Sediment Yield of the Castaic Watershed, Western Los Angeles County California A Quantitative Geomorphic Approach
GEOLOGICAL SURVEY PROFESSIONAL PAPER 422-F
Prepared in cooperation with State of California Department of Water Resources
Sediment Yield of the Castaic Watershed, Western Los Angeles County California A Quantitative Geomorphic Approach
By LAWRENCE K. LUSTIG
PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS
GEOLOGICAL SURVEY PROFESSIONAL PAPER 422-F
Prepared in cooperation with State of California Department of Water Resources
UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1965 UNITED STATES DEPARTMENT OF THE INTERIOR STEWART L. UDALL, Secretary
GEOLOGICAL SURVEY William T. Pecora, Director
For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 - Price 65 cents CONTENTS
Page Page Abstract..______Fl Quantitative geomorphology____-__-__-_-_--_--__-__- F12 Introduction.______1 General discussion._____.___-____-____--______- 12 Statement of the problem and the approach em ployed. ______2 Basic-data collection.______-_____--_-----_-- 12 Acknowledgments and personnel-_-_-----_-__--___ 2 Geomorphic parameters. ______13 The Castaic watershed______2 Relief ratio-.------.------14 Physical description of the area______2 Sediment-area factor.______15 Location and extent______2 Topography and drainage______2 Sediment-movement factor______17 Climate.______3 Total stream length___----_-__-_------17 Vegetation and soils______4 Transport-efficiency factors.______18 Summary of geology. _-_-___-___-______.___ 5 Discussion of results.______19 Sources of sediment______6 Significance of correlations-______-___-___-_-- 19 Long-term channel erosion.____-_--___--_____ 8 Similarity between the Castaic and the San The San Gabriel watersheds______10 Gabriel Mountains watersheds..------20 Physical description of the area______10 Estimated sediment yield of the Castaic water Location and extent______10 shed- ______-_____-_-_---_------20 Topography and drainage______10 Climate. _--__-_.______11 Range of the sediment-yield values for the Cas Vegetation and soils______11 taic watershed______21 Summary of geology.______11 Conclusions.____-_____-____--__-_-___-_-----_------22 Sediment-yield data______11 References-______--__------_----- 22
ILLUSTRATIONS
[Plates are in pocket] PLATE 1. Index map showing the location of selected watersheds, Los Angeles County, Calif. 2. Map of the Castaic watershed, Los Angeles County, Calif., showing the drainage net, approximate lithologic dis tribution, traces of major faults, and sediment-sample locations and particle-size distributions. FIGURES 1-7. Photographs showing 1. View downstream at the single-stage sampling site in the lower reach of Castaic Creek- ______F3 2. The Liebre Mountain area from the south ______-__-----_-_------4 3. The metamprphic-igneous complex in Elizabeth Lake Canyon______-_---___--__- 5 4. The relatively undef ormed Tertiary sedimentary rocks in the southern part of the Castaic watershed.- 6 5. A typical outcrop of the Tertiary sedimentary rocks in the Castaic watershed. ______-___-_-_- 7 6. Rockf all of conglomerate blocks in subbasin 2 that has produced a natural debris dam ______-_--- 9 7. Exposure of the roots of a tree in Ruby Canyon by channel erosion ______10 8. Graph showing relation of sediment yield and relief ratio for watersheds in the San Gabriel Mountains. _ 16 9. Diagrammatic longitudinal section of a watershed that contains three main groups of hills, showing the geometry of the relief ratio and sediment-area factor- ______,__--__---___------16 10-15. Graphs showing relation, in watersheds in the San Gabriel Mountains, of sediment yield and 10. Sediment-area factor ______-_____-___-_----_------_------17 1 1 . Sediment-movement factor ______-______-_-____-__-----_-_------17 12. Total stream length. ---_-_ ____ --___-_____-__.______--______.__.______.__-. 18 13. Transport-efficiency factor Ti______--__--_--___------18 14. Transport-efficiency factor TV------18 15. Transport-efficiency factor TV ------19 in rv CONTENTS TABLES
Page TABLE 1. Weight percentage of granules, sand, and silt-clay in the granule-to-clay size fraction of samples from the Castaic watershed ______-_-______--___-_--_--_____---_-_____----- F7 2. Data on reservoirs and sediment yield of watersheds in the San Gabriel Mountains, Calif______-___-___----- 11 3. Morphometric data and geomorphic parameters of the Castaic drainage basin and of watersheds in the San Gabriel Mountains, Calif-______-_-_------_-----_---_---_- 14
SYMBOLS u Order of a stream, where unbranched tributaries Q Water discharge are designated as first order and the confluence sv Sediment yield of two streams of a given order is designated SA Sediment-area factor, where SA =Ap/cos dg and by the next higher order number Ap is planimetric area Au Area of a basin of order u, where u is the highest SM Sediment-movement factor, where SM=SA y<. order number of the streams contained sin 0g Lu Length of stream or stream channel of order u T Transport-efficiency factors, where Te =Ti, T2, Total stream length T3, ?L _ Number of streams of order u Transport-efficiency factor, where jTi=jR&X£i Total number of streams Gradient of stream channel of order u Transport-efficiency factor, where T2 =2NXRC Transport-efficiency factor, where Tt= . Ground slope, measured orthogonal to contours E Mean basin elevation D Drainage density, where D=2L/AU F Stream frequency, where F=NujAu Intercept value giving the sediment yield of Bifurcation ratio, where Rb=N1l/N1l+i Castaic drainage basin Basin-area ratio, where Ea AuIAu^ r Simple-correlation coefficient RL Stream-length ratio, where RL=LufLu_l rr Rank-correlation coefficient Rc Stream-channel-slope ratio, where Rc =0u/d1l+i H0 Null hypothesis for one-sided tests Kuggedness index, where Rt =DxE a Confidence interval Relief ratio; Rh=H/Lb, where H is basin relief \ Linear-scale ratio and Lb is basin length ox Standard deviation of linear-scale ratios PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS
