G B Waier-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 BY H. K. BARROWS and ROBERT E. HORTON WASHINGTON GOVERNMENT PRINTING OFFICE 1907 CIass^_J>L Book Digitized by the Internet Archive in 2011 with funding from The Library of Congress http://www.archive.org/details/determinationofsOObarr Water-Supply and Irrigation Paper No. 187 Series M, General Hydrographic Investigations, 19 DEPARTMENT OF THE [NTERIOB UNITED STATES GEOLOGICAL SURVEY CHARLES D. WALCOTT, Director DETERMINATION OF STREAM FLOW DURING THE FROZEN SEASON H. K. BARROWS and ROBERT E. HORTON WASHINGTON GOVERNMENT PRINTING OFFICE 19 07 &^ V -p o- FEB 28 1907 ft, dD, CONTENTS. Page. Importance of winter records of si ream How 5 Methods of gaging streams during the open sen son 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, am! needle ice 10 Range of winter gage heights 13 Flow of str< ams 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 Effecl 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 Stat ions 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 Orfonl , X . II 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 ourves for ice cover 43 General considerations - 43 Wallkill River at Newpaltz, X. Y - 43 Kennebec River at North Anson, Me - 44 Connecticut River at Orfonl, N. II 45 3 4 CONTENTS AND ILLUSTRATIONS. Winter records — Continued. Station rating curves for ice cover — Continued. General form of rating curve for ice cover 45 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 1 91 ILLUSTRATIONS. Page. 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 1 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 Hamp- shire , 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 I H T RING THE FROZEN SEASON. Bv II. K. Barrows and R. E. Horton. IMPORTANCE OF WINTER RECORDS OF STREAM FLOW. Estimates of the (low 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 current- meter 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 consider- able 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 condi- tions 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 such 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 per- centage of uncertainty as to the total run-off as well as to its distri- bution. In the Northern States droughts are apt to occur in the late sum- mer 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 mini- mum 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 THE OPEN SEASON. GENERAL STATEMENT. The methods of stream gaging in common use by the United States Geological Survey contemplate especially the determination of dis- charge 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 rat- ing 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 = C\/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 deter- mining the flow. . The flow at dam stations is usually divided — part going over the dam, part through the wheels, and part through by- channels. A weir formula with modified coefficient is used to com- pute 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 thai ilif stream bed is constant in form and position and thai the mean velocity at any given stage will always be the same There- fore a rating curve may be obtained by plotting the results of a suffi- cient number of discharge measurements at differenl stages. In making the measurements an arbitrary number of points, known as "measuring points," arc laid off on a line perpendicular to the thread of the stream, and the velocity and depth are observed. These points art 1 usually at regular intervals from 2 to '_'<) feet apart, depend- ing on the si/.e and condition of the stream. The current meter is commonly used for obtaining velocities, although in 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 measure- ments 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. The most common use of this method is in estimating flood discharge of streams when the only data available are the cross sec- tions, 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. Rarely, 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 forma- tion of ice on streams — (1) the climatic or general temperature con- ditions; (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 Rocky 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 on 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 agi- tated, needle ice will be formed instead of an ice cover. This ten- dency 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 start- ing 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 may be 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 r.t least for some time the formation of an ice cover. Such condi- tions are also potent in assisting the rapid wearing away of the under surface of the ice and, in general, they result in very unstable condi- tions 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 condi- tions, for the reason that very diverse conditions may occur at differ- ent 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 of winter 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 — (a) 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. W'INTKK CONDITIONS. (5) Tendency for ice jams to occur, with eonsequenl backwater, etc. (6) St reams that remain open altogether or freeze over thinly for. short times, owing to — (ii) Exl remes of conditions as noted under (3). (6) High temperature, mainly in the southern portion of the area, suhjee! 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 cur- rent-meter stations and 25 dam stations: Summary of winter conditions at current meter stations. Class. New Eng- land. New York and lower Michigan. Atlantic States. Central States. (1) Smooth, permanent ice cover (2) Tendency for anchor and needle ice to accumulate (3) Unstable ice cover (4) Rough ice cover and piling up (5) Tendency for ice jams (6) Remain open (a) (a) (a) 33 a 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 of winter 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 25 DURATION OF ICE SEASON. 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. Time frozen. Northern Maine Months. 3J-5 Northern Michigan December 1-30 2 -3§ 1J-3 3"-4 Lower New England New York December 1-15.. March 15-31 Pennsylvania 14-2J 1 -2i Illinois December 15-January 15. . February 15-March 1. March 15-31 North Dakota 3J-4J 10 STREAM FLOW DURING THE FROZEN SEASON. A large amount of information relating to the duration of the ice season, especial^ with regard to lakes and navigable streams, was published in the report of the United States Deep Waterways Com- mission. a A few of the results for rivers there given are compiled in the following table : Duration of ice cover on northern sfreams. River. Locality. Connecticut , Do Hudson Illinois Merrimac Mississippi :. .; Davenport, Iowa Do St. Louis, Mo Missouri Bismarck, N. Dak Do Fort Buford, N. Dak. Ohio Cincinnati. Ohio Hartford, Conn Turners Falls, Mass. Albany. N. Y Peoria, 111 Amoskeag, N. H Length of record. Years. 