Mtm _■______---!

Vo|. 38, No. 6 Transactions. American Geophysical Union December 1957

• going into suspension , but part of the same Quantitative Analysis of Watershed Geomorphology mt in the low velocities kwater areas. Examples Arthur N. Strahler een noted close to river ere sand splays or dunes, Abstract—Quantitative geomorphic methods developed within the past few years provide t greatly different from means of measuring size and form properties of drainage basins. Two general classes of de ve been deposited on the scriptive numbers are (1) linear scale measurements, whereby geometrically analogous units of topography can be compared as to size; and (2) dimensionless numbers, usually angles or jam bed. While it is not ratios of length measures, whereby the shapes of analogous units can be compared irrespec is paper to evaluate the tive of scale. of the other bed-load Linear scale measurements include length of stream channels of given order, drainage manner, it is suggested density, constant of channel maintenance, basin perimeter, and relief. Surface and cross- as to the applicability of sectional areas of basins are length products. If two drainage basins are geometrically similar, bed-load and total-load all corresponding length dimensions will be in a fixed ratio. Dimensionless properties include stream order numbers, stream length and bifurcation sand-bed streams a great ratios, junction angles, maximum valley-side slopes, mean slopes of watershed surfaces, terial is carried into sus- channel gradients, relief ratios, and hypsometric curve properties and integrals. If geomet rical similarity exists in two drainage basins, all corresponding dimensionless numbers will -, it may be found practi- be identical, even though a vast size difference may exist. Dimensionless properties can be •ediment load of a water- correlated with hydrologic and sediment-yield data stated as mass or volume rates of flow erosion. Slope is a factor per unit area, independent of total area of watershed. rally recognized bed-load tree, 1955, p. 114]. Exten- Introduction—Until about ten years ago the principles of scale-model similarity [Strahler, 1954a, ccssary to determine the ..omorphologist operated almost entirely on a p. 343; 1957]. Figure 1 illustrates the concept of features as vegetative iescriptive basis and was primarily concerned with geometrical similarity, with which we are pri dumped rock dams, and :he history of evolution of landforms as geological marily concerned in topographical description. ould act as major dctcn- eatures. With the impetus given by Horton [1945], Basins A and B are assumed to be geometrically ice the slope, Bid under the growing realization that the classical similar, differing only in size. The-larger may be cd to gully erosion and iescriptive analysis had very limited value in designated as the prototype, the smaller as the ere direct methods are .radical engineering and military applications, a model. All measurements of length between cor heir quantities, estimates few geomorphologists began to attempt quantifica- responding points in the two basins bear a fixed ust be based upon past :;ra of landform description. scale ratio, X. Thus, if oriented with respect to a upon the best of the bed- This paper reviews progress that has been made common center of similitude, the basin mouths Q' therefrom. n quantitative landform analysis as it applies to and Q are located at distances r' and r, respectively, normally developed watersheds in which running from C; the ratio of r' to r is X. In short, all cor :_xces vater and associated mass gravity movements are responding length measurements, whether they ; 'he chief agents of form development. The treat ction of basic data on sedfc be of basin perimeter, basin length or width, stream on Water Resource;;, ///. ment cannot be comprehensive; several lines of length, or relief (h' and h in lower profile), are in a /, pp. 53-62. October 1951. •tudy must be omitted. Nevertheless, this paper fixed ratio, if similarity exists. ee, C. EL, Computations of . may suggest what can be done by systematic ap- All corresponding angles are equal in prototype Niobrara River near Cody, .!•• v. Paper 1357. 187 pp.. 1955. i proach to the problem of objective geometrical and model (Fig. 1). This applies to stream junction s-u. W. M.. Estimating bed analysis of a highly complex surface. angles a' and a, and to ground slope angles $' and phys. Union, 32, 121-12.5. Most of the work cited has been carried out at /3. Angles are dimensionless properties; hence the ussion of future of reser- I Columbia University over the past five years under generalization ■ that in two geometrically similar Civ. Eng., Ill, 1258-1262. j i contract with the Office of Naval Research, systems all corresponding dimensionless num 1 Geography Branch, Project NR 389-042 for the bers or products describing the geometry must be 1 -tudy of basic principles of erosional topography. equal. District, Tuisa, Oklalwnui References cited below give detailed explanations Studies of actual drainage basins in differing "' techniques and provide numerous examples \ 1. 1957; presented as pari environments show that in many comparisons in itershed Erosion and Sed»" *^ken from field and map study. homogeneous rock masses, geometrical similarity /-Seventh Annual Meeting. j Dimensional analysis and geometrical similarity— is closely approximated when mean values are 1. 1956; open for formal i "e have attempted to base a system of quantita- 58.) considered, whereas in other comparisons, where :ve geomorphology on dimensional analysis and geologic inhomogeneity exists, similarity is def-

05 MILE

order bo./.

