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Home , Drainage basin, Drainage density, Relief ratio

VOL. 12, NO. 5 RESEARCH OCTOBER 1976

Morphometry and in Small Basins Subjectto Diverse HydrogeomorphicControls

PETER C. PATTON AND VICTOR R. BAKER

Departmentof GeologicalSciences, University of Texas at Austin, Austin, Texas 78712

Morphometric parameterssuch as , magnitude, and are practical measuresof potential in small (<100 mi2) drainage basins. Stereoscopicinterpretation of low- altitude aerial photographsprovides the most accuratemaps of basinsfor generatingthese parameters. Field surveysof a high-densitylimestone basin in •;Clltl...... ill I g;,•cta;•11t'ow that I' •A • o•,,,•..... topographlcß maps accuratelyportray the efficientstream system but fail to reveal numeroussmall gulliesthat may form portionsof hillslopehydrologic systems. Flood potentialin drainagebasins can be definedby a regional index computedas the standarddeviations of the logarithmsof the annual maximum stream- flows. High potential basinstend toward greaterrelief, greaterdrainage density, and thus greaterrugged- nessnumbers than low- potential watersheds.For a given number of first-order channels (basin magnitude), flash flood have greater ruggednessnumbers, indicating higher drainage densitiescombined with steep hillslopesand stream channel gradients.Transient controls on flood response,such as differencesbetween local rainstorm intensities,appear to be the major influenceson hydrographsin areas of moderate dissectionand relief. Morphometric parameters for low-potential flash flood regions(Indiana and the Appalachian Plateau) are better estimatorsof frequent low-magni- tude runoff events(mean annual flood), while the sameparameters correlate better with the maximum flood of record in high-flood potential regions (central Texas, southern California, and north central Utah).

INTRODUCTION from regionsof low flood potential. Basinswere selectedon the basisof hydrologicstudies by Beard [1975], which defined The first extensivehydrologic applicationsof quantitative measurem'entsof drainagebasin morphologywere illustrated flood potentialas the standarddeviation of the logarithmsof the annual maximum .Because a proper under- by Horton [1945] and Langbeinet al. [1947]. Horton's mor- standing of the correlationsderived in this study requires an phometricwork has been extendedby many investigators,but only a small percentageof this researchhas been aimed at the appreciationof methodologicallimitations, this report will also considerthe following: (1) the selectionof parameters practical problem of relating flood hydrographproperties to related to flood potential that can be measuredfrom topo- permanent hydrogeomorphiccontrols. The basic method of graphic maps or remote sensingimagery, (2) the resolution relating morphometryto floodsinvolves the identificationand analysis of relationshipsbetween character- capabilitiesof the varioussources of morphometricvariables, istics,meteorological inputs, and flood response. and (3) the distinctionbetween transient and permanentcon- trols [Rodda, 1969] on local flood responsecharacteristics. The most commonlyemployed models identify variablesthat are known to be significantin the processesthat transform MORPHOMETRIC PARAMETERS USEFUL IN drainagebasin input (high-intensityrainfall) to output (flood ESTIMATING FLOOD RESPONSE response).Functional relationshipsbetween various process controls and selectedmeasures of flood responseare usually Drainage area is perhaps the most frequently employed variable in the estimation of stream .Area has been establishedby multiple-regressionanalysis. A standard loga- correlatedboth with frequentrunoff eventsof low magnitude rithmic expressionwould take the following form: [Hack, 1957] and with infrequent runoff eventsof high magni- Qt = aX•bX•.cXsd.ß ß (1) tude [Patton and Baker, 1975]; it has been usedwith runoff in where humid [Benson,1962] and arid [Burkham, 1966] regions. Gray [1970] reviewed numerous examplesfor regions throughout Qt the peak dischargewith t (or some the world. In the present study, drainage areas were deter- other flood hydrograph property such as lag mined from U.S. Geological Survey water supply papers or, time); when necessary,by measurementfrom topographicmaps with regressioncoefficients; a polar planimeter. factors controlling the flood response. Horton [1932, 1945] suggestedthat, in addition to area, streamslope and drainagedensity should be highly correlated In practice this approach has resulted in many 'flood for- with maximum flood discharge.Drainage density,the length mulas,' nearly all of which include basin area as one of the of the channel per unit of drainage area, is controlled by variables.Unfortunately, the approachusually involves many numerous variables, including the relie.f,rainfall, parametersthat are dependentin some way on one another. capacity of the , and resistanceof the to Identifying and quantifying individual factors posesa major [Horton, 1945]. Drainage density has been correlated with difficulty in the establishmentof meaningful statistical rela- measuresof relief and relief ratio [Schumm,1956; Hadley and tionshipsbetween various controls. Schumm,1961], the Thornthwaitesprecipitation effectiveness The purposeof this study is to compare and contrastmor- index and the runoff intensity[Melton, 1957],the intensityof phometric properties of small (<100 mi•') drainage basinsin precipitation[Chorley, 1957], the infiltration capacity[Hadley regionsof high flood potential with drainagebasin parameters andSchumm, 1961], stream [Carlston, 1963; Trainer, Copyright¸ 1976by the AmericanGeophysical Union. 1969], and the mean annual flood [Carlston, 1963;Hadley and 941 942 PATTON AND BAKER: FLOOO POTENTIAL

