherein the State was the maximum temperature much if any above freezing during the entire period. The low flow of 1912 was thereforedue not to lack of precipitation, but to the length and severity ofthe cold wave, which stopped all run-off except from ground waterand undoubtedly retarded to a considerable extent the flow of theground water.1 Follansbee, Robert, Variability of run-oft of Minnesota streams during the low-waterflow of 1910: Eng. News, vol. 65, pp. 536-538, May 4, 1911.a Hoyt, W. G., Gaging Minnesota streams in winter: Eng. News, vol. 68, pp. 499-502,Sept. 12, 1912.s These limits do not apply exactly to all parts of the State, because of differencesresulting from latitude.

FACTORS THAT MODIFY WINTER RUN-OFF.17The table gives also the run-off record for the winter of 1912-13,in which the low flow was about the same as in 1912, though probablydue to different conditions. The precipitation from September toDecember, 1912, preceding the period of low flow in January andFebruary, 1913, was considerably below the normal for that period.During the winter of 1912-13 temperatures were normal or somewhat above and the flow from the ground water was probably littleaffected by low temperature.The table therefore comprises records for a period (in 1910) oflow open-season flow caused by a lack of precipitation, a period (in1912) of low winter flow caused by low temperatures following aseason in which precipitation was above normal, and a period (in1913) of low winter flow caused by a lack of autumn precipitation,the winter temperature being normal. None of the low flows recorded in the table should be accepted as the absolute minimum thatmay be expected, because the available records do not cover a periodof extremely low temperature preceded by a period of deficientprecipitation. Although the low flow in 1910 might have been lowerthan any open-water flow recorded between 1864 and 1910, it wasnot of necessity lower than any closed-season flow within that period,since careful stream-gaging work during the winters of 1911-12 and1912-13 gave results lower in general than were recorded during1910. The years from 1864 to 1910 probably included more thanone period of low precipitation during the fall followed by prolonged low temperature, causing a lower rate of flow than any thathas been recorded, but unfortunately no extensive winter measurements were made until 1911-12. The conditions on the Minnesotastreams, illustrated by the table, are typical of those on streamswhose winter flow is affected by ice.BAROMETRIC PRESSURE.Changes in barometric pressure cause changes in the position ofthe ground-water table and therefore a change in the amount ofground water that reaches the rivers. Observations made byBaldwin Latham 1 in 1881 in England, by Otto Lueger 2 in Germany,and by F. H. King 3 in America, show a variation in the flow ofsprin

water supply or power. CLIMATIC FACTORS. PRECIPITATION AND TEMPERATURE. The climatic conditions that influence stream flow are probably more important than any others, but the conditions are so interrelated that it is difficult to distinguish the effect of one from that of another. Strea