-o.o- o 2 ORDER, F,G. 3 - Regression of number of stream segments on stream order; data from Smith (1953, Plate

found bifurcation ratios of first-order to second- designating stream orders order streams to range from 4.0 to 5.1; ratios of , 1954a, p. 344) second-order to third-order streams to range from measure of the changing length of channel seg 2.8 to 4.9. These values differ little from Strahler's ments as order changes. Because this is a non ;i952, p. 1134]. etry through use of order linear variation, the assumption is implicit that 3 in drainage-network anal- Frequency distribution of stream lengths—Length )f stream segments of each of stream channel is a dimensional property which geometrical similarity is not preserved with in 1 by analysis of the way in can be used to reveal the scale of units comprising creasing order of magnitude of drainage basin. earn segments change with die drainage network. One method of—length Drainage basin areas—Area of a given watershed or drainage basin, a property of the square of analysis is the measurement of length of_____h length, is a prime determinant of total runoff or 'orlon's [1945, p. 291] law of segment of channel of a given stream order. For a sediment yield and is normally eliminated as a that the numbers of stream ■_iven watershed these lengths can be studied by variable by reduction to unit area, as in annual r form an inverse geometric frequency distribution analysis [Schumm, 1956, sediment loss in acre-feet per square mile. In order number. This is generally p. 607]. Stream lengths are strongly skewed right, to compare drainage basin areas in a meaningful ted data [Strahler, 1952, p. but this may be largely corrected by use of loga rithm of length. Arithmetic mean, estimated way, it is necessary to compare basins of the same p. 603] and is conveniently order of magnitude. Thus, if we measure the areas Figure 3. A regression of population variance, and standard deviation serve of drainage basins of the second order, we are of streams of each order as standards of description whereby different order (abscissa) generally measuring corresponding elements of the systems. drainage nets can be compared and their differ If approximate geometrical similarity exists, the ences tested statistically [Strahler, 1954b]. plot with very little scatter area measurements will then be indicators of the Relation of stream length to stream order—Still though the function relating size of the landform units, because areas of similar .ed only for integer values of another means of evaluating length relationships forms are related as the square of the scale ratio. in a drainage network is to relate stream length to .le, a regression line is fitted; Basin area increases exponentially with stream or regression coefficient b is stream order. A regression of logarithm of total order, as stated in a law of areas [Schumm, 1956, p. thm of b is equivalent to stream length for each order on logarithm of ratio rb and in this case has order may be plotted (Fig. 4). Again, the function 606], paraphrasing Horton's law of stream lengths. Schumm [1956, p. 607] has shown histograms of s means that on the average is defined' only for integer values of order. Several the areas of basins of the first and second orders e-half times as many streams such plots of length data made to date seem to and of patches of ground surface too small to have next higher order. yield consistently good fits to a straight line, but channels of their own. Basin area distributions are tt the bifurcation ratio would the general applicability of the function is not yet mensionless number for ex- established, as in the case of the law of stream strongly skewed, but this is largely corrected by a drainage system. Actually numbers. use of log of area. Area is measured by planimeter • stable and shows a small The slope of the regression line b (Fig. 4) is the from a topographic map, hence represents pro i region to region or environ- exponent in a power function relating the two jected, rather than true surface area. Estimation lt, except where powerful variables. Marked differences observed in the of true surface area has been attempted where surface slope is known [Strahler, 1956a, p. 579]. inate. Coates [1956, Table 3] exponent suggest that it may prove a useful QUANTITA1