42 12 87 53 - 18 25 31 24 15 39 Average date of- Closing. Opening. Dec. 12 Deo. 9 Dec. 15 Dec. 17 Nov. 28 Dec. 12 Dec. 19 Nov. 25 Nov. 15 Jan. 15 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. Connecticut River at Orford, N. H. Esopus Creek at ton, N. Y Kings- 1903-4. 1904-5. 1905-6. | 1903-4. 1904-5. 1905-6. Feet. Feet. .3 .7 1.3 1.5 1.7 2.1 2.2 2.1 Feet. .1 .7 1.05 1.15 1.1 Feet. Feet. Feet. . 5 .95 1.1 1.25 1.25 .6 «0 : 6 4 5 .6 1.25 1.5 1.6 .7 «0 .1 .4 January 15 February 1 ^ 1.7 1.85 1.9 2.1 + 2. . 5 .75 .9 Marcii 1 .4 .25 March 30 10 - 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, Imi w hich is formed in ;i (lill'erent manner. Surface ice is formed when I he temperature of a quiet body of w ater becomes 32° F. As the maximum density of water occurs at 39.1°, the temperature of a quiel body of water thai is cooled from the sur- face will gradually increase from the surface downward after a genera] 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 solu- tion 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 affect- ing 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 con- stantly 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 crys- tallization 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 de«ree 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 frW through these masses, but the velocity is very 12 STREAM FLOW DURING 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, indi- cated by the presence of impurities in the ice. A striking illustration of this flow is also given in fig. f , 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 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- W1NTEB CONDITIONS. 13 ice formation shows thai the differences will be sufficient to produce in affect a constantly changing regimen. The formation of needle ice, like that of surface or anchor ice, is due chiefly to radiation of heal from the water mass. Needle ice never forms underneath surface ice and is most frequently formed on cold, clear nights, when the heal 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 lew thousandths of a degree change of tempera- ture, 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 sur- face temperature is below r 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 under- neath 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 con- nection 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 oRept. Commission of 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 of frazil and anchor ice: Canadian Engineer, May, 1897, pp. 6-10; Formation of anchor ice and precise tempera- ture measurements: Trans. -Am. Soc. Mech. Eng., 1905. Ilorton, R. E., Anchor ice and frazi : Paper Trade Journal December 24, 1903. 14 STREAM FLOW DURING 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. In the Chezy formulas « Q = AV_ v=cvrs C is the coefficient dependent on the physical character of the stream bed and the hydraulic radius. The plrysical 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) : A , nn 1.811 0.00281 41.66+—— + 5 — p_ n o ( 4 , 66+ -§-)3 yVR It will be seen that for a given slope and hydraulic radius the mean velocity of a stream is nearly proportional to 1 s-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 are.a 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 con- tact 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 10E. 15 (ho friotional 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 he 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 Hows, 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 is 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 skin 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-w T ood 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 impor- tance 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 pre- vious 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 DURING 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 a found, however, that the position of the point of maximum velocity in vertical velocity curves on Mississippi River was controlled by the direction and veloc- ity of the wind. They give the following expression: ^=(0.317+0.06/) D In this formula D = depth in feet; d=depih of point of maximum velocity; /= relative wind velocity on a scale such that a calm = 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 F+W In this formula A = area of cross 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 pro- duce a material effect on the scale of velocities is apparent from the following considera- tions. 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 ^^ of that of water; a body moving through the air with the same velocity will therefore be retarded -g^ as much as if it moved through water. The above conclusions are confirmed by a comparison of the coef- ficients that have been determined experimentally for use in comput- a Physics and Hydraulics of Mississippi River, p. 305. t> Lowell Hydraulic Experiments, pp. 158-159. STREAM FLOW UNDEB K - K. 17 inglossof pressure occasioned by the flowing of air and water through pipes, the term of expression adopted by Weisbach being used: P=f d~2g In I his fornlula /' loss of pressure in pounds per square inch; / = length of pipe in feel ; \ wading a shorl distance above the bridge a1 low stages. The drainage basin of this stream receives the run-off from the north slope of the Catskill Range and lies for the mosl pari in the tim- bered 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 Hows over a rocky bed through the greater part of its course, hav- ing a total fall of 1 ,200 feet. At the station the bed consists of gravel and rock, ihe main channel lying nearest the right-hand abutment of the bridge, which has a clear span of about 194 feet. About two- thirds 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 ot 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 on the left-hand side hav- ing 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 blue- stone, 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 Oatskill Greek S2 Catskill Creek in this vicinity usually freezes over about December 1, and the general breakup conies 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. Needle 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 CatsMU Creek at South Cairo, N . Y . SEASON OF 1903-4. November 29, ice 0.6 foot; practically the 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 9, 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 1904-5. 