SEDIMENT YIELD OF THE CASTAIC WATERSHED, WESTERN LOS ANGELES COUNTY, CALIFORNIA A QUANTITATIVE GEOMORPHIC APPROACH
By LAWRENCE K. LUSTIG
ABSTRACT in average annual sediment yield and lend added credence to the This report treats the problem of estimating, within a short previous estimate of 250 acre-feet per year. period of time, the long-term sediment yield of the Castaic water Data on the size distribution of the granule-to-clay size shed in the general absence of hydrologic data. The estimate fraction of sediments in the Castaic watershed are presented. provided is based on a comparison of geomorphic parameters for It is shown that the sedimentary rocks and the metamorphic- watersheds in the San Gabriel Mountains, for which long-term igneous complex that occur in the watershed contribute approxi sediment-yield data are available, and for the Castaic watershed. mately equal quantities of sediment in the silt-clay size range of The geomorphic parameters that best correlate with sediment about 8 percent, whereas the granitic rocks contribute one-half yield are (1) a sediment-area factor, defined as SA = AP/COS 8g, of this amount. The contribution of the granitic rocks is less where Ap is the planimetric area of a watershed and 8g is the mean because these rocks crop out over a smaller area. Sediment in ground-slope angle, (2) a sediment-movement factor, defined as the sand-sized range is abundant everywhere in the watershed, and certain suggestions for future debris-dam locations based QUANTITATIVE GEOMORPHOLOGY (3) GENERAL DISCUSSION that is, if sediment yield is some function of water dis The methods of quantitative geomorphology are charge, and the methods of quantitative geomorphology widely applicable to problems involving erosion and should, therefore, be applicable to the problem of sedimentation. The major impetus for studies in this determination of the anticipated sediment yield of a field was provided by Horton (1945), who set forth many given watershed. of the principles and parameters that are today applied In addition to stream discharge, however, sediment to drainage-basin studies. Subsequent investigators, yield is undoubtedly a complex function of a veritable notably Strahler (1950, 1952, 1954, 1957, 1958) and host of climatic, geologic, edaphic, and other character several of his students (Miller, 1953; Schumm, 1956; istics of a watershed. If sufficient data on these char Melton, 1957; Coates, 1958; Broscoe, 1959; Morisawa, acteristics are available, then the methods of multiple 1959; Maxwell, 1960), have enlarged these concepts, regression will enable one to derive an equation express introduced new parameters, and extended the data to ing sediment yield in terms of all the variables. The include a wide variety of geographic regions. In applicability of such an equation, however, will still addition to providing a sound basis for quantitative depend upon qualitative factors such as the arbitrary landform description and comparison, these and other assignation of numerical values for the credibility of studies have led to a better understanding of geologic rocks of various lithologic character. processes and of the interrelationship between geomor- Such procedure is, in any event, precluded in the phic characteristics and the hydrology of drainage basins. problem considered in this report because available hydrologic data for the Castaic drainage basin (pi. 2) Sherman (1932) initially demonstrated that the unit are scarce. Knowledge of the long-term sediment hydrograph varied with basin shape and slope, but Langbein and others (1947) provided one of the first yield from watersheds in the San Gabriel Mountains, mathematical treatments, relating discharge and drain however, is equivalent to knowledge of the cumulative age area. Anderson (1949; Anderson and Trobitz, effect of all the variables operative in that area. 1949) was among the first to apply multiple-regression Determining the role of geomorphic factors in the pro methods to hydrologic problems in watersheds, and to duction of sediment from the watersheds of the San relate forest-cover density to discharge and sedimenta Gabriel Mountains should therefore be possible by tion. Potter (1953) showed that peak flow was cor simple linear regression of each parameter with the relative with the length and slope of the principal known sediment yield. Determination of the same channel, and Morisawa (1959) extended Anderson's geomorphic parameters for the Castaic watershed should multiple regression approach to relate peak intensity of then provide a means by which some reasonable esti runoff with several additional geomorphic variables. mate of anticipated sediment yield can be made. With In a highly sophisticated statistical treatment, Maxwell this approach in mind, the methods of quantitative (1960) computed the correlations among peak discharge geomorphology were applied; a morphometric study of and storm rainfall, cover density, antecedent rainfall, the Castaic and San Gabriel Mountains watersheds and nine geomorphic parameters taken five at a time. was undertaken in a search for significant parameters. In similar fashion, Benson (1962) related the T-year BASIC-DATA COLLECTION annual peak discharge to climatic and geomorphic factors by multiple-regression analysis. The morphometric data listed in table 3 were obtained From the foregoing abbreviated survey of the litera from U.S. Geological Survey topographic maps having ture, it can be concluded that many