channels per square mile [, \>)56, p. 612]. Because of its wide ratio density is a number of p. landform scale analysis, sediment yield would show a j ship with drainage density.^ the relation of drainage de predicting the morphologic pected when ground surfa by land use, has been outlir Constant of channel [1956, p. 607] has used density as a property terme -V-v Pleistocene sediments, maintenance. In Figure 6 area (ordinate) is treated as /*—■ Coast Ranges, Souther of total stream channel lenj California length is cumulative for a gil all lesser orders; it is thus Igneous, metamorphic in a watershed of given orde complex, Coast Ranges, is projected to the horizon, S. California /V* number of true lengths would be obt contour ere nutations correction for slope. CD W An individual plotted pointj en sents a given stream order D rV«~ Carboniferous ' Contour numbered 1 through 5. Using C sandstones o 1 Appalachian Plateau, with most examples given by Schumm, a (crenulatfons dose to a straight line of 45c Pennsylvania tionship is treated as linear here on log-log paper. If the k cept is read at log stream lc P- length of perimeter log of this intercept is taken,! . i ( i -i ■ 1 . i i L_ii ■ 0 100 1000 Texture ratio, T*jr logAQ=logC +1 A__= __:___ Fig. 5 - Definitions of drainage density and texture ratio (Strahler, 1954a, p. 348) ______L -*U_ °d LOG Drainage density and texture ratio—An important inflections on a good topographic map indicate the BASIN indicator of the linear scale of landform elements existence of channels too small to be shown by in a drainage basin is drainage density, defined by stream symbols, their frequency is a measure of AREA Horton [1945, p. 283]. The upper left-hand corne'r closeness of channel spacing and hence also corre FT.* of Figure 5 shows the definition of drainage density lates with drainage density. as the sum of the channel lengths divided by l09..A«o Drainage density is scaled logarithmically on logC basin area. Division of length by area thus yields a 2.6.. _y the ordinate of Figure 5. The grouped points in the 250 number with the dimension of inverse of length. lower left-hand corner of the graph represent In general, then, as the drainage density number basins in resistant, massive sandstones. Here the 0.94 c°= _ Areo increases, the size of individual drainage units, streams are widely spaced and density is low. The Length] such as the first-order drainage basin, decreases next group of points encountered represents typical -10 12 3 proportionately. densities in deeply weathered igneous and meta LOG TOTAL STREAM Figure 5 shows the relation between drainage morphic rocks of the California coast ranges. In CUMULATIVE density and a related index, the texture ratio, the extreme upper right are points for badland?. Fig. 6 - Constant of channelI defined by Smith [1950]. Because the contour Data replotted on logarithm where drainage density is from 200 to 900 miles of Schumm (1956, p. QUANTITATIVE ANALYSIS OF WATERSHED GEOMORPHOLOGY 917

stant of channel maintenance C which is actually channels per square mile [Smith, 1953; Schumm, Badlands, 1956, p. 612]. the slope of a linear regression of area on length. Perth Amboy, Because of its wide ratio of variation, drainage The value of C = 8.7 in the Perth Amboy bad New Jersey density is a number of primary importance in lands means that on the average 8.7 sq ft of surface landform scale analysis. One might expect that are required to maintain each foot of channel sediment yield would show a close positive relation length. In the second example, Chileno Canyon in Badlands, the California San Gabriel Mountains, 316 sq ft of * Petrified Forest, ship with drainage density. A rational theory of the relation of drainage density to erosion intensity, surface are required to maintain one foot of channel Arizona predicting the morphological changes to be ex length. The constant of channel maintenance, with the pected when ground surface resistance is lowered bv land use, has been outlined by Strahler [19566]. dimensions of length, is