QUANTITATIVE GEOMORPHOLOGY

OF THE

SAN DIMAS EXPERIMENTAL FOREST, CALIFORNIA

Technical Report No. 19

Project NR 389-042 Contract N6 onr 271-30: Nonr 266 (50) Office of Naval Research

by

James C. Maxwell

Department of Geology Columbia University New York 27, N. Y.

1960

Department of Geology

Columbia University

New York 27, N. Y.

QUANTITATIVE GEOMORPHOLOGY OF THE SAN DIMAS EXPERIMENTAL FOREST, CALIFORNIA

Technical Report No. 19

Project NR 389-042 Contract N6 onr 271-30: Nonr 266 (50) Office of Naval Research

by

James C. Maxwell

The research reported in this document has been made possible through support and sponsorship by the United States Department of the Navy, Office of Naval Research, Geography Branch, under Project NR 389"042, Contracts N6 onr 271*30 and Nonr 266(50). Reproduction in whole or in part is permitted for any purpose of the United States Government.

1960 Lithoprinted in U.S.A. EDWARDS BROTHERS, INC. Ann Arbor, Michigan Contents

Page

Abstract. vi Introduction. vii Acknowledgments. viii The San Dimas Experimental Forest. 1 Physical geography. 1 Location and general topography. 1 Topography of individual watersheds. 1 Wolfskill Canyon. 1 Fern Canyon. 2 Fern small watersheds. 2 Upper East Fork. 3 Bell Canyon. 3 Bell small watersheds. 3 Volfe Canyon. 3 Climate. 4 Soils. 5 Vegetation. 5 Geology. 7 Bedrock geology. 7 Erosional history. 8 Morphometric properties. 9 General statement. 9 Basic properties. 9 Channel location. 9 Channel order and numbers of streams. 9 Channel length, basin area, and basin perimeter. 9 Basin diameter. 9 Maximum flow length. 10 Relief. 10 Basin azimuth. 11 Maximum valley-wall slope. 11 Derived properties. 11 Basin shape, circularity, elongation. 11 Relief ratio, relative relief. 11 Bifurcation ratio. 12 Drainage density, channel frequency. 12 Measurement and computation precision. 12 Map accuracy. 12 Instrument precision. 13 Data processing equipment and accuracy. 14 Analysis of measurements. 15 Sampling. 15 Means, standard deviations, and extremes. 16 Normal distributions assumed in other studies. 16 Normality tests used in present study. 16 Results of normality tests. 17 Length. 17 Area. 17 Diameter. 18

iii IV

Perimeter. 18 Elevation. 18 Relief. 18 Relief ratio. 18 Relative relief. 19 Elongation. 19 Circularity. 19 Drainage density. 19 Channel frequency. 19 Homogeneity of variance. 19 Statistical inferences. 19 Length, basin area, and diameter. 20 Relief, relief ratio, and relative relief. 20 Perimeter, elongation, and circularity. 21 Drainage density and channel frequency. 21 Analysis of variance. 21 Statistical inferences. 21 Channel length, basin area, and diameter. 21 Relief, relief ratio, and relative relief. 22 Perimeter, elongation, and circularity. 22 Drainage density and channel frequency. 22 Drainage composition. 22 Replication of field observations. 24 Plan of field tests. 24 Channel network. 24 Mean channel lengths and basin areas. 25 Correlation of geomorphic properties and flood discharge. 26 Sources of hydrologic data. 26 Storm characteristics and watershed conditions. 26 Geomorphic properties. 27 Combined equations. 29 Conclusions. 30 Applicability of methods. 30 Analysis of methods. 30 Correlations with flood discharge. 31 References cited. 33 Appendices I Characteristic values of geomorphic properties. 71 II Percent probability of observed departure from normality. 86 IE Topographic maps of watersheds. 93 (There are 7 maps in this Appendix, of which 4 [Wolfskill Canyon, Fern Canyon, Upper East Fork, and Bell Small Watersheds] will be found in the pocket on the inside back cover.) IV Coefficients of correlation. 96 Illustrations

Tables Page

I. Monroe Canyon soil characteristics. 37 II. San Dimas vegetation distribution. 38 HI. Common and botanical names of some species of the San Dimas Experimental Forest. 39 IV. Constants for approximating density of cover types. 40 V. Geologic mapping units. 41 VI. Geomorphic properties. 42 VII. Summary of normality tests. 43 VIII. Summary of homogeneity of variance tests. 44 IX. Summary of analysis of variance. 45 X. Comparison of numbers of stream segments. 46 XI. Comparison of mean lengths of stream segments. 47 XII. Comparison of mean basin areas. 47 XIII. Variables used in multiple correlation. 48 XIV. Coefficients for multiple correlations with peak discharge. 49

Figures

1. Index maps showing relation of San Dimas Experimental Forest to Los Angeles County. 53 2. Index map to watersheds of San Dimas Experimental Forest. 54 3. Precipitation and temperature data of Tanbark Flat, San Dimas Experimental Forest. 55 4. Isohyetal map of San Dimas Experimental Forest. 56 5. Vegetation types of southern California. 57 6. System of channel ordering. 58 7. Relation of stream numbers to stream order. 58 8. Examples of basin diameter determinations. 59 9. Example of relation of observed to mapped topographic features . . 60 10. Relation of stream numbers to order. 61 11. Relation of stream length to order. 62 12. Relation of basin area to order. 63 13. Relation of basin diameter to order. 64 14. Relation of relief to order. 65 15. Relation of basin elongation to order. 66 16. Relation of drainage density to order. 67 17. Relation of channel frequency to order. 68

v Abstract

Methods of quantitative geomorphology, devel¬ Measurement distribution normality was tested oped in regions of humid climate and moderate re¬ by Chi-square and Kolmogorov-Smirnof tests. Cir¬ lief, were tested for applicability to mountainous cularity distributions were normal; channel length, terrain in five fifth-order watersheds in the San basin diameter, perimeter and relief, and drainage Dimas Experimental Forest, San Gabriel Moun¬ density distributions were log-normal. Polymod¬ tains, southern California. Deep canyons, rocky ality of first-order area indicated that it may be cliffs, sharp-crested ridges and many waterfalls useful in detecting multicycle erosional topography. five to 50 feet high typify these watersheds. Their Bartlett’s test for homogeneity of variance showed dense chaparral vegetation consists largely of that logarithms of first-order properties did not chamise, sage, ceanothus, manzanita, and oak, have homogeneous variance. Logarithms of higher which have been grouped in ten associations and order channel length, basin area and diameter, areally mapped. Rainfall totals 20 to 40 inches, drainage density, and channel frequency were of mostly from a few intense winter storms; sum¬ homogeneous variance. These results cast some mers are hot and dry. Stony residual soils are doubt on the assumption made in other studies that generally less than three feet deep. Bedrock of geomorphic properties measured in contiguous gneiss, schist, metadiorite, and granite, inter¬ areas have homogeneous variances. mingled, is deeply weathered, friable to depths ex¬ Differences between watershed logarithmic ceeding 50 feet in places, and fractured by many means of second-order and higher order channel faults of small displacement. Over-steepened inner length and first-order relative relief were found canyon walls, entrenched meanders, and knick-point to be non-significant by analysis of variance. Sig¬ waterfalls indicate recent rejuvenation. nificant differences were found between watershed During two summers’ field work all channels logarithmic means of second- and third-order and basin divides in the watersheds were drawn on basin area and diameter, second-order drainage 1/8000 topographic maps. Channel segment num¬ density, and second-order channel frequency. Laws bers and lengths, basin areas, diameters, perim¬ of stream numbers, of channel lengths, and of basin eters, as well as relief, elongation, circularity, areas were found to apply to the San Dimas water¬ relief ratio, drainage density, and channel fre¬ sheds. A law of basin diameters and a law of basin quency, were measured from these maps. New or relief were postulated and applied. Elongation modified definitions were developed for channels, showed little variation with order. Drainage den¬ basin diameter, elongation, and relief ratio. Meas¬ sity and channel frequency were in inverse geo¬ urement precision was within sources of error metric relation to order. arising from inaccuracies of the base maps and Multiple correlations were computed between limitations of their scale. Field observation reli¬ peak discharge and storm rainfall, cover density, ability was proven by a replication study in which antecedent rainfall, and nine geomorphic proper¬ another investigator using the same definitions and ties taken five at a time. It was concluded that the procedures independently remapped and analyzed methods of quantitative geomorphology are appli¬ two of the watersheds. Results, processed from cable to mountain watersheds, that there are sig¬ punch cards with electronic computers, include the nificant differences between the geomorphic prop¬ mean, standard deviation, maximum and minimum erties of the San Dimas watersheds, and that these of each geomorphic property and its common loga¬ differences account for some of the differences in rithm for each watershed. discharge from these watersheds. Introduction

Quantitative research on morphology of stream- comprehensive analysis of typical mountainous eroded landscapes entered its modern phase with watersheds of southern California and to attempt the publication by R. E. Horton (1945) of a major to relate the observed morphologic properties to paper in which he defined various measurable the hydrologic characteristics. drainage basin properties observed during the years The erosional history of the selected area in the he successfully directed the Horton Hydrologic Re¬ San Gabriel Mountains of southern California is search Laboratory. He found consistent relation¬ complex. Variations in bedrock geology and vege¬ ships between the rank, or order, of stream chan¬ tative cover present a wide range of conditions. It nel segments and their numbers, lengths, drainage was felt that if methods developed for humid, hilly areas, and slopes. Since that time more than a regions of the eastern United States should prove score of other workers have modified, refined, and applicable in extremely precipitous mountainous added to Horton’s list of definable and measurable terrain in an essentially semi-arid environment, watershed properties. They have extended the the range of applicability and soundness of the slowly accumulating store of quantitative landform Horton concepts on which the methods are estab¬ data to include many different geographic regions. lished would be considerably enhanced. A critical They have applied methods of statistical analysis analysis of the morphometric methods and assump¬ to these data to discover new relationships. tions of quantitative geomorphology, with an aim During the decade following publication of Hor¬ of improving the definitions and methods of anal¬ ton’s paper, most of the field work on quantitative ysis was a second objective. geomorphology of fluvially-eroded landscapes was Third, the use of digital electronic computors done in areas of moderate to low relief. Horton’s in statistical analysis was introduced for the first work was done predominantly in Pennsylvania, New time to relate morphological, geological, vege¬ York and adjoining states, in a region of humid tative, and hydrologic data. climate. Other areas studied in the humid eastern The San Dimas Experimental Forest has been states include New England (Langbein, 1947), established by the United States Forest Service, in eastern Tennessee (Miller, 1953), northern New cooperation with the State of California, for re¬ Jersey (Schumm, 1956), southern Indiana (Coates, search in mountain watersheds and watershed man¬ 1958), southeastern Missouri (Ore and White, 1958) agement. A wealth of meteorological, hydrological, and several areas in the Appalachian Plateau ecological, pedological, botanical, and geological (Morisawa, 1959). Work in the semi-arid and arid data has been collected for the area. Many forms regions of the west-central and southwestern of meteorological and hydrological data are being United States was done by Schumm (1956), Schumm continuously recorded. The present investigation and Hadley (1957), Melton (1957), and Smith (1958). is intended to be, in addition to a broadening of the Strahler (1950, 1952, 1958) carried out detailed concepts and methodology of quantitative geomor¬ field and map studies of the Verdugo Hills, southern phology, a contribution to the accumulated knowl¬ California, the first application of Horton princi¬ edge of these watersheds. The author hopes that ples and slope analysis to a mountainous terrain in the description of this area will encourage others a Mediterranean-climate environment, but it re¬ to utilize the data available for further study. mained for the writer to carry out a full-scale,

vii Acknowledgments

Assistance of Professor A. N. Strahler, of Columbia University, who sug¬ gested the study area and supervised the investigation, is gratefully acknowl¬ edged. Charles Bell, William Cromie, Howard Boggs, Michael Rubel, and Diana Maxwell assisted with the field work. The author is grateful to James Trew, who performed the replication study described below, and to P. Carlyle Neely, who wrote the programs and operated the computer for much of the analysis of data. The author’s greatest indebtedness and appreciation are to the office and field staffs of the San Dimas Research Center, and to its former director, Research Forester J. D. Sinclair. Their unfailingly friendly coop¬ eration and the valuable data they had compiled helped make this investigation successful. The research reported here has been made possible through support and sponsorship by the United States Department of the Navy, Office of Naval Research, Geography Branch, through Project NR 389-042, under Contracts N6 ONR 271-30 and N-ONR-266(50) with Columbia University.

viii The San Dimas Experimental Forest

Physical Geography 5200 feet and contains numerous steep-sided V- shaped canyons separated by narrow ridges. Wolf- skill’s long narrow form is unusual compared to LOCATION AND GENERAL TOPOGRAPHY the other more pear-shaped watersheds in the Forest. It is 3.3 miles long and less than one mile The San Dimas Experimental Forest, about 35 wide, oriented with its long axis trending east- miles northeast of Los Angeles, occupies 17,000 northeasterly. acres on the southern slopes of the San Gabriel Another unusual feature of Wolfskill Canyon is Mountains (Figure 1), within the Angeles National the number and size of its waterfalls. Highest in Forest of southern California. This experimental the Experimental Forest are Wolfskill Falls, lo¬ forest is considered to be a representative seg¬ cated on the main stream one-half mile upstream ment of the San Gabriels (Storey, 1948, p. 3) and is from the mouth of the canyon and rising more than also representative of much of the chaparral cov¬ 130 feet above a base elevation of 2050 feet. They ered mountain land in southern California. It con¬ have acted as a local baselevel for the stream tains two major drainage networks: San Dimas above, and for a considerable distance upstream Canyon and Big Dalton Canyon (Figure 2). Each of no other falls occur (Bean, 1946). The next large these has a number of tributary watersheds. Five fall in the main stream is at 3650 feet elevation. of the tributaries, Wolfskill, Fern and Upper East At 4500 feet elevation is the uppermost of a short Fork in the San Dimas network, and Bell and Volfe series of falls. in the Big Dalton network, were studied in this The main stream channel, narrow throughout project. In addition, two groups of small water¬ its upper end, widens to 50 feet or more above sheds, one in Bell Canyon and one in Fern Canyon, Wolfskill Falls. Running water can often be found were studied in greater detail. in the main stream during the dry season. The The San Gabriel Mountain range, oriented on an water disappears into the coarse channel-bottom approximately east-west axis, is 70 miles long, 25 deposits only to reappear further along the stream miles in maximum width, and occupies an area of course. Along much of the length of the main 1400 square miles. The mountains are bounded by stream the channel side walls are bare bedrock, the Mojave desert and Santa Clara river on the extending upward tens of feet. In some places north, by the Santa Ana and San Gabriel valleys on narrow alluvium floored meandering gorges with the south, the San Fernando valley on the west, and overhanging walls have been cut in the crystalline Cajon Canyon on the east. Summit altitudes in¬ bedrock. crease from 5,000 feet at the western end to 10,059 Tributary streams are characterized by very feet (San Antonio Peak) near the eastern end. The steep gradients and have many waterfalls, from 10 range is a deeply-dissected, mature mountain mass, to 25 feet high, but some more than 80 feet high. trenched by many steep-sided canyons. The only Tributary channels are often choked with debris nearly level ground is in the narrow, debris-choked which has moved by creep, sheet wash, and slump flood plains of the major rivers. from the steep adjacent slopes. The narrow chan¬ nel bottoms are usually trenched through the debris into bedrock. TOPOGRAPHY OF INDIVIDUAL WATERSHEDS At the head of Wolfskill Canyon is a small area of about 30 acres whose gently rounded topography Wolfskill Canyon contrasts sharply with the rest of the canyon. The slopes in this area are more gentle, have sigmoidal Wolfskill Canyon, designated Watershed I in profiles, and are covered with a deeper, apparently Experimental Forest studies and in this report, more stable soil. The valley transverse profiles lies in the southeastern part of the San Dimas are broadly up-concave rather than V-shaped. It is drainage system (Figure 2). It includes an area of quite probable that this area is a small remnant of 2.49 square miles,1 with elevations from 1700 to the gently rolling pre-Pleistocene erosion surface (see Erosional History). It has been protected 1 As measured from large scale maps in this study; see from dissection by a group of resistant dacite dikes Measurement Precision below. which cause the uppermost waterfalls in the main-

1 2 stream just below the upland remnant, and by its rock, with a discontinuous veneer of bouldery allu¬ remoteness from regional base level at the head of vium covering the channel bottoms. With the ex¬ an unusually long canyon. ception of Brown’s Flat the slopes are high-angle, Except on the upland remnant, the slopes of unstable repose slopes. A slight steepening of the Wolfskill Canyon are equal to or steeper than the slopes, even that caused by walking on them, often angle of repose of the coarse granular soil cov¬ causes local debris slides. Fern Canyon contains ering them. Small slumps and slides of dry debris the highest point, elevation 5500 feet, in the San are common. Bean (1946) states that the areas Dimas Experimental Forest, a rounded knob on the underlain by granodiorite, in the southwest part of divide at the head of Fern Canyon. the Canyon, have a tendency to develop into steeper Fern Canyon watershed has reached the Davis¬ slopes, on which there is more active sliding and ian stage of early maturity in the N + 1 cycle of soil movement, than those of the remainder of the landmass development although no upland remnant Canyon underlain by gneiss. of the N cycle remains. The rejuvenated main Expressed in terms of the Davisian concept of stream is ungraded and youthful. landform evolution, the rejuvenated streams of Wolfskill Canyon are in the stage of youth. The Fern small watersheds landmass as a whole has reached very early ma¬ turity, with maximum relief and maximum extent Three small tributaries at the head of Fern of steep valley-wall slopes. If the upland remnant Canyon have been mapped by Forest Service per¬ represents the oldest, or N erosion cycle, then the sonnel at a large scale. These watersheds and an succeeding cycle, now in early maturity, may be adjoining area on the same large-scale map are designated the N + 1 cycle. individually designated Watersheds II-1, -2, -3, and -4. They have been measured somewhat more intensively in the present investigation to establish Fern Canyon relationships which could not readily be determined Fern Canyon, designated Watershed II, lies im¬ in the larger canyon watersheds. The Fern small mediately north of Wolfskill Canyon in the San watersheds and adjacent area are located in the Dimas drainage system (Figure 2). It contains northeast corner of Fern Canyon. They contain a 2.20 square miles; elevations range from 2600 to total area of approximately 0.3 square miles with 5500 feet. The watershed, of very roughly pear- surface elevations from 4500 to 5400 feet. Direc¬ shaped form is approximately 2.5 miles long and tions of trunk drainage range from northwest to 1.1 miles wide. In common with the other San southwest. These sub-watersheds have the same Dimas network watersheds, it consists of narrow, steep-sided, V-shaped valleys and narrow, sharp- V-shaped canyons and sharp-crested mountain crested ridges as the other tributaries in Fern ridges. Canyon; all have slightly elongate, pear-shaped A large, shallow closed depression known as outlines. Brown’s Flat occupies approximately 40 acres at Stream gradients in these small watersheds an elevation of 4250 feet on the southern side of have been slightly modified by artificial structures. this watershed. The depression is covered by a In 1938 a mountain wildfire burned into the head of deep sandy loam soil which supports a pure stand Fern Canyon. To prevent excessive erosion of the of tall, widely-spaced Ponderosa pine and a con¬ stream channels and loss of the stream gaging tinuous cover of wild grass. An area of about 150 stations and other instruments in floods which acres on the south canyon wall drains into Brown’s usually follow fires in these mountain watersheds, Flat, and hence does not contribute directly to the a large number of small check dams, one-half to watershed’s channel discharge during a storm. The three feet high, were built in the tributary channels. underground drainage from Brown’s Flat is into A few dams 6 to 16 feet high were built in the main Fern Canyon. Several channels traversing the channels. Sediment soon filled the channels above slope north of and below Brown’s Flat noticeably the dams, locally decreasing the channel gradients. increase in size, apparently because of groundwater The decrease in gradient reduced the capacity of inflow through the shattered and deeply weathered the streams, permitting a gradual accumulation of bedrock. The depression was formed by a major debris along some of the channel banks. The accu¬ pre-historic slump movement on the southern mulation of debris locally has caused a decrease boundary ridge of the watershed. A similar but in steepness of the lowest three to five feet of the much smaller slump block depression exists out¬ valley side slopes. Hence the steepest segment of side the Experimental Forest boundary on the east the valley side slope, which in southern California side of the ridge at the head of Fern Canyon. mountain watersheds is characteristically imme¬ The main stream and tributaries of Fern Can¬ diately above the channel bank, is often several yon have steep gradients with many waterfalls 10 feet above the channel bank in the Fern small wa¬ to 50 feet high. All of the channels are cut in bed¬ tersheds. 3

The Fern small watersheds are in a mature thin veneer of alluvium, apparently less than five stage of erosional development with maximum feet thick, which is scoured to bedrock in the pres¬ slope area and maximum relief. The channels ent channel. within these watersheds would be described as in The remainder of the canyon is very similar to the late youth stage of stream development, with others in the San Dimas system; the tributaries many streams locally approaching a graded con¬ have numerous falls 5 to 20 feet high in narrow, dition. steep-gradient, bedrock channels. Thus, according to the Davisian concept of stage, the landmass of the watershed has passed Upper East Fork early maturity in the N + 1 cycle. Continued re¬ The Upper East Fork of the San Dimas drain¬ moval of mass will decrease relief and decrease age, Watershed III, occupies the northeast corner the percentage of the total area which is steeply of the Experimental Forest and lies immediately sloping. The main stream of the canyon has north of Watershed II. With narrow canyons and reached early maturity throughout much of its mountainous ridges it covers 2.18 square miles. length. Surface elevations range from 2600 feet to 5200 feet. The width of more than 1.5 miles, greatest Bell small watersheds of the watersheds studied, is large relative to its length of 2.6 miles. The four Bell small watersheds are located at The western, lowest third of Watershed III is the upper, northern end of Bell Canyon, forming a constricted to a single large canyon. Two water¬ radial, fan-shaped orientation, and including the falls, about 50 and 80 feet high, occur in this entire headwaters of Bell Canyon. These water¬ narrow canyon. Below the lower fall, near the sheds are designated VIII-1 to VHI-4, from east to outlet of the watershed, the main stream flows in west. Watershed VIII-1 in the northeast corner of a deep bedrock trench, plunging through a series Bell Canyon, has an area of 0.12 square miles. Its of enormous coalesced potholes with smoothly elevation ranges from 2450 to 3475 feet, and its polished, often overhanging walls 20 to 50 feet high. length is oriented southwesterly. Adjacent to it is the largest of these small watersheds, VIII-2, 0.16 square miles in extent, with elevations from 2480 Bell Canyon to 3455 feet, oriented southerly. Watershed VU3-3 Bell Canyon, Watershed VIII, in the western includes the highest point, 3536 feet, in Bell Canyon third of the San Dimas Experimental Forest, is at in its 0.10 square miles. Its lowest elevation is the northeastern head of the Big Dalton drainage 2480 feet, and its principal drainage is southeast¬ system. It has an area of 1.36 square miles, with erly. Watershed VIII-4, the smallest of the Bell surface elevations ranging upward from 1880 feet; Canyon group, has an area of 0.06 square miles, is about 2.3 miles long and 0.8 miles wide. Al¬ elevations from 2400 to 3350 feet, and is oriented though the long axis of the basin is oriented north- east-southeasterly. northeast, near the southern end of the canyon, the All of the Bell small watersheds have steep- main stream curves to the west, so as to leave the gradient channels in narrow, V-shaped canyons watershed approximately one-quarter mile north separated by precipitous, sharp-crested divides. of the southern limit of the basin. Numerous waterfalls, up to 20 feet high, are char¬ Although Bell Canyon has the deep, V-shaped acteristic of both main and tributary channels. The side canyons, narrow sharp-crested ridged, and Bell small watersheds are in the stage of late steep unstable slopes characteristic of the water¬ youth and have youthful channels. sheds of the San Dimas system, its main stream more closely approaches a graded or equilibrium Volfe Canyon form. The high waterfalls and deeply entrenched bed rock gorges characteristic of the lower reaches Volfe Canyon, Watershed IX, is located imme¬ of the main streams of Wolfskill, Fern, and Upper diately west of Bell Canyon, in the Big Dalton East Fork Canyons are absent in Bell Canyon. drainage system. It has an area of 1.18 square There are no falls on the lower two-thirds of the miles. The main stream joins that of Bell Canyon main channel, although near the mouth of the can¬ at an elevation of 1880 feet. The highest elevation yon the channel gradient steepens to more than in Volfe Canyon is 3500 feet. The watershed has a five feet per hundred feet. Throughout the middle symmetric, pear-shaped outline; is approximately and most of the lower course of the main stream, 1.9 miles long and 0.7 miles wide. The main the canyon bottom has been widened by lateral stream flows southward. planation, leaving a discontinuous flood plain 10 to The central section of Volfe Canyon contains 30 feet wide, with a few stretches more than 50 several cone-like summits on the ends of lateral feet wide. The valley floor is covered by a very ridges which extend into and displace the channel. 4