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 ice. 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 down- stream from gage. February 18, stream frozen over except along right bank, where ice becomes honey- combed and is broken. Februarjr 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 -1, 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. January 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 and 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. WINTKK RECORDS. 29 The range of winter gage heights and maximum thickness of ice observed are as follows: Rang* oj wintei observed are as follows: Range of winter i/> P •w 05 <£ m o ° o • ^ * m o°o^ o o M 3 Fh a o O h'JO ent f ing er t tions i o ent f ing er t tion 3 > 03 4^ a oo* 1 ? f Ss "3 o+^b 2 0} PI a3 O is fit o 2 o ■- 1 o o ^ftO CO " — O o u < s P Eh Eh Eh ai o O CJ Feet per Sec- Sec- Sec- 1901 Feet. Sq.ft. sec. feet. Feet. Feet. Feet. Feet. feet. feet. December 9 a 65 106 1.03 110 3.30 2.93 0.37 120 0.92 66 1.67 1902 January 15 90 166 .89 148 3.50 2.84 .66 152 .97 53 2.79 1906 February 16 100 190 .33 62 2.82 2.22 .70 56 1.11 17 3.65 a Gaging made 70 yards below bridge. GAGE HEIGHTS AND DISCHARGE MEASUREMENTS. Stream measurements during frozen season Continued. CONNECTICUT RIVER AT ORFORD, \ II I 'HI.'!. January 24 . January 29 . January 29 . ranuary 30 . February 7. February ~ . 1901. February 3. February 3. February 4 . February 4. February 5. February 5 . 1905. February 2S. March 1 March 1 1906. February 8 . . February 15. February 17. March 14. March 15 Feet. 276 273 27.', 276 278 278 Qj >, U •a 5 > 03 § < a Feet ■per Sq. It. sec. 1,7611 1.69 1.6111 1 . 63 327 327 327 327 327 RSOPUS CREEK AT KINGSTON, N. Y. 1901. December 4.. 1902. January 9 " . . February 28 << Decern ber 11 . December 1 c. 1903. January 14 d. February 24 « 1906. February 15 . 100 116 90 116.6 101.6 104.6 419 706 404 1,170 413 443 1.25 2.39 1.18 2.96 1.03 1.47 236 522 1,690 476 3, 460 250 6.54 9.14 1.60 13 425 6.9 654 7. 1 5.60 6.41 8.94 6.50 6.32 6.70 .13 .20 .10 .58 .40 716 2, 030 741 5,300 Mi! 950 .73 .83 .64 .65 .49 .69 669 1,900 700 638 782 .67 .84 .83 FISH RIVER AT WALLAGRASS ME. 1906. February 15 Do .... . March 15 | 115 Do 9.5 205 0.95 195 3.91 2.66 1.25 0.65 620 0.32 225 95 205 .96 196 3.91 2.66 1.25 .65 620 .32 225 115 312 1.21 378 4.99 3.83 1.20 .9 1,080 .35 580 115 319 1.22 390 5.08 3.92 1.20 .9 1,125 .35 620 0.87 .87 .65 .63 a Partly frozen over: stations 20-70 and 110-115 open. b Partly frozen over: stat : ons 0-25 and 110-116 open. c River frozen over 150 feet below bridge and 200 feet above. Measurements taken at 0.6 depth. Ni ice at bridge. d 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 IS river partly open for a short distance below bridge, but not as much as on February 17. 40 STKEAM FLOW DUEING THE FROZEN SEASON. Stream, measurements during frozen season — Continued. KENNEBEC RIVER AT- NORTH ANSON, ME. Date. height- Gage height . to water surface. — o CJ A OoO« CgojC o Gage height to bottom of ice. i£ a 1904. January 27 . January 28 . March 2 March 4. . . . 1905. February 9. Do.;... 1906. January 9». January 10 a March 2 March 3 March 30... Do Apr 111''... Do. &.... Feet. 240 240 230 230 458 45S 440 440 445 445 447 447 450 450 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 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 Sec- feet. 749 786 529 572 2, (ISO 2,140 1,290 1,120 1,590 1,380 1,600 1,660 1,660 1,710 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 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 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 Feet. 2.0 2.0 1.0 1.0 .1 .1 .1 .1 .0 .0 ±1.0 ±1.0 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 0.24 .25 .15 .16 .28 .28 .37 .35 .32 .30 .26 .26 .28 .28 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 RONDOUT CREEK AT ROSENDALE, N. Y. 1901. December 6 « 1902. January 14. . February 8. February 26. Do.".... 1903. February 25 . 1Q06. February 27. 105 102 80 100 115 117 479 732 489 517 474 555 1.62 1.11 1.32 1.6 .35 423 732 543 684 676 194 7.00 8.81 8.13 8.43 7.9 eb. 15 6.53 8.41 6.71 7.01 7.40 4.51 .47 .40 1.42 dl.42 .50 .46 540 2,330 1,610 1,930 4, 370 .78 .31 .34 .35 247 1,900 359 549 WALLKILL RIVER AT NEWPALTZ, N. Y. 1901. December 11 /. 1902. January 21 January 23 9 . . January 31ft. . February 10 . . February 24.. 1903. February 7.. . February 10 L February 26. . . Mil 1(10 115 85 140 142 130 679 496 1,070 999 757 .78 3.22 1.72 1.20 .74 2.14 2.03 1.24 3,040 332 6,060 1,170 597 288 2, 290 2,030 945 7.24 17.33 9.07 7.78 7.35 11.2 10.9 8.85 6.04 16.41 8.07 6.78 *5. 25 10.45 9.73 7.89 1.20 .92 1.00 1.00 2.10 .75 1.17 860 9,290 1,980 1,160 919 3,580 3,330 1,830 3,250 277 8,300 1,330 619 2,970 2,440 1,230 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. ft Ice badly broken at station 110. i Below rating table; water considerably above top of ice. i Stations 135-142 open. GAGE HEIGHTS AND DISCHARGE MEASUREMENTS. Stream measurements during frozen season Continued. WINOOSK1 RIVER \T RI< BMOND, VT. 41 Gage height Gage height Gage heighl to water surface. in iini torn of ice. 31 t. u u <- Date. . 3 ej £8.2 o o *~ £ ■— *j o ? =3 m O O O ai o> d « o O O ti o Cfl B n s ?°& +^ 60 c 6c> n « 60 n 2 •a c 3 a3 g 3 > a a to is o o o 0J H s o o o *i3 2 & c m „ o Defficien d u c i n water conditi *a2 — • O o Defficien d u c i n water conditi s: < a Q Eh H f- CG o Q O Feet per Sec- Sec- Scc- 1905. Fret. Sq.ft. sec. feet. Feet. Feet. Feet. Feet. feet. feet. March 3 75 75 it*** 114 1.89 2. 30 206 262 5.45 5. 58 2.70 2. 83 2.95 2. 95 1,460 1,610 0. 14 .16 March i 1906. 70 348 1.68 585 5.62 ±3.4 ±2.8 1,650 .35 a Channel open 1,000 feet upstream and one-half mile downstream. Ice very rough, broken, and tilted, reaching to bottom for about two-thirds of section. The follewing table includes some single sets of discharge meas- urements, with a brief description of the conditions. As a rule, these are insufficient in range at a given station to give much infor- mation regarding the winter rating curve. 42 STREAM FLOW DURING THE FROZEN SEASON. «; CQ 2S WJ-M o3 O man O) t^ CO I- CT- X CD ^ N CO ^ N CO CC CD CO CD CD N T iC l- ■/ CO A«Oei5o t< be o i . 52 ^■-■o 5 o ~ — 3 O -T o: r - o ~ — --Z ~ -~ ^ '.