thus a useful means of Constant of channel maintenance—Schumm indicating the relative size of landform units in a [1956, p. 607] has used the inverse of drainage drainage basin and has, moreover, a specific density as a property termed constant of channel genetic connotation. maintenance. In Figure 6 the logarithm of basin Maximum valley side slopes—Leaving now the nents, - area (ordinate) is treated as a function of logarithm drainage network and what might be classified as outhern of total stream channel length (abscissa). Stream planimetric or areal aspects of drainage basins, we length is cumulative for a given order and includes turn to slope of the ground surface. This brings all lesser orders; it is thus the total channel length into consideration the aspect of relief in drainage in a watershed of given order. Length in this case basin geometry. One significant indicator of the is projected to the horizontal plane of the map; over-all steepness of slopes in a watershed is the true lengths would be obtained by applying a maximum valley-side slope, measured at intervals '« number of correction for slope. along the valley walls on the steepest parts of the our crenulotions An individual plotted point on the graph repre contour orthogonals running from divides to sents a given stream order in the watershed, as adjacent stream channels. numbered 1 through 5. Using data of the three Maximum valley-side slope has been sampled examples given by Schumm, the sets of points fall by several investigators in a wide variety of dose to a straight line of 45° slope; thus the rela geological and climatic environments [Strahler, tionship is treated as linear even though plotted 1950; Smith, 1953; Miller, 1953; Schumm, 1956; here on log-log paper. If the logarithm of the inter Coates, 1956; Mellon, 1957]. Within-area variance cept is read at log stream length = 0, and the anti- is relatively small compared with between-area log of this intercept is taken, we obtain the con- differences. This slope statistic would therefore seem to be a valuable one which might relate 10 closely to sediment production. 1000 9 log A0= logC +1 logIL__ Mean slope curve—Another means of assessing the slope properties of a drainage basin is through 8 C> the mean slope curve [Strahler, 1952, p. 1125- ler, 1954a, p. 348) L0G 7 1128]. This requires the use of a good contour topographic map. The problem is to estimate the BASIN topographic map indicate the 6 average, or mean slope of the belt of ground surface Is too small to be shown by AREA 5 lying between successive contours. This may be .-ir frequency is a measure ot FT.' done by measuring the area of each contour belt spacing and hence also corre- 4 with a planimeter and dividing this area by the lensity. loq,.A__ 3 Perth Amboy 8.7 length of the contour belt to yield a mean width. is scaled logarithmically on Chileno Can. 316 The mean slope will then be that angle whose re 5. The grouped points in the 2 /die 425 tangent is the contour interval divided by the rner of the graph represent I 094 --Area ______i mean belt width. Mean slope of each contour massive sandstones. Here the u "Length" L interval is plotted from summit point to basin 0 -paced and density is low. The O I 2 3 4 5 6 7 mouth. Curves of this type will differ from region encountered represents typical LOG TOTAL STREAM LENGTH, FT, to region, depending upon geologic structure and weathered igneous and met* CUMULATIVE logio £L_, the stage of development of the drainage system. he California coast ranges. In Fig. 6 - Constant of channel maintenance, C. If the mean slope for each contour belt is weighted right are points for badlands, Data replotted on logarithmic scales from Schumm (1956, p. 606) for per cent of total basin surface area, it is possible „ty is from 200 to 900 miles of 918 ARTHUR N. STRAHLER to arrive at a mean slope value for the surface of in geological analysis of terrain, the methrv. • the watershed as a whole. be applied to a watershed as a means of Z?' distributed wit Slope maps—Another means of determining both slope steepness and orientation si_^ la, 1952; Mi slope conditions over an entire ground surface of a 1956). watershed is through