The lateral ridges, which extend from the peri¬ and March while less than two per cent occurs be¬ pheral divide toward the center of the canyon, are tween June and September. The rainfall varies generally narrow, sinuous, and sharp crested, as within the Forest depending upon elevations and are most of the ridges in the Experimental Forest. orientation with respect to prevailing storm paths. Near their ends, the ridge crests rise a few tens In southern California, storms moving from the to more than one hundred feet, often rising from a Pacific tend to travel towards the east and north¬ distinguishable saddle in the ridge. Beneath each east. The moist air, forced to rise over the north- terminal summit the base of the ridge usually west-southeast trending ranges of the San Gabriel broadens. The main stream usually swings around and San Bernardino Mountains, delivers much rain¬ the conical base in a sweeping curve. These coni¬ fall upon the south and west slopes. The result is cal summits appear to be the result of canyon en¬ a band of rainfall ranging from 20 to 40 inches trenchment around meander-cutoff remnants which annually on the southerly side of the San Gabriel- were formed during an earlier erosion cycle. San Bernardino Ranges. An isohyetal map of the The southern third of the main channel of Volfe San Dimas Experimental Forest (Figure 4) shows Canyon has a continuous floodplain 50 to 150 feet the detail within a small part of this band of rain¬ wide. The floodplain terminates one or two hun¬ fall. dred feet upstream from the mouth of the canyon, Rainfall was measured by a network of 310 where the channel gradient steepens and the can¬ standard vertical 8-inch raingages, a concentration yon becomes narrower. The floodplain is more of one gage to every 50 acres (Storey, 1939). Such maturely developed than that in Bell Canyon; it is large divergences in rain catch were observed that covered by coarse, bouldery alluvium of undeter¬ other sampling methods were tested, leading to the mined thickness. The main channel, three to five present installation of tilted gages inclined perpen¬ feet deep, does not cut through the floodplain allu¬ dicular to the contiguous slopes. Records from the vium. Near the mouth of the canyon, the alluvial tilted gages were used to correct the previous deposits are absent; the steepened boulder-choked vertical-gage measurements (Hamilton, 1954). channel is on bedrock. The pattern of rainfall (Figure 4) is a result of Description of the Davisian stage of erosion of topographic influences. Air currents passing up the watershed is made difficult by the steepened, Big Dalton Canyon are cooled and yield increasing inequilibrium section of the main stream at the amounts of rain as they ascend. Reaching the mouth of the canyon. It is probable that continued lower parts of Bell, Volfe, and Monroe Canyons, erosion in the upper part of the canyon will de¬ the currents swing eastward and cross a low saddle crease relief and, as the floodplain alluviation con¬ in the Big Dalton-San Dimas divide. After passing tinues, increase the amount of area of low slope. into the San Dimas drainage, these currents en¬ However, the apparent rejuvenation at the mouth of counter others traveling up San Dimas Canyon. the canyon may cause the floodplain to be trenched, The combined currents thence travel eastward, increasing relief. Because the larger portion of the ascending the high ridge which bounds the east side watershed is distant from the influence of the of the Experimental Forest. Increased cooling steepened channel, the watershed is considered to there produces the heaviest rainfall on the Forest. be early mature to mid-mature, with an early ma¬ Areas of comparatively low rainfall near the mouth ture main stream channel. of San Dimas Canyon and in the vicinity of Tanbark Flat are both on the lee side of high points on the Big Dalton-San Dimas divide (Storey, 1948, p. 10- CLIMATE 12). A detailed study of the factors affecting pre¬ cipitation within the Experimental Forest showed The San Dimas Experimental Forest has a sub¬ dependency upon elevation, local slope of the tropical Mediterranean climate (Koppen classifica¬ ground surface, aspect or orientation, topographic tion Csa) in common with most of southern Cali¬ rise within five miles northeastward, and geo¬ fornia. The winters are mild and rainy; the sum¬ graphic position within the Forest (Burns, 1953). mers are hot, dry, and sunny (Figure 3). The sum¬ The combination of cyclonic and orographic mer maximum daily temperatures often exceed 100 effects produces rainfall from several directions. degrees Fahrenheit. The minimum daily winter The northerly storms usually produce small temperatures at elevations above 4000 feet often amounts of precipitation occurring generally at drop below freezing; and some of the precipitation low intensity and at only slight inclinations from occurs as snow (Sinclair, 1954). Over the greater the vertical. Southerly storms are the great rain- part of the Experimental Forest, however, most of producers of the area; and their precipitation is the precipitation occurs as rain. usually of much greater intensity than the northerly Most of the annual rainfall occurs during the storms. The southerly storms are accompanied by winter from extra-tropical cyclones. Seventy eight higher winds than the northerly storms and their per cent of the rainfall occurs between December precipitation usually is inclined a considerable 5 amount from the vertical (Hamilton, 1944, p. 517). found in the soil study, and of 14 soil moisture Most of the precipitation occurs in a few of the plots, are summarized in Table I. winter storms. During a 14-year period, 23 per A local exception to the characteristic residuum cent of the total precipitation fell in 3 per cent of which covers the slopes of the San Dimas Experi¬ the storms. High precipitation intensities are mental Forest occurs on Watershed II, Fern Can¬ characteristic of the region: In 1926, at Opid’s yon. Here, in Brown’s Flat, a shallow closed de¬ Camp in the Angeles National Forest, 0.65 inches pression formed by an ancient land slip, deep or¬ of rain fell in 1 minute, a world record until 1955. ganic zonal soil has developed on 40 acres, or In 1943, 26.13 inches of rain fell in a 24-hour three per cent of the total area of the watershed. period at Camp LeRoy, Angeles National Forest, The soil, a sandy clay loam, has been derived establishing a new record for the United States largely from sediment washed into the depression (Hamilton, 1951, p. 3). by adjacent ephemeral streams.

SOILS VEGETATION

Soils of the San Dimas Experimental Forest, The San Gabriel Mountains are covered by three typical of those of mountain watersheds in southern different vegetation complexes: chaparral, wood¬ California, are of two kinds: (1) Narrow strips of land, and forest (Figure 5). Of these, chaparral, immature alluvial soils form discontinuous borders composed of many different shrubs and a few trees, to the main channels, but these soils occupy less is dominant on the San Dimas Experimental Forest. than one per cent of the five watersheds described It grows at elevations of 1,000 to 6,000 feet above in this study. (2) The watershed slopes are occu¬ sea level, usually on loose soils and steep slopes pied by a shallow, homogeneous residual soil. that favor rapid runoff and high erosion rates when The residual soil is a coarse-textured rock- denuded of the protecting plant cover. It is charac¬ filled sandy loam. Its depth varies from a few terized by evergreen shrubs, usually with thick, inches to more than 6 feet in a few instances. On hard, flat leaves and rigid branching. The species the steep slopes shallower soils are typical and and density of the vegetation vary in relation to age numerous bedrock outcrops occur. The average of the cover, aspect or orientation of the site, ele¬ residual soil depth over the mountain watersheds vation, amount of rainfall and evaporation, and within the Experimental Forest is less than three depths of the soil. During the long hot summers the feet. No profile development or zonation, other chaparral dries and becomes very inflammable. than a downward gradational increase in apparent Wildfires tend to perpetuate and extend the chap¬ density and decrease in organic content, has oc¬ arral into areas originally occupied by other plant curred. The soil shows evidence of active downhill formations. At elevations usually above 5000 feet, creep and dry-sliding. The greater depths of re¬ where winter precipitation often occurs as snow, siduum usually occupy slopes of lower gradient open forests of several coniferous species supplant which typically have fewer rock outcrops and ex¬ the chaparral. The woodland complex generally hibit less creep. grows between 3,000 and 6,000 feet elevation, inter¬ A detailed soil survey has been completed for mingled with chaparral, on northerly-facing hill¬ Watershed Number X, Monroe Canyon, in the Big sides. Dalton Drainage (Rowe and Coleman, 1951, p. 19-21). Ten vegetation types were identified by J. S. Monroe Canyon has lower elevations, (1700 to 3500 Horton (1941, 1944, 1951) in the San Dimas Experi¬ feet) than most of the other watersheds in the mental Forest. These are designated: sage and Forest. The higher watersheds have somewhat barren areas, chamise sage chaparral, chamise steeper slopes, hence a greater percentage of areas ceanothus chaparral, chamise manzanita chaparral, with very shallow soil and exposed bedrock. In broad-leaf chaparral, oak chaparral, woodland Monroe Canyon 110 soil sample plots were exca¬ sage, oak woodland, riparian woodland, and big- vated to bedrock. Depth to bedrock was measured, cone spruce. The percentage of each type covering and samples from the pits were analyzed for tex¬ each watershed is shown in Table II. Common and ture, apparent density, field-capacity and wilting botanical names are listed in Table III. point. Statistical analyses of the results showed no Sage and barren areas are found on dry, steep, significant relationship between these soil charac¬ southerly slopes, and on other very steep slopes teristics and the measurements used to character¬ and rocky cliffs with gradients from 60 to 85 de¬ ize geology, vegetation, and topography. From this grees. The vegetation consists of scattered indi¬ it was concluded that the variations in the charac¬ viduals of white sage, buckwheat, and herbaceous teristics were essentially random, and that the re¬ semishrubs. Minor areas of graded road-surface siduum was a single homogeneous soil type (Rowe which occur in several of the watersheds have been and Coleman, 1951, p. 21). The characteristics as included in this vegetation type. Vegetation density 6 varies from 20% to less than 5%. Areal extent of it is designated chamise manzanita chaparral. The each vegetation type shown in Table II was deter¬ average cover density of these two types is about mined by map planimetry, consequently the sloping 60%. The average height is about 7 feet for the surface areas are somewhat greater than indicated, chamise ceanothus; 5 to 12 feet for the chamise especially for the sage-barren type which includes manzanita. rocky cliffs. If chamise comprises more than 20% Near the heads of the watersheds stream gullies of the total vegetation the area is typed as one of lose their definite channel characteristics and the chamise associations. If there are individuals merge into amphitheatres leading to saddles on the of either California live oak or canyon live oak the divides. These amphitheatres are partially pro¬ complex is called woodland sage. tected by ridges and thus are somewhat less arid The chamise chaparral is one of the most impor¬ than the exposed canyon slopes. At elevations tant chaparral associations of southern California. above 4,000 feet the type may occupy a solid belt In the San Dimas Forest it occupies the hot, dry where slopes are moderate on upper portions of south-facing slopes and the ridgetops. The domi¬ south facing ridges. The vegetation of these sites nant species, chamise, is not a broad sclerophyll; contains less than 20% chamise and may be domi¬ its leaves are small and linear. Associated with nated by manzanita, hoaryleaf, ceanothus, Christ- the chamise are the xerophytic hoary-leaf ceano- masberry, or other broadleaved shrub species. At thus, white sage, black sage, bigberry manzanita, higher altitudes chaparral whitehorn is common Eastwood manzanita, and other minor chaparral and Christmasberry almost lacking. This type is species (Horton, 1951, p. 12). The presence of designated broadleaf chaparral and is intermediate chamise to an amount of more than 20% of the total between the xeric chamise chaparral on south¬ vegetation distinguishes chamise chaparral. The facing slopes and the mesic oak chaparral on the chamise chaparral of Bell Canyon had an average cooler north-facing slopes. Broadleaf chaparral cover density of 48% (i.e. 52% of the surface is not has a cover density of about 80% and an average vegetated) in 1934 (Horton, 1941). The shrubs height of 7 to 10 feet. average about 5 feet high but range up to 15 feet The north-facing slopes, with lower evaporation high. A comparatively light litter layer accumu¬ losses, support a more dense vegetation designated lates under this association. oak chaparral. At lower elevations the dominant On the drier sites, intermediate between sage- species is California scrub oak. Above 4,000 feet barren type and the pure chamise, is a chamise the California scrub oak is usually replaced by sage chaparral association. The distinction between interior live oak. At this altitude the oak chaparral sage and chamise sage is sometimes difficult to sometimes occurs on south-facing slopes, where make, but usually a break of slope or change of the oak is usually associated with chaparral white¬ exposure will make it quite sharp. The percentage thorn, bigberry manzanita, and Eastwood manzanita. of sage varies from zero in the pure chamise to a An unusual feature of the north-facing association theoretical maximum of 80% in the chamise sage. is the occasional occurrence of dense stands of Below 2500 feet elevation white sage is character¬ Pacific poison oak. In these stands the poison oak istic, but black sage and buckwheat are the sage grows as a shrub, reaching heights up to 6 feet, associates at higher elevations. Chamise sage with trunk diameters of a few inches. Oak chap¬ chaparral has cover density somewhat less than arral has a vegetation density of about 80%, and the other chamise types, an average height close grows to an average height approximating that of to 5 feet, and ranges up to 8-10 feet high. No at¬ broad leaf chaparral, with some individuals more tempt was made in the mapping to separate the than 20 feet high. Considerably more litter accu¬ pure chamise from chamise sage because, accord¬ mulates on the ground under this type than under ing to Horton (personal communication, 1959), pure the chamise type. stands of chamise are almost non-existent in the The oak woodland association occurs on the San Dimas Forest. Some sage is almost always more humid of the north-facing slopes. Canyon present in the more xeric chamise type. live oak dominates this association. In drier por¬ Two other chamise associations occur in the tions interior live oak is abundant. California live chaparral group. On sites slightly less arid than oak becomes important where the soil or drainage those of the chamise sage, hoaryleaf ceanothus conditions provide more moisture. The oak wood¬ occurs with the other chaparral shrubs. If chamise land covering much of watersheds I, II, and in is and ceanothus are each present to an extent of at entirely of the canyon live oak type. Areas domi¬ least 20% the vegetation is called chamise ceano¬ nated by the more mesic California live oak have thus chaparral. In areas of its best development been included in riparian woodland. Most of these the ceanothus overtops the chamise. However, the areas are in watersheds Vn, VIII, and EX, hence ceanothus is relatively short-lived and is even¬ the large percentages of riparian woodland shown tually supplanted by chamise. If bigberry or East- in Table n for these watersheds. In general, older wood manzanita occurs over 20% in this association, stands of oak woodland have very little understory 7 because of dense shading. Oak woodland averages Geology 15-18 feet in height with some stands more than 30 feet high. It produces an amount of ground litter comparable to that of oak chaparral. BEDROCK GEOLOGY Bigcone Douglas fir, locally called bigcone spruce, is found at altitudes between 2,500 and The San Gabriel Mountains are a complexly 6,000 feet. The bigcone spruce forest and its asso¬ faulted horst, outlined and transected by three ciated chaparral and woodland types constitute a major fault zones and many minor faults. The San tension zone between the chaparral of lower ele¬ Andreas fault zone borders the north and east vations and the coniferous forests which prevail in flanks of the mountains; an unnamed fault zone ex¬ the more humid and cool higher elevations in tends from the area north of San Fernando, through southern Californian mountains. North-facing the Tujunga Creek drainage, to form the scarp slopes in this tension zone are occupied by stands along the south side. A third zone branches from of bigcone spruce or canyon live oak woodland; the latter and extends eastward, controlling the south-facing slopes are often covered with oak east and west forks of the San Gabriel River. These chaparral. principal faults are usually not sharply defined, but A few artificial plantations and a small stand of are composed of systems of roughly parallel frac¬ ponderosa pine have been included in the spruce tures and brecciated zones 50 feet or more wide forest category in Table II. The small plantations along which repeated movements have occurred. of Coulter pine and knobcone pine are located in Branching faults are common. In addition to the Watersheds V and VII, which are not included in the major faults there are numerous well-defined geomorphic study. The ponderosa pine covers less small faults of only a few feet displacement. The than 10 acres in a shallow land-slump depression, San Gabriel fault block is composed of pre-Creta- called Brown’s Flat, in Watershed II, Fern Canyon. ceous schists, gneisses, and granitic rocks, sur¬ Surrounding and underlying the tall widely-spaced rounded on all sides by Tertiary and Quaternary pines is an area of 40 acres of grassland. This is alluvial deposits and interbedded volcanics. Thus the only grassland in the Experimental Forest. it is largely similar to the other fault-block ranges A complex of woodland associations, including of southern California. The intensive faulting and riparian species, occurs in the canyon bottoms. fracturing has greatly increased the permeability Although these trees cover only a small part of the and groundwater storage capacity of the crystalline watersheds, their location near the stream chan¬ rocks, and aided the very deep weathering of the nels and springs and their daily draft on the avail¬ bedrock. able moisture enable them to exert a direct influ¬ Bedrock of the San Dimas Experimental Forest, ence on summer stream-flow. The major associa¬ representative of much of the San Gabriel Moun¬ tion is dominated by California live oak, which tains, includes both metamorphic and granitic borders the main stream channels, but which may rocks. The oldest rocks in the Experimental not require as much water as the other riparian Forest comprise the San Gabriel Formation (or species. These latter include California laurel, complex), thought by Miller (1934) to be of early white alder, California sycamore, bigleaf maple, pre-Cambrian age. In the western San Gabriel and several species of willows, all of which are Mountains this complex has been divided into three found near seeps, springs, or in the main channels mappable units, the Placerita metasediments, the wherever there is a permanent supply of water. Rubio diorite, and the Echo granite. Of the Place¬ This type of vegetation has an herbaceous under¬ rita metasediments, little can be mapped as a sep¬ story which is lacking in the chaparral types. Poi¬ arate unit because they have been so extensively son oak vines, using other vegetation for support, intruded—first by diorite, then by granite—that occur frequently. only small remnants remain in the form of layers, J. S. Horton (1944) has determined general re¬ lenses, and shreds. The numerous, small, widely lations of vegetation cover density to cover age, scattered, mappable bodies of Rubio diorite are cover type, and the geologic origin of the parent thought by Miller to be remnants of once larger material of the soil. These relations permit the masses, remaining after the wholesale attack of calculation of prevailing cover density at a given granite magma upon the Rubio diorite and earlier time after a watershed has been burned. The con¬ metasediments. During this attack both the meta¬ stants determined by Horton and the general equa¬ sediments and the diorite were extensively cut, tion used to calculate cover density from these locally injected lit-par-lit, and variably digested constants are given in Table IV. Values of cover by the Echo granite, which is usually foliated, gran¬ density for successive years were calculated and, ulated and variably contaminated. with precipitation data and geomorphic character¬ The next younger identifiable formation in the istics, were correlated with annual flood discharge Experimental Forest is the Wilson diorite. It is a from the watersheds studied. medium-grained, massive to very moderately 8 foliated quartz diorite. It occurs as small irregu¬ begun to assume their east-west trend and had lar to sill-like bodies sharply cutting the rocks of been repeatedly subjected to uplift and erosion the San Gabriel complex. It is probably of late (Nevadan and Laramide revolutions). Igneous ac¬ Mesozoic age. tivity along the border faults during the Miocene A few small scattered masses of buff-colored epoch produced volcanics along the flanks of the granodiorite which occur in the gneiss may be the mountains and in the shallow seas which surrounded same as the Lowe granodiorite identified by Miller them. Continued uplift and strong erosion through¬ in the western San Gabriel Mountains. Numerous out Miocene and Pliocene time is evidenced by the aplite, granite, and pegmatite dikes, thought to be fan and fluvial sediments now comprising shales, offshoots of the Lowe granodiorite, sharply cut all sandstones, and conglomerates overlying the Mio¬ of the older formations in irregular branching net¬ cene volcanics. By the end of the Pliocene the works. The granodiorite and associated dikes are landmass had been reduced to gently rolling hills younger than the Wilson diorite, but are also of and broad valleys. Remnants of this pre-Pleisto- late Mesozoic age. cene erosion level are preserved on broad ridge- Sharply cutting the pre-Tertiary formations are tops in the western half of the San Gabriel Range. a suite of Tertiary dikes of quartz-latite porphyry, Pine Flats, Barley Flats, Pine Mountain, Josephine lamprophyre (or gabbro-diorite), and diabase. The Peak, Mt. Lawler, Strawberry Peak, and Condor latter two are sometimes laced with narrow string¬ Peak in the southern third of the Tujunga quadrangle, ers of quartz. The basic dikes are commonly fine¬ and San Gabriel Peak, Mount Markham, Mount Lowe, grained and more resistant to weathering and ero¬ and Mount Wilson in the northern part of the Pasa¬ sion than the gneisses and acidic intrusives they dena quadrangle all rise to an altitude of between cut. These resistant dikes are rarely more than a 5,350 and 6,152 feet (Miller, 1928, 1934). These few feet wide, and have little influence on larger summits, several of which are platform-like, bevel topographic features, although they frequently an irregular mixture of plutonic and steeply dipping cause small waterfalls where they are crossed by metamorphic rocks. streams. An exception is the very resistant dacite The low-level, old age pre-Pleistocene surface dike, two feet wide, which controls the 100-foot was strongly uplifted during the Pleistocene Cas- high upper part of Wolfskill Falls near the mouth cadian revolution. Tertiary sedimentary formations of Wolfskill Canyon. along the flanks of the mountains were folded and For the present study it was necessary to cate¬ tilted nearly to the positions in which they are now gorize the rocks present. Miller (1934) had desig¬ found. The shallow seas surrounding the mountains nated all of the rocks under the San Dimas Experi¬ withdrew to the west, leaving the present broad, mental Forest as belonging to the “San Gabriel flat lowlands. Uplift of the mountains progressed Formation” which he described as “mainly Place- as a series of rapid elevations followed by still- rita metasediments or Rubio metadiorite injected stands and valley widening. At least four old ero¬ by much Echo granite and often cut by later plu- sion levels can be distinguished within the San tonics.” Bean (1943, 1944, 1946), who mapped the Dimas forest. Each new uplift caused inner can¬ area in greater detail, described it as one in which yons to be incised into basin floors of the previous the various rocks do not occur in large, easily dif¬ still-stand. Traces of older basins are preserved ferentiable bodies, but as small intrusions which in the heads of the present canyons. Nickpoints are intimately associated with other small bodies. progressed up the major channels. These uplifts He described the rocks as “gneisses and schists, are considered as a single event by Miller. The which represent either highly metamorphosed sedi¬ total uplift in the San Dimas area was at least 2000 ments, or injected, somewhat metamorphosed, ig¬ to 2500 feet and may have exceeded 4500 feet. The neous rocks.” The portions which were originally sediments produced during this period built great sedimentary and originally igneous are not known. alluvial fans along the flanks of the mountains. Bean divided the rocks into four groups according Another marked uplift or rejuvenation of the to the dominant type of the group. He also mapped southern block of the San Gabriel mountains oc¬ five different types of dikes. The classification curred in the Late Pleistocene (Wisconsin?). This used in this study (Table V) is based on Bean’s di¬ caused V-shaped, over-steepened canyons 400-450 vision except that only two dike types, those which feet deep to form in the somewhat wider older can¬ cover at least 30 per cent of the area of the small¬ yon floors. Erosion during this stage removed est drainage basins in which they occur, have been much of the very large alluvial fans which had retained. been built during the earlier Pleistocene stages. New alluvial fans were built with surfaces at lower elevations than the remnants of the older, uptilted, EROSIONAL HISTORY early Pleistocene fans. By late Pleistocene major streams in the San Dimas area had reached early Prior to Miocene time the major east-west bor¬ maturity and had begun to meander in the canyon der faults were established. The mountains had bottoms. Less than 25,000 years ago the most 9 recent uplift caused the meandering streams to en¬ Channel Order and Numbers of Streams trench their channels. The entrenched meanders Ordering is a means of designating the sequence are about 200-250 feet below the floors of the older or succession, in terms of the joining of tributar¬ early-mature floodplains of the canyon stage. The ies, of channels within a drainage network. A sys¬ impassable meandering gorge at the mouth of the tem of channel ordering was first proposed in North Fork (Watershed V) of the San Dimas River, Germany by Gravelius (1914, p. 5) and was used in the very deep gorges of lower Fern Canyon and the United States by Horton (1932, 1945) and other Upper East Fork, and Wolfskill Falls, 130 feet high, hydrologists (Wisler and Brater, 1947). Gravelius’ are all results of this latest uplift. method as modified by Strahler (1952, p. 1120) was used in this study to eliminate ambiguity and sub¬ jective decision. Strahler’s method designates the Morphometric Properties smallest fingertip tributaries as first-order chan¬ nel segments. Confluence of two channel segments of the same order forms a channel segment of the GENERAL STATEMENT next higher order. (Figure 6). Because numbers are used to designate the different orders, and One of the principal objectives of this investi¬ there must be, by definition, a successively in¬ gation was to determine which of the many meas¬ creasing sequence, stream ordering is an ordinal urable geomorphic properties would most effective¬ level of measurement (Siegel, 1956, p. 24ff.). ly describe the rugged, chaparral-covered moun¬ Order is an enumerational property, achieved by tain watersheds in southern California. To accom¬ counting. In this study the order, u, of each chan¬ plish this purpose twelve basic properties, and nel and the number, Nu, of channels of each order seven additional properties derived by combination were determined within each watershed (Figure 7). of the basic properties, were studied. These basic and derived properties are discussed below and Channel Length, Basin Area, and Basin Perimeter summarized, with their units of measurement, in One or more of the three basic size properties Table VI. All of the properties studied, except of channel length, basin area, and basin perimeter, slope and gradient, were measured on large-scale, have been used by hydrologists and geomorpholo¬ field-corrected topographic maps. gists investigating watersheds. Gravelius (1914) related mainstream length to watershed area. Horton (1932, 1945) expressed length, area, and BASIC PROPERTIES perimeter in terms of order. V. C. Miller (1953) measured length, area, and perimeter although he Channel Location expressed perimeter as the area of a circle; The location of every channel in the drainage net Schumm (1956) used length and area; Melton (1957) of each watershed was determined by field inspec¬ used length, area, and perimeter. tion and plotted, in the field, on a topographic map. In the present study, the entire network of Aerial stereophotographs were used to help obtain drainage channels within a watershed was first the correct planimetric location of the channels drawn on a map and the order of each channel de¬ and tributary basin divides. Difficulties encoun¬ termined. The curvilinear map length, Lu, of each tered and criteria established for the recognition channel segment of each order was measured along of channels are discussed below (see Replication of the channel, from its head at the junction of the Field Observations). Four criteria were found to two channels segments of the next lower order (or be adequate. Accuracy of drainage network map¬ at the upper end, if first-order) to its junction with ping was verified by the replication study. In moun¬ a channel of the same or higher order. Area, Au, tainous terrain in a climate having a prolonged dry of the planimetric projection of the basin drained season stream channels are not always readily by each channel segment was measured from the identifiable. Most reliable and most frequently used map. For each second-order and higher order is the criterion that stream eroded depressions channel, basin area includes the basins of all the usually have well-defined, nearly vertical banks. lower order channels tributary to the higher order In many cases debris or litter carried by running channel. Perimeter, Pu, was measured on the map water was draped over branches and roots of vege¬ along the topographic drainage divide, starting and tation protruding over and into the channel. In ending at the lower end of a channel of a given other cases debris was oriented in sub-parallel order, and including all tributary basins. flow-lines along the sides of the channel. Direct Basin Diameter evidence of water erosion and deposition, similar to that caused by extreme sheet erosion of slopes, To express the length of a basin, and for use in was usually found within the channel boundaries. describing the orientation and shape of the basin, 10 a straight line here termed basin diameter, Ld, tended to the basin divide. Horton (1945, p. 279) was drawn approximately parallel to the main mentions such a measure of extended stream stream of the basin. This property is essentially length measured along a stream and extended to the same as basin length defined by Schumm (1956, the watershed line. Elsewhere Horton (1945, p. p. 612) as “the longest dimension of the basin par¬ 291) says “the distance along the course of a allel to the principal drainage line.” Schumm does stream from its mouth extended to the watershed not clarify whether “longest dimension” is to have line is called mesh length.” Horton gave no nu¬ more or less emphasis than “parallel to principal merical values for this property, and he may not drainage” when the two are in conflict. As it is have measured it. Recently Maner (1958, p. 672) recognized that subjective judgment is required to used a similar property, which he called “length”, locate a straight line “approximately parallel” to a defined as “maximum watershed length . . . meas¬ sinuous line, and because scientific procedure re¬ ured approximately parallel to mainstream drain¬ quires the repeatability of a measurement, free as age from dam-site to watershed divide.” Although far as possible from subjective error, a detailed Maner measures a curvilinear length (1958, per¬ definition of diameter is required. Fortunately, in sonal communication) it is not clear to what extent almost all cases encountered in practice the loca¬ his “approximately parallel” line approaches the tion of the diameter is much more obvious and maximum meander length of the channel. simple than the following definition implies. Basin Broscoe (1959, p. 6, Fig. 2) extended stream diameter, Ld, is here defined as the length of the profiles to a headward reference point defined as horizontal projection of the straight line extending the upper end of the longest flow path, orthogonal from the mouth of the basin to its headwater divide, to the contours, leading to the channel head. This with the following criteria applied according to the length he designated Lg a special case of Horton’s procedure described below. length measure, overland flow. Maximum flow length, Lf, in this study is de¬ Criteria. The diameter must be a straight line fined as the curvilinear length of a drainage basin and measured from the basin mouth along the longest 1) be essentially parallel to the longest drainage channel and its extension perpendicular to the line, countour lines above the channel head to the basin 2) divide the main channel into segments such divide, and measured on the projection to a hori¬ that the sums of segment lengths on opposite zontal surface. It is the sum of Broscoe’s Lg, and sides of the diameter are approximately the channel length, Lu, for a basin of order, u. equal, Flow lengths were measured of all basins in the 3) be parallel to the line which separates oppo¬ Fern and Bell small watersheds. The path, or tra¬ site-facing valley slopes, jectory, itself is referred to below as the longest 4) bisect the basin area, flow path. 5) be the longest diameter. Application. The first criterion listed below is Relief to have the greatest weight and the last the least weight. If the channel is essentially: The elevation of the mouth of each basin (the straight and longer than one-half of diameter, lower end of each channel) was determined from use criteria 1, 2, and 3 the contours of topographic maps. For use in com¬ straight and shorter than one-half of diameter, puting the relief of the basin, the elevation of the use criteria 1, 3, and 4 upper end of the diameter was determined for all curved and longer than one-half of diameter, use basins. The upper elevation of the longest flow path criteria 5, 3, and 2 and the maximum elevation were also determined curved and shorter than one-half of diameter, in all basins in which flow length was measured. use criteria 3, 4, and 5 Many geomorphic and hydrologic studies since Gravelius (1914) have used a measure of maximum Although this definition seems very cumbersome, basin relief. In the San Dimas Experimental Forest its use can be learned with very short practice and many low-order basins occupy a side-hill position serves as a guide to reduce subjective decision. on the flanks of long ridges (Figure 8) and are so Elaborate application is necessary in relatively disposed that the highest point is often not at the few instances (Figure 8). point on the divide farthest from the basin mouth. In other basins the highest points are residual lo¬ cal summits or monadnocks which rise sharply Maximum Flow Length above the adjacent divides or, in a few cases, are The length of a drainage basin is sometimes on subsidiary ridges in the interior of the basins. measured along a curved line instead of a straight To eliminate the spurious effects induced by use of line. An obvious line to follow is the channel, ex¬ such unusual summits basin relief, H^, in this study 11 was measured as elevation difference between the or road. At each observation station where slopes basin mouth and upper end of the diameter. This were measured, the maximum valley-wall slope on definition generally leads to a value less than the both sides of a straight stretch of channel and the maximum relief. The upper end of the diameter corresponding channel gradient were measured. and of the longest flow path frequently fall on a The channel segment over which the gradient was saddle or low point on the divide between two op¬ measured occasionally included waterfalls a few posed basins. To ascertain the relations among feet high. the three similar properties, basin-length relief, Hd, maximum relief Hmax, and relief of the longest flow path, Hf, all were computed for those basins DERIVED PROPERTIES for which flow lengths were measured. Basin Shape, Circularity, Elongation Basin Azimuth Several different combinations of basic linear Basin diameter can serve also as an axis for and areal properties have been used to describe determining the azimuth in which the drainage is the planimetric shape of a drainage basin. Miller directed. In mountainous watersheds of southern (1953, p. 8) defined basin circularity, Rc, as the California, orientation of a basin affects both the ratio of basin area to area of a circle having the precipitation it receives with respect to the pre¬ same perimeter. This is similar to the Cox coef¬ vailingly southwesterly approach of storms, and its ficient of roundness of a plane section of sand water loss by evapotranspiration. These factors in grains (Cox, 1927, p. 180). Melton (1957, p. 5) turn affect the vegetative cover and the rates of used a ratio of channel length to basin perimeter erosion in the basin. Basin azimuth, a, is defined as a shape index. Both this and Miller’s circu¬ as the number of degrees of arc in a horizontal larity ratio fail to discriminate between departures angle measured from the direction of geographic from perfect circularity due to irregularities in north clockwise to the mouth direction of the basin gross outline and those due to crenulations in the diameter. perimeter. Schumm (1956, p. 612) used an elongation ratio, Re, defined as the ratio between diameter of a Maximum valley-wall slope circle with the same area as the basin and maxi¬ Maximum slope, 6>max, of the valley-walls lead¬ mum length of basin parallel to the principal ing down to stream channels was sampled in each drainage line. Although Schumm stated that the of the watersheds. The slope was measured in the elongation ratio is the same as the Wadell spheri¬ field, using a Brunton compass and Abney hand city ratio used in petrology the latter explicitly level. Several profiles extending from channel to requires use of the maximum diameter of a plane ridgetop and many valley-side measurements figure, whereas in many natural drainage basins showed that valley walls in the San Dimas Forest any straight line dimension approximately parallel have a nearly constant slope from the bottom to to the principal drainage line is shorter than the within a short distance from the top. Where not maximum diameter of the basin. uniform the maximum value occurs near the foot Basin elongation ratio, Re, is here re-defined of the slope. Although an effort was made at each as the ratio of the diameter of a circle having the measurement to determine the slope over a dis¬ same area as the basin to the diameter of the tance of 100 feet to minimize the effect of minor basin. This, except for the definition of diameter, surface irregularities, very dense chaparral vege¬ is the same as Schumm’s elongation ratio. Elonga¬ tation often prevented visibility between two points tion ratio was computed for every basin of each separated more than 20 feet, even when intense order. In order to test the usefulness and applica¬ light beams were used. Average length of the slope bility of a perimeter-based shape index, basin cir¬ measurements is 48.5 feet. cularity, Rc, as defined by Miller was computed No attempt was made to randomize the sampling for many basins of several orders. formally. Only those slopes which lead directly to a channel bank are included in each sample. Valley Relief Ratio, Relative Relief walls which are separated from the channel by a flood plain, those which contain rock cliffs, and Ratios of basin relief to some other length di¬ short, oversteepened basal slopes caused by chan¬ mension have been found to be closely correlated nel scour are omitted. Otherwise an effort was with other geomorphic properties and with sedi¬ made to distribute the measurements uniformly ment discharge. Schumm (1954, p. 2) defined relief throughout each watershed, within the limitations ratio, Rh, as the ratio between total relief of a imposed by the impenetrability of the chaparral. basin and longest dimension of the basin parallel Most of the measurements are located near a trail to the principal drainage line. Melton (1957, p. 5) 12 defined relative relief, Rhp, as the ratio of basin shed, can vary if one or two first-order channels relief to length of perimeter. This measure also is are added or omitted. Hence the highest-order sensitive to irregular crenulations in the perimeter point should not be considered more reliable or as noted above in discussion of basin shape. Using more exact than any other point when fitting the curvilinear basin length, Maner (1958, p. 672) com¬ bifurcation ratio line to the points in the scatter puted a relief-length essentially analogous to diagram. It is interesting to note the apparent up- Schumm’s relief ratio. concavity of the trend of the points in Figure 7. The relief ratio, Rh, is here defined as the ratio This trend has been noted in other watersheds of basin-diameter relief, H^, to basin length, Ld, (Schumm, 1956, p. 603). in the same units. This ratio could equally well be Drainage Density, Channel Frequency called the gradient of the basin diameter. This property is closely related to Reliefenergie studied Drainage density, D, or total length of channels by European geomorphologists (Neuenschwander, per unit drainage area, is a widely used geomorphic 1944, p. 74ff.) and still widely used (Ichikawa, 1958, index of scale of topographic texture. In this study p. 16). Relief ratio was computed for all basins. both length and area were measured from maps. A Relative relief, Rhp, as defined by Melton (1957, similar index, introduced by Melton (1957, p. 4), p. 5) was computed for those basins the perimeters the density of first order channels, Dx, is the total of which were measured. length of first order channels in a basin of second or larger order, divided by the basin area. Melton found Dx useful in determining the relations among Bifurcation Ratio planimetric properties of basins. The ranking of tributary channels and basins Probably the earliest use of a quantitative geo¬ within a watershed is accomplished by ordering as morphic property was by Belgrande in his study of described above. An indicator of the frequency of the Seine (Horton, 1932). Belgrande determined the channel segment branching within the watershed is ratio of the area of a watershed to the number of the ratio of number of channels of one order to streams within it. The reciprocal of Belgrande’s number of channels of the next higher order, desig¬ ratio was used by Horton (1932) and called stream nated the bifurcation ratio, Rb, by Horton (1945, density, and later (Horton, 1945) stream frequency. p. 286). Thus Rb = Nu/Nu+1 where Nu is number Following Horton, channel frequency, F, is defined of stream segments of order u. He noted that when here as the total number of channels within a basin the numbers of channels, Nu, are plotted against divided by the basin area. A corollary index, the order, u, on semi-log graph paper (or the loga¬ frequency of first order channels, Fx, is used as rithms of numbers of channels against order on defined by Melton (1957, p. 4): the number of first linear graph paper) the points on the scatter dia¬ order channels in a larger order basin, divided by gram appear to lie close to a straight line (Figures the area of the basin. This index can be used with 7 and 10). Because order number involves only an Dx to determine whether an increase in drainage ordinal level of measurement, the degree of corre¬ density is due to headward growth of channels or to lation between number of streams and order num¬ an increase in the number of first order channels. ber must be tested by nonparametric measures such as Spearman or Kendall rank-correlation (Siegel, 1956, 202 ff.). Bifurcation ratio, Rb, has Measurement and Computation been defined as the antilog of the slope of a straight Precision line fitted by inspection equally to all points of a scatter diagram of the logarithms of numbers of MAP ACCURACY channels of each order plotted against order num¬ ber (Maxwell, 1955, p. 520). This definition avoids Base maps used in this study are special large- the statistical inferences of linear regressions scale maps prepared by the staff of the San Dimas which are not mathematically justifiable with or¬ Research Center. They were modified from photo¬ dinal measurements. However, in the discussion of graphic diapositive enlargements of U. S. Geologi¬ analysis of measurements below, values of bifurca¬ cal Survey topographic maps of the area. These tion ratios were obtained from lines fitted by the topographic maps, published in 1940, are of the least-squares method. This method, which has been 7i-minute series with a scale of 1/24,000 and con¬ used in several other studies of bifurcation ratio, tour interval of 25 feet, and were surveyed during was used as a choice of convention. The reason for 1925 and 1933 by plane-table rather than photo- fitting equally to all points, instead of requiring the grammetric methods*. The 7|-minute maps show line to pass through the point of the highest order, is illustrated in Figure 7. In a watershed which is *A photogrammetrically surveyed 7|-minute map of part apparently fourth order, the number of channels of of the Experimental Forest became available after the fourth order, and conversely the order of the water¬ study started. 13 considerable detail, although many minor errors Special maps of the Fern and Bell small water¬ and a few major ones exist. A close study of the sheds areas had been made by the Forest Service. maps and observation of the terrain during field These were made at a scale of 1/2400 by plane- mapping of the drainage network convinced the au¬ table methods. Because they were made by special¬ thor that much of the topographic mapping was ists for hydrological and ecological studies, they done from the ridge crests without descending into depict the ground surface very accurately. Lengths tributary canyons. Most of the substantial topo¬ scaled from these maps are believed to have errors graphic errors are in cul-de-sac tributary canyons due to map inaccuracy of less than five feet. in the central areas of the watersheds. Usually these tributary canyons cannot be clearly seen from the boundary ridges. Some of the errors INSTRUMENT PRECISION agree closely with misleading views obtained from nearby ridgetops. One of these gross errors is Channel lengths were measured from the maps shown, with the corrected drainage net, in Figure using a dial-type map measurer, Dietzgen Number 9. In addition, there were numerous small errors 1719B, graduated to 1/32-inch, and a straight flat of the head of a first- or second-order channel in¬ scale graduated to 0.02-inch. Readings on the map correctly joined with the lower reaches of another measurer could be estimated accurately to 1/64- separate channel, of channels shown where ridges inch and were recorded to the nearest 0.01-inch. exist, and of ridges shown where channels occur. The readings from the flat scale were estimated Such errors, corrected, can be seen in the drainage and recorded to 0.01 inch. It was found that many net maps, Appendix III, prepared by the author for of the nearly straight first-order channels and this study. The fact that a plane-table survey was some of the second-order channels could be meas¬ completed, with generally good fidelity, in such ured more quickly and as accurately with the densely brush-covered precipitous terrain is a straight scale as with the map measurer. Repeated great tribute to the skill of the topographers. measurements on widely separated dates by vari¬ The San Dimas Research Center photographi¬ ous operators showed most of the readings to be cally enlarged the 7i-minute U. S. G. S. maps to a reproducible within plus or minus 0.01-inch and all scale of approximately 1/8,000. Both the negatives except the Fern Canyon and fifth-order readings to and diapositives were made on plastic base mate¬ be within plus or minus 0.02-inch. The Fern Can¬ rial of high dimensional stability to reduce errors yon readings were reproducible within 0.03-inches. arising from differential swelling during photo¬ The much longer, more meandering fifth-order graphic processing. Modifications and revisions length measurements were reproducible within were made directly on the diapositives. Most of plus or minus 0.1 inch. Because the map scale is the modifications consisted of redrawing areas of approximately 1/8000, the full scale channel length very steep topography where the contour lines were measurement errors are less than plus or minus so closely spaced and heavily drawn as to make the 0.0025 miles for all but Fern Canyon, 0.0038 miles map almost illegible. The redrawn contours fol¬ for Fern Canyon, and 0.0125 miles for all fifth- lowed the original, often incorrect, ones. The re¬ order channels. In the field mapping of the drainage visions consisted of redrawing some contours on network there was often some doubt about the exact watershed divides, and redrawing trails and roads, location of the heads of first-order channels. Some when surveys by the Research Center revealed of the channels may have been drawn as much as errors in the maps. 50 feet longer or shorter than their true length, For the present geomorphic investigation, oza- and a few may have errors up to 100 feet. Most are lid-type dry process contact prints were made believed to be correct within plus or minus 20 feet. from the revised, film-base large scale maps. The Thus the accuracy of first-order channel lengths is scales of these ozalid base maps were carefully limited by field mapping errors rather than map determined by comparison with new copies of the measurement errors. corresponding U. S. G. S. maps. Repeated meas¬ Basin diameters were all measured with a flat urements were made parallel and perpendicular to scale graduated in 0.02 inches. Because the diam¬ the grain of the paper of the ozalid maps, to deter¬ eters are straight lines with well-defined termini, mine the extent of differential shrinkage. The av¬ they could be measured more precisely. The maxi¬ erage error (difference between E-W and N-S mum measurement error is approximately 0.013 scales) was one-half of one percent, and the great¬ inches at map scale, or plus or minus 0.0015 miles est difference was 1.32% (on Wolfskill map an unu¬ at full scale, for all diameters. sually long and narrow sheet). Because the mean Basin perimeters were measured with a less of the N-S and E-W scales was used to determine precise map measurer, Dietzgen Number 1718, each map scale, length properties scaled from the graduated to 0.5 inches and read to 0.1 inches. maps may have an error, due to map scale, of plus Most of the perimeter measurements used in the or minus 0.25% (0.66% for Wolfskill Canyon). quantitative analysis were measured on the detailed 14