Schumm, 1961]. Becauseof the interactions between process goodnessof fit between dischargeand with de- and form variables summarizedby the drainage densitymea- creasingfrequency of the runoff event. This suggestedthat sure [Horton, 1945; Strahler, 1958] and becauseof the wide higher-magnitude events are most important in the estab- range of naturally occurring values of drainage density lishmentof the drainagenetwork. Shreve's[1967] methodof [Schumm,1956] it is an important variable. Certainly, in a very ordering has been advocatedby a number of investigatorsas simplistic view, drainage density measuresbasin efficiencyin being more descriptiveof network form in relation to stream- removing excessprecipitation inputs. flow. The number of first-order (Shreve magnitude) In an analysis of flood potential one might expect flood has been correlatedwith the peak dischargeof Appalachian prone regions to be characterizedby high drainage density streams [Morisawa, 1962] and central Texas streams[Patton values indicating low infiltration capacity, relatively short and Baker, 1975]. In addition, Blyth and Rodda [1973] noted steepslopes, and low vegetativecover, all of which would lead that the number of flowing first-order streamsincreased with to the rapid concentrationof flood runoff. Low-flood poten- total rainfall and rainfall intensity. They noted that during dry tial regions might be expected to have low drainage density periods, flowing first-order streamsconstituted less than 20% values, reflecting the inverse of the above conditions. The of the total flowing length of the network. At the maximum erodibility of the terrain, a function of local geology or relict extent of the network the total length of first-order streams drainage systemsthat result from paleoclimates,can add con- constituted over 50% of the total basin stream length. siderablecomplexity to this generalization. The importance of basin relief as a hydrologic parameter A technical problem with the use of drainage density is the has been noted by numerous investigators[Sherman, 1932; difficulty of measurement,particularly when large basinsare Horton, 1945; Strahler, 1958]. With increasingrelief, steeper considered.This problem can be circumventedby employing hillslopes,and higher streamgradients, time of concentration the line intersection-estimatingprocedure. First introducedby of runoff increases,thereby increasingflood peaks. Thus all Carlston and Langbein [1960] and later modified by McCoy other conditionsbeing equal, the greater the relief of a basin, [1971] and Mark [1974], the techniqueinvolves superimposing the greater the rate of hydrograph rise. In order to compare a grid over the drainage net and counting the number of relief amongbasins of varying sizes,two dimensionlessparam- intersectionsof drainage lines along a traverseline. Drainage eters were calculated. Relief ratio [Schumm,1956] is the ratio density can then be calculated from severalempirical equa- of basin relief to basin length. Basin relief is measuredby tions employing the quotient of the number of intersections averagingthe elevationof the divide and subtractingthe eleva- (N) and the traverse length (L): tion of the outlet. Basinlength is measuredparallel to the main stream. Ruggednessnumber [Melton, 1957] is the dimension- DD = 1.414NIL (2) lessproduct of drainagedensity and relief; and thereforeareas from Carlston and Langbein [1960] of high drainage densityand low relief are as ruggedas areas of low drainagedensity and high relief. Areasof potentialflash DD = 1.8 ß i .•tx,/ L, (3) flooding might be expected to have the highest ruggedness from McCoy [1971] numbers incorporatinga fine drainage texture, with minimal length of overland flow acrosssteep slopes,and high stream DD = 1.571N/L (4) channel gradients. The combination of these factors might from Mark [1974]. result in far higherflood peaks for an equivalentrainfall input This techniquewas usedfor calculatingdrainage density for than for basinshaving a low ruggednessnumber. six basins in north central Utah. For comparison,drainage THE PROBLEM OF NETWORK RESOLUTION densityfor the six basinswas also calculatedby measuringthe total stream length and dividing by drainage area. Equation Leopoldand Langbein[1963] noted that in geomorphicsys- (3) gave the bestresults, showing less than 10%error (Table 1). tems the ability to measuremay always exceedany ability to Consideringthe rapidity of the techniquethe error was accept- forecast.Although the presentstudy is concernedwith aspects able. of the network geometry that have adjustedto climatic and Stream order has been directly correlatedwith dischargeby geologicfactors, only a portion of a drainageform of a net- numerousworkers [Blyth and Rodda, 1973;Rodda, 1969;Stall work. can be attributed to these deterministic factors. The rest and Fok, 1967]. Stall and Fok [1967] noted an increasing has been ascribedto topological randomness[Shreve, 1966,