the slope map [Strahler, Relief ralio-Schumm [1956, p. 612] has dev__4 Figure 8 ilk 1956a]. (1) A good topographic map is taken. (2) and applied a simple statistic, the rdief^ On this map the slope of a short segment of line dimensionless defined as the ratio between total basin relief Si drainage normal to the trend of the contours is determined at a large number of points. These may be recorded is, difference in elevation of basin mouth 2 a horizontal as tangents or sines, depending upon the kind of summit) and basin length, measured as the Ion!! the relative dimension of the drainage basin. In a general« contour h to map desired. (3) These readings are contoured the relief ratio indicates overall slope of the w_2' with lines of equal slope, here called isotangents. the ratio of shed surface. It is a dimensionless number r__S entire basin (4) The areas between successive isotangents are correlated with other measures that do not d«a measured with a planimeter and the areas summed on total drainage basin dimensions. Relief ra_I_ for each slope class. (5) This yields a slope fre simple to compute and can often be obtain* quency percentage distribution. Because the entire ground surface has been analyzed, the mean, llckin detaUed inf°rmati0n on toPogniptyb standard deviation, and variance are treated as' Schumm [1954] has plotted mean annual sedi t population parameters, at least for purposes of ment loss in acre feet per square mile as a function comparison with small samples taken at random of the relief ratio for a variety of small drama- from the same area. fo basins in the Colorado Plateau province [Fig T Lines of equal sine of slope, or isosines, may The significant regression with small scatter il also be drawn. The interval between isosines on the map becomes the statistical class on the histo suggests that relief ratio may prove useful in estimating sediment yield if the parameters for i gram. Sine values are designated as g values Summit because the sine of slope represents that proportion given climatic province are once established of the acceleration of gravity acting in a down- Hypsometric -*-iy_i_-Hypsometric analysis, or the relation of horizontal cross-sectional drainai. slope direction parallel with the ground surface. basin area to elevation, was developed in its Rapid slope sampling—-The construction of modern dimensionless form by Langbein and othen slope maps and their areal measurement is ex 11947]. Whereas he applied it to rather large water- tremely time-consuming. Experiments have shown that essentially the same information can be sheds, it has since been applied to small drainage Area basins of low order to determine how the mass a achieved by random point sampling [Strahler, 1956a, p. 589-595]. Both random coordinate- sampling and grid sampling have been tried. In the random-coordinate method a sample square is Mode scaled in 100 length units per side. From a table of SEDIMENT random numbers the coordinates of sample points LOSS are drawn for whatever sample size is desired. The (ACRE FT grid method does much the same thing, but is not PER Ml*) flexible as to sample size. Point samples, which are easy to take, were \ compared with the frequency distribution meas ured from a slope map. Noteworthy is the ex-, tremely close agreement in means and variances, and even in the form of the frequency distributions,' including a marked skewness. Tests of sample variance and mean are discussed by Strahler [1956a]. *-<_-». Chapman [1952] has developed a method of analyzing both azimuth and angle of slope from contour topographic maps. Although based on Fig. 7 - Regression of sediment loss on petrofabric methods and designed largely for use relief ratio, after Schumm (1954, p. 218) QUANTITATIVE ANALYSIS OF WATERSHED GEOMORPHOLOGY 919