1/2400-scale small watersheds maps. The meas¬ gree, were read to one-half degree. The downhill urements are repeatable within plus or minus 0.2 direction of the gradient was usually measured by inches at map scale, or 0.008 miles in the small only one of the observers. The other would check watersheds and 0.025 miles for the measurements the quadrant of the measurement by subjective ori¬ on the canyon maps. entation. No analysis was made of the field meas¬ Basin areas were measured using a compensa¬ urement errors, but it is believed that the slope ting polar planimeter, Post Number 1600D. Vari¬ and gradient readings were reproducible within ous degrees of precision were used for the different plus or minus one-half degree, and the direction watersheds; consequently the measurement errors measurements reproducible within plus or minus vary between watersheds. Repeated readings were two degrees. made, tracing each area clockwise and counter¬ clockwise with the planimeter pole both to the left and to the right of the tracing point. This proce¬ DATA PROCESSING EQUIPMENT AND dure compensated for any small errors of adjust¬ ACCURACY ment of the instrument. The mean of the repeated readings was recorded. One-half of the maximum Most of the computations necessary for the range of the sets of readings was the basis for es¬ analysis of measurements were carried out on timating the precision of the measurements. In modern mass data processing equipment. Individ¬ Fern and Volfe Canyons the measurement errors ual measurements of geomorphic properties were were within plus or minus 0.05 square centimeters, transcribed into digital punch cards by key punch or 0.00012 square miles at ground scale. In upper machines. The correctness of the punching was East Fork Canyon the discrepancies were less than verified by a duplicate but separate punching which 0.1 square centimeters, which represents 0.00024 was automatically compared with the first punching. square miles on the ground. The half-maximum- These verified cards were further checked by read¬ range value for Wolfskill and Bell Canyons were ing a listing of the data from the cards compara¬ 0.02 square inches, or 0.0025 square miles full tively with the original data. It is possible that in scale. The small watersheds in Fern and Bell Can¬ the approximately 36,000 four-digit numbers thus yons were also measured to a precision of plus or recorded a few incorrectly recorded digits may minus 0.02 square inches, but at the much larger have escaped detection. The relatively small map scale this represented an error of only second-order and higher order sets of data, in 0.00003 square miles on the ground. The above which a single incorrect value would have had a precision applies to the first-, second-, and third- greater influence on derived results, were checked order areas. Most of the fourth-order and all of with proportionally greater care. Later, when the the fifth-order areas had to be arbitrarily subdi¬ data were sequenced for normality tests, extreme vided for measurement. This led to a loss of pre¬ values were examined for gross errors and none cision. The loss was greatest for the fifth-order was found. Thus it is believed that undetected areas measurements which were repeatable to errors, if any, in the transcribing of data to punch plus or minus 0.2 square inches, or 0.025 square cards exist only in mid-range values of low order miles. Previously published measurements (Sin¬ properties and do not affect the results within the clair, 1953) obtained by planimetering the fifth- accuracy reported. order watersheds as shown on small scale USGS All of the properties which had been measured maps, differ from those of this study by a maximum from maps were converted to standard units of of 0.10 square miles and an average of 0.04 square miles or square miles by multiplying by appro¬ miles. priate map scale factors in an electro-mechanical Azimuths of the basin diameters were measured computer, an IBM 602A. New data cards, with the with the calibrated head of a drafting machine, data in a floating-point format suitable for elec¬ Bruning Model 2701. The instrument is graduated tronic computers, were prepared by machine from in minutes of arc, but was read only to one-half the standardized cards. Using an IBM 650 elec¬ degree and the readings recorded to one degree. tronic computer, the means, standard deviations, The readings were reproducible to one-half degree. and extremes for each order of each property were Valley-wall slope and direction, and channel computed. All of the sets of data which were suffi¬ gradient and direction were measured in the field. ciently large were sequenced and grouped by the At each location, slope and gradient measurements 650 for Chi-square tests. Values of Chi-square were made independently by the observers at oppo¬ were computed from grouped data with a desk cal¬ site ends of the line of measurement. If the meas¬ culator. Homogeneity of variance and analysis of urements did not agree they were immediately re¬ variance computations were similarly completed done. The instruments, a Keuffel and Esser Brunton- with a desk calculator using statistics computed on type pocket transit and focusing Abney hand level, the 650. graduated respectively to one minute and one de¬ The calculations on the electromechanical 602A 15 were in fixed-point numbers, hence contained no group of observations. Statistical description often errors due to machine rounding-off. Because the relies heavily upon charts and diagrams. Statisti¬ map scale constants were rounded to six digits the cal analysis, on the other hand, is used to infer results were as accurate as the original unstand¬ conclusions about a large group of observations, ardized values. In the floating-point format used the population, from a smaller group of actual ob¬ in the 650, round-off errors of one in the tenth servations, the sample. The methods of parametric digit could occur. In summations of the larger statistical analysis are largely based on the condi¬ samples this error theoretically could exceed one tion that a sample must be obtained in such a way in the sixth digit although the probability of this that each observation in the population has an was less than one percent. The maximum probable equal and independent chance of being included in error due to machine rounding was less than one the sample, i.e., a random sample. in the seventh digit. Both the 602A and the 650 In the present study all of the basins within each have extra circuits built in to check against possible watershed were measured. The objective was to machine error. In the 650 each digit of each num¬ find characteristic values for each geomorphic ber is checked several times during each operation property within similar watersheds. The bases of as the number is moved about within the machine. similarity were unknown but presumably were de¬ There was no evidence of machine malfunctioning terminable, whether related to watershed shape in the data output. and orientation, rock type, climatic condition, or Data for the multiple regressions were punched some combination of these and other conditions. into coded paper tapes and processed on an LGP- Analysis of the observations will indicate some of 30 electronic computer. The programs used com¬ the geomorphic properties which may be useful for puted correlation coefficients, partial correlation defining distinctive populations of watersheds. coefficients, variance of coefficients, analysis of Assuming that the effort to measure all values variance, and t-tests for significance. Computa¬ of a given property in each watershed was success¬ tions were performed in floating point with nine¬ ful, the sets of measurements could be viewed digit accuracy. Because of possible cumulative either as populations or as samples. Each set is round-off error, and because of low accuracy- the population of all measurements for a specified only three or four digits—in some of the input data, watershed. Population parameters could be obtained the computed statistics are accurate to only five or and directly compared, without estimation from six digits. sample parameters. Such a viewpoint would limit The use of punch cards, paper tapes, and mass comparisons to the five watershed populations and data processing techniques and equipment in this might prohibit estimation of the parameters of study was the first application of these techniques larger populations. in quantitative geomorphology. Melton (1957) used Alternatively, each set of measurements could edge-punched cards, which were manually proc¬ be viewed as a sample. This viewpoint assumes essed, to file and sort his data conveniently. Com¬ that there exist other chaparral-covered water¬ puter processing of topographic coordinates was sheds in southern California which are not signifi¬ widely used prior to this study for photogram- cantly different from those studied. Each set of metric and cartographic purposes but had not been measurements could be considered as a sample applied to geomorphic analysis. More recently from the population consisting of the same geo¬ several other investigators have used mass data morphic property in all basins of the same order processing in projects related to landform analysis in watersheds similar to that in which the set or and evaluation (Wood, 1959; Bryson and Dutton, sample was measured. The San Dimas and Big 1960; Dacey, 1960). Evaluation of geomorphic prop¬ Dalton Watersheds had been carefully selected as erties often requires the analysis of a large num¬ representative of San Gabriel Mountain watersheds ber of measurements. It is expected that the pres¬ and of mountain chaparral watersheds in general. ent rapid evolution of data processing techniques The bases on which any one of the studied water¬ and equipment will accelerate progress in quanti¬ sheds are similar to or different from others was tative geomorphology. not known at the beginning of the study, hence any bias in selecting the samples is indeterminable. Throughout the following analysis of measurements the assumption is made that each set of measure¬ Analysis of Measurements ments is a random unbiased sample. Results of the analytical procedures may be con¬ sidered as descriptive statistics. For example, the SAMPLING normality tests may be considered as describing the particular sets of measurements without infer¬ Statistical description is used to express quanti¬ ence to any populations. Certain modifications of tatively and succinctly various characteristics of a degrees of freedom would have to be made in such 16 cases but the direction of this modification is such a sample have a normal distribution. Particularly, that a deviation found significant when considered inferences from t-tests, F-tests, and analysis of as a sample deviation would also be significant variance are valid only when the samples used are when considered as a complete set. Similarly F- normally distributed. Sample and population distri¬ values in the analysis of variance tests may be butions of various geomorphic properties are them¬ considered simply as descriptive ratios between selves, aside from statistical considerations, sub¬ two variances, without carrying the test to the jects of geomorphic interest. final step of statistical inference. Complete math¬ Miller (1953, p. 10) used analysis of variance to ematical rigor in the statistical inference depends compare means of samples of four different geo¬ upon future verification of the unbiased nature of morphic properties. He noted (p. 14) that “when the sample. frequency distribution (of basin area) was studied by means of class intervals on an arithmetic scale that there is invariably extreme skewness to the MEANS, STANDARD DEVIATIONS, AND right, and that by converting the areas into logs a EXTREMES more nearly symmetrical, normal distribution was obtained.” However, he gave no evidence of tests The mean, standard deviation, maximum and for the normality of any of his sample distributions. minimum of each property measured was computed Schumm (1956, p. 607) stated, “Frequency distri¬ for each order in each large watershed. The same bution histograms of the stream lengths and basin values were computed also for the two sets of areas show marked right skewness, which appears small watersheds. Means, pooled standard devia¬ to be fully corrected by plotting log values on the tions, maximum maxima, and minimum minima abscissa.” No tests other than graphic plotting were computed for the combined total of all basins were made to check the distributions. Melton (1957, of each order measured. The results of these com¬ p. 23) discussed the question of normality of distri¬ putations are listed in Appendix I. butions of geomorphic properties, but did not per¬ The values listed in the columns headed “Log” form normality tests because the size of samples are the antilogarithms of the means of the loga¬ taken in any category was insufficient to allow de¬ rithms of the measurements. The antilogarithms tection of moderate departures from normality. He were tabulated to permit direct comparison with used analysis of variance extensively, but tested the arithmetic means of the measurements. The means of samples, which tend to be normally dis¬ variances of most of the logarithmic measurements tributed even when the populations have moderate were used in analysis of variance tests summa¬ departures from normality. Coates (1958, p. 13) rized in Table IX. No figures were tabulated in the sampled a number of geomorphic properties. He Log columns for standard deviation because it is grouped the data into classes, computed means, thought that the antilogarithms would be meaning¬ standard deviations, and variances, and showed less and the logarithmic values could not be com¬ distribution characteristics in tables or histograms. pared with the corresponding arithmetic values. Apparently no analysis of normality other than tab¬ The antilogarithms of the extremes of the loga¬ ulation and plotting of histograms was done. rithms are the same as the arithmetic extremes so were not tabulated. Standard deviation was computed using the quan¬ NORMALITY TESTS USED IN PRESENT STUDY tity N-l, rather than N, as a divisor. This was done to follow the tacit assumption that each group The number of individual measurements of each of basins, of a single order in a given watershed, property was sufficiently large for the lower order represented a sample from a population composed basins to permit rigorous testing of sample nor¬ of the same order basins from all watersheds mality. Variates in each of the large samples were which were not significantly different from the grouped into twenty equal intervals. The grouped given watershed. The bases of similarity which data were tested for goodness of fit to a normal were undefined were assumed to be definable. The distribution having the same mean and standard sample standard deviation so defined was then con¬ deviation as the sample, using a Chi-square test. sidered to be a best estimate of the standard devia¬ The sample groups were combined where neces¬ tion of the population. sary to meet two restrictions: that for each group the expected or normal frequency was not less than one, and that not more than twenty percent of the NORMAL DISTRIBUTIONS ASSUMED IN OTHER expected frequencies were less than five (Dixon STUDIES and Massey, 1957, p. 22). Chi-square was computed for each sample,and the probability for each Chi- Several of the methods used in geomorphic sta¬ square value was obtained from Chi-square-degrees- tistical analysis require that the measurements in of-freedom tables. Degrees-of-freedom were taken 17 as three less than the sample size. The probabili¬ Distributions of the log lengths were found to be ties are tabulated as percentages in Appendix II not significantly different from normal at the one- and are summarized in Table VII. Each percentage percent level. However, it was noted that if a ten- value tabulated is the probability of obtaining as percent level of significance had been used, none large or larger a Chi-square as was observed, of the first-order and only three of the second- under the null hypotheses that the sample was a order log distributions from the large watersheds random sample drawn from a normal population. would be considered normal. The larger alpha, For those sets of measurements which were not ten percent, reduces the chances of making a type sufficiently large to satisfy the restrictions of the two or beta error, of accepting as normal a non¬ Chi-square test a Kolmogorov-Smirnov test for normal distribution. goodness of fit (Massay, 1951; Birnbaum, 1952) For samples taken from the small watersheds was used. This test is based on the maximum dif¬ the log transformation generally reduced the dis¬ ference between the cumulative sample distribution parity between the sample and normal distribution, and a cumulative normal distribution.. The distri¬ as indicated by either Chi-square or K-S differ¬ bution of the maximum difference is known for ence, but the results were not conclusive regarding completely specified normal distributions. How¬ the non-normality of the arithmetic distribution. ever, as Massey (1951, p. 73) points out: The samples for third- and fourth-order segment lengths were too small for Chi-square tests. The The distribution (of d, the maximum differ¬ K-S test did not indicate that either the arithmetic ence) is not known when certain parameters or logarithmic distribution was non-normal, nor of the population have been estimated from did it clearly indicate that the log distribution the sample. It may be expected that the ef¬ more closely approximated the normal. fect of adjusting the population mean and Lower order distributions appeared, upon sub¬ standard deviation to those of the sample, jective inspection, generally to be monomodal with either by calculation or by visually fitting a a strong right skewness, which apparently caused straight line on normal probability paper, the non-normality and which was apparently elim¬ will be to reduce the (actual) critical level inated by log transformation. of d. If the (theoretical critical value of d) is exceeded in these circumstances, we may safely conclude that the discrepancy is sig¬ Area nificant, i.e., that the distribution is not Departure from normality of the area distribu¬ normal. tions for larger samples was highly significant, Therefore, the percentages tabulated in Appendix with probabilities much less than one-tenth per¬ II should be considered as maximum probabilities cent. For the first-order basins in the large water¬ of obtaining as large, or larger, a difference be¬ sheds the distribution of logarithms of the areas tween each sample distribution and a normal dis¬ was also significantly different from normal, ex¬ tribution having the same mean and standard devia¬ cept for Volfe Canyon, which was significantly non¬ tion as the sample. The exact probabilities are normal at the five-percent level. smaller. For a given sample size the probability In the Fern small watersheds the log area dis¬ is an indication of the maximum deviation; it can tributions seem to approach normality more be used as a qualitative index of goodness of fit, closely than the arithmetic distributions, as shown the larger probability indicating generally a lesser by the K-S differences. For Fern No. 4, which was deviation. large enough for Chi-square testing, the arithmetic distribution was significantly non-normal, the log distribution not. All of the Fern small watersheds RESULTS OF NORMALITY TESTS are in the upper part of Fern Canyon (Figures 2 and 4), above 4,500 feet elevation. Length The Bell small watersheds, which, except for Using a one-percent level of significance the Bell No. 4, are larger than the Fern small water¬ lengths of first- and second-order channel segments sheds, show no consistent relationship. In the two were found to be significantly non-normally distri¬ larger of the Bell small watersheds neither the buted, with the exception of the measurements from arithmetic nor logarithmic distributions were Bell small watershed No. 3. No reason was ap¬ normal. parent either from the maps or in th^ field for this Upon subjective inspection most of the sample variation. It seems plausible that if the lengths distributions, both arithmetic and logarithmic, ap¬ population is non-normal, an occasional sample peared polymodal, with some right skew in the might deviate sufficiently from its population dis¬ arithmetic distributions. The Fern small water¬ tribution to yield a distribution that was not signif¬ shed samples appeared essentially monomodal, icantly different from a normal distribution. with a strong right skewness in the arithmetic dis- 18 tributions. The multi-level, or multi-cycle nature samples barely met the restrictions for the Chi- of the large watersheds has been described above square test, it is felt that a larger sample might in the discussion of erosional history. From analy¬ have shown non-normality of the arithmetic distri¬ sis of the measurements it appears that first-order bution. For all of the small watershed samples basin area, or some other factor which affects area the log distribution more closely approached the (such as infiltration capacity), is sensitive to either normal distribution. elevation above base levels or to duration or stage of erosional development or to both. It further ap¬ Elevation pears that the Fern small watersheds are within a single geomorphic stage, that the effects of the The samples of elevation were not expected to earlier rejuvenations have reached the headwater have either normal or log normal distributions. If basins and the effects of the latest rejuvenations a watershed had an elongate elliptical shape with a have not yet reached the 4500-foot level in Fern greater number of individual basins concentrated Canyon. near some central elevation and a few at high and The discovery of this quantitative evidence for low elevations, the sample distribution might ap¬ the sensitivity of first-order basins to the effects proximate a normal distribution. Such a watershed of interruptions of the geomorphic cycle, and its would not usually occur in nature. Of the measured implications regarding the up-valley migration of samples, none of the first-order distributions was knick-points, may become a powerful tool of quan¬ normal; two of the second-order distributions were titative geomorphology if confirmed by additional not significantly different from normal. studies. Locally it could provide a quantitative basis for relating the tilted, dissected alluvial fans Relief surrounding southern Californian mountain ranges to multiple erosion levels within the mountain wa¬ All of the first-order distributions of relief tersheds. On a much broader level it could contrib¬ were found to be significantly different from normal ute to the basic understanding of the evolution of at the one-percent level. Of the second-order re¬ fluvial topography. lief distributions, one was significantly non-normal at the one-percent level, another at the five-percent level. The remaining three second-order distribu¬ Diameter tions were not significantly different from normal. Distributions of first-order diameters of the Four of the five logarithmic transformations of the large watersheds were significantly non-normal. non-normal first-order distributions were normal. The non-normality of second-order diameters was All of the second-order logarithmic distributions not significant at the one-percent level, except for were normal at both the one- and ten-percent levels. Fern Canyon, but was significant at the ten-percent The first-order logarithmic distributions showed level for Wolfskill, Fern, and Upper East Fork some moderate polymodality, even though most of canyons. Non-normality of the first- and second- them were not significantly different from normal. order log diameter distributions was not significant This, in connection with the polymodality of the at the one-percent level. Those for the first order, area distributions, led to the tentative hypothesis except for Fern Canyon, were significant at the that first-order basins are sensitive to stage of de¬ ten-percent level. For higher orders and for the velopment of their watersheds, and that there are Small Watersheds, tests did not show any distribu¬ two or more stages of development present in most tions to be non-normal. Consistently, except for or all the five watersheds studied. Bell No. 3, the approximation to normality was closer for log diameters than for diameters as Relief ratio shown by higher probabilities. Three of the first-order relief ratio distribu¬ tions were non-normal at the one-percent level; Perimeter all were non-normal at the ten-percent level. Log¬ As noted previously, perimeter was not meas¬ arithmic transformations of the two which were ured in all basins or in all watersheds. For the arithmetic normal were non-normal. Logarithmic samples obtained, arithmetic distributions in the transformations of the three which were arithmetic large watersheds were non-normal, whereas the non-normal were normal at the one-percent level log distributions were not non-normal. For the but only one was normal at the ten-percent level. small watersheds, neither the arithmetic nor loga¬ Three of the second-order arithmetic distributions rithmic distributions were non-normal, even for are non-normal at the one percent level; all are those samples large enough for Chi-square testing. non-normal at the five-percent level. All of the The arithmetic samples showed a moderate right second-order logarithmic distributions were not skewness. Since the larger of the small watershed different from normal at the one-percent level, 19 although one was significantly different at the five- suggestive because two of the samples of elongation percent level. Because relief ratio is a quotient of ratio included basins which were not in the circu¬ relief, and first-order relief was non-normal, it larity samples. was not unexpected that first-order relief ratio was non-normal. Although the results did not pro¬ Drainage density vide quantitative proof of the general distribution of relief ratio, there is qualitative evidence that None of the arithmetic distributions of first- the distributions of single homogeneous populations order drainage density was normal. The distribu¬ of this property are logarithmically normal. tions of logarithms of first-order drainage density were not significantly different from normal at the one-percent level, but one, Wolfskill, was non¬ Relative relief normal at the five-percent level. The second-order This property was computed only for three wa¬ arithmetic distributions were not significantly dif¬ tersheds in which perimeter was measured. The ferent from normal at the one-percent level but arithmetic distribution of one sample was signifi¬ two departed from normality at the five-percent cantly non-normal. The logarithmic distributions level of significance. The second-order logarith¬ were normal at the one-percent level, but two mic distributions were also not significantly dif¬ were non-normal at ten percent. The departure ferent from normal at the one-percent level, but from normality was greater for two of the three one distribution was different at the five-percent arithmetic distributions than it was for their cor¬ level. The probability of the observed departures responding logarithmic distributions. from normality was consistently higher, except for Wolfskill Canyon, for the logarithmic distributions, than for the arithmetic distributions. From this it Elongation was concluded that the distribution of the logarithm Four of the five samples of first-order elonga¬ of drainage density is not significantly different tion ratios had distributions significantly different from normal. from normal. Logarithmic transformations of those four samples yielded three distributions not Channel frequency significantly different from normal at the one- percent level; one which was. A logarithmic trans¬ Five first-order and five second-order channel formation of the arithmetic distribution which was frequency distributions were tested by Chi-square normal had less departure from normality than the tests. All departed significantly from normality arithmetic distribution. Of the five second-order even at the stringent one-tenth percent level. Loga¬ samples, three were arithmetically non-normal; rithmic transformations of the first-order distri¬ logarithmic transformation normalized one of butions were significantly non-normal at the one them. Logarithms of the two samples which were tenth-percent level, except for Volfe Canyon. The arithmetically normal had less departure from distribution for this canyon, Watershed IX, was not normality, as measured by Chi-square. Thus it significantly different from normal at the one- appeared, in a qualitative sense, that logarithmic percent level, but was different at the five-percent distributions of elongation ratio tend to depart less level. Of the logarithmic transformations of the from normality than arithmetic distributions of second-order circularity distributions, only that this property, when sampled from homogeneous for Upper East Fork, Watershed m, was signifi¬ populations. The non-normality of the area distri¬ cantly different from normal. Thus within water¬ butions apparently was not compensated by dividing sheds, first-order channel frequency in the Experi¬ by diameter in the computation of elongation. mental Forest is neither normally nor log-nor¬ mally distributed. Second-order channel frequency may be log-normally distributed. Circularity Three sample distributions of circularity ratio HOMOGENIETY OF VARIANCE were tested. None departed significantly from normal. The logarithmic transformations of these Statistical Inferences distributions showed greater departures from nor¬ mality, one being significantly non-normal at the Statistical inference drawn from analysis of the one-percent level; another was non-normal at the variance of sample means depends upon an assump¬ five-percent level. It was notable that for arith¬ tion that the samples were drawn from normally metic values of the two properties, elongation distributed populations having equal variances. tended to be non-normal and circularity normal, The assumption that variances are equal or homo¬ but for logarithmic values the opposite relation geneous is, fortunately, amenable to testing. Bart¬ seemed to hold. However, the comparison is only lett’s test (Dixon and Massey, 1957, p. 179) for 20 homogeneity of variances, used in this study, uses This was due entirely to an unusually small value an approximation of the F-ratio to test for signifi¬ for Fern Canyon which had only two fourth-order cant differences among the variances. Pooled var¬ basins, of nearly the same diameter. iance and other terms needed for Bartlett’s test From the foregoing it appears that in the three were computed on a desk calculator from sample basic properties of channel length, basin area, and standard deviations derived by an IBM 650 digital diameter, first-order basins are sensitive to dif¬ computer. Except for circularity, which had been ferences or changes in erosional history. Within found to have an arithmetic normal distribution, the San Dimas Experimental Forest, second-order only the sets of logarithms were tested for homo¬ values of these properties give a much better basis geneity of variances. The arithmetic data were ex¬ for comparing watersheds. The number of meas¬ cluded from consideration for analysis of variance urements of third- and fourth-order properties by their non-normality. The results of the homo¬ was not large enough to determine whether appa¬ geneity tests are summarized in Table VIII and rent differences in variance were significant. are discussed below. Volfe Canyon, Watershed IX, had consistently less variation among first-order properties, which may indicate that interruptions in erosional history, Length, Basin Area, and Diameter which increased first-order variation in other wa¬ Significant differences were found among the tersheds, had less effect in Volfe Canyon. The variances of the five sets of logarithms of first- writer considers it more probable that erosional order stream lengths. Variance of first-order changes which have only partially affected other stream lengths in Fern Canyon was significantly watersheds have progressed closer to completion greater than average for the watersheds studied; in Volfe Canyon. that in Volfe Canyon was less than average. No significant differences were found among the vari¬ Relief, Relief Ratio, and Relative Relief ances of the second-, third-, or fourth-order sets, considering each order separately. The observed None of these measures of relief had homo¬ differences among second-order lengths were geneous variances among sets of the same- order, small. Observed differences among the third- and except for the very small sets of fourth-order log¬ fourth-order sets were large, factors of 2.5 and 10 arithms. Among the sets of logarithms of relief, respectively, between extremes. The small num¬ except for fourth-order values, the variances of ber of values from each watershed made these Watersheds n and III, Fern and Upper East Can¬ relatively large differences non-significant. yons, were consistently greater than those of the Results of homogeneity tests of the variances of other watersheds. Among the fourth-order log re¬ logarithms of basin area were similar to those for lief sets, the variance of Fern Canyon was based length. Significant differences were found among on only two measurements, of nearly alike values, the first-order statistics but not among those for hence was very small. The fourth-order variance the higher orders. Among the first-order vari¬ for Upper East Fork was greater than for the ances the observed value for Volfe Canyon was other three sets of relief logarithms. The signifi¬ lowest, that for Fern Canyon a little higher than cant differences among variances of the relief average, and that for Upper East Fork was highest. ratio logarithm sets are not so consistently ar¬ The observed differences among the second-order ranged. Excluding the unusual Fern Canyon fourth- variances was small, and among the third- and order value, the Volfe Canyon variances are fourth-order area logarithms was of less magni¬ smaller, order by order, than those of other water¬ tude than among third- and fourth-order length sheds. The variances of Fern Canyon are larger logarithms. than average and for the second- and third-order Homogeneity of variance among the sets of loga¬ sets are largest. The largest variance of the first- rithms of basin diameter followed the same pattern order sets was that for Bell Canyon. Relative as for channel length and basin area. Variances of relief was calculated for only three watersheds, II, first-order sets were significantly different; those III, and VIII, in which perimeters were measured. for higher orders were not. The variance of the The differences among the variances of these three Volfe Canyon measurements was again least among sets were not significant at the two percent level the first-order variances; that of Upper East Fork but were at the five percent level. Fern Canyon was the greatest. Differences among the second- had the largest variance. order variances were very small; range of vari¬ The results of homogeneity of variance tests ances for logarithms of the third-order diameters indicate that, at least in the San Dimas Experi¬ was comparable to that for third-order length loga¬ mental Forest, differences between means of meas¬ rithms. Variances of fourth-order diameter loga¬ ures of relief cannot properly be compared on a rithms had a very large range, the largest variance watershed basis by analysis of variance. This re¬ being four hundred times greater than the least. striction probably applies to most of the watersheds 21 in the San Gabriel Mountains. Whether it pertains ANALYSIS OF VARIANCE to other areas with less complex erosional his¬ tory is not known. However, future investigations Statistical Inferences using measures of relief should include tests of Analysis of variance yields an estimate of the homogeneity of variance if analysis of variance is probability that means of populations from which to be used. The results of tests of relief proper¬ samples have been obtained are equal. A very ties support the conclusion that geomorphic varia¬ small probability is taken as basis for the infer¬ tion, presumably related to erosional conditions, ence that the population means are unequal. Popu¬ is least in Volfe Canyon and greatest in Fern and lation means are estimated from sample means. Upper East Fork Canyons. As discussed above, assumptions basic to analysis of variance include normality of the sample and Perimeter, Elongation, and Circularity population distributions and homogeneity of popu¬ Drainage basin perimeters were measured only lation variances. These assumptions have often for first-order basins in Watersheds II, ni, and not been tested in previous geomorphic investiga¬ VIII. Inhomogeneity among the variances of the tions. Although moderate departures from homo¬ perimeter logarithms was not significant at the geneity of variance do not greatly affect analysis five-percent level, but was significant at ten per¬ of variance results, the effect of large departures cent. Upper East Fork had the greatest variance is not known. and Bell Canyon the least. Inhomogeneities among Analysis of the variance of the means of loga¬ variances of the first-, second-, and third-order rithms of each order of each geomorphic property sets of elongation logarithms were significant at were computed, using a desk calculator, from the one-percent level. No regular ranking was ap¬ means and variances computed by an IBM 650 parent from order to order: among first-order digital computer. Inferences from the results are ratios, Watershed Vin had a larger than average considered to be valid only for those sets of meas¬ variance; among second-order sets, the variance urements which have homogeneous variances and of the set for Watershed I was much larger than no significant departure from normality. To facili¬ average; Watersheds I and VIII had variances tate comparison with results of other studies anal¬ much less than average of the third-order group. ysis of variance was computed for sets of data The three sets of circularity measurements and which were not normal and of homogeneous vari¬ their logarithms had variances that were signifi¬ ances. The results of these latter analyses should cantly non-homogeneous. Bartlett’s test was ap¬ be considered as descriptive statistics and not plied to the arithmetic values of this property in used as a basis for inference. For convenience in addition to the logarithmic values, because the dis¬ tabulation these descriptive statistics have been tribution of untransformed values had been found listed in Table IX as “percent probabilities”. to be not different from normal. The variances for These “probabilities”are not valid inferences and the Fern Canyon sets were larger than those of the are intended only as expressions of a descriptive other two watersheds tested. ratio of variances. For analytical purposes the non- underlined figures in Table IX should be converted Drainage Density and Channel Frequency to F-ratio values by using the appropriate degrees of freedom (k-1, and N-k, where k is the number of Tests of homogeneity of variances of these two watersheds and N the total number of observations). closely related properties produced unexpected Such F-ratios should then be considered as de¬ results. Differences among third-order variances scriptive statistics of the between-means to the were significant even though those among second- pooled variance ratios. Results of valid analyses and fourth-order variances were not. The first- of variance also are summarized in Table IX and order variances of both drainage density logarithms discussed below. and channel frequency logarithms were, as ex¬ pected, significantly non-homogeneous. Differences Channel Length, Basin Area, and Diameter among variances of first- and second-order drain¬ age density logarithms were small, although the Analyses of the variance of second-, third-, and differences among the first-order variances was fourth-order channel length logarithm means found to be significant at the one-percent level. showed no significant differences between means. The significant inhomogeneity of third-order loga¬ The means of logarithms of first-order lengths rithms of drainage density and channel frequency had an F-value of 32, which would indicate highly was due in both cases to unusually small variance significant differences between means if the meas¬ of the Volfe Canyon values. In all instances, all urement sets had homogeneous variances. Loga¬ orders of both properties, whether homogeneous or rithms of second-order basin areas had highly sig¬ not, the Volfe Canyon sets of logarithms had the nificant differences between watershed means. Dif¬ least variance. ferences between means of third-order area loga- 22