- CO •- O X ~ I - — ~ ' ~ • >~ c-ri-c i- :c ro »-" CI <~ x oONiOccioioosooco«;t 05 S3 . i . b£>05 £"_• w , a3 O o3 *-• O O o" 00»M1CO"CICCC';C e ,_• oo >o - 'CD X X C- ~. r- ■— jT ro . « O ^ C C - /. OCT" '/. C C-l ?) X 'C ■^lOQOiOCM^TCO* : r- : ^ n o ^ n n oo ^'cj , ©O'-*IMc — < t ^f cn 5 ^Z © r- cs io c c>^^CN » iCNCONO'O'OCONiONiO ^lOCNiO^'XCCNcD DCCC^tCNCNiO ,>■ oi .ro cd t •— • — ci ~ D r* :c — t ^ r^ r^ t-- ^(NWlOrOrHMrHpjCCr^CNHrHrHr-irH t^ wcocd^iooh <£;'-*locoC*I >1 >> >> >i (>, >, >,,- or ff 03 S— !— t—CaC3C3CQCCcnca J-333t.^t-^t-tH^PPP 05503,3050505050,05 05 «.2i5 s£ - u B..3 W> 5 ra g 2 6 3 ,3 "3 m J3 05 _ «?■* 05 *" + J " o«oo S 05 ' -_ _ — _. ~ _0)T- ■■ = £ s "2 6 n CUD 0^ can; *±a% ■r. -=? +» i ■ " 05 Si oc„ w oj p 05 o c 3 05 >- — c 05 +J -o s 2 05 J" > °s a > 05 — g M j "^ 3 T3 m t3 a -a t; — — 05 rr b—. O - 05 05 ^X2 ii^5 O.X2 m > > m >xS > 05 > a3c3S3c3GG3;>03 *j •» -^ * — g a sgO WINTKK RECORDS. 43 STATION RATING CURVES FOR ICE COVER. GENERAL CONSIDERATIONS. At several stations sufficient data Lave been gathered to con- struct a rating curve for conditions of ice cover, applicable to aver- age ice conditions within the range of winter gage heights, hut 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. N VELOCITY - FT PER SEC. 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 gag- ing, 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. 3000 4-000 5000 6000 CU. FT. PER SEC. 1904 DISCHARGE MEASUREMENTS = O 1905 " " = 9 1906 " " = • • FIGURES DENOTE DISTANCE FROM WATER SURFACE TO BOTTOM OF1CT. Fig. 5.— Rating curve under ice cover, Kennebec 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 0URVE8. 45 more gagings would, perhaps, enable a scries 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 2000 3000 4000 DISCHARGE-CU. FT. PER SEC. 5000 6000 1903 DISCHARGE MEASUREMENTS = © 1904 " " = O 1905 " " = O 1906 " " = • FIGURES 0ENOTE 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 bot- tom 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 Ken- nebec, 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 STREAM FLOW DURING THE FROZEN SEASON. which they were made, and have been given little weight in draw- ing 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 open- water 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 con- structed for different thicknesses of ice) will be approximately par- allel 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 dis- charge compared with that for the same gage heights in open chan- nel, 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 of 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 espe- cially 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 conse- quent 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 CURVES. 47 *£■■ •qjd.ip 8*0 ' .-.•(> 0.95 .98 .99 1.00 .98 ficient ing to eiocit •qid.ip i;'0 ' ***°! . d Coe red uc cn a r- cn o •uinuiixn|\; i-cooosn <« o Depth of thread of maximum velocity. •qidopjo &£«-? n tuoojodnj 6 ' ' ' ■|.>'M ui OC <* OOCN d ' ' -< o CO . — >. go 4.J, °i 5E cu cp Q C cu •s o •qjdop jo luooj.xl u i -rait- o o CO 'O CO OJ 1 - d ■199] II] OCOOOCN cn -) -i oi u cu ft ft p •qidop jo juoojod uj CO o d OCN CD rH « O •;ooj ui d COCO '3 > 08 u f-t CU > B o u . *** CO ^l og 0) « t- •111111111X13 JV «oo« lO CD >0 tC d •uiotjoa rh 0*0 00 r- — .CO -H d ■dox oocn ira CO >0 CO CN d •if z CftCNOO-H CO rf Tf UO d ldep 8-0+Z-0 00 tP -^ (N ■qjdap 8"0 ' "M'M -^>o d OOCN O qjdop s - o >oco'Oio d qidopc-o CO t^ CO CO - CO cn cn Ol CN 1*1 "£* O CO COCO CC •mdoppnox »^cocom « 1*1 (■bijiui uiojj ooireisiQ ^ 001 JO UIOJ 'S -}oq oi'jqSioq oS«o | £ ooBjans jojbav oj jqSioq oSey IS ^CN d o cn C£ > s- £ X. a a > - c r. a 3 0.93 .93 .83 .55 .96 38 .71 .78 1.02 1.07 1.00 1.02 00—11-1-01 COCK © "O -TOM- l-l-'JiOfrri", >- / - / f / O 0.78 .66 .64 .57 .42 .38 .28 . 19 .52 .86 .90 .82 .85 .86 — • -r s ,oo cn f co co co — cr. — - x rJ«CO>OCOCNCOrHCO CO »o co — •- — d COCOO-*00 — oo co co d co -h oi ^ c i -f -r -ceo pi 1-i rH i-i 0.86 .68 .83 .70 cc*co oo ooiiCH a- tOCOCO »C OOCDI-CK 1- COt^uOCN i^cdood U50i0 COCNCO 0»0 ■"*• Oi co cn oi oi •toco^Hi-ocufl —i cooox-f cr -h-hc-1-ho-hOO rH -hO-hOI i- o ClOOlOtcO-HM n-'ClrH CD CO CO 00 0.50 .85 1.70 1.86 2.13 1.72 1.28 .74 & OiO o OOOO -h H- uo O CO »0 o 0000CNO5COCN00CO t- 00 CO M CN I- 00 Oi O CC CD co »o »o t~ -hpcocOCO CO CTMCOrtiOiOCNai O t-hOcDI- .rH doddddco»o oo lOrfco'co •* cr. ooooooo CN CO »-0 CO 00 OS O i-H OOOO CN co -f 35 1- (M CO 00 CO CO U3 00 c4 s o t- > a c q > k E OC "c c a s 1 a a > t. r t) -r o c 1 cu s 48 STREAM FLOW DURING THE FROZEN SEASON. .SbijO cp 3 6.1 •qjdap 2 1.04 1.01 1.00 1.02 8'0+S'O •qjdap vo CM ■* CO O r~oooo oo d •mnuiix-BjAi rtCCtN O t^OOOO r— d Depth of thread of maximum velocity. •qjdap jo juaoaad uj r~co c-- co *tfi CD »0 »0 d •J99J ui IN001O o S, >> ■a *^ Bo *-, a O oj 0) ft 0) A CP •qjdap jo juaoaad uj t^O". 00 00 d o "J99J UJ -#CO O d^-id ft ft P •qjdgp jo juaoaad uj O 00 "3 > E o . "-' ID T3 > O 3 o o a> ^ ft oj a> .5 >> o o > •uinuiix'Bpi t^ o: CO O 'r-i •uiojiog COOO ^ d "dox T-H CO ^ d •^ d9 P 8W0 o»ra ■* IONH d 'ih •qjdap 8'0 r-oooo d ' ^h ■qjdap g-o co r^ o lOCD^H d ' i-i ■qjdep c-o ca ooo t^ en CO d 'i-i •a-eapi CN CD ^ ^ io r~ t-i oo d ' rH •go; jo ssau^oiqx 1.10 1.10 1.10 1.10 •3D! Mopq qjdaa; .Feet. 13.2 12.4 11.5 12.4 •qjdap" ibjox Feet. 14.3 13.5 12.6 13.5 ■juiod jbijiu! mojj aou'tfq.siG Feet. 130 150 170 •901 JO UIOJ -}oq oj ViSieq 9§B0 ■*? CNI tc,co aa^uM oj jqSiaq aSao g P ■ CD o CN > s- ck E n < > l- E c ■ $ ~ S X O O O OS NSOOOOOOOO ©©©©©© © ©©©©©<©©©© JO C 1 -r CO © 00 © WOfMiO--^iO(N(NCO 00 © © 00 © 00 CO ©©©©©©©©© --f 00 -h co co co t- co co o f- -h © oo »o oo oo © oo oo oo oo r--©ooooQo©aor^-QO OHOOINN CO CO TT -f CO CO i— ( i-i CM CM CO CO CO rH CM OOiOCO^N iOcO-tiO tMCNTjiiOCNcOOiOOO T-IricNeO'^'tcOHtN 00 O CO CM O 00 CM © i-H i-H (M i-t O l-t iO ' CO »o iO OC CO CO © ■©©©©©© »o © 00 t- CO © ©^ 'rH NhNfhO'' ©COOOOrH © ct re M © to CM WhC^hM -h x — - Ml- cr. * oo lo r-. i>- i-O ?i CO ci co © © 00 00 © o © CO tO (M © CM -f CM i— t © iO © © CM* CM i-H r-i t-h r-i r^ cm co r-i co © T-H T-H © © © © Oi f>i rH rH rH r-i cm -rf io or CO' © rH ■ rH CO CO »-0 CO CM t- -H 00 r-H 00 CM CO 00 CM 00 © ■'tf (M t-H CM CM t-- CO CO©©^h >o ■* ci n< — • ci so — • co — ' i - /• f / r ~. / -. / / — — E • BOgh •3 5.5 s ■qidap jo in. ioi»d u i ■ i.i.ij ii [ Sol? 8 OS "<*t 00 -* "* 'Q 'O I~ OS CO S co rr * ' ■* — § § ^ co 5E •llldop 1.1 d to to (~ X co co cc IS l - l - i - l - o fooiniOHHrf lOMONOI-l-l. oc CO l.Mj III m ■ o es Cliici CO CO *o CI CO n W h* t^- 00 Ol O) CI CI CI O) Ol CO CO CI cooowcoosr^h-^ CI MCI — CI CO CI CO ■ilid-M' JO CT- -h "2 * 'O CO Ci -h cC 'X CI X 'O X CifClOM O t-^hOOOO— ; u[ •^ I' M W W h I- O 