TABLE 1. Drainage Density Values for Basinsin North Central Utah Accordingto Various Calculation Procedures

Measured Drainage Basin N/L* 1.571N/L*'• 1.414N/L*•: Density, mi/mi •'

City Creek 6.04 9.49 8.54 8.87 Centerville 4.72 7.50 6.65 6.67 Farmington Canyon 5.37 8.44 7.60 7.47 Ricks Creek 4.93 7.74 6.97 7.50 Parrish Creek 4.72 7.44 6.68 7.36 Holmes Creek 6.53 10.26 9.23 8.96 Thecoefficients derived by' regression analysis for these basins are DD = 1.442N/L,R•' = 0.9979, and P < 0.0001. *N/L is the numberof intersectionsper traverselength in miles. tFor the coefficient1.571, error rangesfrom 1.1 to 13%. :•For the coefficient1.414, error rangesfrom 0.3 to 9.2%. PATTON AND 13AKER:FLOOD POTENTIAL 943

The most detailed network analysisof Bee Creek (3.4 mi•') BE utilized low-altitude black and white aerial photographsat a 1:13,000 scale (Figure 1). Photographic mapping on stereo pairs was usedto interpret the most subtlechanges in shadow that could be interpreted as a stream channel. Besidesthe continuouschannel network, many small discontinuousgullies which develop on the slopesof Bee Creek were easily inter- preted from the stereo pairs. This technique resolved316 un- branched (first-order segmentsor first-magnitude links) in the continuousnetwork exclusiveof the slope system. The total number of first-order collectors, dis- continuousgullies plus first-order segments,was 995.