rithms were significant at the ten-percent level logarithms of circularity had variances which were but not at five percent. Differences between fourth- non-homogeneous, consequently their means could order watershed means of basin area logarithms not validly be compared by analysis of variance. were not significant. The polymodal first-order The variances ratios for these sets were moder¬ sets of basin area logarithms had a variance ratio ately large. The inconclusive results of tests of of 60. Results for diameter logarithms were simi¬ these three measures of drainage basin size and lar to those for basin area logarithms. Significant shape suggest that there may be no important dif¬ differences were found among second- and third- ferences between watersheds for second-order and order means. No significant differences were found higher order values of these properties but that among the means of the small fourth-order sets of there probably are differences between first-order measurements. The first-order sets, which had watershed averages. large inhomogeneity of variances, had a between^- means to pooled variances ratio of 42. These re¬ Drainage Density and Channel Frequency sults indicate that, except for first-order channels, there is little difference in average channel lengths The sets of logarithms of second-order drainage among the watersheds studied. Conversely there density, and of second-order channel frequency are significant differences between second-order were normally distributed and of homogeneous var¬ means and between third-order means of both iances. The differences between the means of these basin area and basin diameter. sets were highly significant. Variance ratios of means of the third-order drainage density loga¬ rithms and channel frequency logarithms indicate Relief, Relief Ratio, and Relative Relief significant differences between means of these Only the small sets of fourth-order properties properties, if the moderate (significant at one-half and the incomplete sets of perimeter logarithms percent) departures from homogeneity of variances and relative relief logarithms had been found to do not invalidate the analyses of variance for these meet the prerequisites for analysis of variance. properties. Fourth-order drainage density loga¬ The fourth-order sets probably met conditions only rithms had valid significant differences between because the small number of values in each set watershed means. The between-means to pooled provided scant basis for discrimination of non¬ variance ratio of fourth-order channel frequency homogeneities of variances. The two incomplete logarithm means indicated significant differences first-order sets provided only three watershed between watershed means, although the measure¬ means and variances, instead of five. Analysis of ment sets did not have homogeneous variance. variance showed that differences between means of Logarithms of first-order drainage and channel fourth-order relief ratio logarithms were signifi¬ frequency sets, which had non-homogeneous vari¬ cant at the five-percent level but not at two percent. ances, had between to pooled variance ratios of, Differences between log relief fourth-order means respectively, 70 and 64. The results of analysis of were significant at ten percent but not at five per¬ variance of log drainage density and log channel cent. No significance was found to differences be¬ frequency means indicate that these properties tween the three first-order log relative relief provide a significant basis for distinguishing dif¬ means. Other orders of the several relief proper¬ ferences and similarities between watersheds. ties had between-means to pooled variance ratios ranging from approximately 6 to 36. DRAINAGE COMPOSITION Perimeter, Elongation and Circularity R. E. Horton (1945) formulated from observed Differences between the three watershed means relationships a group of laws of drainage compo¬ of first-order perimeter logarithms were found to sition relating numbers of streams, stream lengths, be significant at three percent but not at two per¬ stream slopes, and basin areas respectively to cent. Only the fourth-order sets of elongation loga¬ order number, by geometric series. The geometric rithms met the requisites of normality and homo¬ ratios of these series were called respectively the geneity of variances; means of these sets had no bifurcation ratio, length ratio, slope ratio, and significant differences. The ratios of between- area ratio. The law of basin areas had been im¬ means to pooled variances for the second- and plied by Horton but was first explicitly stated by third-order logarithms of elongation were quite Schumm (1956, p. 606). Schumm also established a small. This indicates that differences between the new law of drainage composition which related watershed means may be non-significant. Large basin areas and channel lengths as a linear func¬ differences between the variances make accurate tion whose slope was designated the constant of evaluation of the analysis of variance results im¬ channel maintenance. Because these laws were possible. The sets of first-order circularity and of postulated to be geometric series, graphs of the 23 relationships on semi-logarithmic coordinates ap¬ be formulated: the mean diameter of basins of pear as sets of points lying on straight lines, with each order within a higher order watershed tend slopes which are the geometric ratios. For con¬ closely to approximate a direct geometric series venience these ratios are referred to below as in which the first term is the mean diameter of the watershed ratios to distinguish them from other first-order basins and the ratio is the diameter ratios. Each of the watershed ratios has a single ratio. value for each watershed. The relationship of eight Logarithmic plots of mean drainage basin relief geomorphic properties to basin order was investi¬ (or, more exactly, diameter relief) against order gated in the present study. Figures 10 through 17 also fall close to straight lines (Figure 14). Hence, are graphs of the laws of drainage composition a law of basin relief, which describes this relation, based on these eight properties. Logarithms, base is postulated: the mean relief of basins of each 10, of the watershed ratios are given in each case, order in a watershed tend closely to follow a direct because these are the regression coefficients of geometric series in which the first term is the the regressions of the logarithms of each property mean relief of the first-order basins and the ratio on order. is the watershed relief ratio. Obviously this law The law of stream numbers, as stated by Hor¬ will be valid only for watersheds of low to inter¬ ton, seems to apply well to the San Dimas water¬ mediate order; the maximum regional relief quickly sheds (Figure 10). The logarithms of bifurcation becomes a limiting factor as order increases. It is ratios were all similar, the greatest being 0.70, unfortunate that the phrase “relief ratio” thus has for Fern Canyon, and the least 0.62 for Upper East two meanings. The use of “relative relief” for the Fork. The San Dimas channel length-order data do relief of the diameter would improve terminology not seem to fit a geometric series closely (Figure if that term had not already been used by Melton 11). In the five watersheds studied, the fifth-order for the ratio of relief to perimeter. The logarithm channel segment is shorter than would be expected of watershed relief ratio found in this study ranged if a semilog linear relation based on the first four from 0.21 for Volfe Canyon to 0.26 for Fern Can¬ orders were extended to the fifth order. In other yon. It is notable that Fern Canyon had the largest words, the functions appear to be concave up when watershed ratios for stream numbers, channel plotted on semilogarithmic coordinates. Strahler lengths, basin areas and relief. The significance (1953) found similar relations for several other of this fact has not yet been determined. watersheds. Much of this apparent departure from The derived geomorphic properties of elonga¬ linearity may be due to Strahler’s revision of tion, drainage density, and channel frequency Horton’s method of stream ordering. Horton con¬ showed much less variation with basin order (Fig¬ sidered the length of a fifth-order stream to extend ures 15, 16, and 17). The largest value of the slope from the mouth of a fifth-order watershed to the of mean elongation plotted logarithmically against head-water extremity of its furthest fingertip trib¬ order was 0.015. In general, the mean elongation utary. Strahler’s revision, which eliminated sub¬ of first-order basins was less than that of higher jective choices about the trunk stream, considers order basins. This may indicate that first-order the fifth-order segment to extend only from a junc¬ basins start as insequent gullies unaffected by tion with a fifth-order (or higher order) segment processes which control the shape of better inte¬ up to the highest confluence of two fourth-order grated higher order basins, or it may indicate that segments. Such fifth-order segments would, on a recent rejuvenation affected the shape of many the average, be shorter than fifth-order streams first-order basins but has not yet affected the as defined by Horton. Broscoe (1959, p. 5) gave a higher order basins. It is probable that in regions similar explanation for this apparent non-linearity. characterized by dendritic drainage patterns, elon¬ When more data are available, for sixth-order or gation is independent of order. higher order watersheds, it will be possible to as¬ The semi-logarithmic graph of drainage density certain which method of ordering yields results against order showed that this property decreases most closely fitting Horton’s law and, conversely, with increase in order (Figure 16). The points what function best fits channel lengths as defined scatter widely about a straight line, but all water¬ by Strahler. sheds show the same inverse relationship. No con¬ Mean basin area measurements seem to follow sistency in the departures from linearity was ap¬ closely the law of basin areas as stated by Schumm parent. The largest value of decrease in log drain¬ (1956, p. 606). The logarithms of watershed area age density per unit increase in order was 0.025, ratios were all between 0.71 and 0.72 except that for Fern Canyon; the least was 0.019, for Volfe for Fern Canyon which was 0.78 (Figure 12). A Canyon. Semilogarithmic plots of channel frequency plot of mean basin diameters on a logarithmic against order showed a relationship similar to that scale versus channel order is very closely fitted of drainage density (Figure 17). Departures of the by a straight line (Figure 13). From this observa¬ plotted points from straight lines were less than tion another law of drainage basin composition can those of the drainage density—order plots. The 24 logarithm of channel frequency ratio was largest dry season, stream channels are often indistinct. for Fern Canyon (-0.079); least for Wolfskill Can¬ Mechanical erosion by rolling and sliding of rock yon, (-0.063). The larger channel frequencies in debris produces linear depressions, called debris the Big Dalton drainage, Watersheds VIII and IX, chutes, which resemble but are not stream chan¬ compared with corresponding orders in the San nels. Leaves fallen from wilting chaparral during Dimas drainage, Watersheds I, n, and III, are ap¬ the dry season often conceal small channels bridged parent on the graphs. A similar but less conspic¬ by dense vegetation. Formal definition of the prop¬ uous segregation can be seen on the drainage den¬ erties to be studied was required for uniformity in sity-order graphs. This tendency of channel fre¬ the field mapping and for reproducibility in the quency-order plots to segregate into groups sug¬ replication study. gests that channel frequency may be a useful prop¬ In the San Dimas area four criteria were found erty for distinction between watersheds which are to be sufficient to distinguish a stream channel: in the same physiographic province but which have the presence of stream banks, the presence of sus¬ subtle geomorphic and hydrologic differences. pended and oriented debris, the presence of wash marks, and continuity with a larger channel. It was observed in the field that inclined linear depres¬ sions which frequently carried running water, de¬ Replication of Field Observations veloped well-defined nearly vertical banks. Those eroded by loose debris did not. This criterion was the most reliable and most frequently used. Debris PLAN OF FIELD TESTS or forest litter carried by running water was often draped over branches and roots of vegetation pro¬ Quantitative geomorphic analysis tacitly assumes truding over and into the channel. In some instances objectivity, or at least freedom from significant debris was oriented in sub-parallel flow-lines subjective bias, in the collection of field measure¬ along the sides of the channel. Wash marks, small ments. Little, if any, evidence has been presented rill marks, terracettes, and dams of fractional- to substantiate this assumption. Reproducibility of inch size, similar to those produced by sheet ero¬ an observation, measurement, or result is a funda¬ sion, were often found within the channel bounda¬ mental criterion of validity in physical science. ries. The last criterion, continuity with a larger Although this test of reproducibility is often pre¬ channel, was not applicable to the few first-order cluded by practical considerations in the geological channels which drained into Brown’s Flat in Fern sciences, it should be applied where possible. Canyon. This caused no difficulty because the other To test the reproducibility of the field mapping criteria were applicable. Usually at least two of and measurements of the present study, independ¬ the four criteria were recognized in each channel ent duplicate studies of two fifth-order watersheds mapped. were made. After the author had mapped the chan¬ Inaccuracy of the large-scale base maps used nel network and drainage divides and measured was another practical problem affecting the repli¬ maximum valley-wall slopes in Wolfskill and Bell cation study. An enlarged portion of the map of Canyons, Mr. James Trew of Brown University in¬ Upper East Fork Canyon (Figure 9) shows some of dependently mapped and measured the same prop¬ the map inaccuracies encountered in the field work. erties. Mr. Trew’s work was done for part of his Figure 9b shows first-order stream channels dissertation for the Master of Science degree found where the contour lines of the map indicate a (Trew, 1956) under the direction of Professor ridge. Above the center of the area another channel Richard Chorley, Brown University Department of crosses a ridge indicated on the original map. Geology. With the exception of two half-days during which the identification of channels was field-verified with Maxwell, Trew mapped the drainage network CHANNEL NETWORK of Bell and Wolfskill Canyons independently and without reference to Maxwell’s maps of the same Geomorphic properties are usually compared watersheds. Difficulty in recognizing the more according to the order of the channel or drainage obscure channels, inaccuracy of the base maps, basin with which the properties are associated. and the physical impossibility of checking every Determination of the order of a channel is depend¬ square foot of the rugged mountain watersheds led ent upon the correct identification of its tributary to discrepancies between the two drainage networks channels. This, in turn, depends upon the field ob¬ as mapped by the two investigators. Subjective server’s ability to recognize a stream channel. errors in identification of first-order channels led Simple criteria for defining a stream channel were to two kinds of differences. One channel may join found to be elusive. In chaparral-vegetated moun¬ another in either of two ways, here arbitrarily tainous terrain, in a climate which has a prolonged called A-type and B-type junctions. The confluence 25 of a channel with another of the same order forms the topography is more rugged than usual for the an A-type junction and a higher order channel re¬ San Gabriel Mountains and when access to the sults. If one channel joins another of a higher or¬ area, both in space and in time is limited; then a der, forming a B-type junction, the order of the reproducibility of approximately ten percent may higher order channel is not affected. The dotted be expected. The errors of reproducibility in enu¬ lines in Figure 6 show the effect of a channel meration of higher order channels depends upon mapped by only one investigator. On the left an the type of junction of incorrectly mapped (omitted) A-type junction has increased the number of first-order channels. The mean bifurcation ratios second-order and higher order segments. The for the original and replicate channel enumerations addition of the first-order segment generally de¬ is also shown in Table X. These results seem to creases the average length of first- and second- indicate that the bifurcation ratio is only slightly order segments and the average area of first- and affected by differences in channel enumeration. second-order basins by adding a new, smaller basin and by substituting only a part of the original basin. MEAN CHANNEL LENGTHS AND BASIN AREAS Results of the drainage network mapping and channel enumeration are listed in Table X. The After Trew completed his field mapping, and table shows the number of segments of each order before any comparisons with Maxwell’s data, Trew mapped by each investigator, with differences made measurements of his channel lengths and listed as percentages of the channels mapped by basin areas. For these measurements he used Maxwell. The fact that some of the differences are definitions and procedures as described above positive and some negative can best be understood under the discussion of geomorphic properties and in terms of the types of tributary junctions. A de¬ measurement precision. Trew’s replication meas¬ tailed comparison of the Bell Canyon maps re¬ urements did not include first-order basin areas. vealed that Trew found three A-type first-order The results of the replication measurements are junctions more than did Maxwell, while the latter shown in Tables XI and Xn, which list mean values found twenty three more B-type first-order junc¬ of stream length and basin areas respectively. To tions than did Trew. Two of the A-type first-order facilitate a roughly quantitative evaluation of the junctions caused the positive second- and third- significance of the difference between correspond¬ order differences. ing means, the estimated standard errors of Max¬ There are at least three reasons why the dif¬ well’s means are also listed. It can be seen that, ferences are greater in the Wolfskill Canyon data. except for first-order means, the differences be¬ Although Wolfskill Canyon is almost twice as large tween means of the same order are less than one as Bell Canyon, Trew spent most of his field time estimated standard error. A somewhat improved in Bell. Trew refers to this (Trew, 1956, p. 90-91) estimate of the significance of the difference be¬ as *. . .the predominance of time spent in the field tween means is possible for second- and third- being in Bell Canyon, where existing conditions al¬ order basin areas in Table Xn. Trew calculated lowed more exacting work to be done... In contrast, estimated standard deviations for these properties. much less field time was spent in Wolfskill Canyon From these the estimated standard errors of dif¬ and the area was much less accessible.* Accessi¬ ferences of means were calculated (Table XII). bility in upper Bell Canyon is by moderately well- Standard errors listed for the fourth-order basin maintained contour trails at 300-foot vertical in¬ areas are based only on the standard deviation of tervals; a paved road diagonally transects the lower Maxwell’s samples. half of the canyon. These trails and road intersect Some understanding of the causes of the differ¬ many of the Canyon’s tributaries. By contrast the ences between means was obtained from a compari¬ contour trails in Wolfskill Canyon are vertically son of the field maps. On both the Bell and Wolf¬ separated by 1000 feet and are partially abandoned; skill maps, Maxwell extended quite a few first- the road in the lower fifth of the Canyon follows the order channels slightly further headward than did canyon bottom and provides poor access to tribu¬ Trew for the same channels. In several instances taries. In addition to differences of accessibility Maxwell mapped minor bends in channels which and of duration of study, there is a difference in Trew mapped as straight. These two factors ac¬ topography. Wolfskill Canyon is more precipitous, count for the larger first-order mean length found with greater local relief and many narrow, well- by Maxwell for Bell Canyon. In Wolfskill Canyon concealed small tributary canyons not visible from almost all of the first-order channels which Trew the bordering ridges. omitted were small. This bias overweighed the Thus it appears that in the area studied trained opposite effect of the previous two factors. One of observers working independently may be able to the A-type first-order streams which Trew mapped enumerate the first-order channels with a repro¬ in Bell Canyon formed a smaller-than-average ducibility of approximately five percent except when second-order channel, which also made an A-type 26 junction producing a smaller-than-average third- log-normally distributed geomorphic properties order basin. The smaller third-order mean length which had homogeneous variances, were grouped reported by Maxwell for Bell Canyon was appar¬ in multiple correlations. Eighteen variables, in¬ ently caused by two of the pairs of second-order cluding discharge, the dependent variable, were channels mapped by him which joined just a short tested. These variables and their definitions are distance above a fourth-order channel. This listed in Table XHI. formed an unusually short third-order segment. A logarithmic linear form was used for the es¬ The differences between means of the same order timating equation. Logarithms of annual peak dis¬ in Wolfskill Canyon were due almost entirely to charge were assumed to have a normal distribu¬ omission of short channels by Trew. The greater tion, although it is recognized that, because they sinuousity of channels mapped by Maxwell may are extreme values, annual peak discharges can be account for the difference in fourth-order channel shown theoretically to have a Gumbel-type ex¬ length means. treme-value distribution, which departs signifi¬ From the results tabulated it was concluded cantly from log-normality for long records. Sev¬ that mean channel length and mean basin area for eral studies by the United States Army Corps of second-order and higher order basins have been Engineers and United States Geological Survey objectively measured, within the natural varia¬ have shown that for records of a few decades dura¬ bility of the property, in this region of rugged to¬ tion the log-normal is a useful approximation of pography and dense vegetation. First-order chan¬ flood discharge distribution. nels, intrinsically more difficult to recognize, have not been so accurately measured. Factors which have influenced the objectivity of the map¬ STORM CHARACTERISTICS AND WATERSHED ping and measurements have been identified. CONDITIONS