analysis of terrain, the method might distributed within a basin from base to top [Strah- curve is a plot of the continuous function relating ) a watershed as a means of assessing /tT) 1952; Miller, 1953; Schumm, 1956; Coates, relative height y to relative area x. steepness and orientation simultane- 1956]. As the lower right-hand diagram of Figure 8 Figure 8 illustrates the definition of the two shows, the shape of the hypsometric curve varies )—Schumm [1956, p. 612] has devised dimensionless variables involved. Taking the in early geologic stages of development of the a simple statistic, the relief ratio, drainage basin to be bounded by vertical sides and drainage basin, but once having attained an e ratio between total basin relief (that a horizontal base plane passing through the mouth, equilibrium, or mature stage (middle curve on _ in elevation of basin mouth and the relative height is the ratio of height of a given graph), tends to vary little thereafter. Several i basin length, measured as the longest contour h to total basin height H. Relative area is dimensionless attributes of the hypsometric curve t the drainage basin. In a general way, the ratio of horizontal cross-sectional area a to are measurable and can be used for comparative io indicates overall slope of the water- entire basin area A. The percentage hypsometric purposes. These include the integral, or relative . It is a dimensionless number, readily ith other measures that do not depend .inage basin dimensions. Relief ratio is Percentage hypsometric :ompute and can often be obtained .iled information on topography is Summit curve: plane ^ J^ 1.0 III 1 [1954] has plotted mean annual sedi- <=l* acre feet per square mile as a function .8 :' ratio for a variety of small drainage \ H ic Colorado Plateau province [Fig. 7]. _=_ ■ *i . xant regression with small scatter £_\6 - x*, x iat relief ratio may prove useful in \£&r. sediment yield if the parameters for a .4 tic province are once established. trie analysis—Hypsometric analysis, or Mouth i of horizontal cross-sectional drainage °.2 OJ to elevation, was developed in its CC lensionless form by Langbein and others 0 1 1 1 1 ireas he applied it to rather large water- 0 . 2 . 4 . 6 . 8 1 . 0 is since been applied to small drainage Area a Area A >w order to determine how the mass is (entire basin) Relative area, -j-

Y Model hypsometric Characteristic curves function: of erosion cycle*. Inequilibrium (young) stage Equilibrium >^ (mature) stage Monadnock phase

0 Relative area I. 7 - Regression of sediment loss on relief ratio, after Schumm (1954, Fig. 8 - Method of hypsometric analysis (Strahler, 1954a. p. 353) p. 218)

______■ 920 ARTHUR N. STRAHLER Vol. 38, No. 6 Langbein, VV. B., and others, Topographic charac area lying below the curve, the slope of the curve teristics of drainage basins, U. S. Geol. Suro. Water- at its inflection point, and the degree of sinuosity Supply Paper 968-C, 157 pp., 1947. of the curve. Many hypsometric curves seem to be Maxwell, J. C, The bifurcation ratio in Horton's Relating; closely fitted by the model function shown in the law of stream numbers, (abstract), Trans. Amer lower left corner of Figure 8, although no rational Geophys. Union, 36, 520, 1955. Melton, M. A., An analysis of the relations antoni or mechanical basis is known for the function. elements of climate, surface properties, and geo Abstract—The yield j Now that the hypsometric curves have been morphology, Of. Nav. Res. Proj. NR 389-042, Tech. inherent watershed plotted for hundreds of small basins in a wide Rep. 11 (Columbia Univ. Ph.D. dissertation), 102 pp., 1957. of vegetation, and variety of regions and conditions, it is possible to flow which produce; observe the extent to which variation occurs. Miller, V. C, A quantitative geomorphic study of drainage basin characteristics in the Clinch Mountain sediment measuring Generally the curve properties tend to be stable in area, Virginia and Tennessee, Of. Nav. Res. Proj. sources of variation homogeneous rock masses and to adhere generally NR 389-042, Tech. Rep. 3 (Columbia Univ. Ph.D. study of the yield to the same curve family for a given geologic and dissertation), 30 pp., 1953. sediment yields. Such! climatic combination. Schumm, S. A., The relation of drainage basin relief to sediment loss, Pub. International Association of sediment, to evaluate Conclusion—This paper has reviewed briefly a criteria for design of Hydrology, IUGG, Tenth Gen. Assembly, Rome, which multiple regre variety of geometrical properties, some of length 19'54,1, 216-219, 1954. dimension