0 I 2 Km An •dditic•nal mapping sourcewas the Austin west quad- I I I rangle,with a 1:•4,000 scaleand a 20-ft contourinterval Fig. 1. Drainage map of Bee Creek basin near Austin, Texas, (Figure 2). The drainage network composition interpreted constructedby detailed stereoscopicinterpretation of panchromatic from the topographic map (Figure 3) was lessdetailed than aerial photographsat a 1:13,000 scale. that revealed by the low-altitude stereomapping.Only 109 first-order streams were resolved. 1967;Smart, 1969]. Whatever the purposeof the investigation, An absolutebasis of resolutioncapability for BeeCreek was however, the detailed mapping of the drainage network is the established by detailed field surveys for selected subbasins initial step in quantitative drainage basin studies.The most (Figure 2). The features which acted as first-order stream precisedata, of Course,comes from field determinations.Be- segmentsin the field were found to be preciselythose segments cause this method is slow and often costly, standard topo- mapped as discontinuousgullies in the detailed stereoscopic graphic mapshave becomea favorite sourceof data. interpretation of low-altitude black and white aerial photo- In order to compare the resolution capabilitiesof various graphs.The gullieswere found to averageless than 100 ft in scalesand types of drainage network data sources,a number length and were characterizedby broad shallow channelscut of detailed studies were completed on Bee Creek, a small in rock (Figure 4). The frequency of first-order in the of the Colorado , near Austin, Texas. The selectedsubbasins was 290 per squaremile. The extrapolated hydrologyof Bee Creek was describedby Tinkler [1971]. The number of 986 gullies over the entire basin comparesremark- basin is developedon deeply dissectedmarl and limestone ably with the number estimatedby detailed stereoscopic .It is characterizedby steepslopes, brushy vegetation, interpretationof the aerial photographs. thin , and a high relief ratio (0.03). A number of studies similar to the one discussed above have

'-. - ...... BEE GREEK STUDY BASINS

\\

A xxx I / \\\ I // / \\\, •'• ,:',• TOPOGRAPHIC

,,, , / , •oo ,,, BI,,

• // / /2 • / B2 / {- [ 0 50 I00Meters •// 0 50 I00 Meters xx •, /1/ xNxx

Fig. 2. Drainagemap of BeeCreek constructed by the 'methodof V's,' usingthe Austinwest 7.5' topographicquadrangle map (1:24,000 scale).Subbasins A, 13,and C were mappedby detailedfield surveywith compassand tape. 944 PATTONAND BAKER:FLOOD POTENTIAL

beendone for basinsin centralTexas [Baker et al.[ 1975].In general,high relief gullied basins are not resolved adequately by 1'24,000scale topographic maps, while low-relief basins - 60

.....

showvery little difference between field surveys, topographic 40 I,I maps,and detailed stereoscopic interpretations of low-altitude ._l aerialphotography. In the high-reliefbasins the hydrologic significanceofthe gullies iscertainly much less than that of the continuouschannel network. The gullies probably constitute a -O componentof thehill slopehydrologic systems. Their high Fig.4. Measuredcross section of a first-ordergully in theBee Creek channelroughness and irregular gradients clearly distinguish drainagebasin. them from the more efficientchannel system shown on the the analysisof unregulatedflow recordsfrom 2900 topographicmap. Purely as a practicalexpedient for regional stations in the under 1000 mi: in area and comparisons,large-scale topographic maps were utilized for with recordlengths equal to or exceeding20 years. the streamflowestimates in the presentstudy. Clearly, how- The flashflood warning index was developed as a regional ever,the accuracyof suchmaps for predictingflood response from diverseterrains needsto be testedin future research. measureof the rate of riseof streamflow.The completedaily recordsof 260 stationswere analyzedand regionalizedover SELECTIONOF STUDY BASINS the entireUnited Statesto representwarning times for 1-mi•' drainageareas [Beard, 1975]. This index was used in thisstudy Hydrologicallydiverse areas in whichto examinemorpho- asa generalguide for locatingregions subject to flashfloods. metricmodels of floodresponse were established by employing The flashflood magnitudeindex map of the United States s,everal measures of regionalflood potential. Two of themea- (Figure5) developedby Beard[1975] allowed a readymeans of sureswere developedby Beard [1975]. The first is the flash distinguishinghigh- from low-flood potentialregions. The floodmagnitude index, which equals [ZX•/(N- 1)]•/•', where X is the deviation of an annual maximum streamflow from the studyareas selected to representhigh flash flood potential were centralTexas, the WasatchMountains in north central Utah, mean(expressed as a logarithm)and N is the numberof events and the San Gabriel in southern California. The in therecord. The secondmeasure is theflash flood warning regionsof lowpotential'selected areIndiana and the Appala- index,which equals •}max/{•arn, where •}max is theannual max- chian Plateauprovince in westernPennsylvania, Maryland, imumpeak flow and Qa,,, is the average rate of flow for a 3-day Ohio, West Virginia, and Tennessee. periodprior to andincluding the day of occurrenceof thepeak flow. Flood prone areaswere also designatedby their historic The flash flood magnitudeindex is an estimatorof the ratio tendencyto experienceflash floods. A flashflood is variously definedas (1) a suddenflood in a usuallydry ,resulting of rareflood events to commonflood events as they would be from a cloudburst[American Geological Institute, 1972], or (2) representedon a plotof dischargeversus exceedence frequency a local flood of great volumeand shortduration, generally per 100events in a standardlog Pearsontype 3 frequency .resultingfrom heavyrainfall in the immediatevicinity [Web- analysis[Beard, 1975]. Beard [1975] applied this criterionin ster, 1965].The hydrologicimplications of thesevague defini- tionsare that (1) the rate of riseof the flood hydrographis 400 extremelyrapid and (2) becauseof the intensityof rainfall requiredfor the generationof a flashflood the drainagearea - I I affectedis relativelysmall. In his descriptionof flashfloods Low-Altitude Aerial - ß PhotoStereo Pairs along the WasatchMountains in Utah, Woolley[1946] in- ß TopographicMap cludedhydrographs for PriceRiver (drainage area of 530mi •') and San Rafael River (drainagearea of 1690mi •') which dem- IOO _ ß S-190B onstrated the rapid rise of flood stage as a result of - x S-190A