00 I- CO-o i- x t^ ro — ' x ci >o ci Oi ro '-< co r^ oo co co W lO TrJI 00 o M « r-i OO^NiOOOOOiOO oo - ;c x •_: 00 C-l CO "-O CI 0 ^ N CI lo [- Oi iO « •dox x o o «- io co co t- co o '- -r c: O X I- CO X X :0 NONCDOOQWH ffiOCiOQOOOiO *H;dap C » Ci h h 05 s — — C: S'O+o'O O CI i-t t- OS 04 iH OS •qidap 8"0 00 T tjh os Ci l~ co co CO 01 OS r~ 11 00 OS l^ cc ii ^i 30 X IO N (M »0 CC ^ 30 CO'-'C.NXHON •qidap o i» o o co co co i-i r- — < ci os co os co o r~ ci r~ if CI CO CO 00 O CO CI o •qidop : ; > IRR 187—07- 50 STREAM FLOW DURING THE FROZEN SEASON. .S Mo o c — ' q; 3 O CD •iftdap 8'0+S'O •qidop tj-Q •uinuiixTjjn I - --CK OO O O OS 00 O nOOHOOCOO O MiiOOnOOl r-< oioojoooiq o oooooao o o o o o o o o> o CM •* O 00 00 CO CO OS CO cc s s_ 7 I re f: Sj -TlOfoO^OO ©coooooooico oo oc x x x — oc x x y: r_ o. oo oo as oo CO ^H t^ ^f CO CM co O H H lO iO CO N S CO IO >— i r- co r~ o oo »ra CO 00 00 00 00 OS 00 00 00000000000500 00 00 00 OO i^ 00 00 00 00 o o £ x t3cj£o 't^dop jo ^uaoJ9dui iO OJ Ol r-i a; N iO Os o o c cc -r ■— . ~ C t l--rcOMWHO cm to cm co co ^ -^ co -^ co co co co ■■cr ^ ? to co co -^ -f to •^89 J ui i^GOOMTr © Ol (M W Q h lO iO H^(NrH(MCOM ££ •i^dap jo q.uaojadui NH(NOCHTfN ^ iO rf< -j c C- C) '* -f /^X'OOiOQO j oo r— to t- oo i - x -o — r- oo i>- i>- r-- oo co co r^ w !>■ •^aaj ui co ^ tf tp tp o to ^OOCO^OOOD CO tF -* CO Tfi IO ^ NHOSNNNN co tp co co ^r to •** ■qidap jo ^uaojadui CI ~ a-'^OJOON CO ONOiMCCNC iO 'f Ol O) LO O ^ ( O - co as r- as r- co NOO^NOOH *o:ox O O ■* Ol CO O N 00 O ""tf CO O OS CO t^- CM iO 00 "tf 1 O "* o cr- m coooi'* S iO 00 M Q iO 05 CO OS CO i— I i-h 00 ^ O l-H rH H i-i ■T»dap 8 . 0+g . N (M O -^ N 00 ^ OliON^COOCO CD O N M 00 Tf C-l O CO to Tf CO i-h co NWCCO CM jC CO O -^ tO CO' co. O to ■ifttfap S'O »~CI^COHOOH oo co' »o e<» cm o co co to -^ as ^- ■* as r^. co as cc as cc o i COCOOiHOtO O i-l H ^H r-t ^H •tftdyp 2*0 OS W N LO CO N CD O 'I 1 00 CD tO O CD a. t- o co oo ■* ■* C ^ / D ■* h o r^ cm co cm co oi a. o co r- co. *^ i— < io ■tftdap 2*0 co as cc co t— -*■ co OXOOCOtOHN CM CM O CO 00 i-t O CO OS 00 CD ^ CM I>- N r-i CO iO CO 00 CO CM 00 I"-- tO »0 1— i CD tO 00 !>• ^cM t^- CD CO -^ C.'C '/ -t -D?1M 'O ~- ~- I - OS -tfi r-- iO OS tO CO "t CO o co CM o CO lo ■'cr CO >— i CO CM o -^ iO CN CO o to ■90T jo sseu^oiqx ■^totoooooo as ooooooo ^^r-*CMCOCOas00 »o ^CNWWCOON ooooiooto r- CO -co as hococC'Ooo iO ^idto'tocoi>-CD ■mdep Fjox |0!NtNN>000 J i-O t^ £^ t-^ t^ 00 00 IO OcOMCMiOCOO t-^ cot^t^t^t^oood iO COCMHO^NCO t~^ lo i>I r-I t^ t^ oo t^ •^uiod IBI^TUI UI0.1J a0U13').STlJ ■j - ooooooo ^ co "cr rs: c-1 -o O T OOOOOOO co -r xci o o -r OOOOOOO CO T Jl CM co cr ^ -Hr-iCNCNmM •801 }0 IU0J Ptiid fc, CO VERTICAL VELOCITY CURVES. 51 a J. ■§g£ -*.3 « 5 U»dep so t .to obsSooo o oioooooo o M I'i-'I ' SO IIIUUHM'IV r r r / cc f o. 00 ■*■ O Q 00 OS OS 00 00 / i : . - ' / / / / 00 00X00 00 00 00 00 00 00 03 00 00 00 00 00 = = §£■ £"S|g - t ~- - 'Ml'I'M' J" 111. '.'.I. Hi 11 I — gcoi-io — cc- o xxc. — .or^oo i~ 'O T??Ciro T"f CO f^f^M Mfl W fO TO |.MJ ii! 00 00 CD ""*• 00 CO IO „ _, — , ~l ~, -i J I — r — / — — — — — -I — ~ 3 ■Ul.I. ip;o } 1 1 . i. > j . »< i u[ •),.,.! Ill •qpiap jo in .),> j.i'l u | i- - -r ?; ^ ".- « o ww-Hrtxci^ o • StD^ONN ■ 1-1-Xil-l- 1- 1^ Cl Cl TO io i— X ci co to to to ■"»■ to nONOfflrti' Ci CO CO CO CO "3* CO — — — o ■ — •J,MJ UI -*im~ io **r - ~x> a 1- U3 TO Cl I- Cl Cl 00 o o— ooo— — o a. o •iiinui!xi;]\; IG CO cc X — O CO CI cc co ■*** "^ Cl cc •lUOJJOJJ •dox •q-jdap - 8"0+ IO Oi CI TO CO — 3 rr ^ io IO ^: io 1 CO CI IO t^ — o i CO CO CO CO 00 t^ ' O O Q O O Q g - it t x Cl sc c: -r — — CI CI C [s, ■* K(to' — X C. X f C I CO — — CO CO CI Cl 00 — 00 O TO TO — CJ O i-O — CO TO TO — Cl Cc »0 O >OiOQlOOiCQ C. O O O iO o O O — O H io f io CO o ts, — ' ci — — i — ' — ci — — ' ci — — — — cn — Cl CM CO t^ — I^ 00 co -^r -^ -*r io io *o >o t~ TI< CO CO CD CO t>- CO ogooooq -o -r x ci o cr -r 38888 8 0.90 ,79 .90 .88 .91 .88 i - o> r * -*r — cc / i - / xo> 36 o 0.32 .50 .35 .32 .51 .40 cuo oo x r i — Cl — — Cl 0.70 .80 . 69 . c.ti .81 .73 Cl -^ CO CO CO 0.05 .21 .14 .09 .18 .13 CNOt^iOOO • d — 1.37 2.35 2.09 1.97 1.52 0.60 .95 1.30 .92 .78 1.08 .63 1.25 1.35 1.15 1.20 1.83 1.82 1.65 1.38 1.07 1.87 1.66 1.39 1.38 CO Oi oo — — • CO f~« O OS ^J* • 1.32 2.35 2.03 1.87 1.52 1.19 1.86 1.82 1.65 1.38 1.58 CO LCjlOIOlOCO -^ o t^O— ICOtN 00 co io »c »o tp ^r Cl i-O cc TO iO CM ^CH IO IO CO "^ IO OOOOO ' IO IO (X — Cl TO CO *cf IO o ci ■o T Cl o en ~~ a TO t> a : a a i-s > 3 o IO o C! a CD 52 STREAM FLOW DURING THE FROZEN SEASON. 5 <3 co C , E.- S S * S 56 2 8'0+iTO •qjdap e - COi-l 00 Oi O 00 00OJ00O5 00 OOOOOOOOOiOOOiOO oo CD00OIO1 CT> 00 Oi t- 00 •uinuiix-epi •itfdap jo luaoiadui •J99J ui •iH dap jo q.uaojadui •qjdap jo jueojadui •jaaj ui •UiniUTXBI^ •iuoj40{j; •dox ■iljdap 8 - 0+o"0 ■q^dap 8'0 •i^dap g'O OOOOOOO CC HOJOINHOOQC 00 O Ci Cs OS OS O * . *. C. C ~- O OS OS «rtlNTf CC ^-< O) OS 'cF OS 1^ CO OS LO 00 CO TP r-< CO 00 00 C r-i OS lO 00 CO 00 •q^dap (TO ■aot jo ssau^oiqx HCOO-jH CO O OO 00 OOMN CD CO 00 CO <-h o »-0 CO LQ lO LO 00 o»ooooooo NiQOiOcDOr- ICO LOOOOiOOOCN r. M 'X) CO CO t-- 00 NWWU5O0MHH coojccoQrHaici H CO cc iO io io ^ c lOQOOONCOMCO NCOrHN CD 00 co .— i — i r- ooi— CO WOOt^-0000000000 GO co oo co t^- 00 ci :i :o oo 1-h v y, -jo cd io ONiCN CO NcD23 H ---iaiOi— I GO CO 00 CO lO ooo as > CD 10 *o •q.tiiod {•Bi^mi uiojj eou'B^sia oooooooo CO-^iOcCNCOQO •aot jo mo:* -j;oq o^ ^qSiaq qSvq *80'BJ.mS ja^AY 05. ^qSTeq dSvo •5 a VERTICAL VELOCITY CURVES. 53 a 00) H fa. 2.9-S o -o -qidap r. 8"0 t.""M c I>«P C7 ~- c c r CO 001^ OOIC = C_ 1.00 1.00 1.00 1.00 ■i|)'l-M' S"0 QUJOM <* i- -r O O 1 - CO CO / / ~. s / 9»o?00<£ /■ / r. / / / d •ninuiis i|\ ^f OS OO t- CM QC50-H — I IOOQIO CM i-i~oooo x oooocmco i- ncioooo oo d Depth of thread of maximum velocity. llKUJ.nl II | "T^^O 1 ~ l*00O« OS CO •*« CO OS O COCO"* * BQ HN CM i-H — CM "* CM CM « d l.i.il ll[ WiOOOO i-5 'HCMCO CO C "5 CO 00 CO CO >o 'cM i-i i-< ■il j dap jo lii.i.ij.nl u] [DHiOCI 00 nifiOC 00 CM iO "* OS 00 iNCIi £ IOCIOv: 1 Q — 1 - - -o -o d o •J.MJ U] iO — ' -J^1 lO oi co co co C cct 93 5E t-i CD q»dapio fefeSS 5 (u.iajjduj d ' ' ' o> S N cc -r riOO O o. ft X P COCO 00 OS •jaaj ui d • ' ' CM IO CM CO +^> "S o T > "3 o FH 0) > s u -o 3 c t ° a 0) o (H 0) ft +d 0) IB C °3 o > ■umuiprB^ O CO CM CO os as oor- CO O CM CM ■OOIM 30 OCMO-* CO CM CM — •uiojjoy lOOOO d '»-i oooooo »o lO »o CO »0 CO CM •doj. ONOM Oi-l "** CM NOCHO iO t^o>»o OCOCOO Ot-00"J" •m dap z 8'0+S'O cooo-.o o ■* IO « U5 ^Ji -.c 00 o 131 00 CO IO as Oi co 00 aiooioo qjdap 8"0 O 00 CM 00 OCM 1>CO -H 10 CO C> CO t ' C-l 00 CO 10 t^ CC O 1^ CO CM OOOCO •qjdap s'O °? .