The momentary peak discharge produced from a watershed by a given storm is a result of accu¬ Correlation of Geomorphic Properties mulated depth of rain that falls, the intensity (depth and Flood Discharge per unit time) of the precipitation, and the wetness of the watershed preceding the storm. The maxi¬ mum rainfall during a sixty-minute period and SOURCES OF HYDROLOGIC DATA during a twenty-four hour period were used as measures of both total storm rainfall and its inten¬ The present sharp-crested ridges and deep, sity. Wetness of the watershed was estimated by precipitous canyons of the San Gabriel Mountains the depth of rain which fell in the seven-day and are the-result of repeated uplift of the range dur¬ twenty-one day periods prior to the beginning date ing vigorous down-cutting by streams. Sheet ero¬ of the storm. The flood-reducing effect of vege¬ sion during rainstorms, and soil creep, slump, and tative cover was computed according to methods slides deposit debris in the stream channels. Most used by Anderson (1949, p. 570): of this sediment is removed from the mountains An estimation of average cover density on during infrequent large floods, whose erosive ef¬ the watershed at the time of the storm was fectiveness is generally related to the magnitude of assumed to represent a single-valued quan¬ their momentary peak discharges. Peak discharge titative expression of cover effectiveness in turn is related to storm and watershed proper¬ (Anderson and Trobitz, 1949). The assump¬ ties. Quantitative estimation of the relationship tion is reasonable, for practically all of the between flood peak discharge, storm character¬ beneficial effects of cover tend to increase istics, and watershed properties is possible with with increase in cover density: the protec¬ the statistical technique of multiple correlation. tion of the soil from beating rain, the pro¬ Channel flow from the watersheds studied in duction of leaf litter which further protects this investigation is continuously measured by the soil and retards surface runoff and ero¬ recording gages on specially designed flumes. sion, and the secondary effects on soil struc¬ From these measurements the annual maximum ture and permeability. The cover density momentary discharge for each year and each water¬ for the actual watershed condition for each shed was tabulated, a total of 113 annual peak dis¬ storm was obtained by applying the density- charges from 1935 to 1957 inclusive. Records for age relations for various cover types on var¬ Watersheds II and in were interrupted for one year ious geologic types as developed by J. S. during World War II. Storm characteristics of 460 Horton of the California Forest and Range floods, including all annual flood producing storms, Experiment Station. are published for the San Dimas Forest (Reimann and Hamilton, 1959). These data, together with the These density-age relations are given in 27

Table IV. The percentage area of each watershed versus Q was 0.795. The multiple correlation co¬ covered by each vegetation type, shown in Table II, efficient for P21, the twenty-one day prior rainfall, was multiplied by the appropriate density-age fac¬ P24, and Cd versus Q was 0.807. Thus these three tor for each year of flood record. These percent¬ variables alone appear to account for nearly 65 ages were added, for each watershed, to give an percent of the variation in discharge. To check average cover density for each year. In Water¬ whether the inclusion of prior rainfall would affect sheds I, n, and in, which had been damaged by the relative quality of P60 as a predictor, P60, P21, wildfires in recent years, the amount of damage and Cd were correlated with Q. The multiple cor¬ to each vegetation type was estimated from fire relation coefficient for this was only 0.677. An un¬ maps. The area of undamaged cover was reduced expected result appeared in these correlations in accordingly. the coefficients of estimation, or regression, of To test for independence of the storm and water¬ cover density. In all the above correlations except shed condition variables simple correlations be¬ that of P24, P7, and Cd versus Q, the estimating co¬ tween each of the variables were computed. As efficients of cover density were positive. This expected, a highly significant correlation was found would indicate that the magnitude of flood peak between maximum sixty-minute rainfall and max¬ discharge increases as the vegetative cover on a imum twenty-four-hour rainfall. Anderson (1949, watershed increases. Because theory and observa¬ p. 571) had found a similar result. Seven-day ante¬ tion both refute this inference it is quite evident cedent precipitation was found to be highly corre¬ that the correlations are incomplete, that signifi¬ lated with twenty-one-day precipitation. This was cant pertinent variables have been omitted. to be expected inasmuch as each seven-day period was a one-third estimate of the corresponding twenty-one day period. Simple correlation coeffi¬ GEOMORPHIC PROPERTIES cients between each of the four precipitation varia¬ bles and discharge were found to be highly signifi¬ The influence of geomorphic properties on flood cant. Unexpectedly, the simple correlation coef¬ peak discharge is more complex and less well ficient between cover density and discharge was known than that of storm characteristics. The ef¬ small and not significant. It is thought that the fect of only one property, watershed area, has effect of watershed area probably masked the been well-established by measurements. In gen¬ effect of cover density. Significant positive simple eral, for small to moderate size watersheds, as correlation was found between maximum twenty- watershed area increases, flood peak discharge four hour storm rainfall and both seven- and increases. Anderson (1949, p. 575) investigated the twenty-one day antecedent precipitation. Maximum combined effect of bifurcation ratio, slope ratio, sixty-minute storm rainfall was significantly and and length ratio, and found it to be not significantly positively correlated with twenty-one day, but not related to peak discharge. Potter (1953) found that with the seven-day antecedent precipitation. Be¬ a geomorphic property involving the length and cause no a priori reason is known to exist for gradient of a watershed’s principal waterway was storms following dry periods to be less intense significantly related to peak discharge per unit than storms following wet periods, the positive area. The property investigated was correlation between antecedent precipitation and . . .designated as the T-factor and may be storm intensity is assumed to be indicative of some defined as the length of the principal water other factor, such as long-term climate cycles, way divided by the square root of the chan¬ rather than of cause and effect relationship. nel slope. Since velocity varies as the Five multiple correlations between annual peak square root of slope, the T-factor is indic¬ discharge, cover density, and the precipitation ative of time of channel flow. Considered variables were computed to determine which com¬ with area and peak rate of runoff in a mul¬ bination best estimated discharge as the dependent tiple correlation it is also indicative of time variable. The first two related only storm inten¬ of concentration, channel storage, and water¬ sity and cover density to discharge. For sixty- shed shape. (Potter, 1953, p. 69). minute precipitation, P60, and cover density, Cd, the multiple correlation coefficient was 0.556; for In the present study a characteristic value of twenty-four hour precipitation, P24, and Cd it was each geomorphic property was available for each 0.786. Thus when only these variables are consid¬ of the five watersheds studied. When combined ered, P24 seems to explain more of the variation in with the 113 records of peak discharge these char¬ peak discharge, Q. When watershed wetness, as acteristic values permitted unique solutions of es¬ measured by rainfall prior to the flood-producing timating equations having not more than five geo¬ storm, was considered, more of the variation was morphic variables. accounted for. The multiple correlation coefficient The computation of multiple-variable estimating for P7, seven-day prior rainfall, and P24 and Cd equations was simplified by establishing a new 28 dependent variable which expressed the variation order area, diameter, relief, drainage density, in peak discharge after allowance for the variation channel frequency, and relief ratio, and watershed explained by storm characteristics and watershed bifurcation, length, diameter, and area ratios. condition. Each value of the new dependent variable Fifth-order diameter and area had the two highest was formed by subtracting from the original de¬ simple correlations with unexplained discharge, as pendent variable its corresponding value of log Q indicated in the preceding paragraph. Length ratio calculated by the best four-variable estimating yielded the third highest simple correlation. equation. This gave 113 values of unexplained dis¬ Second-order channel frequency and diameter, in charge. It was recognized that this procedure would that order, were next highest. The remainder, yield inexact values of the estimating coefficients with the exception of bifurcation ratio and area and multiple correlation coefficients because the ratio, yielded approximately similar correlation estimating coefficients used in the four-variable coefficients. Correlation with bifurcation and area equation were almost certain to be different from ratios was very low. those in a nine-variable equation. However, it was Next, multiple logarithmic correlations of pairs believed and later demonstrated that the second- of geomorphic variables and unexplained discharge order partial correlation coefficients, which had were computed. Fifth-order area was first used been relatively large in the four-variable equations, as one of the independent variables, successively indicated that the four-variable equation gave a with each of the other variables except fifth-order useful approximation of the portion of the dependent diameter. Then fifth-order diameter was substi¬ variable which would be estimated by the corre¬ tuted for area and paired successively with the sponding three terms of an eight-variable equation. same other independent variables, in correlation The first geomorphic variable added to the cor¬ with unexplained discharge. All of the multiple relation was area of the fifth-order watersheds. correlations using fifth-order diameter had larger As was expected, fifth-order area was significant¬ multiple correlation coefficients than those in¬ ly correlated with peak discharge. The correlation volving fifth-order area. Fifth-order area and di¬ of area with discharge often, unfortunately, con¬ ameter were not included in the same correlation ceals other significant effects. This was well ex¬ because they were highly correlated with each pressed by Anderson (1957, p. 922) who states: other. Using the results of the three-variable corre¬ . . .‘area’ can well be called the devil’s own lations, a number of four-variable correlations variable. Almost every watershed character¬ were computed. Fifth-order area or diameter was istic is correlated with area. So every char¬ included as one of the independent variables in all acteristic that is left out as a separate var¬ of these correlations. It was found that when cor¬ iable is in part hidden in ‘area’. Big water¬ related with the bifurcation, length, area, and di¬ sheds are not like little watersheds and the ameter ratios and with mean second-order relief differences may be disguised in the term ratio, the combination of fifth-order diameter and area. Therefore, it is dangerous to ascribe second-order area gave better estimates of unex¬ physical significances to the regression co¬ plained discharge than did the combination of fifth- efficients of the area variable. order diameter and second-order diameter. The An effort was made to find other geomorphic vari¬ opposite, i.e. that second-order diameter gave ables which might separately express the effects better estimates than second-order area, when combined in area. When fifth-order diameter was used with fifth-order diameter, was found when the substituted for area in simple logarithmic linear third independent variable was second-order relief, correlation with unexplained discharge, the corre¬ drainage density, or channel frequency. Second- lation coefficient was 0.441, which compared fav¬ order channel frequency was found to be highly orably with 0.388 for log area versus log unex¬ correlated with second-order area, diameter, and plained discharge. When second-order basin area drainage density, hence it could not be used as an was added the correlation coefficient was increased independent variable with any of these three. The from 0.388 to 0.427. When diameters were used in¬ largest multiple correlation coefficients among stead of areas, the multiple correlation coefficient the four-variable correlations were for those rose from 0.427 to 0.448. which included fifth-order diameter and second- A series of simple and multiple logarithmic order drainage density as two of the three inde¬ linear correlations was computed to find which pendent variables. combination of variables gave the best prediction, To confirm the apparent relative effectiveness as measured by the multiple correlation coefficient. of the variables, two series of five-variable and The variables and corresponding correlation coef¬ two series of six-variable multiple correlations ficients of these equations are tabulated in Appen¬ were computed. In the first series of five-variable dix IV. The geomorphic variables considered were correlations, fifth- and second-order diameters, fifth-order area and diameter, means of second- second-order drainage density, and successively 29 six other geomorphic properties were used. In the rainfall, cover density, and geomorphic variables. second five-variable series, fifth- and second- It is quite probable that more of the variation will order areas were substituted for diameters. Very be explained when better measures of storm con¬ little difference was found among the multiple cor¬ ditions are available. All precipitation values used relation coefficients of these two series, although were measured at the main San Dimas Experimen¬ those for the series using areas were generally tal Forest rain gage located at Tanbark Flat. slightly larger. For the two six-variable series, Thorough investigation has indicated that this gage second-order relief ratio and drainage density samples local rainfall accurately. Precipitation were paired with fifth- and second-order diam¬ data measured within each watershed would probab¬ eters or, alternatively, areas, and successively ly correlate more closely with watershed peak dis¬ five other properties. When the multiple correla¬ charge. tion coefficients of these equations were rounded The estimating, or regression, coefficients to three significant digits they were alike except listed in Table XIV show the effect of change in for the equation of diameters with diameter ratio, one variable when the others are held constant. A which was very slightly larger. very large range was found for estimating coeffi¬ These results indicate that, for the sample of cients of the geomorphic variables from equation peak discharges and geomorphic properties that to equation. For the two equations which had the was studied, fifth- and second-order areas or di¬ largest multiple correlation coefficients, the esti¬ ameters, together with second-order drainage den¬ mating coefficients of the geomorphic variables sity and relief ratio, provide a good estimate of were approximately ten times greater than the cor¬ the variability in peak discharge which can be ex¬ responding coefficients in the other three equations. plained by geomorphic variation between water¬ The standard deviations of the geomorphic varia¬ sheds. Several other geomorphic variables im¬ bles also were larger by factors of three to six prove the estimating equation slightly, and about in the first two equations. In these two equations equally. Several of these may be related to another, all of the estimating coefficients were significant, unidentified, geomorphic property which would im¬ being one to three standard deviations different prove the estimating equation more than any of from zero. In the remaining three equations, only these taken singly. fifth-order area or diameter was consistently dif¬ ferent from zero. The partial correlation coefficients, also listed COMBINED EQUATIONS in Table XIV, indicate relative influence of the several variables. Storm intensity has the largest The results of the correlation of storm charac¬ partial correlation coefficient, 0.77. Cover density teristics and watershed condition with peak dis¬ is second only to storm intensity; antecedent pre¬ charge, and the correlation of geomorphic proper¬ cipitation accounts for less of the variation in peak ties with unexplained discharge determined the se¬ discharge than does cover density. In the equation lection of variables for correlations which would having the largest multiple correlation, the geo¬ combine both. Five nine-variable multiple corre¬ morphic variables have approximately equal par¬ lation equations were computed. The equations tial correlation coefficients. Evaluating the signi¬ were of the form: ficance of the partial coefficients is difficult be¬ cause of complications in the degrees of freedom. log Q = k + b4 log P24 + b2 log Cd + b3 log P21 For the first three variables, P24, Cd, and P21, 113 + b4 log A5 + log A2 + b6 log D2 + b7 log different groups of data were available. For the geomorphic variables there were five groups of R2 + b8 log Ra approximately 22 identical values each, correlated Numerical values of the estimating coefficients, with 113 different values of peak discharge. If, in their standard deviations and the partial correla¬ using a t-test to evaluate the significance of the tion coefficients for each term are listed in Table partial coefficients, the sample size is taken as XIV. The largest coefficient of multiple correlation 113, the coefficients are all significant. If five is obtained was 0.8965. This was for the equation used for sample size N, the t-value cannot be cal¬ using fifth- and second-order areas and the area culated, because the degrees of freedom, N-m ratio, with P24, Cd, P2i, D2, andR2, to estimate Q. (where m is the number of variables) is negative. The equation using fifth- and second-order area Without drawing a probability inference, an in¬ and mean second-order relief with the same other dication of the influence of the geomorphic varia¬ variables had the smallest multiple coefficient, bles can be seen in the increase in multiple corre¬ 0.8888. The coefficient of multiple determination lation coefficient from 0.807 for the best four- for the best correlation was 0.8037, indicating that variable equation to 0.897 for the best nine-variable more than 80 percent of the variation in peak dis¬ equation. Pertinency of the five geomorphic vari¬ charge can be explained by this combination of ables is indicated by the increase in partial corre- 30