geomorphic param a scale of 1:24,000. These maps depict the moun eters can exert an effect upon the discharge from a given tainous terrain of the areas studied in considerable watershed. This conclusion is true if, as shown for detail. Some errors, both of location and of omission of example by Hack (1957), first-order stream channels, do occur, however. Several examples of such errors have been cited by Coates (1) (1958) and Maxwell (1960), among others. Maxwell because proved their occurrence in the San Dim as watershed Au =f(Nu, Lu, Si, 0, ...) (2) of the San Gabriel Mountains by a careful field check and revised the maps involved accordingly. Time and discharge is therefore a function of these same limitations prevented a similar correction of the maps variables. It is reasonable to suppose then that certain employed in the present study, and for this reason the geomorphic parameters will also affect sediment yield effect of typical map discrepancies upon the data if should be noted. SEDIMENT YIELD OF THE CASTAIC WATERSHED, CALIFORNIA F13 The morphometric properties most readily altered by of the original set of values, occurred, and the variance omission of first-order streams are: stream-channel from the mean of the means was within the limits of order, number of streams, stream-channel length, error of the measurements. It was concluded, there basin order, and drainage density and other derived fore, that a random sample of 100 ground-slope angles parameters. Such parameters are a function of map was sufficiently large to be representative of the pop scale (Giusti and Schneider, 1963, for example), and ulation of ground-slope angles of each watershed. any first-order stream channel can generally be shown The value of the sine of each of the 100 ground-slope to be of much higher order number if detailed mapping angles within each watershed was recorded, and the on a larger scale is undertaken (Leopold and Miller, mean value (sin 0g) was computed. The reasons for 1956), however. The values obtained for drainage computing the sine rather than the tangent of the density (table 3), for example, may be less than the angles will be discussed later. The cosine of the mean true values because drainage density is proportional to ground-slope angle was also computed to calculate SA, total stream-channel length. Basin-order designations sediment area (SA =Ap/cos 0g). These data are listed are also less, for similar reasons. The values obtained in table 3. can still be used for comparative purposes, however, because they have been affected to the same degree; Elevations at each random location in a basin were the fact that the maps including the basins studied are read from the maps, and the means of each set of 100 of equal scale obviates the difficulties imposed by the values (E) were computed (table 3). These values are discrepancies of these maps. thought to be representative of the mean basin eleva Stream order and basin order were designated in tions. Proportional dividers were used to interpolate accord with Strahler's (1952) modification of the between adjacent contours to the nearest 5 feet. This usage of Gravelius (1914) and Horton (1945). Stream- same procedure was followed in measuring elevation channel lengths were measured with dividers set at differences along stream channels. These values were 0.01 mile. The use of dividers provided more consistent used to compute the mean stream-channel gradients of replicate results than could be obtained with a map streams of each order (0J within each basin (table 3). measurer. This was particularly true for measurement The number of streams of each order (Nv) within a of the lengths of highly sinuous streams. The mean basin was determined by inspection, and relief ratio stream-channel length of streams of each order (La) (Rn=HILi,} was computed in accord with Schumm's and the cumulated lengths of streams of each order (1956) procedure. All other parameters that are listed (SLu) were computed for each watershed; the values in table 3 are derived properties that require stream are listed in table 3. length, basin area, stream-channel gradient, or the Drainage areas were measured with a compensating number of streams of a given order for then- computa polar planimeter, and the mean values of replicate tion. These derived parameters are: drainage density sets of measurements were recorded. Areas of sub- (D=2L/AU), stream frequency (F=NU/AU), bifurcation basins of each order (Au) within a given watershed ratio (R6=Nu/Nu+i), stream-length ratio (RL=Lu/Lu_i), were cumulated in order to verify total drainage area. basin-area ratio (Ra=Au/Au_i), stream-channel-slope The results accorded to the nearest 0.05 square mile. ratio (Rc eu l9u+i), and the ruggedness index (Rt = The mean area of each basin order (Au) and the DXE}. cumulated area of each basin order (1ZAU} were com puted for each of the seven watersheds (table 3). GEOMOBPHIC PARAMETERS Random-number overlays, of a size sufficient to Each of the parameters listed in table 3, obtained as cover the area of each watershed, were prepared to described in the preceding section, was considered both determine the mean ground-slope angle of each basin. individually and in various combinations for possible The procedure, as described by Strahler (1954) is correlation with the sediment yield of the watersheds simple. At each of 100 random locations within each of the San Gabriel Mountains. Although a trial-and- basin, the slope was measured over a 200-foot reach error approach will suffice in seeking the correlation of orthogonal to contour lines. The mean ground-slope individual parameters with sediment yield, the choice angle (0g) was calculated from these sets of 100 measure of combinations of these parameters must be governed ments to the nearest one-half of a degree. Replicate by consideration of both the relationship between two measurements of slope at alternative sets of 100 random parameters of a paired set and the expected influence locations were made within the largest of the watersheds of the paired set upon sediment yield. One would not, that were studied to test sufficiency of sample size. for example, expect a product of mean stream length The expected reduction of the standard deviation of of a given stream, order and mean basin elevation the means of these replicate sets, compared to that (LU XE) to produce an explicable correlation with 776~ Q5 O 65 . 