or its products, others dimensionless, Schumm, S. A., Evolution of drainage systems and The studies are discus which may be applied to the systematic descrip slopes in badlands at Perth Amboy, New Jersey, functions; and the effe Bui. Geol. Soc. Amer., 67, 597-646, 1956. nificant variables. tion of drainage basins developed by normal Smith, K. G., Standards for grading texture of ero processes of water erosion. Among the morpho sional topography, Amer. J. Sci., 248, 655-668, logical aspects not mentioned are stream profiles 1950. Introduction—Many hydrol^ and the geometry of stream channels. These, too, Smith, K. G., Erosional processes and landforms in erate within watersheds, and are subject to orderly treatment along the lines Badlands National Monument, South Dakota, Of. variable 'material,' with highl] Nav. Res. Proj. NR 389-042, Tech. Rep. 4 (Colum As a consequence, we have suggested. The examples of quantitative methods bia Univ. Ph.D. dissertation), 128 pp., 1953. working out the end results, presented above are intended to show that, com Strahler, A. N., Equilibrium theory of eroskoil yield, of all these processes operi plex as a landscape may be, it is amenable to slopes approached bv frequency distribution analy of a watershed. Also, when we quantitative statement if systematically broken sis, Amer. J. Sci., 248, 673-696, 800-814, 1950. down into component form elements. Just which of Strahler, A. N., Hypsometric (area-altitude) analy yield, we have equal difficulty sis of erosional topography, Bid. Geol. Soc. Anetn share each process contribut these measurements or indices will prove most 63, 1117-1142, 1952. need to predict sediment yielc useful in explaining variance in hydrological Strahler, A. N., Quantitative geomorphology of erosional landscapes, C.-R. 19th Intern. Geol. Conf, reservoirs and channels; we properties of a watershed and in the rates of erosion and sediment production remains to be Algiers, 1952, sec. 13, pt. 3, pp. 341-354, 1954a. processes and the contributior Strahler, A. N., Statistical analysis in geomorphic seen when they are introduced into multivariate parts of watersheds in order to 1_ research, /. Geol., 62, 1-25, 1954b. sources and evaluate how effetl analysis. Already there are definite indications of Strahler, A. N., Quantitative sloDC ana'ys55. s,i- those sources would be in redur. the usefulness of certain of the measures and it is Geol. Soc. Amer., 67, 571-596, 1956a. Several research workers hav. only a matter of continuing the development of Strahler, A. N., The nature of induced erosion and aggradation, pp. 621-638, Wenner-Gren Symposium pie regression analysis offers analytical methods until the most important geo Volume, Man's role in changing the face oftheEont, difficulty. This paper reviews morphic variables are isolated. Univ. Chicago Press, Chicago, 111., 1193 pp., 1956b. to see how multiple regressic References Strahler, A. N., Dimensional analysis in geomm- phology, Of. Nav. Res. Proj. NR 389-042, Ted- useful and some ways to make Chapman, C. A., A new quantitative method of to Rep. 7, Dept. Geol., Columbia Univ., N. Y., 43 pp., useful. pographic analysis, Amer. J. Sci., 250, 428-452, 1957. Why is multiple regressior 1952. sediment yield studies? It te Coates, D. R., Quantitative geomorphology of small Department of Geology, Columbia University, New I «•* want to know:: how the 27, N. Y. drainage basins in southern Indiana, Of. Nav. Res. of watersheds contribute to Proj. NR 389-042, Tech. Rep. 10 (Columbia Univ. Ph.D. dissertation), 57 pp., 1956. (Manuscript received April 1, 1957; presented as pari how well we can predict the ; Morton, R. E., Erosional development of streams and of the Symposium on Watershed Erosion and -em watershed by study of the their drainage basins; hydrophysical approach to inent Yields at the Thirty-Seventh Annual Meet** errors in each are evaluated in! Washington, D.C., May 1, 1956; open for formal du quantitative morphology, Bui. Geol. Soc. Amer., 56, cussion until May 1, 1958.) Hiving us a measure of how gc 275-370, 1945. and some clues as to where toi ment. The studies which this pape cusses were based on the hypot yield from whole watersheds is