lation coefficients of the first three variables. be meaningfully applied to mountain watersheds of After having much experience using multiple cor¬ precipitous slopes and high relief, despite greater relation to investigate watershed discharge and difficulties of conducting field operations in moun¬ sediment production, H. W. Anderson (1957, p. 123) tainous terrain than in areas of more moderate has criticized routine dropping of “non-significant” slopes and lower relief. Probably the greatest dif¬ variables: ficulty encountered in applying the quantitative methods was in identification of stream channels. Frequently, in the past, variables have been This was overcome by defining stream channels in dropped “because they were non-signifi¬ terms of recognition criteria which had logical cant”. The arbitrary choice, say the five- bases in theory, which were readily visible, and percent level, for this decision is statistical which excluded channel-like depressions not formed nonsense. Why we should choose to drop a primarily by concentrated stream flow. That the measure which is unbiased, small, but dif¬ definition and recognition criteria were adequate fering from zero, and substitute the biased was verified by a replication study, in which an¬ value of zero is not clear. other investigator, working independently but using The statisticians do not suggest that we the same definition and criteria, obtained consis¬ make any such arbitrary decision at the tent results. five-percent level; they tell us we must de¬ Generalizations, such as the laws of stream cide on the basis of the risks we are willing numbers and of basin areas, were found to be valid to take of (1) retaining a variable whose ap¬ for chaparral covered mountain watersheds. Char¬ parent effects are really due to chance and acteristic values of the many geomorphic proper¬ (2) dropping a variable with real effects. ties investigated were consistent with those found The ‘real effect’ of a variable which is elsewhere, and were consistent with subjective de¬ worthwhile retaining in analyses relating scriptions of the investigated area. Thus it was sediment yield (or peak discharge) to water¬ concluded that concepts which were developed in shed variables is one which would affect the humid, hilly eastern United States are suffi¬ the results, most importantly affect the ciently general to be applicable to mountainous partial effects of the other variables. The areas in a Mediterranean climate. added possibility that the several small ef¬ fects may add up to an important effect makes dropping of individual variables ANALYSIS OF METHODS risky. Analysis of the methods of quantitative geomor¬ Regarding the interpretation of partial-corre¬ phology, during application of these methods to lation coefficient-significance tests, Croxton and mountain watersheds, revealed that a few of the Cowden (1955, p. 735) state that these do not tell definitions of geomorphic properties contain am¬ us that we should necessarily exclude a non-signi¬ biguities. Resolution of difficulty with the identifi¬ ficant variable from our analysis, since it may cation of channels has been mentioned above. Some contribute some useful information even though its of the methods used in previous studies for meas- significance has not been demonstrated. The au¬ using drainage basin shape failed to discriminate thor believes that inclusion of the above geomor- between gross differences in shape and minor phic variables contributes useful information in at crenulations in basin perimeter. To overcome this least two ways. Directly, their inclusion improves difficulty a shape index based on basin diameter the estimation of flood peak discharge by making was proposed and applied. Partly to facilitate def¬ allowance for basic differences between watersheds. inition of the shape index, but primarily to provide Indirectly, an estimation of the relative influence a more adequate definition of a basic property, of different aspects of the landscape on flood peaks basin diameter was explicitly defined. A somewhat is provided, indicating which properties might be lengthy definition was needed to accomodate all most fruitful for further investigation, and giving anticipated conditions. Fortunately, the definition a clue to cause and effect relationships between was generally easy to apply. After review of the streams and the equilibrium forms they produce. several methods used to express the relative relief of drainage basins, one based on the diameter was Conclusions used. Because quantitative geomorphology is a very recently established branch of science, it is to be expected that many significant basic proper¬ APPLICABILITY OF METHODS ties have not as yet been identified and defined. New definitions used in this study are tentatively The results described above indicate that presented with the expectation that they may be methods of quantitative geomorphic analysis can improved by future work. 31

Methods of geomorphic analysis often include should include tests for normality of distributions comparison of means by statistical analysis of var¬ and homogeneity of variance. iance. Inference from analysis of variance is valid only when the populations compared are normally distributed and have equal variances. In some CORRELATIONS WITH FLOOD DISCHARGE previous studies of watershed morphology the nor¬ mality of sample distributions was tested. Tests Storm rainfall, watershed cover, antecedent for homogeneity of variance of geomorphic data precipitation, watershed area, mean second-order had not been made prior to the present study. The basin area, mean second-order drainage density, results of normality tests in this study indicated mean second-order relief ratio, and watershed that first-order drainage basin areas are sensitive area ratio were correlated with 113 measurements to interruptions in their erosional development. of annual peak discharge. The multiple correlation Consequently, measurements of first-order basin coefficient was 0.8965. Several other multiple cor¬ area are likely to be polymodal and non-normal relations indicated that fifth-order and second- when grouped on a watershed basis. The non¬ order diameters, mean second-order relief, and normality found in first-order basin areas in the watershed diameter ratio were also useful in esti¬ San Dimas Experimental Forest may indicate a mating peak discharge. Partial correlation coeffi¬ very useful means of objectively determining the cients indicated that storm rainfall, watershed area affected by a younger erosion cycle encroach¬ cover, and antecedent precipitation accounted for ing upon forms developed to a later stage by an more of the variation in discharge of fifth-order earlier cycle of erosion. Homogeneity of variance watersheds than did any of the geomorphic varia¬ tests revealed that groups of the same order and bles. It was concluded that there are significant property from adjacent watersheds had significant quantitative differences in geomorphology between differences between variances. It is not known the watersheds of the San Dimas Experimental whether this condition is characteristic only of Forest, and that these differences account for San Dimas watersheds, or of mountain watersheds, otherwise unexplained differences in flood peak or whether it is often true of watersheds in gen¬ discharge from these watersheds. eral. Future studies which use analysis of variance N

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-■ References Cited

Anderson, H. W., 1949, Flood frequencies and Nat’l Acad. Sci. - Nat’l Res. Council, Sympo¬ sedimentation from forest watersheds: Amer. sium on Quantitative Methods in Geography. Geophys. Union Trans., v. 30, p. 567-584. Dixon, W. J., and Massey, F. J., 1957, Introduction _, and Trobitz, H. K., 1949, Influence of some to statistical analysis. Second edition: McGraw- watershed variables on a major flood: Jour, of Hill Book Co., Inc., New York, 488 pp. Forestry, v. 47, p. 347-356. Gravelius, H., 1914, Flusskunde: Goschensche _, 1957, Relating sediment yield to watershed Verlagshandlung, Berlin, 176 pp. variables: Amer. Geophys. Union Trans., v. 38, Hamilton, E. L., 1944, Rainfall measurements as p. 921-924. influenced by storm characteristics in southern Bean, R. T., 1943, Geology of the Big and Little California mountains: Amer. Geophys. Union Dalton watersheds: open file report, San Dimas Trans., v. 25, p. 502-518. Experimental Forest, U. S. Forest Service, _, 1951, The climate of southern California; Calif. Forest and Range Experiment Sta. in Some aspect of watershed management in _, 1944, Geology of watershed V, VII, and southern California: Calif. Forest and Range lower VI: open file report, San Dimas Experi¬ Experiment Sta., Misc. Paper No. 1. mental Forest, U. S. Forest Service, Calif. _, 1954, Rainfall sampling on rugged terrain: Forest and Range Experiment Sta. U. S. Dept, of Agriculture, Tech. Bull. 1096. _, 1946, Geology of watersheds I, II, III, and Horton, J. S., 1941, The sample plot as a method IVA: open file report, San Dimas Experimental of quantitative analysis of chaparral vegetation Forest, U. S. Forest Service, Calif. Forest and in southern California: Ecology, v. 22, p. 457- Range Experiment Sta. 468. Birnbaum, Z. W., 1952, Numerical tabulation of the _, 1944, Vegetation distribution on the San distribution of Kolmogorov’s statistic for the Dimas Experimental Forest: open file report, finite sample size: Jour. Amer. Statistical San Dimas Research Center, U. S. Forest Ass’n., v. 47, p. 425. Service, Calif. Forest and Range Experiment Broscoe, A. J., 1959, Quantitative analysis of Sta. longitudinal stream profiles of small water¬ _, 1951, Vegetation; in Some aspects of water¬ sheds: Office of Naval Research, Geography shed management in southern California: U. S. Branch, Project NR 389-042, Tech. Rept. No. Forest Service, Calif. Forest and Range Experi¬ 18 (Columbia University, N. Y.), 73 pp. ment Sta., Misc. Paper No. 1. Bryson, R. A., and Dutton, J. A., 1960, The vari¬ Horton, R. E., 1932, Drainage-basin characteris¬ ance spectra of certain natural series: Nat’l tics: Amer. Geophys. Union Trans., v. 13, Acad. Sci. - Nat’l Res. Council, Symposium on p. 350-361. Quantitative Methods in Geography. _, 1945, Erosional development of streams Burns, J. I., 1953, Small scale topographic effects and their drainage basins; hydrophysical ap¬ on precipitation distribution in San Dimas Ex¬ proach to quantitative morphology: Geol. Soc. perimental Forest: Amer. Geophys. Union Amer. Bull., v. 56, p. 275-370. Trans., v. 34, p. 761-767. Ichikawa, M., 1958, On the debris supply from Coates, D. R., 1958, Quantitative geomorphology of mountain slopes and its relation to river bed small drainage basins of southern Indiana: deposition: Science Reports of the Tokyo Columbia University, Dept, of Geology Technical Kyoika Daigaku, Sec. C, v. 6, p. 1-29. Report No. 10, Office of Naval Research Project Langbein, W., 1947, Topographic characteristics NR 389-042. of drainage basins: U. S. G. S. Water-Supply Cox, E. P., 1927, A method of assigning numerical Paper 968-C, p. 125-157. and percentage values to the degree of roundness Maner, S. B., 1958, Factors affecting sediment de¬ of sand grains: Jour. Paleontology, v. 1, p. livery rates: Amer. Geophys. Union Trans., 179-183. v. 39, p. 669-675. Croxton, F. E., and Cowden, D. J., 1955, Applied Massey, F. J., 1951, The Kolmogorov-Smirnov general statistics. Second edition: Prentice- test for goodness of fit: Jour. Amer. Statistical Hall, New York, 944 pp. Assn., v. 46, p. 68. Dacey, M. F., 1960, Description of line patterns:

33 34

Maxwell, J. C., 1955, The bifurcation ratio in semi-arid cycle of erosion: Amer. Jour. Sci., Horton’s law of stream numbers (abstract): v. 255, p. 161-174. Amer. Geophys. Union Trans., v. 36, p. 520. Siegel, S., 1956, Non-parametric statistics for the Melton, M. A., 1957, An analysis of the relations behavioral sciences: McGraw-Hill Book Co., among elements of climate, surface properties, Inc., New York, 312 pp. and geomorphology: Columbia University, Dept, Sinclair, J. D., 1953, A guide to the San Dimas Ex¬ of Geology Technical Report No. 11, Office of perimental Forest: U. S. Forest Service, Naval Research Project NR 389-042. Calif. Forest and Range Experiment Sta., Misc. Miller, V. C., 1953, A quantitative geomorphic Paper No. 11. study of drainage basin characteristics in the _, 1954, Erosion in the San Gabriel Mountains Clinch Mountain Area, Virginia and Tennessee: of California: Amer. Geophys. Union Trans., Columbia University, Dept, of Geology Techni¬ v. 35, p. 264-268. cal Report No. 3, Office of Naval Research Con¬ Smith, K. G., 1958, Erosional processes and land- tract N6 ONR 271-30. forms in Badlands National Monument, South Miller, W. J., 1928, Geomorphology of the south¬ Dakota: Geol. Soc. Amer. Bull., v. 69, p. 975- western San Gabriel Mountains of California: 1008. University of California, Dept, of Geological Storey, H. C., 1939, Topographic influences on Sciences Bull., v. 17, p. 193-240. precipitation: Proc. Sixth Pacific Science Con¬ _, 1934, Geology of the western San Gabriel gress, v. 4, p. 985-993. Mountains: Calif. University Publications in _, 1948, Geology of the San Gabriel Mountains, Mathematical and Physical Science, v. 1, California, and its relation to water distribution: p. 1-114. U. S. Forest Service and Calif. Dept, of Natural Morisawa, M. E., 1959, Relation of quantitative Resources, Div. of Forestry, Berkeley, Calif., geomorphology to stream flow in representative 19 pp. watersheds of the Appalachian Plateau Province: Strahler, A. N., 1950, Equilibrium theory of ero¬ Columbia University, Dept, of Geology Techni¬ sional slopes approached by frequency distribu¬ cal Report No. 20, Office of Naval Research tion analysis: Amer. Jour. Sci., v. 248, p. 673- Project NR 389-042. 696, 800-814. Neuenschwander, G., 1944, Morphometrische _, 1952, Hypsometric (area-altitude) analysis begriffe: University of Zurich, Doctoral thesis: of erosional topography: Geol. Soc. Am. Bull., Emil Ruegg & Co., Zurich, 134 pp. v. 63, p. 1117-1142. Ore, H. T., and White, E. D., 1958, An experiment _, 1953, Revisions of Horton’s quantitative in the quantitative analysis of drainage basin factors in erosional terrain. Hydrology Section characteristics: The Compass of Sigma Gamma Am. Geophys. Union, Washington, D. C. 1953 Epsilon, v. 36, p. 23-38. (Abstract). Potter, W. D., 1953, Rainfall and topographic fac¬ _, 1954, Quantitative geomorphology of ero¬ tors that affect runoff: Amer. Geophys. Union sional landscapes: 19th International Geol. Con¬ Trans., v. 34, p. 67-73. gress, 1952, sec. 13, pt. 3, p. 341-354. Reimann, L. F., and Hamilton, E. L., 1959, Four _, 1958, Dimensional analysis applied to flu- hundred sixty storms: U. S. Forest Service, vially eroded landforms: Geol. Soc. Am. Bull., Pacific Southwest Forest and Range Experiment v. 69, p. 279-300. Sta., Misc. Paper No. 37. Trew, J. R., 1956, Slope development in the San Rowe, P. B., and Coleman, E. A., 1951, Disposition Dimas Experimental Forest, California: of rainfall in two mountain areas of California: Master’s thesis, Brown University, Providence, U. S. Dept, of Agriculture, Tech. Bull. 1048. R. I. Schumm, S. A., 1954, The relation of drainage Wisler, C. O., and Brater, E. F., 1949, Hydrology: basin relief to sediment loss: Publ. International John Wiley & Sons, Inc., New York, 419 pp. Assoc, of Hydrology, I. U. G. G., Tenth Gen’l. Wood, W. F., and Snell, J. B., 1959, Predictive Assembly, Rome, v. 1, p. 216-219. methods in topographic analysis I: relief, slope ___, 1956, Evolution of drainage systems and and dissection on inch-to-the-mile maps in the slopes in badlands at Perth Amboy, New Jersey: United States: U. S. Army Quartermaster Re¬ Geol. Soc. Amer. Bull., v. 67, p. 597-646. search Center, Technical Report EP-112. _, and Hadley, R. F., 1957, Arroyos and the

Table I MONROE CANYON SOIL CHARACTERISTICS O 45 •H •H ft ft aS 3 o O P co o P ■< CD ^ t «a* S ft •H rH > O P r—i O o CO •H « ft p O ft Pi co P P o o O 3 rH to O O rH T3 >» rO CtJ H* O •H rH TS ft •H •H -3 P O u ID 4> aS ft O oJ >> co P rS (M O bfi d o 00 3 o CO 1 « • ro •H •S rH 3* •H TJ p P p CO bO Pi CO P C<1 O C oS O ID o « o HN fO ft ft rH ft •H CO T3 3 p JD 43 O r-i ft ■rl Ha) p P X> J ^ P(fl rH -H •H P 43 . 4S CO •H *H T3 •H c W o o c O o o P 3 d> > | > O O o 3 O JJ o Pi *H CO ctf P tH O a p OOP o co P w « X o co « £ Ctf O 3 cm p o •H O T3 rH •H O 31 i3 ft 2 rH ft 43 1 rrJ >3 p co rH ■H P (N P t3 3 0> « nf to T 3 p O V P oo 3 o bo 23 cti C O P O & «5 P co tD •H P s p O CO 3 o p bfi «

From Rowe and Colman, 1951 37 38

Tabic II San Dimas Vegetation Distribution Cl, u o (O entage of Watershed Area Covered by Vegetation Type J3 O •H y -3 as rC C •H C X pH 3:2 CO X XS Q CD •h 4J X O •H cd X a 3 TS o c/5 Ul ►» *-> • Vi ♦ • •• • •• U <1> O 3 3 rH rH 05 X T) O rH O • • ft H 3 c3 •• U U cd co cd r* o H nj cd 3 cd ft cd hC 4> cd / rH rH cSJ rH pH (SI CO H rf o rH 05 <0 rf CO ro rH rf o ft 05 H 05 • a 0 « m • • * a / rH HI pH rf HI rH rf HI CO CO pH OJ rf C'- to rH rf M o o ft M co ft I « «► * * • a • • • CH rH M CM O CO * a • a a • a • • • H? CO O o M pH HJ rH ro CO c 05 • a « e « • 0 a a • rH H" rH H rf ft H « • « • a • © • • pH rH H- pH HJ O (M Tf rH rH CO rf ft ft CO rf

From the files of the San Dimas Experimental Forest 39

TABLE HI

COMMON AND BOTANICAL NAMES OF SOME SPECIES OF HIE SAN DIMAS EXPERIMENTAL FOREST

Alder, white...•••••••••o..o.«»...... o....Alnus rhombifolia Berry, Christaoas.....Photinia arbotifdlia Budswheat, California...o.••«»»...... •....Erigonum Fasciculatum Ceanothus, deerbrush...•».••»••••«..«o....o«Ceanothus integerrimus Ceanothus, hairy...,...«..««««C. oliganthus Ceanothus, hoaryleaf...... o.0.oo*.a.a*»«.*o.«..,•»C. crassifolius chamise*oo«...«.....a.*.oo.o..«.o«.««.«*»■•...«.oo«a.*..oaAdenostcsaa £asciculatusi Laurel, California.•»•«••»«*«•*..•**«#4».««*Umbellularia californica Manzanita, bigberry...... 0.«.•••••••••••••••*«.•••*««•••*Arctostaphylos glandulosa Manzanita, Eastwood...••«••••••.••••«..o«.*o»...... Arctostaphylos glandulosa Maple, bigleaf....oAcer marophyllum Mountain-mahogany, birchleaf• *.••••••••••••••••• •Cercocarpus betuloides Oak, California live..***..•••••...... Quercus agrifolia Oak, California scrub....• • .•••<>• •••oQ* dumosa Oak, canyon live (Golden Oak).....••••••••••••••«•••»§• chrysolepis Oak, interior live..••••••••••**•••••....Q. wislizeni Pine, Coul ter...... •••••••...... o.....o.. ..Pinus coulteri Pine, knobcone••••...... o.»..o.»»...<>«• •.• .P. attenuata Fine, ponderosa...... ««...*..*otoP. ponderosa Poison oak, Pacific...... Toxicodendron diversilobun..*...(Rhus diversiloba) Sage, black...... Salvia mellifera Sage, white.....•••••••»••• .S. apiana Spruce, bigcone•••••••••<«•«•••.Pseudotsuga macrosarpa Sumac, laurel...... Rhus laurina Sumac, lemonade.....R. integrifolia Sugarbush...... ••....•••««•«R. ovata Sycamore, California..••••••••••.•••«o...... o..«o.•«•••.«Platanus racemosa White thorn, chaparral.....o.«.« ..««.««»««.«• o »•...... Ceanothus leucodermis Willows...... Salix :.spp. Table IV Constants for Approximating Density of Cover 40 Types for Southern California Watersheds for Burned Areas "t" fears After a Fire^ O ft rH o o > 3 ft (U g (5 O O 0) b£ a I i ft! O F~ft O iH & S ft 43 •H r-* d Otf 3 3 d o X 6 cr> co o H 4> O') to ro C5 O 3 01 ft o O 3

0 o O C •H TO CO O 41 P m o OH to Q £ d 3 3 G • O j* 3* TO rH TO O X •H rH O’ rH < i—I et5 o O O d 3 O 01 3 CO 01 Cl o (N G IH 3 ►» g a. o 3 O ro -O a 43 O •H •H t3 O 43 rH 43 •H 23 P d o S3 to p r“+ G d o f d r* N d CO o rH rH 3 d d d 3 ft 3 3 ro d d Is ft o g o a ft o t- »n O rH rH rd 3 T3 g (0 tuO O 3 • •H co O »r> o rH rH CH p 4) 01 £ 3 d 01 3 >> o •H •H 43 rH K O 43 rH 33 43 S co •H P o o rH P CO O ro d CO bfl > O 3 ft d 3 d 01 d 3 3 o d o O (.4 P • t3 •H ft O r- O O rH Tf ro <51 3 d 3 w q >> WO o o G 3 • ■—*s •H O T3 rH T3 •H > <5 ft rH O’ <3j H rH O ro Tf O O rH o ID d O d O M 3 O 3 d 3 3 to 01 bO O « •H O 43 T3 ft O H 43 •rH - —H P O rH O cO cDro to o o O Cl O d- co P G G 3 d £ wd w G 3 d ft d 3 3 d d 3 o o £ O ft • ft O 01 Sd 3 G O 3 •H CO TO O o o o CO P £ 3 3 Cl 01 d to o *fq O 43 A ft T3 O •H co 3S CO -3 d o o rH uo 4> to O rH O O 00 P t3 3 3 d G G d 3 3 03 03 G d bO G c3 *n 3 O >> £ G Cl ft p G Cl • ,-H 3 01 03 bO O 3 3 •H -Q rH TJ E-< rH O 43 < rH rH o O o o ■ft to L.O £ G 3 d 3 d ft 3 3 d d « O rH co rH rH o ft o O rH ro P tO d CO d O d bO G » ft cO rH rH 3 O O rH ro O o o P co 3 G d G bC G <* •rj co X CO 43 d 41 •rl 3 O M O o o rO ai P T3 § 3 d 3 G 3 d *ri 3 £ js O 01 ft P Cl to 01 oi « ft CH O O o ro 4) to a bO G O 3 01 9 p I rH o 'd •rH ft •ri o ft ft O O P P H- P P P • « u H O G o > G G 3 01 G 3 d 3 O O G 3 G 9 t»-> II I H « P p £ d 3 TJ -3 rH 43 •H *3 en ft H Ol P 3 3 3 £ G 01 3 d 3 N 3 o o G •s 41

Table V

GEOLOGIC MAPPING UNITS

1. Granodiorite, buff-colored, may be same as Lowe granodiorite, and meta- diorite; mostly in southwest Wolf ski 11 Canyon.

2. Quartz diorite. includes some fine-grained (quartz) diorite or meta- diorite, Wilson quartz diorite, diorite gneiss and schist; interfingering augen gneiss, leucocratic gneiss and other gneiss, varying amounts of granite, granodiorite and associated dikes.

3* Augen gneiss predominant; some other gneiss, (quartz) diorite and metadiorite, granite, granodiorite and associated dikes.

4. Banded gneiss predominant; considerable (quartz) diorite and meta¬ diorite; some augen gneiss, granite, granodiorite and associated dikes.

5. Dacite dikes and quartz diorite.

6. Dacite dikes and augen gneiss.

7. Dacite dikes and banded gneiss.

8. Pegnatite dikes. 42

Table VI

GEOMORPHIC PROPERTIES

Symbol Name Units Dimensions

u Order Enumerative Dimensionless

Number of channel segments of order u Enumerative Dimensionless

Length of channel segment of order u Miles L 2 Area of drainage basin of order u Sq.miles L

Perimeter of basin of order u Miles L

Basin diameter Miles L

Plow length along channel,to divide Miles L

Basin relief, measured on diameter Feet L

Basin relief, measured on maximum flow path Feet L

Maximum basin relief ■^max Feet L oc Basin azimuth (downstream direction of diameter) Degrees Dimensi Onless

Maximum valley-side slope Degrees Dimensionless

Channel gradient Degrees Dimensionless

R Basin circularity Dimens ionless c Basin elongation ratio Dimensionless

Relief ratio Dimensionless

Relative relief Dimensionless

Bifurcation ratio Dimensi onless

D Drainage density Mi.per sq .mi • P Channel frequency (stream frequency) No.per sq.mil 43

TABLE YII

Summary of Normality Tests^

PROPERTY CONCLUSION

Channel length All log-normal

Area First order polymodal; higher orders log-normal

Diameter All log-normal5 higher orders may be arith-normal

Perimeter Three measured were log-normal

Elevation Not arith-normal; not log-normal

Relief Log-normal

Relief ratio Inconclusive; not arith-normal; may be log-normal

Relative relief Inconclusive; not arith-normal; may be log-normal

Elongation Inconclusive; probably log-normal

Circularity Normal

Drainage density Log-normal

Channel frequency May be log-normal

1 See Appendix II for tabulation of tests. 44

TABLE Till

Summary of Homogeneity of Variance Tests

Order 1st 2nd 3rd Ijth

Property Percent probability of homogeneity

Log length -.05 65-75 25-35 25-50

Log basin area .05-0.1 56-60 60-70 75-90

Log diameter —.05 95-98 25-35 25-50

Log perimeter 5-10

Log relief -.05 -.05 .05-0.1 25-50

Log relief ratio —.05 -.05 -.05 50-75

Log relative relief 2.5-5 v\ in 0 0 1 1 1 1 • Log elongation • 0.5-1.0 50-75

Circularity —.05

Log circularity —.05

Log drainage density 0.5-1.0 10-25 0.1-0.5 25-50

Log channel frequency -.05 10-25 0.1-0.5 1-2.