2 F14 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS TABLE 3. Morphometric data and geomorphic parameters of the Castaic Mean area Mean length Mean chan Mean Mean Stream Basin Area of basin of basin Number Total length of of streams of nel slope of basin ground- frequency Watershed order of order u of order u of streams streams of order u streams of elevation slope angle (number per (sq mi) (sq mi) of order u order u (miles) (miles) order u (feet (ft) (degrees) sqmi) per foot) 5 /li =83.28 3i=0.45 #1-187 £i=1.07 ft=0.189 .Fi=2.25 ,42=79.60 ,42=1.85 #2=43 2^2=245.54 £a=5.n 02=. 078 -Fj=.54 ,43=82.12 ,43=6.32 #3 = 13 2£s=269.42 Zs=20.72 03= .043 3240 40.5 -F3=.16 ,44=111.72 ,44=27.93 #4=4 2^4=294.62 £4= 73.66 §4 =.027 .Fi=.04 ,45=137.63 ,45=137.63 #5 = 1 2£s=307.49 £5=307.49 §6=. 014 -Fs=.01 3 ,4i=2.29 ,4i-.18 #i-13 2£i-8.13 Zi=.63 ft =.292 .Fi=5.68 ,42=1.94 At =.39 #2=5 2£2=9.89 £2=1.98 02 =.201 3010 33.5 ^2=2.58 ,43=3.34 ,43=3.34 #3 = 1 2£3=12.17 13=12.17 §3=. 083 -Fs=.30 3 ,4i=4.30 ,4i = .72 #1-6 2£i=6.31 £i=1.05 ft =.207 .Fi=1.40 ,42=4.41 ,42=2.21 #2=2 2£2=8.60 £2= 4.30 62=. 060 2620 30.5 .F2=.45 ^3=4.50 ,43=4.50 #3=1 2£3=8.80 £3=8.80 0s=. 038 -F3=.22 3 ,4i=6.69 ,4i-.39 #1-17 2£i = 15.50 £i=.91 ft = .279 -Fi=2.54 ,4.2=8.06 ,42=2.69 #2=3 2i2=21.47 £3=7.16 §2=. 142 3485 34.0 -F2=.37 ,43=10.79 ,43=10.79 #3=1 2£3=23.72 £3=23.72 &=. 055 ^s=.09 4 ,4i=10.54 ,4i-.88 #1-12 2£i = 19.02 £i=1.59 ft =.155 .Fi=1.14 ,42=7.54 ,42=1.89 #2=4 S£2=23.50 £2=5.88 §2=. 109 ^2= .53 .3305 33.0 ,43=9.95 ,43=4.98 #3=2 2£3=27.21 Zs=13.61 §3=. 059 -F3=.20 ,44=16.17 ,44=16.17 #4 = 1 2£4=30.27 £4=30.27 ft=.020 -F4=.06 3 ,4i= 16.81 A t _ *>A #1-49 2£i -46.26 £i=.94 ft = .228 -Fi=2.91 ,42=12.43 142=1.78 #2 = 7 2£3= 55.66 £2=7.95 92=. 109 4050 33.5 ^2= .56 ,43=28.10 ,43=28.10 #3=1 2£3=61.24 £"3=61.24 93=.073 ^3=.04 Big Tujunga...... 5 ,4i =43.52 ,4i=.32 #1-136 2£i- 116.01 £i = .85 ft = .216 -Fl=3.13 ,42=53.61 ,42=1.73 #2=31 2£2=156.98 £2=5.06 fa =.091 F3= .58 ,43=54.71 ,43=6.84 #3=8 2£3 = 176.32 £3=22.04 03 = .056 4540 30.5 -F3=.15 ,4i=64.35 ,44=32.18 #4=2 2^4=185.11 £4=92.56 §4 =.046 -F4=.03 ,45=82.00 ,46=82.00 #6=1 S£5= 189.07 Z5= 189.07 §5= .018 -F6=.01 sediment yield. Although each of the variables in this RBHLIEP RATIO example may indeed bear some relation to sediment The relief ratio of a watershed (Schumm, 1956) is yield, their relation to each other is not obvious, and defined as Rh=H/Lb, where H is the difference in the results of a correlation between the pair and sedi elevation between the basin divide and mouth and L^ ment yield would defy explanation. In this sense, all is the maximum basin length measured along a line as possible combinations of parameters have not been nearly paraUel to the principal channel as possible. tested for correlation with sediment yield. The relief ratio is therefore a dimensionless number The parameters discussed below are, except for relief that approximates overaU watershed slope. Because ratio, those which are interpreted as meaningful and of lack of adequate maps, or for ease of computation, which correlated well with sediment yield. Certain of relief ratio has often been correlated with sediment the parameters to be described appear in this report yield in preference to treating hypsometric data as for the first time, and comparison with previous results suggested by Langbein and others (1947) and Strahler is therefore not possible. Among the more common (1952). In addition, it is logical to assume that the parameters, such as drainage density or ruggedness energy input of such hydrologic factors as runoff and index, only total drainage area provided a good corre discharge should be, in part, a function of this param lation with sediment yield. As previously indicated eter. Morisawa (1959) found that relief ratios of (equations 1, 2, 3), if this were not true, then the rela watersheds in the Appalachian Mountains correlated tionship between sediment yield and various parameters weU with peaks of discharge and rainfall-runoff inten that are a function of drainage area could not be sities, and Hadley and Schumm (1961) obtained a good investigated. The relationship between sediment yield correlation with sediment yield in the Cheyenne River and drainage area will, however, be held in abeyance drainage basin. Accordingly, relief ratio for each of for discussion in a subsequent section of this report. the watersheds in the San Gabriel Mountains was The linear-regression lines that relate sediment yield among the first parameters determined during the with each of the following geomorphic parameters were morphometric study for this report. The linear regres fitted by the least-squares method. Correlation co sion of sediment yield with relief ratio for the basins efficients computed for each pair of variates are cited studied is shown in figure 8. The rather poor correla below where appropriate; the statistical significance of tion (r=0.658) between these variates is apparent, and these coefficients will be explained in a subsequent the data are included here for illustrative purposes subsection entitled "Discussion of results." only. SEDIMENT YIELD OF THE CASTAIC WATERSHED, CALIFORNIA F15 drainage basin and of watersheds in the San Gabriel Mountains, California Drainage Transport efficiency factors density Rugged- Bifurcation Stream -length Basin-area Stream- Sediment- Sediment- (mile per ness index ratio ratio ratio channel-slope Relief ratio area factor movement sqmi) ratio factor Ti T, Ts TO=4.35 £5/£4=4.17 A6/A4=1.23 §i/§2=2.42 2.23 7,225 iX-sS £s/£2=2.63 A3/A2=1.03 §3/§4=1.59 0.058 180. 