*:" CO CO -H 00 IOCOCNN 010000 COr-lrHr-l lOOOOO •qjdap yo ^2!j2 I-CO CM 00 ■JOCOt- CM CM -HO Ofoo i-i io««o cm os as co oo oo *UT?aiAr i i* 1 io cc io io tiooNL-: co oioosoo os •aai jo ssamcorqj, ~OOOQ O OMOO O O 00 CM 00 O-l ^unji^if f i~ cc 10 co cc »o "^ 10 io 10 l«l d •aoi MOjaq qjdag ■« 00 -J" 00 ""l" CO 00 CM IO O -H IO CM 00 -H CC £> co -i< d i-^ io r-i ci ci ci oi co »d 'r io -r ■q:jdap iinox ■g CM 00 CM 00 O tji 1^ OS IO CO OS CO CM CO i-H .^ ^i i< r~ r- d c-i oi oi cm ci co id io io »o l*i •juiod IHI^IUT UIOJJ OOUBJSId ■^ oomo ^ O N 00 Oi 0000 CO ^ CO ^1 OOOO NCOOiO •801 JO UIO^ -^oq o; iqSiaq a§t;o ^4j •aoBjjns ja^BA\ o^ jqSiaq aSuo « 5 S 10 O CO ■0 CD CO o t CN > a a a > B c c J CO »c; i a 3 F- a ■— Z C a a > u a 3 FH a > c 1* a 3 80 — a> o 5 5 ' co •■: ?l CI CO -o CO O *r d-Hi-i O'JiOOCO -H ONCON I - CM i-O I' iO 1^ I- O 10 I OC CO CM 1 Or^rt XhoiC 0-5rH f^-H 00 ^1 d>-< ^-Oi CM CM 10 OlCO—i IO OrHrt -J" t^ ■«■ Ol OC 00 -H O iO 00 CM IO00O OS CO "^i 'Ji CO CO 54 STREAM FLOW DURING THE FROZEN SEASON. 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Decemlier 11 Mean of 8 curves '_---'/ > 'y 7 O ■* O 'O — < CM « CM CM -h CD CD CD CD 1 5 3 Cl iO 00 lC t^ " cm cm cm o J W O: O N CiO ^ CO CM CM r-i CO Tt< GO CM CD IH CO CM ^ rn OOOON-f — i CO CM i-H — i CM 00 Ol CD t^. CM CO CM CM —i ClCGO -^ 00 CD -f C. CM iO CO »-• CO CM CM ^H CM 'O iO LO CD CD iO O O0 iO O 00 CD CM CO rp -^ CO CO •C CO O CD •-* CM CM ^ iO ^ ^ **j« o o o o o CM CO ■* CD 00 64 STREAM FLOW DURING THE FROZEN SEASON. a o 'A o rt > iu ou CO ■< PS £ >M W O 0> 5| Z 8'0+S'O ■mdaps-o •lunuxixBK o o g >> „_ 'J T) l>> Ol +J o> c ,d > ti - +3 B •qq.dap jo jaaojadui "J.88J ui ■mdep jo •+99J UI ■qjdap jo lirao J9d uj •^93j ui §3 Ol -— i Ol i— < O O O C-J O". 3 C-l C Cj O CI >— ( Ol CO CI t— I fflooiooo o o oi o o o oi o aooioo o C. J- X X Q CO CO CO CO CO CO Ol 00 GO Ol Ol CT> CO CO C- CO ~ ~ Ol O ~ '--!-'" CI lO CO CO ** -F Ol i— i - — ~. O- C- ~ O ~ CO 'CO. 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T3 CD C t> 11 CO CD ft +^ CD .5 O o CD > 'TdnuiprBji 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 •uioqqog; oooo OCONN .82 1.95 .90 1.50 .80 .15 .00 .00 .65 .62 1.27 .20 •dox 2.00 1.60 1.30 1.74 1.00 1.86 1.70 1.80 1.98 .42 1.00 .90 1.15 1.15 1.30 .28 2 •qjdap g-o+g-o 2.22 2.58 2.44 2.60 1.26 2.25 2.15 2.56 2.66 - CM 00 00 ^CH O CO Oi CO CM O "^ -^ 00 CO •qqdap 8-0 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 •qadap 2"0 2.77 2.91 2.68 2.63 1.38 2.20 2.55 2.79 2.81 CM O CM OC- O O O t^ ^Ji -*l lO CO 00 t-~ •qidap g-o 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 •uBajAi 2.23 2.54 2.38 2.52 3 IN 1.29 2.26 2.17 2.53 2.65 X CM oi o cm co i-< r^ oo to cm .-h ^ "^r oo co o CM •301 J o ssanjprqx Feet. 0.80 .80 .80 .80 C X CO o o o o CO o o o o c OOOOOOO NNOOON CO o> •eoi a ^oyaq qidaa Feet. 6.8 10.3 10.8 12.3 c OOOOCOOO ^QOCOCH c oc CM 00 CM 00 CM »0 CO io »o "^ t^ o; o r~- CM •qidap moj, Feet. 7.6 11.1 11.6 13.1 ac 5.2 7.0 5.2 8.8 10.2 11.2 8.5 o oc •quiod I'BTq.Tui ukuj aou'Bq.sia ~ oooo ^COCCOIrH »o o o o o N^COOOH "OOOOOOO CM -^i CO GO O — h CM •801 -joq oq "q :o moq qSiaq aS^o SJ £ •30 jajt;A\. oq. BJJtlS jqSraq aS^o 00 o lO 00 oo 4 P CO o On > u cc P cc 1- a r~ a c ; P. cc a 5 a 1= a > s »o c a 1 CC IN r- cc a J* a > a •a c fi s a VERTICAL VELOCITY CURVES. 69 1 s c O 0; •§g?3 £•= .- O O g >, +a 03.5 O ■a a> ■qqdep r. so t r.'li SO O ro ci — o — . — • o o ooooo o ooooi ooooc ■ifldapg-o - - ?l - O l • l- fl — ' X 3- 3* I *- 31 31 31 31 31 8C> — * O SO O U?<0 rH ~H JjO". Cl'XsiJ-O)?* 31 ■llltl.l,! .1" jim.ijoiI hi ■l.Ki.I hi •ilidapjo niooaod ii] ■^93J Ul iljilop JO lii.i.u.id hi i>NOOO«)U5h 00O100t^-00O"lO"lC71 95 59i59""iw | " =o 00 S00O0 91OOIX1S1O100 ao co -f co • cm co o^cii-aioi-i'o -f 'OCOCOCOCOCOCOCMOl CO o o oo o t^ o i^- o m " ' ci -! 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CI ^ o a h id CM nnoohioiocooocono NCjDNNONONONClONN i--cor^r--r-t^.r--.cDr^i>-ic>irH r - ci ro co ^ no o r^ t-^ co CC' oo co C W O O C-l Ci CI C M iO h Oh >-ioaOriHO-*NCDOHOCl ,_, ,_, h CI CI 01 r *O^C001COrHXNCOONiO(N cmnowwohooncohooo tH rH CS Cq N C^ W iH CN CN IOCNiOI^-TtiTjHTjicOCOCN^-iOO ^h c-i oi c-3 cn c0 io »o ICOHICOCOO i-H I CM CM 1-4 rH i-H CM CM* ^CMO:00aicO00c0"*yivOOSTti00 ^HHH^^rHrHHHlNHH CO COO o t HHNNr ^C0OOlC0c0»OTTiT}iTPC0O00CM CO Tfi o O O lr^- co co 00 iO CO O co CO co co^t^t^cocococ^ocJcoc^cjcocm' CO .lOO'OO^OiOQiOOiOOiO 5 00 CjCOtF i— iT-tCMCMCOCOTt'Tl-'iOUOCOCO fj^ CM •-0 O iO O 'O w '0 c-c o ic o io i— It— I CM CM CC CO Th tji UO iO CO O VERTICAL VELOCITY CURVE8. 71 w ^ ■qjdap so t ,-.ii twdopg ii •UUIUHXHIV riT:: i-:i- c r. = c s z o © E ■-. ja -r 5 H *» a) C c Sjgf Se 111,1,.! |,, Hi, >. ij.nl II) o fgc-i i- o -r •l-'.'J 111 'i|l,l,ip jo lusoaaa u] ■jooj ur q»dap j,, Ui.i.i.i.1,1 ii i },>, O M - Cl C (M M — -— Cl ci re Ti ncxOHHuj M -H " r-i rt c ■-; vr: •301 JO U10J -loq o^ jqiswq aSiifj fc, CO •aonjjns jojiiav oj jqSioq d2vj 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. VERTICAL VELOCITY CORVES. 7'A eg M i-i»i • S(i+,-d -,|i,l..p. ;i i c a ;j. - - — v> .- / / / / / - : ~j j - iniiuix i.'iv c-;i:r J i-Nr:irixto-f?)cii-- \\< >' | 'UIMIU I9ddjQ ■ ioNMi ci re 1 - ~ -h -tZNOOONHN ^-* C-l O ^H o >i-li-IOi-H-lOO©Oi-l©00 ■ © i-H O rH O .- i M m _ m ?l - r-c r- . ■XlioojaA treap[ ■ -i- -^ c ~ x ~ x -* ci ~ ci » t x n - z rr rr rr c c n oo-i-tf ooou: .- — •-. ci 05 «3 Oi oa THL:rti--i«^iof t 'to-HOorcc ie :c i - ci c 3 x ~ I CI — i CI CI CI •ao'r japun mcfofi •aoBjjns •i-.IAJll.) Jo JJlHUtl^J .NNOHtOX-)OCiO»OXNOCiCCC.C'l-ini-OOJMOM P 5? ci re >* ■» t^ io eo ■* ira ci ce ce to ce ci ci rA ci re' ci or) d oi so to i~ t^ os oo 5 x o *^ cr n ir c x '-e r- o t-~ o ic oo >-e re ^QO^rt'HCOHOOCOCO^iO^t'Or-INNmr-IO^mNCOin r ^ ci ci -t ■* o »o io to r~ re to ic i-h i-h re re re -r -t< -t< io to cs »e i^ t~ oo ~h r~ -r tt* co ci to ci 'X ci 'X 00' 'Xi o ~h as -r< ci i-e * o w re re t~ re --< n* -* re o O O £ 3** . ST3 o3 08 g a a +J 03 Q oj ■gES 03.G O QUO ■J CB g O 03 O^ 74 STREAM FLOW DURING THE FROZEN SEASON. 'to R 03 « +^> l> O T3 CP pq O ^ • O) S 3 ti Hjdap 8-0+S-O S-i o £© Is •qidap 5-o o go co ooo o H S o3 o conoo •uinuiix^pf u o fQTJiCCiOH c •umtuixi^H o T3 2 **» CO 3 lO ce ■s^ > ■d s o gSMi-J +^> o s.g oooo—.o.--tm iococo csco N N h l-; t co d p MS fiS o wi go oo t- i^ ■*■* co co cq t^ lO Tji co oo ONCO ^ CO lO «££ VERTICAL VELOCITY iri:\ i:s. 