-.05 should he read as “less than five hundredths percent",05 should he read as "much less than five hundredths percent" • 45

TABLE IX

Summary of Analysis of Variance

Order 1st 2nd 3rd lith operty Percent Probability of Equal Means

Log length —.0$ 35-U51 10-50 25-50

Log basin area —.05 -.05 5-10 10-25

Log diameter —.05 -.05 1-2.5 10-25

Log perimeter 2-31 1 0 • Log relief —.05 —.05 vn. 5-io

Log relief ratio — .05 —.05 .05-0.1 2.5-5

Log relative relief 30-w

Log elongation -.05 90-95 10-20 99-99.5

Circularity 0.5-1.0

Log circularity 0.1-0.5

Log drainage density —.05 — .05 1-2.5 0.5-1

Log channel frequency —.05 — .05 0.1-0.5 0.5-1

-.05 should be read as "less than five hundredths percent".05 should be read as "much less than five hundredths percent" •

1. Probability inference is valid only for underlined values5 see text* 46

TABLE X

Comparison of Embers of Stream Segments

Bell Canyon Wolfskill Canyon

Order Maxwell Trew $ Biff. Order Maxwell Trew $ Biff Hi % 386 366 -5.2 ^109 366 -10.5 90 1.1 h2 96 *2 S9 S3 -13.5 24 25 4.2 Hj 21 -19.0 h3 17 N4 4 4 0 H4 5 5 0 1 1 1 h5 H5 1

Rb 4.51 4.48 -0.4 lb 4.51 4.4s -2.0 47

TABLE XI

Comparison of Mean Lengths of Stream Segments

Bell Canyon Wolfskill Canyon

Order Maxwell Trew s— Order Maxwell Trew X El 0.0493 0.044 0.0017 0.0713 0.0S1 0.0021

e2 0.OS39 0.0S2 0.0063 r2 0.1096 0.11S 0.0096

0.1^5 0.147 0.0179 0.1910 0.220 0.0291 r3 E3 0.3142 0.32S 0.061s 0.2930 0.27^ 0.0915

2.011 2.000 2.839 2.710 L5 l5 (lengths in miles)

TABLE XII

Comparison of Mean Basin Areas

Bell Canyon Wolfskill Canyon

Order Maxwell Trew Order Maxwell Trew Sx-y O.OOS67 0.00S6 0.00095 i2 *2 0.0156 0.01S 0.0020

O.O3S7 O.O33 0.0061 0.06l0 0.070 O.OI76 *3 *3 O.OS54 0.0S6 0.2242 *4 *4 0.236

1.357 1.370 2.4915 2.470 A5 (areas in square miles) 48

TABLE XIII

Va-RIABT.ES USED IN MULTIPLE C0EEELATI03JS

Symbol Definition Units Q, Maximum yearly peak discharge cfs.

p6o Maximum 60-minute precipitation during stoim inches Maximum 24-hour precipitation during stoim inches p24 7-day precipitation prior to date of storm inches P7

P21 21-day precipitation prior to date of storm inches

°d Cover density on the watershed percent

Fifth order watershed area so . miles a5

*5 Fifth order watershed diameter miles

a2 Mean second order basin area sc^. miles x 10^

d2 Mean second order basin diameter miles x 10^

h2 Mean second order relief feet

D2 Mean second order drainage density miles~P

C2 Mean second order channel frequency miles~P

*2 Mean second order relief ratio x 103

*b Watershed bifurcation ratio

% Watershed length ratio

Ea Watershed area ratio

*d Watershed diameter ratio COEFFICIENTS FOR MULTIPLE CORRELATIONS WITH PEAK DISCHARGE rQ e fH u 05 r>» £ 05 05 M •H rO •H •H •H K X -rj- o O CO o o O CT\ in pH cn CO ir\ cn K0 O OJ O cn CO K0 cn Cn M OJ 1 1 1 • • • • • • vo -d* vo Jt vo VO VO vo vo Q O o o to o o h- OJ 1—I 0- r— o o rH r— o o o r— rH OJ fL rH 1— rH cn • • • • • • OJ • VO vo vo 3 O CO r— iH CO O C0 o in CO o r— r— CO o o OJ CT\ m rH -4- CTv rH rH O o o rH I 1 i • • • • • ♦ • vo vo vo o CO o o o o CO o r— c— o c— O o o o c— OJ CO o o OJ OJ cn o m n- OJ OJ in OJ r—1 CO P4 • • • • • • • ed s J=t -Z}- CO o CO OJ in t"- o in c~ rH o cn fH rH o fd OJ rH r— CO CO 1— r~- cr\ OJ cn cn m »cJ in • • • • • • • vo £> -d* CO o o CO in o o o in m OJ OJ O CO cn CO rH rH rH O o LTv c— o rH rH CO cn cn OJ CVJ • • • • • * • vo vo 3 to CO o O o cn OJ in o cn Cn m rH c— OJ n r— r— in rH c— m cn m in r— OJ rH OJ rH p I • • • • • OJ • • vo vo s vo CO o o CO rH in cn f—1 in ON m OJ in rH o o CO rH cn r— OJ o rH p5" cn cn cn 1 r • • • • • • • o S3 a in cn OJ Pi rH OJ cn Jp cn • • vo o r— in o o in rH in OJ Ph cn • • • ci vo CO ft rH rH o ft o A c— cn CM • • • CO o to o in CO CO rH o co CO rH cn cn CT\ H •rl cn -p P u p* j=y y> yj o o o + y) o d OJ OJ cn CM 1—1 in 'd 1—1 & rH fQ rH rC5 fH rH Q rQ Ph + + a5 + + o y> yj o o yj o y) VO co OJ n- Ln OJ c$ 49 50

TABLE XIV (continued)

*1 S1 *1 sb ryx

k -362.0 O.O38 7.736 O.O39

2.001 0.164 P24 1.967 0.159 0.771 0.767

c -10.64 1.806 0.500 -8.551 1.687 0.445

0.376 0.070 P21 0.281 0.068 0.282 0.366 26.08 0.276 6.164 1.921 0.300 a5 76.36 63.55 a2 171.5 0.256 3.395 13.50 0.028 d2 444.5 163.I 0.258 4.242 7.510 0.055 h -196.6 71.07 0.262 5.926 26.48 0.022

Ea 451.8 l66.4 0.257

h2 -8.897 24.51 O.O36

Multiple r O.S965 0.8888 Illustrations

Vx't) h-fM

Figure 1. Index map showing relation of San Dimas Experimental Forest to Los Angeles County. SAN DIMAS EXPERIMENTAL FOREST

Figure 2. Index map to watersheds of San Dimas Experimental Forest. ANNUAL RAINFALL, INCHES RAINFALL, INCHES TEMPERATURE, DEGREES ANNUAL RAINFALL WILLBEEQUALEDOR EXCEEDED San Dimas ExperimentalForest. Figure 3.Precipitation andtemperature dataofTanbark Flat, NUMBER OFTIMES INIOOYEARS 56 57

San Francisco

«»;jj;s;»;ss;;ni ponderosa pine CHAPARRAL WOO0LAND * CHAPARRAL-GRASS

San Diegoj

Figure 5. Vegetation types of Southern California. 58 30

HUMBER OF CHAHHELS ZO /O S 3 7- 2 / \ / 2 ORDER / 3 4- 5 OF CHANNELS 27 28 Figure 7.Relationof streamnumberstoorder. A B 3 4 9 70 / 2 NUMBER / System ofchannelordering. CHANNEL ORDER First Order Second Ordei- Fourth Order— Third Order—* 59

Figure 8. Examples of basin diameter determinations. 60

B. Same map showing corrected locations of channels and divides.

Figure 9. Example of relation of observed to mapped topograhic features. NUMBER OF CHANNEL SEGMENTS Figure 10.Relationofstreamnumberstoorder. CHANNEL ORDER 61 L 62

SEGMENT LENGTH, MILES Figure 11.Relationofstreamlengthtoorder. CHANNEL ORDER BASIN AREA, SQUARE MILES Figure 12.Relationofbasinareatoorder. CHANNEL ORDER 63 64

DIAMETER, MILES Figure 13.Relationofbasindiametertoorder. CHANNEL ORDER ii

RELIEF, FEET Figure 14.Relationofrelieftoorder. CHANNEL ORDER 65 DIAMETER OF CIRCLE O o < 2 UJ H UJ

o I

30

25 - 0.023 - 0.019

- 0.020 20

- 0.025

- 0.022

T I 2 3 4 5

CHANNEL ORDER

Figure 16. Relation of drainage density to order. 68

CHANNEL FREQUENCY NUMBER OF SEGMENTS PER SQUARE MILE Figure 17.Relationofchannelfrequencytoorder. CHANNEL ORDER Appendices

APPENDIX I 71 Characteristic Values of Geomorphic Properties

WATERSHED I, WOLFSKILL CANYON_ I First Order n v Second Order Third Order Fourth Order roper y_Arithmetic Log ' Arith Log Arith Log Arith Log Number 1)09 96 21 5

X .07130 .06013 .10961) .071)70 .19095 .11)731) .29300 .20136 Channel s .01*267 .09837 .13337 .2001*7 length max .2650 .1)79 .1)67 .1*82 miles min .011*0 .013 .028 .029 X .0031*85 .00261*0 .015633 .0111*23 .060990 .01)5195 .221)21) .18071* Area s .002771 .013186 .0531)93 .16136 sq. miles max .0178 .0683 .2501 .1)61)3 min .0001* .0010 .0083 .0721) X .10809 .0981*0 .20771 .10693 .38671 .35939 . 7lil)l)0 .70915 Diameter s .01)736 .08795 .15016 . 2671)9 miles max .336 .1)83 .771 1.156 min .026 .01)5 .11*8 .1)93 o) * Perimeter ' s miles max min X 332lt.li 3250.7 3111.9 301*0.2 2887.5 2785.8 2778.1) 2715.7 Elevation s 701). 5 668.3 609.6 61)3.8 feet max 511)0 1)367 3935 3390 min 1768 1825 1828 1965 X 377.6 31)0.2 671.8 635.lt 1061.0 1018.8 151*2.6 1501). 7 Relief s 161*. 6 207.1 293.1) 391.1 feet max 1088 111*0 1765 2070 min 35 115 1)60 1193 X .68130 .651)77 .65705 • 61*808 .51)1)60 .53689 .1*0660 .1)0185 Relief s .1801*3 .18890 .08712 .06607 ratio max 1.1*906 1.5677 .651)0 .1*623 min .1285 .321)0 .2960 .3006

Relative^' s relief max min X .60385 .58927 .65387 .67217 .67130 .6671*8 .67803 .6761)6 Elongation s .11)082 .17121 .07105 .05179 max 1.6853 1.1)690 .7672 .71)28 min .3500 .391)5 .5366 • 6159 2) * Circularity ' s max min X 21). 770 22.781 21). 687 21). 370 25.170 23.713 22.173 21.976 Drainage s 10.005 8.091 10.858 3.361 density max 59.00 62.00 66.79 27.27 miles min lt.38 7.92 13.1il) 17.95 x 1)96.6 378.8 1)20.1)3 31)2.93 356.23 309.71) 269.1)3 2 51t. 69 Channel s 382.3 31)3.52 205.08 109.52 frequency max 2500. 3000.0 81)3.1) 1)55.8 miles “2. min 56.2 78.1 115.1 176.6

1) Tabulated value is antilog of mean of logarithmic distribution. 2) Not measured in this watershed. 72 APPENDIX I

Characteristic Values of Geomorphic Properties

WATERSHED II, FERN CANYON Second Order Third Order Fourth Order Property First Order Arithmetic Log Arith Log Arith Log Arith Log Number 1*65 92 19 2

X .05272 .01)21)3 .091*61* .06853 .20681* .13756 .871*00 .83538 Channel s .03705 .08593 .15255 .3592 length max .268 .1*72 .51*5 1.128 miles min .005 .011 .005 .620 X .002711 .001952 .012501 .008685 .052500 .038388 .1(7810 .1)1)1(13 Area s .002568 .011)679 .01*1273 .2503 sq.miles max .0171* .091)1) .1681 .6553 rain .0002 .001)4 .0082 .3011 X .09270 .08317 .17733 ~ .1581*3" .35011 .30870 .98350 .98232 Diameter s .Oh559 .09397 .171)81) .6859 miles max .291 .573 .71)7 1.032 min .020 .059 .131 .935 .28021* .25608 Perimeter 3)' *s .13337 miles max 1.133 min .088 X 1*311.6 1)253.0 1*110.2 1*01*2.8 1)073.1) 1*012.5 1)025.0 1*025.0 Elevation s 678.8 727.2 703.5 0 feet max 5260 5065 1)909 1(025 min 2650 271*2 2912 1)025 X 287.8 21)6.7 515.6 1*56.0 790.0 695.7 1306.0 1301*. 8 Relief s 161.2 250.6 365.9 792 feet max 1015 1222 1516 1362 min 35 98 156 1250 X .59975 .56170 .58762 . 51*511* .1*8236 .1(2682 .2526 .25156 Relief s .22163 .21(252 .26667 .1038 ratio max 1.3658 1.1)711) 1.131*0 .2758 min .1155 .221)9 .2172 .229!) .2192)4 .20381 Relative"^3); s* .08012 relief max .1*1*39 min .0301* X .61527 .59939 .67885 .66363 .72795 .71617 .7735 .76552 Elongation s .13872 .1521)5 .11*636 .1571) max 1.2613 1.2901) 1.2080 .881)8 min • 11(91 .391)5 .5689 .6622 .55512 .50917 Circularity^ s .19158 max 1.5303 min .0078 X 2l(.l)l8 21.737 21i.902 23.51)2 21). 708 21).065 18.17 18.128 Drainage s 15.516 8.1)32 5.896 1.68 density max 206.00 52.86 36.83 19.36 miles min 5.52 9.59 16.52 16.98 X 686.lt 512.3 575.11) 1*66.72 1)89.93 1)32.56 288.5 285.32 Channel s 553.1 397.55 21)0.12 60.1) frequency max 5000. 211)2.9 975.6 331.2 miles ***■ min 57.5 81).7 160.6 21(5.8

3) N = 150 APPENDIX I 73

Characteristic Values of Geomorphic Properties

WATERSHED III, UPPER EAST FORK First Order Second Order Third Order Fourth Order Arithmetic Log Arith Log Arith Log Arith Log Number 317 70 17 5 X .06808 .05607 .10*1*46 .07386 .23818 .18136 .31110 .22605 Channel s .01800 .08367 .16399 .22990 length max .33h .*4*47 .559 • 593 miles min .0114 .008 .025 .070 X .003612 .0025h2 .016713 .011716 .078691; .06113 .25876 .19121 Area s .003hi8 .017395 .058967 .21296 sq.miles max .0238 .1051 .2215 .5526 min .0003 .0020 .0221 .0669 X .10223 .08968 .19859 .13977 .Ujllil •h065h .72300 .66609 Diameter s .05*468 .09680 .I8*j*i8 .319h9 miles max .312 .175 .823 1.120 min .025 .058 .199 .393 X .26360 .23753 Perimeter s .12756 miles max .831 min .087 X 3925.1 3882.5 3795.1 3752.7 3808.9 3800.2 3710.8 3706.7 Elevation s 56!t.6 553.5 261.0 191.1 feet max 5120 1755 *421x3 3882 min 2583 2660 3272 3105 X 298.7 253.2 2j82.0 112.1 809.0 731.8 108*4.0 101*4.1 Relief s 172.2 256.0 356.1 [ih9.0 feet max 928 1195 1195 1595 min 51 50 328 720 X . 561*00 .53175 .17058 .13896 .36182 .31090 .29223 .2 8 835 Relief s .19117 .18255 .13392 .05363 ratio max 1.1.529 1.0001 .6126 .3720 min .2110 .1C6! .1697 .2216 X .21562 .20190 Relative s .08086 relief max .702), min .0628 X .61*773 .63129 .70000 .68639 .70635 .68856 .71355 .71077 Elongation s .131*25 .11226 .16881 .07165 max 1.0832 1.1673 1.0211 .8151 min .3501* .3959 .5021 .6127 X .58ooo .566io Circular5ty s .1211*6 max .9756 min .2915 X 21.030 22.062 22.093 21.022 19.231 18.727 19.726 19.265 Drainage s 1C.031 7.350 1.665 1.795 density max 76.67 19.79 29.55 25.72 miles” min 3.66 11.60 12.77 11.9? X 513.3 393.1 101.70 328.18 263.63 21(2.90 258.26 237.51 Channel s 155.0 276.18 107.11 111.83 frequency max 3333. 1500.0 189.5 379.7 miles” min 12.0 68.6 115.8 I 137.2 APPENDIX I

Characteristic Values of Geomorphic Properties

WATERSHED VIII, BELL CANYON_ p, . First Order Second Order Third Order Fourth Order oper y Arithmetic Log Arith Log Arith Log_Arith Log Number 386 89 21* 1*

X •OJU928 .01*111 .08388 .0601*5 .11*051* .11279 .31625 .29789 Channel s .03267 .05960 .08762 .12369 length max .256 .229 .332 .686 miles min .011 .006 .023 .220 X .001681 .00131; .008668 .006661* .038683 .029583 .085350 .080223 Area s .0011*83 .006071* .023795 .032092 sq. miles max .0136 .0288 .0803 .1202 min .0002 .0006 .0030 .0653 X .07302 .06728 .15330 .13976 .28600 .26390 .69075 .67667 Diameter s .03652 .06263 .09857 .16665 miles max -27U .332 .650 .668 min .Oil! .028 .096 .361 .21292 li) * .22783 Perimeter*1' s .09651 miles max .601. min .101 Z 2677.1 2677.7 2529.6 2505.3 2663.8 2615.6 2551.2 2569.7 Elevation s 361.6 351.5 381.7 103.0 feet max 3525 3535 2965 2660 min 2222 2270 1920 2650 Z 213.7 191.5 380.2 356.7 577.2 557.8 870.0 861.3 Relief s 91.. 2 139.2 168.5 162.0 feet max 750 735 880 1000 min 1.0 80 290 735 X .57979 .56607 .50071 .68068 .61601 .60033 .36638 .36365 Relief s .15951. .15235 .10713 .06869 ratio max 1.0062 1.1685 .6017 .3856 min .2296 .2658 .2268 .2793 1*) ^ .22826 .21903 Relative s .061.67 relief max .3758 min .1081. X .62861 .62210 .67206 .65903 .76069 .73562 .68116 .67330 Elongation s .13789 .16621 .09326 .12506 max 1.2017 1.2776 .9778 .8651 min .1835 .6566 .6251 .5856 . 5171.9 .50182 Circularity^ s .12200 max .7873 min .21.63 Z 35.526 32.111. 31.122 29.360 26.310 21*. 801* 30.190 30.060 Drainage s 23.1.76 11.267 9.362 3.221 densi ty max 307.50 71.05 68.33 36.08 miles min 9.00 13.75 13.30 26.38 Z 996.9 775.5 766.68 605.66 572.66 1*1*2 • 1*6 619.80 610.16 Channel s 802.6 676.51 505.86 126.65 frequency max 5000. 5000.0 2333.3 772.6 miles'* min 73.5 183.5 137.0 683.6 1*) N - 53 APPENDIX I 75

Characteristic Values of Geomorphic Properties

WATERSHED IX, VOLFE CANYON First Order Second Order Third Order Fourth Order Property_Arithmetic Log Arith Log Arith Log Arith Log Number 314) 73 16 3 * .05087 .01)1)95 .08730 .06301* .21388 .16796 .30300 .25638 Channel s .0261*1* .07295 .1261*9 .21257 length max .158 .1)39 .1*1*3 .51)1 miles min .013 .009 .018 .132 X .001932 .00151*2 .00961)9 ,007723 .01*9050 .01)21)78 .21903 .19599 Area s .0011*37 .007175 .021*857 .13321 sq. miles max .0083 .01)79 .1033 .3728 min .0003 .0013 .0129 .1386 X .07871 .07290 .16U8 .15392 .37062 .35719 .68333 .68016 Diameter s .03081) .06851 .10023 .08182 miles max .189 .1)05 .539 .771) min .021 .01)9 .217 .615 * Perimeter^' s miles max min X 2670.1 261)6.3 2578.5 2553.0 2377.3 2360.0 231)9.3 231)8.0 Elevation s 31)7.8 356.9 293.7 96.li feet max 3250 3108 2839 21)05 min 1900 1890 1882 2238 X 239.2 220.3 1)38.7 i)ii.i 738.2 718.8 989.0 972.5 Relief s 96.3 150.1 169.2 212.6 feet max 555 835 998 1157 min 35 107 1)73 750 * .58756 .57221) .52775 .&762 .38350 .38111 .2801)9 .27080 Relief s .13818 .11102 .OU)98 .081)01 ratio max 1.1)250 1.0273 .1)823 .3315 min .1181) .3506 .3087 .1835

Relative 5)y *s relief max min X .61885 .60771) .67165 .65927 .66519 .65109 .71)200 .731)1)7 Elongation s .11571 .11)020 .11)81)2 .13231 max 1.0396 1.3385 1.0723 .8901 min .1602 .1)518 .1)815 .6355

Circularity^ s max min X 31.721) 29.152 30.101 28.852 25.577 25.U.3 25.682 25.655 Drainage s 20.100 8.928 3.057 1.1)1)6 density max 31)6.67 51.91) 33.35 27.30 miles min 5.32 15.60 20.22 21). 52 X 803.3 61*8.6 637.99 553.07 1)07.18 398.1)2 392.33 392.31 Channel s 551).6 1)17.29 90.03 1).06 frequency max 3333. 3076.9 620.2 396.8 milesmin 120.5 187.8 271).5 388.9

5) Not measured in this watershed 76 APPENDIX I

Characteristic Values of Geomorphic Properties

WATERSHED II-l, FERN NUMBER ONE First Order Second Order Third Order Arithmetic Log Arith Log Arith Number 19 3 1

X .02516 .01902 .05233 .OljOOl* .359 Channel s .0173)4 .01)761 length max .058 .107 miles min .005 .020 X .001563 .001262 .006867 .006095 .o5Wi Area s .001302 .003630 sq. miles max .0062 .0102 min .0006 .0030 X .067ii7 .06556 .11733 .11078 .1)08 Diameter s .01665 .01*528 miles max .107 .157 min .01*0 .068 X .17879 .17268 .33300 .32319 1.102 Perimeter s .01)91*7 .09711) miles max .313 .1)27 min .111 .233 X 1)91*7.5 1)91)5.0 5035.3 5031). 7 i*6io Elevation s 163.0 112.0 feet max 5180 5100 min 1)730 1*906 £ 202.6 196.7 306.7 301.7 727 Relief s 50.2 65.1) feet max 286 363 min 128 235 % .571)25 .56831 .521)21 .51631 .3371)7 Relief s .08395 .111)82 ratio max .721)1) .651)5 min .3983 .1)379 X .22082 .21552 .17731 .17687 .121)91) Relative s .01)636 .15173 relief max .2971) .1910 min .121)8 .1610 X .62378 .61110 .79968 .79522 .61*505 Elongation s .13072 .09650 max .9122 .9089 min .1)1)33 .7259 Z .51)158 .53059 .73553 .73373 .56292 Circularity s .11198 .06392 max .7953 .8092 min .3586 .691)1) X 18.186 15.077 11). 091 13.885 18.272 Drainage s 12.051) 2.975 density max 1)8.75 17.25 miles-1 min 6.67 11.35 5? 928.5 631.87 583.56 1)22.79 Channel s 1)91). 8 321.62 frequency max 1667. 1000.0 miles-* min 172.li 1)05.1) APPENDIX I 77

Characteristic Values of Geomorphic Properties

WATERSHED 11-2, FERN NUMBER TWO__ Property First Order Second Order Third Order Arithmetic Log Arith Log Arith

Number 22 it 1

X .02605 .02112 .05050 .03722 • Wilt Channel s .01836 .02910 length max .082 .068 miles min .006 .007 X .OOlhhS .00112li .005600 .001*529 .0655 Area s .001263 .00321it sq. miles max .0060 .0083 min .0005 .0013 X .07282 .0671*0 .10325 .10199 • it86 Diameter s .02893 .01850 miles max .135 .121* min .032 .082 X .17800 .16960 .31250 .29879 1.21*3 Perimeter s .05923 .1011*2 miles max .31*3 .l*0li min .095 .187 X 1975.5 1*973.8 1*973.2 1972.8 “558? Elevation s 129.1 75.2 feet max 5188 5033 min 1*750 1*877 231.1* 217.0 287.2 281.8 61*7 Relief s 82.7 63.7 feet max 386 357 min 99 217 X .61396 .60975 .52812 .5231*2 .25211* Relief s .07522 .08023 ratio max .7935 .6037 min .1*931* .1*326 X .21*698 . 21*231 .19078 .17866 .09858 Relative s .01*697 .07393 relief max .3359 .2562 min .1537 .1017 X .58107 .56118 .77165 .710*60 . 591*21 Elongation s .16122 .23067 max 1.01*95 1.01*90 min .31*99 .1*961 X .50655 .1*9083 .65207 .63751* .53273 Circularity s .11821* .15671 max .6962 .8369 min .2671 .1*672 X 22.1*89 18.796 25.286 23.51*1 18.611 Drainage s 13.027 11.790 density^ max 1*1*. U* 1*2.31 miles- min 5.00 16.1*0 X 1069.0 1005.73 808.72 1*12.21 Channel s 582.5 868.97 frequency max 2000. 2307.7 miles”* min 166.7 512.8 78 APPENDIX I

Characteristic Values of Geomorphic Properties

WATERSHED II-3, PERN NUMBER THfpSE_^_ rZTTTIIZ First Order Second Order Pr0perty Arithmetic Log Arlth Number 13 1