97 116. 16 1146.94 481.12 694.64 Ni/Ns=4.QO £2/£i=5.34 A2/Ai=.96 §4/§5 = 1.93 #6=3.73 #t=4.18 #o=1.15 #.=1.94 NilNz=2.6Q £"3/£"2=6.15 A3/Ai=1.72 §i/§2=1.45 3.64 10,956 NilNs=5M £2/£i=3.17 A2/Ai=.85 §2/§3=2.42 .340 4.01 2.18 46.25 36.86 40.62 #6=3.80 #t=4.66 #o=1.29 #e = 1.94 -ZVi/.ZV2=3.00 £"3/^2=2.05 As/A2=1.02 §i/§2=3.45 1.95 5,109 NjN3=2.00 £2X1=4.09 A2Ai=1.03 §2/§3=1.58 .061 5.23 2.59 22.00 22.68 32.34 #6=2.50 #t=3.07 #o=1.03 #«=2.52 Ni/N3=5.67 £3/12=3.31 A3/A2=1.34 §i/§2=1.96 2.20 7,667 N3/N3=3.QO £2/Ii=7.86 A2/Ai=1.20 §2/§s=2.58 .230 13.01 7.18 102.95 47.67 49.52 #6=4.34 #t=5.59 #"a=1.27 Sc=2.27 Ni/Ni=3M £4/£3 =2.22 A4/43=1.63 §i/§2 = 1.42 £s/£2=2.31 43/A2=1.32 1.87 6,180 .139 19.28 '10.34 70.53 39.33 42.67 SSS £2/Ii=3.70 §3/§4=2.95 #"&=2.33 #t=2.74 #a=1.22 #e=2.07 Ni/Ni=7.00 £s/l2=7.70 A3/A2=2.26 §i/§2=2.09 2.18 8,829 Nt/N3=7,QO £2/11=8.46 A i/Ai =.74 §2/§3=1.49 .070 33.70 18.34 428.68 102.03 128.96 #6=7.00 #t=8.08 #a=1.50 #0=1.79 Wi/JV2=4.39 Is/£4=2.04 A6/A4=1.27 §i/§2=2.37 NzlN3=3.88 Z4/Zs=4.20 A4/As=1.18 §1!/§3=1.62 2.31 10, 487 N3/Nt=4.00 £s/£2=4.36 Ai/Ai=l.Q2 §3/§4=1.22 .078 95.17 47.40 674. 98 345. 32 479. 21 Ni/Nt=2.QO £2/£i=5.95 A2/Ai=1.23 §4/§s=2.56 #"&=3.57 #L=4.14 #o=1.18 B.-1.94 Good correlation between relief ratio and sediment tion of drainage area, with which stream discharge and yield is absent probably for two reasons, aside from the many geomorphic parameters are indeed interrelated, a <|>bvious difficulties and ambiguities involved in deter parameter, herein termed the "sediment-area factor," mining the maximum basin length (Lj,) as defined. was computed. Sediment area is defined as SA =AP/cos First, several of the watersheds in question (pi. 1) 6g, where AP is the planimetric area of a watershed possess nearly identical basin relief but differ drastically and 6g is the mean ground-slope angle for values obtained in maximum length. This difference is an obvious at 100 random locations, as previously described. consequence of variation in basin shape. Because relief Consideration of the simple relationships shown in ratio is an indirect function of basin shape, this param- figure 9 provides the rationale for the sediment-area ^ter cannot provide consistent correlation with sedi expression. Figure 9 is a diagrammatic longitudinal ment yield in the absence of similarity of shape. section of a watershed that contains three main groups Second, relief ratio is a measure of the slope of a of hills, the steepest of which occurs in the divide area. ^urface, the horizontal projection of which is taken as If we wish to find the total length of slopes that are ihe drainage area of a watershed. Sediment yield, exposed to erosion in this two-dimensional portrayal, however, is a function of sediment availability and then, assuming symmetry of the hills, we would compute might be expected to be more closely related to total ij/cos 0J+2Z2/COS02+2.L3/COS 03, (4) surface area than to planimetric drainage area in certain drainage basins. Clearly, two basins can be equal in which gives the desired result, namely planimetric area and yet differ in total surface area (5) because of topographic variation. One could not expect equal sediment yields from 100 square miles of hori If we add the interhill lengths, which are also on the zontal mesa and from 100 square miles of rugged surface exposed to erosion, then the total length in any mountains, to cite an extreme example. For these two-dimensional portrayal clearly will be much greater reasons, a substitute for the relief-ratio parameter was than Z6. Lh is basin length, as used in the relief ratio devised as described in the following discussion. expression, and it is measured in the horizontal plane. Figure 9 suggests that one approximation to total sur SEDIMENT-AREA FACTOR face length in two dimensions can be derived from the To approximate watershed surface area with a mini- relief ratio, H/Lb ; the length EC is such an approxima Jnum of computational difficulty and yet avoid elimina tion and it can easily be obtained. F16 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS 1000 ~l \ I I I I I I I I 1 I I I I I I I I I I I I T~TT 0.01 0.10 1.0 10.0 RELIEF RATIO Rh = H/Lb FIGURE 8. Relation of sediment yield and relief ratio for watersheds in the San Gabriel Mountains. The vertical line represents the relief ratio of the Castaic watershed; its intercept (Ic) with the curve gives the sediment-yield estimate provided by this parameter, r =0.685, 7c=33.17. FIGURE 9. Diagrammatic longitudinal section of a watershed that contains three main groups of hills, showing the geometry of the relief ratio and sedim«nt-area factor. Lb is basin length; .ACis basin relief or H; Si, 82, Ss are lengths of hillslopes; Li, Li, Ls are horizontal orojeotions of Si, Sz, and Ss, respectively; 61, 61, fa are angles of hillslopes. SEDIMENT YIELD OF THE CASTAIC WATERSHED, CALIFORNIA F17 1000 F both gravitational and shearing stresses and the nature of the material available. Because the sine of the angle of slope is the ratio of the gravitational stresses to the shearing stresses that act upon either bedrock or its sediment cover, the sine of this angle is a geomorphic parameter of significance and is more meaningful than I- 100 b other