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Studies of Longitudinal Stream Profiles in Virginia and Maryland

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Studies of Longitudinal Stream Profiles in Virginia and Maryland By JOHN T. HACK SHORTER CONTRIBUTIONS TO GENERAL GEOLOGY GEOLOGICAL. SURVEY PROFESSIONAL PAPER 294-B Preliminary results of a study of the form of small river valleys in relation to geology. Some factors controlling the longitudinal profiles of streams are described in q'uantitative terms UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1957 UNITED STATES DEPARTMENT OF THE INTERIOR FRED A. SEATON, Secretary GEOLOGICAL SURVEY Thomas B. Nolan, Director For sale by the Superintendent of Documents, U. S. Government Printing Office Washington 25, D. C. - Price 75 cents (paper cover) CONTENTS Page Peg* AbstractL 45 Relation of particle size of material on the bed to stream IntroductionL 47 lengthL 68 Methods of study and definitions of factors measuredL 47 Mathematical expression of the longitudinal profile and Description of areas studied L 49 its relation to particle size of material on the bedL 69 Middle River basinL 50 Mathematical expression in previous work on longitudinal North River basinL 50 profilesL 74 Alluvial terrace areasL 50 Origin and composition of stream-bed materialL 74 Calfpasture River basinL 50 Franks Mill reach of the Middle RiverL 76 Tye River basin L 52 Eidson CreekL 81 Gillis FallsL 52 East Dry BranchL 82 Coastal Plain streamsL 53 North RiverL 84 Factors determining the slope of the stream channelL 53 Calfpasture ValleyL 84 Discharge and drainage areaL 54 Gillis FallsL 85 Size of material on the stream bedL 54 Ephemeral streams in areas of residuumL 85 Channel cross sectionL 61 Some factors controlling variations in size: conclusions_ _ _ 86 Summary of factors controlling channel slopeL 61 The longitudinal profile and the cycle of erosionL 87 Factors determining the position of the channel in space: the References cited L 94 shape of the long profileL 63 IndexL 95 Relation of stream length to drainage area L 63 ILLUSTRATIONS Pag e Page PLATE99. Drainage map of Calfpasture, North, and 24. Profiles of hypothetical streams showing effect Middle river basins, VirginiaL In pocket of river length on profileL 63 10. A, View of falls in Eidson Creek; B, view of 25.LRelation of length to drainage area L 64 sandstone outcrop in East Dry Branch _ _Facing 80 26.LGraph comparing measured and calculated FIGURE 8. Index map of parts of Maryland, Virginia, and values of stream length and drainage area in West Virginia showing areas studiedL 46 basin of Christians CreekL 67 9. Plan and sections of hypothetical river valley 27. Relation of length to size of bed materialL 68 showing quantities measuredL 47 28. Variations in size of material on the bed of Gillis 10. Plan of river bed showing grid layout L 48 FallsL 69 11. Longitudinal profiles of principal streams in 29. Relation of channel slope to stream length at all areas studiedL 49 localities studiedL 69 12. Drainage map of Nelson County, Va. L 51 30. Graph of profile of Gillis FallsL 70 13. Geologic sketch map of headwaters of the South 31. Graphs of the equation S= HP for various values Branch of the Patapsco River, Md. L 52 of k and n L 71 14. Geologic sketch map of part of the Maryland 32. Graphs of the integrals of the function klLn_ 72 Coastal Plain L 53 33. Relation of size of bed material to length in four 15. Relation between drainage area and discharge streamsL 72 in the Potomac River basinL 54 34. Comparison of computed profiles with actual 16. Relation between drainage area and slope at all profilesL 73 localitiesL 55 35. Map of Middle River near Franks Mill showing 17. Plan of short reach of Middle River above Franks changes in relative amounts of different types MillL 56 of rock in the stream bedL 75 18. Relation between slope and median size of bed 36. Median particle sizes of lithologic components of materialL 57 bed material in Middle River near Franks Mill 76 19. Relation between slope and the ratio of particle 37. Rate of decrease in size of sandstone component size to drainage area L 58 with distance of travelL 76 20. Relation of slope to particle size for streams in 38. Relations between distance of travel of three two groups having different drainage areas__ _ _ 59 lithologic components and percent of the 21. Three-component diagram showing general rela- component in the bed loadL 78 tions between slope, drainage area, and size, 39. Sketch map of Middle River at bed below Franks based on equation 2L 60 MillL 79 22. Relation of drainage area to width and depth_ _ 61 40. Size and composition of bed material at locality 23. Relation of drainage area to depth-width ratio_ __ 62 592 showing lateral changesL 80 UT IV ILLUSTRATIONS (Continued) '14 Page Page 41. Relation of size of bed material to amount of 45. Relation of slope to length typical of seven areas limestone presentL 80 of different geology L 88 42. Sketch map and profile of lower Eidson Creek _ _ _ 81 46. Longitudinal profiles typical of four areasL 88 43. Longitudinal profile of East Dry Branch, and 47. Longitudinal profile of East Dry Branch and relation of reddish sandstone pebbles and boul- Middle River L 89 ders to reddish sandstone outcropsL 83 44. Relation of channel slope to length of streams in areas of contrasting lithologyL 87 TABLES Page Page TABLE 1. Measurements at locality 654, Calfpasture River, stone in the accumulation downstream from the to show variations in size of bed material in a cliff of figure 38L 79 short reachL 55 5. Grid analyses of material on a talus slope on the 2. Values of the constants j and m for four streams_ _ _ 73 east side of the Calfpasture River valley, locality 3. Comparison of profile equations computed from 625L 84 data on size of material on the bed, with profile 6. Median size and amount (percent) of lithologic equations computed from actual elevations in components of bed material at localities on the streamsL 73 Gillis Falls, Md. L 85 4. Parameters obtained by grid analyses, showing 7. Particle-size and slope data in short streams whose size and amount of boulders of tufa and lime- channels contain fine-grained soil materialL 86 8. Principal measurements at selected localitiesL 91 SHORTER CONTRIBUTIONS TO GENERAL GEOLOGY STUDIES OF LONGITUDINAL STREAM PROFILES IN VIRGINIA AND MARYLAND By JOHN T. HACK ABSTRACT Streams in seven areas of Virginia and Maryland, in the Appala­ the profiles of some of the streams studied may be expressed by two chian and adjoining Piedmont and Coastal Plain provinces, with simple equations. One, a logarithmic equation, applies where the different kinds of stream profiles and in geologically different terrane, particle size remains constant. This equation is were selected for study. In each of the areas measurements were H=k loge L-I-C made of stream length, drainage area, channel slope, channel cross section, and size of material on the stream bed. More than 100 where H is the fall from the drainage divide, L is the length from the localities were examined, on streams whose drainage areas range drainage divide and k and C are constants. It is a straight line on between 0.12 and 375 square miles. The measurements are com­ semilogarithmic graph paper. The other equation applies where pared on a series of scatter diagrams and relations among some of the the particle size changes systematically in a downstream direction variables that affect channel slope are discussed. The data for the and has the general form streams studied indicate that the slope of a stream at a point on the channel is approximately proportional to the 0.6 power of a ratio H— L(.+0 +C, when n does not equal —1 n+ 1 obtained by dividing the median size of the material in the stream by the drainage area of the stream at the same point. This relation where H is the fall from the drainage divide, L is length and k, n, means that for a given drainage area the channel slope is directly and C are constants. When C is zero this is a simple power equation proportional to a power function of the size of rock fragments on and plots as a straight line on logarithmic graph paper. The two the bed, and for a given size of bed material the channel slope is equations provide a wide variety of curves which are easily derived inversely proportional to a power function of the drainage area. It and offer a simple method of comparing many stream profiles. is also shown that the ratio of depth to width decreases downstream Because the size of the bed material has been demonstrated to in all streams studied. Streams in areas of softer rocks such as have an important effect on stream slopes and may show systematic shale or phyllite tend to have deeper cross sections than streams in changes along the stream, an attempt is made to analyze the factors more resistant rocks, such as sandstone. that control the changes. Detailed size-distribution analyses, in A very uniform relation between stream length and drainage area which stream-bed samples were separated into lithologic components, exists in all the streams studied, such that length (measured from a were made in areas where the sources of the bed material are known. locality on the stream to the source along the longest channel above These studies show that coarse material enters the stream wherever the locality) increases directly as the 0.6 power of the drainage area.
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