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 differ- ence 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 prob- ably 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 continu- ous to the surface (fig. 7, b). Varying degrees between a and b 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 // vertical velocity curves under smooth ia cover. Difference as re- gards maximum River and station. Cage Number \ \ erage Average velocity. Ratio hi' heignl . of curves depth. \ elocit v. 1 to 2. Top(l). Bottom (2). Feet ixr int. Feet. second. Kennebec, North Anson, Me... 3.48 is 2.6 1.17 0.22 0.62 0.35 4.17 lit 2.5 1.30 .30 .112 .48 4.77 9 2.9 1.33 .40 .57 .71) Connecticut, Orford, X. II 4.15 IS 4.0 1.04 .50 .f,t; .76 5.59 / 4.6 1.08 .27 .72 .38 (i.(K) 7 4.9 1.11 .32 .72 .44 6.70 21 5.8 1.23 .41 .(15 .63 Fish, Wallagrass, Me 3.91 8 2.5 .90 .23 .51 .45 5.04 8 3.6 1.25 .(14 .74 .86 26 5 1.6 8.0 2.12 2.18 .59 .37 .65 Wallkill. Newpaltz, X. Y .57 .39 .66 .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 on vertical velocity curves under very rough ice cover. River and .station. Number of curves Average depth. ! Difference as re- gards maximum Average j velocity, velocity. Top(l). Bottom (2). Ratio of 1 to 2. Rondout Creek, Rosendale, X. V Wallkill. Newpaltz, N. Y Winooski, Richmond, Yt Mean . Feet. 5.3 14.6 6.2 Feet yer second. 0.74 2.98 1.99 1.02 .81 1.11 0.55 .89 1.05 .83 1.86 .91 1.96 1.28 RELATION OF DEPTH AND VELOCITY TO FORM OF CURVE. It is evident from the foregoing tables that for a given mean veloc- ity 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 lie- come 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 natter as the stage increases. COMPAEISON 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 VELOCITY 0.G0 0.60 1.00 TERMS OF MEAN VELOCITY = 1.00 Mean of 78 curves without ice cover Mean of 42 curves with ice cover 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 conse- quence of tins 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 0URVE8. T'.i slightly less in the case of ice cover. The bottoms of the two curves arc 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 hack 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 tabic 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. 0.20 0.40 0.60 0.80 1.00 VELOCITY IN TERMS OF MEAN VELOCITY = 1.00 1.20 GAGE HEIGHT NO. OF CURVES AVERUGE DEPTH AVERMjE VELOCITY Jan. 10, 1906 3.48 18 2.6 1.17 Mar 2, 1906 4.17 19 2.5 1.30 Mar 30, 1906 417 9 2.9 1.33 Fig. 9. — Vertical velocity curvi : 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 ordi- nates 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 0.40 0.60 0.80 1.00 1.20 VELOCITY IN TERMS OF MEAN VELOCITY = 1.00 &A&E HEIGHT AVERft&E DEPTH AVERAGE VELOCITY Jan. 21, 1902 7 24 6.7 1.04 Jan. 31, 1902 9.01 9.0 2.16 Jan. 23, I90E 17.33 21.3 3.93 Fig. 10.— Vertical velocity curves under ice cover; average of curves at stations 80, 90, 100 for different stages, Wallkill 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 VERTICAL VELOCITY 0URVE8. SI noted that they si ill preserve about the same distance apart, viz, 0.60 depth. (See table on pp. 73-74, and fig. L4,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 0.40 VELOCITY 0.60 0.80 1.00 IN TERMS OF MEAN VELOCITY =1.00 Feb. 1305 6AGE HEIGHT NO OF CURVES AvERJkGE DEPTH AVERAGE VELOCITY 4 15 18 4.0 1.04 6.10 21 5.8 /.23 6 00 7 4.9 l.ll 5.59 7 4.6 I.0B Feb. 1906 . . Mar/906 Alar. 1906 Fig. 11.— Vertical velocity curves under ice cover, showing change in form of curve with change of stage, Connecticut River at Orford, N. II. 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. ibb 187—07 6 82 STREAM FLOW DURING THE FROZEN 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 0.40 0.60 0.90 1.00 VELOCITY IN TERMS OF MEAN VELOCITY = 1.00 Feb. 1906 &A&E HEI&HT NO OF CURVES AVERAGE DEPTH AVERAGE VELOCITY 3.31 5 04 2.5 5.6 0.90 I.Z5 Mar. 1906 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 aver- age relation was found on the upper Mississippi by A. O. Powell, assistant engineer, under the direction of Col. Charles J. Allen, Corps of Engineers, IT. S. Army, in 1882 and 1890,° the variation being a Ann. Rept. Chief of Engineers, U. S. A., 1890, pt. 3, p. 2104. VERTICAL VELOCITY CURVES. 83 between 0.87+ and 0.88 + . No data arc given, however, as to con- ditions 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 aver- age value for the 13 curves being 0.82, with a range of 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.S depth is 1.002, the range being from r . ^^^ > \ 'VS. /A \ \ \ \ i -t / t / / / / / ^^''' 020 40 60 80 100 VELOCITY l/N TERMS OF MEAN VELOCITY = 1.00 Winooski River at Richmond Yt . 8ED NO OF cuavts 4VEH&&E DEPTH xvehh&e velocity Gravel Clay & Cobbles 26 S 16 8.0 2.12 2 Id Wall kill River at Nerrpaltz N Y Fig. 13.— Effect of depth on form of vertical velocity curves under ice cover. 0.9S to 1.04, there being, however, but one set of curves with a greater value than 1.02. This relation is shown graphically by con- necting 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 1 1 , 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 cor- responds 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 0.60 ^^ ^ "v. ^\^V. NS \ \ \> \ 1 1 \ / y J / _^ ^-: <^ 0.40 VELOCITY 0.60 80 100 TERMS OF MEAN VELOCITY = 1.00 Rondout Creek at Rosen dale, Al. Y. Wall hi 1 1 River at Mwpa/tz, N.Y. Winooski River at Richmond, Vt. BED NO. OF CURVES AVERAGE DEPTH AVERAGE VELOCITY Rook ClayS cobbles SandbgmYel 4 4 5 S3 14.6 6.2 0.14 2 99 1.99 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 VERTICAL VELOCITY CURVES. 85 as well for Curves tinder ice cover as with open seel ion, and I he 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 l<> mean velocity. Maximum 0. II 10 0(> Mid depth 0.2 mid 0.8 deptli The accuracy of the method being assumed to be proportional to the square root of the number of observations, and either of the single- point methods being adopted as a basis, the computed probable range of error for the two-point method would be Range for single point 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. Average of 7 curves . Highest Lowest 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 observa- tion. a 1.013 1.04 .98 From curve. & 1.004 1.02 .99 Depth under Feet. 5.0 6.3 3.5 Mean velocity. Feet ver second. 1.10 1.39 .56 a Mean from 0.2 and 0.8 velocity as observed. b 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 River at Orford, N. H., meter suspended from cable — Continued . MARCH 15, 1906, GAGE HEIGHT 5.59. Observed velocity Ratio: Velocity from curve. Ratio of velocity determined by the 0.2 ahd 0.8 method to the mean velocity. Depth under ice. Mean velocity. 0.2 depth. 0.8 depth. Actual observa- tion. From curve. 