trigonometric ,functions of slope. To determine whether a relationship existed between sediment yield and the movement of sediment toward the drainage net, a parameter, herein termed the '^sedi ment-movement factor," was defined as SM=SA Xsm 6g, where SA is sediment area, as previously defined, and sin 8g is the mean of the shies of the ground-slope angles at each of 100 random locations in a given watershed. Sediment area is included hi this expression for sediment movement because it is logical to consider the product of the forces acting upon the sediment and the availa bility of that sediment. The regression of sediment 10 100 1000 yield with SM is shown hi figure 11. The correlation SEDIMENT AREA FACTOR (SA =AP /cos6 coefficient is 0.940, suggesting that, like SA, the defined FIGUEE 10. Relation of sediment yield and the sediment-area factor for watersheds sediment-movement factor is a significant geomorphic in the San Gabriel Mountains. The vertical line represents the value of the sedi parameter. ment-area factor in the Castaic watershed; its intercept (7p) with the curve gives TOTAL. STREAM LENGTH the sediment-yield estimate provided by this parameter. r=0.929, /c =223.41. Total stream length also correlated well with sediment Difficulties will arise, however, when one attempts to yield (r= 0.935); the linear regression is shown hi figure extend the approximation just cited to the three- 12. Although greater length of an individual stream dimensional problem. Symmetry of hills will not implies that more sediment deposition can occur along necessarily prevail and, moreover, relief ratio will vary its course, greater total stream length within a water with basin shape as previously mentioned. For these shed implies both greater precipitation and runoff and reasons the sediment-area factor, namely SA =AP/ greater sediment-availability and sediment-movement cos 8g, was used in this report. The expression is, hi effect, an approximate integration of the general ex 1000 p pression Li/cos Qt within the watershed. Because the mean ground-slope angle was obtained from a random sample of slope values hi a given watershed, it represents the mean, of all slopes hi that watershed, and Ap, of course, is equivalent to SZ*. The sediment-area factor is thought to represent the 100 true surface area of a given watershed and, therefore, the availability of sediment within that watershed, to a first approximation. The regression of sediment yield with SA is shown in figure 10. The correlation coeffi cient is 0.929, clearly suggesting that this parameter is superior to relief ratio for the areas studied. 10 SEDIMENT-MOVEMENT FACTOR The valley-side slopes in a watershed have a direct bearing on problems of sediment-yield estimation. Other factors being equal, one can state qualitatively that an increase in steepness of slope will result in both 10 100 1000 an increase in the rapidity of runoff and a greater supply SEDIMENT MOVEMENT FACTOR ( SM = SA x sin 89 ) of sediment provided to the drainage system for trans FIGURE 11. Relation of sediment yield and the sediment-movement factor for water sheds in the San Gabriel Mountains. The vertical line represents the value of the port. The downslope movement of sediment, upon sediment-movement factor in the Castaic watershed; its intercept (/c) with the curve which the supply of sediment depends, is a function of gives the sediment-yield estimate provided by this parameter. r=0.940,7p=279.40. F18 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS 1000 nets, and the gradients of these streams are obviously related to transport efficiency. The regression of sediment yield with T2 is shown in figure 14; the corre lation coefficient is 0.886. The third and last of the transport-efficiency 100 factors is defined as T3= (M+N2) (RcJ + (N2+N3) (Re2/3) + . . . +(Nn-i+Nn)(RC(n_u/n), where N is the num ber of streams of each order, designated by the appro priate subscript, and Rc is the ratio of the stream-channel slope of each stream order to the next higher order, as designated by a subscript. This expression for T3 can be seen by inspection to be an adjustment of that for T2. It weights the streams of lower order and their respective gradients more heavily to accord with the greater abundance of these streams and is therefore 10 100 1000 TOTAL STREAM LENGTH (2t), IN MILES FIGUEE 12. Relation of sediment yield and total stream length for watersheds in the San Gabriel Mountains. The vertical line represents the total stream length of the Castaic watershed; its intercept (7c) with the curve gives the sediment-yield estimate provided by this parameter. r=0.935, 7C=226.26. possibilities. Thus, it would be expected that total stream length be related to sediment yield. TRANSPORT-EFFICIENCY FACTORS Although total stream length (Si-) might be con sidered a measure of transport efficiency, it is apparent 10 1000 upon reflection that both the unit hydrograph and the TRANSPORT EFFICIENCY FACTOR (T, = RJ,XZD sediment yield of two watersheds may vary con FIGUEE 13. Relation of sediment yield and the transport-efficiency factor T\ for siderably, despite equal values of Si. Both the number watersheds in the San Gabriel Mountains. The vertical line represents the value of individual stream channels that compose Si and of Ti in the Castaic watershed; its intercept (7c) with the curve gives the sediment- the gradients of these channels, among other factors, yield estimate provided by this parameter. r=0.944, 7c=168.50. can cause such variation. For this reason three 1000 r I I I I I I I I additional geomorphic parameters were defined and computed in an attempt to more closely reflect trans port efficiency Te ; these parameters are herein desig nated as Tlt T2, and T3. The