X .05131 .01*1*58 .1*89 Channel s .02632 length max .105 miles min .011) £ .003338 .0021*35 .0856 Area s .002972 sq. miles max .0118 min .0005 Z .10051) .09753 .557 Diameter s .02617 miles max .161 min .060 X .25962 .21)590 1.31)9 Perimeter s .09168 miles max .1)88 min .126 X 1)973.8 1)972.1 1*525 Elevation s 136.5 feet max 511)0 min 1)735 X 303.0 296.7 990 Relief s 6U.li feet max 1|02 min 219 Relief x .57930 .57606 .33662 ratio s .06276 max .6913 min .1)529 X .231)99 . 22859 .13899 Relative s .05611 relief max .3292 min .11)50 Z .58756 . 57081) .59270 Elongation s .11*71*0 max .9101 min .3723 Z .51701) .50596 .59110 Circularity s .10561 max .6829 min .3087 X 19.962 18.312 13.505 Drainage s 8.371 density max 36.00 miles min 8.90 X 56hi.9 163.55 Channel s 527.8 frequency max 2000 miles min 81). 7 APPENDIX I 79

Characteristic Values of Geomorphic Properties

WATERSHED Il-k, FERN ADDITIQNALS First Order Second Order Third Order Arithmetic Log Arith Log Arith Log Number 70 13 h

X .031406 .02730 .08662 .06907 .08650 •Ola72 Channel s .02316 .05755 .07751 length max .128 .205 .182 miles min .007 .020 .003 X .001201 .000970 .007623 .005598 .023775 .019269 Area s .0008h9 .007283 .017795 sq.miles max .00142 .0279 .01*91 min .0002 .0022 .0078 X .06h0lt .05999 .1351*6 .12582 .19850 .18091 Diameter s .023614 .0531*3 .09660 miles max .139 .238 .315 min .030 .071 .109 X .161*66 .15601* .37562 .31*908 .68150 .61*921 Perimeter s .051*69 .15893 .23663 miles max .328 .751 .972 min .069 .229 .1*01* X 1*91*8.0 1*91*5.1 1*853.8 1*852.2 1*827.2 1*826.1 Elevation s 168.1* 12l*.7 119.3 feet max 5181* 1*953 1*920 min 1*515 1*550 1*670 3c 188.14 175.3 305.3 281.2 361*. 2 325.1 Relief s 69.6 108.7 172.8 feet max 393 1*1*0 551 min 5>6 79 11*0 X .£6609 .5531*2 .1*3821 .1*2325 .35151 .31*038 Relief s .11182 .1071*9 .101*96 ratio max .8092 .5619 .1*953 min .2165 .2107 .21*33 X .22120 .21277 .16177 .15256 .10838 .091*85 Relative s .55613 .50651* .52601* relief max .31*86 .2365 .1591* min .0593 .0603 .0362 X .59586 .58577 .68238 .67102 .92060 .86578 Elongation s .111*19 .12771* .1*0163 max .9956 .8990 1.5108 min .3637 .1*592 .6112 X .51013 .50057 .581*15 .57733 .57730 .571*51 Circularity s .09597 .08801 .06527 max .7121* • 7176 .6531 min .2671 .3809 .1*995 X 30.1*71 28.150 29.630 28.681 30.805 30.355 Drainage s 12.167 7.277 6.1dl density nisuc 61*. 29 1*2.35 1*0.26 miles min 8.21* 11*. 29 26.27 X 1267.7 919.1A 786.35 755.07 725.91 Channel s 871.2 1*89.87 21a.35 frequency max 5000. 1818.2 1025.6 miles“2- min 238.1 186.3 516.1* 30 APPENDIX I

Characteristic Values of Geomorphic Properties

WATERSHED VIII-1, BELL NUMBER ONE_ Pr nprtv First Order Second Order Third Order Fourth Order Qpe y_Arithmetic Log Arith Log Arith Log_Arith Number 55 9 2 1 X .03936 .0351*1* .09000 .08358 .03800 .03571 .531 Channel s .01879 .09176 length max .103 .262 miles min .018 .002 X .000955 .000805 .007689 .001*631* .015950 .009889 .1219 Area s .000660 .007138 sq. miles max .001*1 .0211* min .0003 .0011 X .05735 .05857 .13588 .11816 .11*100 .12513 .679 Diameter s .01832 .08037 miles max .101 .259 min .030 .050 X .18807 .18275 .35833 .30531 .38050 .32378 1.669 Perimeter s .08185 .19763 miles max .288 .692 min .079 .136 £ 2916.0 2909.9 2738.1 2728.7 2987.0 2987.0 21*1*6 Elevation s 189.1 183.8 feet max 322lt 3006 min 2518 2558 sr 203.2 197.1 88l.O 363.7 31*6.5 332.2 992 Relief s 50.9 283.3 feet max 315 893 min 122 177 X .69887 .681*1*5 .68287 .60381 .51358 .50288 .27670 Relief s .13339 .28261 ratio max 1.8099 1.0890 min .8256 .3382 X .26503 .26150 .28032 .22562 .19882 19838 .11257 Relative s .08265 .09805 relief max .3887 .8320 min .1668 .1315 X .59832 .58706 .67711 .67287 .87811 .87661 .58021 Elongation s •1221*3 .07612 max 1.0858 .7606 min .3799 .5028 X .50636 . 1*961*8 .63038 .62872 .98367 1.13288 .58992 Circularity s .09619 .08863 max .7587 .7878 min .2077 .5038 X 1*6.651* 88.019 80.853 38*61*1* 83.907 83.105 29.385 Drainage s 15.918 18.933 density max 81*.00 62.73 miles min 22.00 26.39 X 1825.9 1338.96 1050.88 1893.62 1283.16 51*9.55 Channel s 718.7 996.91 frequency max 3333. 2727.3 miles'^ min 283.9 851.1 APPENDIX I 81

Characteristic Values of Geomorphic Properties

WATERSHED VIII-2, BELL NUMBER TWO First Order Second Order Third Order Fourth Order Arithmetic Log Arith Log Arith Log Arith Log Number 75 16 5 2

X .03963 .03533 .051)38 .02758 .081*00 .06600 .23950 .23893 Channel s .02071 .08765 .06626 length max •118 .11)1 .192 miles min .012 .000 .026 X .00101*0 .000821* .001*750 .003890 .016080 .013103 .063100 .060596 Area s .000863 .00361*0 .008876 sq. miles max .001*9 .0121 .0275 min .0002 .0008 .0032 X .05896 .05536 .10912 .09896 .18100 .16962 .37800 .37800 Diameter s .0213I1 .05132 .06973 miles max .133 .21)1) .283 min .022 .oil .090 X .15057 .11)310 .28725 . 261*9 i* .51180 .88799 1.0880 1.0780 Perimeter s .05022 .11685 .16108 miles max .326 .525 .721 min .068 .117 .272 X 2985.8 2979.9 291)0.5 2936.8 2879.8 2878.6 2657.0 2657.0 Elevation s 187.5 11)9.1 76.0 feet max 3282 3078 2939 min 2533 2598 2753 X 206.0 19I1.O 338.1) 319.8 896.0 886.2 720.0 719.5 Relief s 71.0 113.1 105.6 feet max 375 577 620 min 90 171) 380 X .67258 .66377 .6211)6 .61209 .55195 .58296 .36079 .36050 Relief s .11099 .11171) .11239 ratio max 1.07W .8163 .7155 min .1)1)86 .1)1)79 .8189 X .26178 .25678 .23286 .22863 .19081 .18872 .12831 .12680 Relative s .05201 .08500 .03200 relief max .1)551 .2885 .2367 min .1526 .1537 .1587 X .59271) .58503 .69001 .67362 .76527 .76150 .78210 .73883 Elongation s .0961)3 .15305 .08887 max .911)9 .9858 .8738 min • 1)021) .3936 .6612 X .51601 .50551 .63221 .62883 .69815 .69185 .65530 :6552S Circularity s .10226 .10113 .10552 max .7967 .8286 .8168 min .2905 .Soil .5835 X 1)6.196 1*2.892 81.336 39.090 37.167 36.527 32.956 32.980 Drainage s 17.81)9 13.723 8.386 density max 95.00 60.75 51.88 miles min 13.81 21.23 32.17 X 11)96.3 1811.27 1189.97 1082.01 929.60 700.60 697.23 Channel s 1065.5 991.88 686.75 frequency max 5000. 3750.0 2187.5 miles*2 min 201).1 861.5 685.7 82 APPENDIX I

Characteristic Values of Geomorphic Properties

WATERSHED VIII-3, BELL NUMBER THREE First Order Second Order Third Order Fourth Order Arithmetic Log Arith Log Arith Log Arith Number 39 6 2 1 X .01)079 .03681 .111)83 .101492 .11300 .10776 .315 Channel s .01866 .0631)6 length max .099 .21)3 miles min .012 .071) X .001062 .000933 .008900 .008028 .025850 .025372 .0979 Area s .000558 .005269 sq. miles max .0026 .0195 min .0003 .0056 S .06328 .06009 .17917 .17090 .214500 .2W)18 .5145 Diameter s .02033 .06769 miles max .106 .312 min .025 .131) T .16038 .i5a3 .39183 .3901)3 .68350 .68192 1.387 Perimeter s .Oljli23 .03632 miles max .251) .1)38 min .076 .31)6 X 3007.9 2997.6 2965.8 2960.0 2852.0 2852.0 21)69 Elevation s 21)9.0 197.3 feet max 3308 3079 min 251)3 2lt67 X 201). 9 195.6 1)67.2 1)55.9 579.5 578.0 1031 Relief s 61.2 118.2 feet max 3a 683 min 61) 332 X .62a8 .61650 .50838 .50523 .1)1)831) .1)1)832 .35828 Relief s .09755 .06067 ratio max .8672 .5767 min .3869 .1)11)6 X .21)1)79 .21)031) .2251)7 .22115 .16051) .16053 .11)078 Relative s .0U)61) .01)651 relief max .31)28 .2953 min .1302 .11)86 X .58265 .5731U) .59777 .59158 .73615 .73606 .61)781 Elongation s .10381 .09659 max .8399 .7569 min .3711 .5050 X .5081)2 .1)9321) .69750 •66l80 .68678 .685614 .63950 Circularity s .121)26 .28670 max .8057 1.2773 min .21)88 .5363 X 1)2.106 39.1)79 32.533 32.086 29.510 29 J4I46 28.815 Drainage s 15.302 5.852 density max 86.67 39.1)3 miles-1 min 15.62 25.23 X 1227.0 657.65 616.53 51)7.68 51)3.29 1)90.30 Channel s 696.0 251.60 frequency^ max 3333. 1000.0 miles-2' min 3814.6 359.0 APPENDIX I 83

Characteristic Values of Geomorphic Properties

WATERSHED Vlll-b, BELL NUMBER FOUR_ First Order Second Order Third Order Property Arithmetic Log Arith Log Arith Number 13 3 1 X .01*107 .031*51 .09367 .05175 .256 Channel s .02550 .11901* length max .095 .231 miles min .012 .020 X .002071 .001703 .011200 .006683 .0617 Area s .001260 .0131*50 sq. miles max .001*2 .0267 min .0005 .0026 X .07336 .06921 .13600 .12323 .1*1*7 Diameter s .02539 .071*05 miles max .125 .218 min .035 .071* X .18850 .17905 .39833 .35201 1.191 Perimeter s .0621*8 .25203 miles max ♦318 .687 min .0911 .222 X 2772.8 2762.3 2685.7 2685.1* 231*9 Elevation s 250. 1* 1*2.1 feet max 3150 2710 min 2386 2637 X 255.9 21*8.0 1*11.0 391*.0 921 Relief s 66.9 11*3.8 feet max 393 560 min 166 273 X .68536 .67877 .61277 .60551 .39023 Relief s .09953 .11169 ratio max .8983 .6987 min .51405 .1*865 X .26570 .26236 .21739 .21197 .11*61*6 Relative s .0I428I .05686 relief max .31*55 .261*9 min .1831* .151*1* X .67828 .67275 .75372 .71*857 .62703 Elongation s .09191 .10598 max .9031 .81*58 min ♦ 5522 .6379 X .68361* .66731* .67815 .67776 .51*660 Circularity s .17819 .02838 max 1.21*82 .7109 min .5203 • 6606 X 21.676 20.267 23.771 23.086 18.023 Drainage s 7.379 6.831 density max 31*. 1*1* 30.38 miles” min 7.89 16.71* X 726.1* 701*. 56 595.38 275.53 Channel s 522.6 1*1*5.88 frequency max 2000. 1153.8 miles'"2 min 238.1 262.2 84 APPENDIX I

Characteristic Values of Geomorphic Properties

FIFTH ORDER VALUES LARGE WATERSHEDS

Watershed I II HI VIII IX Property

Channel length 2.839 1.870 2.251) 2.011 1.209 miles

Area 2.1)915 2.2038 2.1790 1.3571) 1.1809 sq. miles

Diameter 2.5602 2.1)639 2.5622 2.2157 1.8610 miles

Elevation 1765 2565 2565 1880 1880 feet

Relief 2695 2900 2560 1520 1610 feet

Relief .19937 .22291 .18923 .12993 .16358 ratio

Elongation .69569 .67981) .65008 .59333 .65782

Drainage density 19.266 18.501 17.811 2U * li06 21).907 miles“l

Channel frequency 213.53 262.73 201.93 371.30 370.06 miles'^ APPENDIX I 85

Characteristic Values of Geomorphic Properties

WEIGHTED MEANS AND EXTREME EXTREMES

Property Order 1st 2nd 3rd 1th 5th

X .05833 .09615 .19365 .36581 2.036 Channel length max .33i< .179 .559 .593 2.839 miles min .oo5 .001 .005 .029 1.870 X .002692 .012611 .051911 .22998 1.8825 Area max .0238 .1051 .2501 .6551 2.1915 sq. miles min .0002 .0006 .0030 .0153 1.1809 X .09126 .18017 .36106 .7089 2.3332 Diameter max .336 .573 .823 1.156 2.562 miles min .01)4 .028 .091) .361 1.861 X .26169 Perimeter max 1.133 miles min .087 X 3123.1 3228.3 3078.7 3039..'1 2131.0 Elevation max 5260 5065 1)909 1)025 2565 feet min 1768 1825 1828 1965 1765 X 285.3 ■>03.6 785.9 1168.0 2257.0 Relief max 1088 1222 1765 2070 2900 feet min 35 50 156 720 1520 X .6ol39 .555i6 .1)1)11)9 .32771 .18100 Relief ratio max 1.1906 1.5677 1.131)0 .1)623 .2229 min .1155 .1061) .1697 .1335 .1299 X .21783 Relative relief max .7021 min .0301 X .62188 .67397 .70170 .71609 .65535 Elongation max 1.6153 1.1)690 1.2080 .8901 .6957 min .1191 .391)5 .1815 .5856 .5933 X .56727 Circularity max .97<6 rri n .0078 X 27.909 26.606 21).388 23.319 20.978 Drainage density max 316.67 71.05 66.79 31). 08 21.91 milesmin 3.66 7.92 12.77 lb.97 17.81 X 703.2 562.88 128.09 361.67 283.91 Channel frequency max 5000 5ooo 2333 772.6 371.3 milesmin 12 68.6 115.1 137.2 201.9 86 APPENDIX II

Percent Probability of Observed Departure from Normality

Watershed I, Wolfskill Canyon

ORDER 1 2 3 h PROPERTY Prob. Test Prob. Test Prob. Test Prob. Test Channel length —o.i1^ Chi —0.1 Chi 10-5 Chi 92 K-S 65 K-S Log chan, length 5-2.5 Chi 5-2.5 Chi 70 Chi 85 K-S 93 K-S Area —0.1 Chi —0.1 Chi 2k K-S 76 K-S in 1—1 o o i . Log area • Chi io-5 Chi 82 K-S 99 K-S

Diameter —0.1 Chi 2.5-2 Chi 23 K-S 98 K-S

Log diameter 8-5 Chi 65-55 Chi 9h K-S 99.8 K-S Perimeter

Log perimeter

Elevation —0.1 Chi —0.1 Chi

Log elevation —0.1 Chi —0.1 Chi

Relief —0.1 Chi 97.5-95 Chi

Log relief 1-0.5 Chi Uo-30 Chi

Relief ratio io-5 Chi 2.5-2 Chi

Log relief ratio —0.1 Chi 70-60 Chi

Relat. relief

Log relat. relief

Elongation -0.1 Chi -0.1 Chi

Log elongation 5-2.5 Chi —0.1 Chi Circularity

Log circularity

Drain, density —0.1 Chi U5-U0 Chi

Log drain, density 5-2.5 Chi 35-30 Chi

Channel freq. —o.o5 Chi —0.1 Chi

Log channel freq. o.5-o.l Chi 20-15 Chi

1) -0.1 should be read as "less than one tenth percent"; —0.1 as "much less than one tenth percent". APPENDIX II 87

Percent Probability of Observed Departure from Normality

Watershed II, Fern Canyon

ORDER 1 2 3 k

PROPERTY Prob. Test Prob. Test Prob. Test Pr ob. Test

Channel length —0.1 Chi —0.1 Chi 2-1 Chi Not determinable, 62 K-S N = 2 35-30 Chi Log CxQan. length 2-1 Chi uo-75 Chi It H 32 K-S

Area —0.1 Chi —0.1 Chi 92 K-S tt K

Log area -0.1 Chi 25-20 Chi 95 K-S tt It

Diameter —0.1 Chi -0.1 Chi 28 K-S « tt

Log diameter 15-10 Chi 6o-5o Chi hh K-S H H

Perimeter -0.1 Chi

Log perimeter h$-35 Chi

Elevation —0.1 Chi —0.1 Chi

Log elevation —0.1 Chi -0.1 Chi

Relief —0.1 Chi 30-25 Chi

Log relief i5-io Chi U5-35 Chi

Relief ratio —0 • 1 Chi o.5-o.i Chi

Log relief ratio io-5 Chi 5o-Uo Chi

Relat. relief 15-10 Chi

Log relat. relief 30-20 Chi

Elongation —0.1 Chi io-5 Chi

Log elongation 5-2 Chi 20-15 Chi

Circularity i5-io Chi

Log circularity —0.1 Chi

Drain, density —0.1 Chi 30-25 Chi

Log drain, density 38-32 Chi U5-U0 Chi

Channel freq. —o.o5 Chi —0.1 Chi

Log channel freq. -o.o5 Chi 65-60 Chi 88 APPENDIX II

Percent Probability of Observed Departure from Normality

Watershed III, Upper East Fork

ORDER 1 2 3 U

PROPERTY Prob. Test Prob. Test Prob. Test Prob. Test

20-10 Chi Channel length ——0«1 Chi -0.1 Chi 21* K-S 87 K-S

Log chan, length 5-2.5 Chi 20-10 Chi io-5 Chi 66 K-S 87 K-S

Area —0 • 1 Chi —0.1 Chi 1*2 K-S 62 K-S

Log area -0.1 Chi 50-1*0 Chi 65 K-S 89 K-S

Diameter —0,1 Chi 2-1 Chi 56 K-S 99 K-S

Log diameter 5-2.5 Chi 65-55 Chi 83 K-S 91 K-S

Perimeter —0.1 Chi

Log perimeter 6o-5o Chi

Elevation —0,1 Chi 10-5 Chi

Log elevation —0,1 Chi io-5 Chi

Relief —0.1 Chi -0.1 Chi

Log relief 100-99*5 Chi 20-15 Chi

Relief ratio —0.1 Chi -0.1 Chi

Log relief ratio 60-55 Chi 50-1*0 Chi

Relat. relief -0.1 Chi

Log relat* relief 100-99.9 Chi

Elongation 15-10 Chi 20-15 Chi

Log elongation 30-25 Chi 30-25 Chi

Circularity 1*0-30 Chi

Log circularity 2-1 Chi

Drain, density -0.1 Chi 30-25 Chi

Leg drain, density 1*5-140 Chi 6o-55 Chi

Channel freq. —o.o5 Chi —0,1 Chi

Log channel freq. -o.o5 Chi 1-0.5 Chi APPENDIX II 89

Percent Probability of Observed Departure from Normality

Watershed VIII, Bell Canyon

ORDER 1 2 3 b f) PROPERTY Prob. Test Prob. Test Prob. Test Prob. Test

Channel length —0.1 Chi 0.5-0.1 Chi 50-140 Chi 90 K-S Ii5 K-S

Log chan, length Chi Chi 20-10 Chi 88 K-S io-5 5-2.5 85 K-S

Area ——0,1 Chi 2-1 Chi 80 K-S 99.9 K-S

Log area —0.1 Chi 65-55 Chi bb K-S 99.8 K-S

Diameter —0.1 Chi 15-10 Chi 86 K-S 97 K-S

Log diameter 2.5-2 Chi 90-85 Chi 29 K-S 87 K-S

Perimeter -0.1 Chi

Log perimeter 70-60 Chi

Elevation -0.1 Chi -0.1 Chi

Log elevation ——0.1 Chi -0.1 Chi

Relief -0.1 Chi 2.5-2 Chi

Log relief io-5 Chi 25-20 Chi

Relief ratio 5-1* Chi 1-0.5 Chi

Log relief ratio —0.1 Chi 80-75 Chi

Relat. relief 20-15 Chi

Log relat, relief 5-1* Chi Elongation o.5-o.i Chi -0.1 Chi

Log elongation —0.1 Chi 10-8 Chi

Circularity 90-85 Chi

Log circularity 20-15 Chi

Drain, density —0.1 Chi 5-2.5 Chi

Log drain, density 20-10 Chi 60-50 Chi

Channel fbeq. ——o.o5 Chi —0.1 Chi

Log channel freq. o.5-o.i Chi 25-20 Chi 90 APPENDIX II

Percent Probability of Observed Departure from Normality

Watershed IX, Volfe Canyon

ORDER 1 2 3 k

PROPERTY Prob. Test Prob. Test Prob. Test Prob. Test

Channel length —0.1 Chi —0.1 Chi 20-10 Chi 91 K-S 86 K-S 70-50 Chi Log chan, length 10-5 Chi 80-75 Chi 98 K-S 69 K-S

Area ——0.1 Chi -0.1 Chi 99.9 K-S 61* K-S

Log area 2. £-2 Chi 6o-5o Chi 59 K-S 66 K-S

Diameter —0 #1 Chi 6o-5o Chi 87 K-S 9k K-S

Log diameter 5-2.5 Chi 70-60 Chi 58 K-S 95 K-S

Perimeter

Log perimeter

Elevation —0.1 Chi 15-10 Chi

Log elevation —•0.1 Chi 1-0.5 Chi

Relief —-0.1 Chi 80-75 Chi

Log relief 18-12 Chi 75-70 Chi

Relief ratio -0.1 Chi 5-1 Chi

Log relief ratio 2-1 Chi 5-3 Chi Relat. relief

Log relat. relief

Elongation -0.1 Chi -0.1 Chi

Log elongation 5-3 Chi 1-0.5 Chi Circularity

Log circularity

Drain, density —0.1 Chi 2.5-1 Chi

Log drain, density 10-35 Chi 5-3 Chi

Channel freq. —o.o5 Chi -0.1 Chi

Log channel freq. 2.5-2 Chi 30-20 Chi APPENDIX II 91

Percent Probability of Observed Departure from Normality

Watersheds II-l, 2, 3, and hs Pern Small Watersheds, First Order Only

WATERSHED II* -1 II- -2 II-3 II-U

PROPERTY Prob. Test Prob. Test Prob. Test Prob. rest

Channel length 10-5 Chi 20-10 Chi 88 K-S -0.1 Chi 65 K-S 16 K-S Chi 20-10 Chi Log chan, length 30-20 80 K-S 10-30 Chi 77 K-S 70 K-S

Area 23 K-S 5.7 K-S 1*6 K-S 0.5-0.1 Chi

Log area 88 K-S 28 K-S 95 K-S 85-80 Chi

Diameter 96 K-S 78 K-S 96 K-S 30-25 Chi

Log diameter 98 K-S 93 K-S 98 K-S 50-I4O Chi

Perimeter 90 K-S 35 K-S 80 K-S 50-^5 Chi

Log perimeter 98 K-S 63 K-S 75 K-S 99.5-99 Chi

APPENDIX II

Percent Probability of Observed Departure from Normality

Watersheds VIII-1, 2, 3, and h} Bell Small Watersheds, First Order Only

WATERSHED VIII- -1 VIII*-2 VIII-3 VIII-1*

PROPERTY Prob. Test Prob. Test Prob. Test Prob. Test

Channel length 0.5-0.1 Chi 0.5-0.1 Chi 20-10 Chi 83 K-S

Log chan, length 20-10 Chi 95-90 Chi i5-io Chi 98 K-S

Area —0.1 Chi —0.1 25-20 Chi 51 K-S

Log area —0.1 Chi o.5-o.i Chi 10-9 Chi 72 K-S

Diameter 50-145 Chi 145-35 Chi 2-1 Chi 97 K-S

Log diameter 95-90 Chi 90-80 Chi 1-0.5 Chi 98 K-S

Perimeter io-5 Chi i5-io Chi 15-10 Chi 92 K-S

Log perimeter 30-25 Chi 85-80 Chi 30-25 Chi 97 K-S

93

2000 1000 0 94 8o»)tipP

APPENDIX III: Fern Small Watersheds APPENDIX IV 95

COSPPICIENTS OP COKRELATION, WITS UNEXPLAINED DISCHAKG-E AS DEPENDENT VARIABLE

Multiple Correlation, Independent Variables Independent Simple Variable Correlation a5 d^ a5,a2 d-5»a2 <15,d2 <15,112 <15 ,D2

a5 0.327 0.441 *5 0.222 .4267 .4603 a2 d2 0.251 .4110 .4476

.4886 h2 0.241 .3907 .4421 .4274 .4764 .U396 .4889 .4890 »2 0.233 .4286 .4885 .4745 0.256 .4i4o .4596 .4643 .4607 .4728 .4889 °2 .4759

0.159 •3SS3 •4513 .4278 .4747 .4699 .4703 .4890

o.o46 .4438 .4606 .4481 .4444 .4885 \ •3S79 .4776

Ei 0.288 .4274 A531 •4279 .4630 •4539 .4594 .4887

*a 0.015 .3956 .4428 .4888 .4684 .4530 .4438 .4885

0.232 .4116 .4499 .4848 •4787 .4665 .4499 .4886

Multiple Correlation, Independent Variables Independent Variable

h2 .4890 .4890 .4892 .4392 •

.4890 .4892 R2

.4390 •4893 .4391 .4891 •

E1 .4890 .4854 .4892 .4392

K .4890 .4892 .4892 .4392

% .4890 .4896 .4900 .4892