1.006 1.04 .95 0.974 1.13 .90 1.011 1.05 .97 1.003 1.01 .99 Feet. 4.6 5.7 3.2 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 varia- tion 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 depth Highest Lowest '. Average of 4 stations, vertical velocity curves Highest Lowest 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 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 l<' LOW DURINO KltoZKN SEASON. 87 SLOPE DETERMINATIONS VXD VALUES OF n IN KIT- TER'S FORMULA, UNDER ICE CONDITIONS. In 1906 two sets of slope 1 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 1 1 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, 0.65 feet; gage height to bottom of ice, 5.15 feet; gage height to top of ice 6.67 feet; discharge, 2,070 second-feet.] Dis- tance of sec- tion from gage. Width below ice. Area below ice. Veloc- ity. Wet- ted Per- imeter. Hy- draulic Radius. Dis- tance be- tween sec- tions. Differ- ence in eleva- tion of water surface. Slope. Aver- age Hy- draulic ra- dius. Aver- age veloc- ity. n. Feet. 516 250 100 Feet. 302 340 329 Sq. ft. 2,110 1,890 1,730 Ft. per sec. 0.98 1.10 1.20 Feet. 605 685 659 Feet. 3.49 2.76 2.63 Feet. 266 | 150 Feet. 0.026 .043 0.000098 .000287 Feet. 3.12 2.70 Ft. per sec. 1.04 1.15 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 sur- face in holes cut in the ice. These were located on each bank at sec- tions 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 B^LOW DURINC4 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 iee, 4.18 feet; gage height to top of ice 6.67 feet; discharge, 2,070 second-feet.] H C 3 a QJ (13 o rl +j i 3 oj -a £ 03 u-, 60 £ G oj tn o P £ °a 5^ "3 XI "2 o ,Q 03 a) !i '3 o "3 > ft 03 o 3 03 u -a M qj a •° o QJ T3 §8 5 0)T3 M03 03 tn tl a) < 3 t> QJ bo o3 a) t> <1 QJ oj 0) o . c _. qj ego QJ O 03 ~ 'St* qj ^ b Q Slope. n. .F7. per T^i per Feet. Feet. Sq.ft. sec. .Feei. JYrf. .Fee/. .Feei. sec f 1 Feet. 0. 020 0. 000091 0.030 516 295 1,800 0.83* 592 3.04 1 220 2.67 0.90 ll .020 .024 . 000091 . 000109 .030 .033 296 330 1,530 .98 662 2.31 1 ] .030 .000153 .030 I 196 2. 2S 1.01 2 .031 . 000158 .031 100 319 1,440 1.04 640 2.25 ! u .030 . 000153 .030 Conclusions. — The mean value of n for the February obsevations 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 sur- face and bottom, which were nearly equal to each other. The United States Engineer Corps c recently made some current- meter 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 Inter- national Meteorological Congress, Chicago, 1893. d a Water-Sup. and Irr. Papers Nos. 76 (1903) and 95 (1904) . b Humphreys and Abbot, Physics and Hydraulics of Mississippi River, p. 190. c Rept. Chief of Engineers for 1897, p. 4092. dThe four great rivers of Siberia: Bull. U. S. Weather Bureau No. 11, 1893. STREAM FLOW DURING THE FROZEN 8EASON. 89 CONCLUSIONS. PRACTICABILITY OF WINTER ESTIMATES OF FLOW. The classification of current-meter gaging stations on page ( .) indi- cates 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 sta- tions south of the area subject to ice cover. About one-third of these stations usually have a smooth, permanent ice cover, and it is prob- ably 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 hydrog- rapher, 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 current- meter 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 deter- mined 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 pos- sible to give more attention to the study and completion of station rat- ing curves — the direction in which the most effort should be expended in the immediate future. N DEX. Page Air. friction of 15 17,77 Anchor ice, character of 13 S< e also Ice. Barnes, II. T., on Formation of ice 11,13 Bed, friction of, comparison of ice friction and 77 Bliskirk, N. Y., gaging station at, condi- tions at 42 velocity curves at. for ice cover 57 Catskill Creek, gaging station on, condi- tions at 20-29, 38 velocity curves on, for ice cover 47,73 Catskill Mountains, streams in, measure- ments of 21 Chemung, N. Y., gaging station at, condi- tions at 42 needle ice at, figure showing 12 velocity curves at, for ice cover 47, 73 Chemung River, gaging station on, condi- tions at 42 needle ice in, figure showing 12 velocity curves on, for ice cover 47, 73 Chippewa, Wis., gaging station at, condi- tions 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 03 Connecticut River, discharge of, relation be- tween ice cover and open flow in . <:o gaging station on, conditions at 29-30, 39 ice on, thickness of 10 slope determinations on 87-88 rating curve for ice cover on 45-40 figure showing 45 velocity of, variations in 85-80 velocity curves on, for ice cover. 48-51,73,74,77 figure showing 81 Cost of measurements under ice cover, dis- cussion of 24 Current meter, measurements by, cost of. . . 24 measurements by, methods of 22-24 use of 90 Current-meter stations, ice. conditions at. 9,20-38 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, condi- tions at 42 velocity curves on, for ice cover 51, 74 Page. Discharge measurements, accuracy of 89,90 effect <>f freezing on \f ( 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 con- sulted 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, System- atic geology and paleontology; D, Petrography and mineralogy; E, Chemistry and physics; F, Geography; G, Miscellaneous; H, Forestry; I, Irrigation; J, Water stor- age; K, Pumping water; L, Quality of water; M, General hydrographic investiga- tions; N, Water power; O, 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 ss. 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. 76 pp., 3 pis. WS 95. Accuracy of stream measurements CseconiT 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. Hydrograpny of the Susquehanna River drainage basin, by J.C. Hoyt and R. H.Anderson. 1904. 215 pp., 28 pis. I II SERIES LIST. WS 116. Water resources near Santa Barbara, California, by J. B. Lippincott. 1904. 99 pp., 8 pis. WS 147. Destructive floods in the United States in 1904, by E. C. Murphy and others. 1905. 206 pp., 18 pis. WS 150. Weir experiments, coefficients, and formulas, by R. E. Horton. 1906. 189 pp., 38 pis. WS 162. Destructive floods in the United States in 1905, by E. C. Murphy and others. 1906. 105 pp., 4 pis. WS 180. Turbine water-wheel tests and power tables, by Robert E. Horton. 1906. 134 pp., 2 pis. (Out of stock.) WS 187. Determination of stream flow during the frozen season, by H. K. Barrows and Robert E. Horton. 1907. 93 pp., 1 pi. Correspondence should be addressed to The Director, United States Geological Survey, Washington, D. C. December, 1906. o lr'08 LIBRARY OF CONGRESS 019 953 636 9 /