first of these factors is defined as Ti=!SB XSL, where Rt is the mean bifurcation ratio and Si is, again, total stream length. T\ may be regarded as an adjustment of total stream length to more closely reflect the nature of the drainage net, the individual segments of which compose Si. The regression of sediment yield with TI is shown in figure 13; the corre lation coefficient is 0.944, which is slightly higher than that for Si alone. The second transport-efficiency factor is defined as 10 100 1000 10,000 T2= SA/"X Rc, where SAT" is the total number of streams of TRANSPORT EFFICIENCY FACTOR (T2 =SNXiFc) all orders and Rc is the mean stream-channel-slope ratio FIGUEE 14. Relation of sediment yield and the transport-efficiency factor T2 for watersheds in the San Gabriel Mountains. The vertical line represents the value for a given watershed. The total number of streams is, of Tt in the Castaic watershed; its intercept (7c) with the curve gives the sediment- again, a factor that reflects the vagaries of drainage yield estimate provided by this parameter. r=0.886,7=175.15. SEDIMENT YIELD OF THE CASTAIC WATERSHED, CALIFORNIA F19 more satisfactory from a mathematical viewpoint. TI, T2, and T3. Establishing such a relationship is If basin hydrology and sediment yield are considered, incidental to this report, however. More pertinent however, Tz may be the superior geomorphic param to the problem under consideration, that of estimating eter of the two because of the importance of the princi- the sediment yield of the Castaic drainage basin, are piil channel of a drainage net and water discharge, as the results of the relationship, namely the intercept indicated by Langbein and others (1947), Potter values Ic that are shown on the regression plots of (1953), and others cited in this report. One should not, sediment yield with each of the geomorphic param however, conclude that the tributary streams of lower eters (figs. 8, 10-15). older are necessarily of little consequence; they are the The vertical line shown on each of these regression connecting links between the available sediment and plots represents the value of each of the respective it 3 ultimate transport by streamflow in the principal geomorphic parameters computed from morphometric c lannel. Sediment yield at a basin mouth may de- analysis of the Castaic drainage basin. The intercept pi jnd upon the transport efficiency of the principal values (7C) given are obtained by the intersection of c lannel, but the sediment supply to this channel each regression line with these vertical lines. Each d spends, in turn, upon the efficiency of the tributary value of /c was computed by substituting the value of streams of lower order. Accordingly, the parameter a parameter in the Castaic drainage basin into the d jfined here, namely T3, and to a lesser extent T2 as appropriate regression-line equation, obtained for the well, is thought to reflect the transport efficiency within watersheds of the San Gabriel Mountains. The value a watershed. The regression of sediment yield with of any Ic can, of course, also be obtained graphically is shown in figure 15; the correlation coefficient but with less accuracy. The reliability of the series for this pair of variates is 0.842. of sediment-yield values obtained by this procedure DISCUSSION OF RESULTS depends upon (1) the degree of significance of the correlation between sediment yield and each of the As previously stated, sediment yield represents geomorphic parameters for the watersheds of the San tiie cumulative interaction of a large number of climatic, Gabriel Mountains, and (2) the degree of similarity geologic, edaphic, and other watershed character between the Castaic drainage basin and those in the istics. The results of this study indicate, however, San Gabriel Mountains. Discussion of these two points tiat sediment yield is also a function of the geomorphic follows. parameters given in the following equation: SIGNIFICANCE OF CORRELATIONS (6) Although several of the parameters involved can be considered as either populations or samples for each where SA is sediment area or an availability factor, watershed, the watersheds will herein be treated as &M is a sediment-movement factor, and Te is a transport- samples for statistical purposes. This treatment will efficiency factor, here used in substitution for SL, allow demonstration that the six watersheds of the San Gabriel Mountains comprise a sample of sufficient size to be representative of a population of watersheds. The significance of the correlations obtained from this sample of six basins can be determined by application of Fisher's t test for small samples (Ezekial, 1941, p. 318). The statistic t is defined as t=- (7) where n is one less than the size of the sample, and r is the correlation coefficient to be tested for significance. To test the null hypothesis that the correlation coeffi cients discussed in this report are equal to zero, namely i i 1 10 100 1000 10,000 TRANSPORT EFFICIENCY FACTOR sA =fsM=rTe =rBh=0, (8) ( T3 = (N, + N2 ) (Rc 1/2 ) + (N2 + N3 ) (Rc 2/3 ) + ... + 'IGUBE 15. Relation of sediment yield and the transport-efficiency factor Ta for at the 95-percent level of significance (a=0.05), values watersheds in the San Gabriel Mountains. The vertical line represents the value of t were computed for each of the geomorphic param of Tz in the Castaic watershed; its intercept (Ic) with the curve gives the sediment- yield estimate provided by this parameter. r=0.842, Ic=202.75. eters and ^-distribution tables were consulted. The F20 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS probabilities for SA, SM, 2L, and TI are approximately of vegetative cover, result in sediment yields of greater 0.01, and those for T2, T3, and Rh are 0.03, 0.055, and magnitude than might otherwise occur, other factors 0.185, respectively. It can be concluded, therefore, being equal. Given disparate basin geometries in that the correlations obtained are significant at the cluding relief, slopes, drainage density, and other chosen level of confidence, except for relief ratio and factors equivalent dynamic changes are unlikely to perhaps T3, which may or may not be significant, and produce identical results. Because the dynamic prop that SA, SM, SL, and 7\ would be significantly correlated erties of the Castaic drainage basin are unknown, the with sediment yield at the 99-percent confidence level, differences in balance that relate to the expected sedi had a=0.01 been chosen for the test. ment yield cannot be evaluated in a comparison with The assumption of Fisher's t test, however, includes the watersheds in the San Gabriel Mountains. the requirement that the variates, or, in the strict sense, Simple tests of geometric similarity between water the errors, be normally distributed. Because uncer sheds (Strahler, 1958) can be applied to the Castaic tainty exists whether this condition is fulfilled by the and San Gabriel Mountains watersheds, however, in data, Spearman's rank-correlation coefficient (Miller order to compare the geometric properties alone. The and Kahn, 1962, p. 335) was also computed and tested. ratio between such linear-scale factors as the mean The rank-correlation coefficient can be expressed as length of first-order streams or the mean area of second- order drainage basins in two watersheds, for example, (9) can be computed and designated as \£1 and Xl2, respec tively. If geometric similarity between the two water where xt, yt are the variates expressed as ranks, and n is sheds exists, then such X's or linear-scale ratios should the sample size or the number of pairs of variates. closely correspond. Such ratios were computed for Because this statistic is nonparametric, it does not each of the watersheds studied, and the Castaic water require the restrictive assumptions of the t test for shed was compared with each of the Sari Gabriel application. A test of the null hypothesis of equation 8 Mountains drainage basins in turn. Although the for the rank-correlation coefficients of each geomorphic individual values of X did not exhibit close correspond parameter and sediment yield leads to conclusions ence, mean values of the linear-scale ratios ranged similar to those previously obtained. The coefficients from 0.96 for the comparison of Castaic with the Big for SL, SA, SM, and Eh are 0.943, 0.886, 0.886, and Santa Anita drainage basin to 1.14 for that of Castaic 0.029, respectively, and are 1.000 for Tl} Tz, and T3. with San Dimas drainage basin, except for the compari For a one-sided test such as this, a rank-correlation son of Castaic with Sawpit, which gave a mean value coefficient of 0.829 or more is significant at the 95- of 1.98. The computed value of Langbein, W. B., and others, 1947, Topographic characteristics Morisawa, M. E., 1959, Relation of quantitative geomorphology of drainage basins: U.S. Geol. Survey Water-Supply Paper to stream flow in representative watersheds of the Appa 968-C, p. 125-157. lachian Plateau province: Tech. Rept. 20, Proj. NR 389- Langbein, W. B., and Schumm, S. A., 1958, Yield of sediment 042, Office of Naval Research, Geography Branch, 94 p. in relation to mean annual precipitation: Am. Geophys. Murphy, N. F., 1949, Dimensional analysis: Virginia Poly tech. Union Trans., v. 39, p. 1076-1084. Inst. Bull., v. 42, no. 6, 40 p. Leopold, L. B., and Miller, J. P., 1956, Ephemeral streams Potter, W. D., 1953, Rainfall and topographic factors that affect hydraulic factors and tbeir relation to the drainage net: runoff; Am. Geophys. Union Trans., v. 34, p. 67-73. U.S. Geol. Survey Prof. Paper 282-A, 36 p. Rowe, P. B., 1962, Watershed management and upstream sedi ment production: Pacific Southwest Inter-agency Co mm. Lustig, L. K., 1963, Distribution of granules in a bolson environ Minutes, Tuscon, Ariz., Mar. 8, 1962, p. 20-22. ment in Short papers in geology and hydrology: U.S. Geol. Schumm, S. A., 1956, Evolution of drainage systems and slope in Survey Prof. Paper 475-C, p. C130-C131. badlands at Perth Amboy, N.J.: Geol. Soc. America Bull., Maxwell, J. C., 1960, Quantitative geomorphology of the San v. 67, p. 597-646. Dimas experimental forest, California: Tech. Rept. 19, Sherman, L. K., 1932, The relation of hydrographs of runoff to Proj. NR 389-042, Office of Naval Research, Geography size and character of drainage basins: Am. Geophys. Union Branch, 95 p. Trans., v. 13, p. 332-339. Melton, M. A., 1957, An analysis of the relations among elements Strahler, A. N., 1950, Equilibrium theory of erosional slopes of climate, surface properties, and geomorphology: Tech. approached by frequency distribution analysis: Am. Jour. Rept. 11, Proj. NR 389-042, Office of Naval Research, Sci., v. 248, p. 673-696, 800-814. Geography Branch, 102 p. 1952, Hypsometric (area-altitude) analysis of erosional Miller, R. L., and Kahn, J. S., 1962, Statistical analysis in the topography: Geol. Soc. America Bull., v. 63, p. 1117-1141. geological sciences: New York, John Wiley and Sons, 483 p. 1954, Statistical analysis in geomorphic research: Jour. Geology, v. 62, p. 1-25. Miller, V. C., 1953, A quantitative geomorpbic study of drainage 1957, Quantitative analysis of watershed morphology: basin characteristics in the Clinch Mountain area, Virginia Am. Geopbys. Union Trans., v. 38, p. 913-920. and Tennessee: Tech. Rept. 3, Proj. NR 389-042, Office of 1958, Dimensional analysis applied to fluvially eroded Naval Research, Geography Branch, 30 p. landforms: Geol. Soc. America Bull., v. 69, p. 279-300.