_ cloudbursts.However, these rapid rises were probably a result

_ of runofffrom only a fewmuch smaller tributaries. Similarly, _ in centralTexas, rapid runofffrom BleidersCreek (drainage area of 16 mi•') on May 11 and 12, 1972,as a resultof 16 in. of concentratedin 4 hourscaused a rapid riseon the Comal _ River hoursbefore the runofffrom the dry ComalRiver basin peaked(Figure 6). Furthermore,flash floods may produce recorddischarges on smallstreams even though the runoff in the major drainagesmay be of a far lower recurrenceinterval.

_ For thesereasons the studywas restrictedto basinsless than

_ 100 mi •' in area.

,, _ Whereit was possible,published morphometric data were _ usedto generatepredictive equations. However, for two re- gions,central Texas and north central Utah, data were specifi- _ callygenerated for this studyby topographicmap analysis. The drainagenetwork was interpretedfrom 1:24,000 scale

I maps using$trahler's [1957] crenulationmethod. The stream I 2 3 4 5 6 networkwas orderedby the $trahler [1957]and the Shreve ORDER [1966]method. Areal measurements were made with a polar Fig. 3. ttorton'.s[1945] law of streamnumbers as interpreted from planimeter,and linear measurements were made with a map variousdepictions of the BeeCreek drainage network. wheel. PATTONAND BAKER: FLOOD POTENTIAL 945

Fig.5. Locationofstudy areas in relation to the regional variation inthe flash flood magnitude index for the United States(simplified from Beard [1975]). The symbols are T, centralTexas; W, Wasatchfront; S, southernCalifornia; I, Indiana; and A, the Appalachian Plateau.

Streamdischarge records were gatheredfrom published sedimentsof the Gulf Coastal Plain. This diversity resultsin a U.S. GeologicalSurvey records and U.S. ForestService open wide rangeof drainagebasin morphometric characteristics. file reports.The logPearson 3 frequencyanalysis was used to Relief, measuredas relief ratio, is highly variable, ranging calculateexceedence probabilities from the annualpeak data from low valueson the Gulf CoastalPlain (0.010) and in north [Beard,1974]. Where discharge data werenot available,re- centralTexas (0.007) to highervalues in the Llano gionalrunoff equations were employed [Patton and Baker, (0.020)and on the Edwards Plateau (0.030). The same trend is 1975].Morphometric and dischargedata werereduced and analyzedby standardstatistical techniques, including correla- tion, discriminantfunction, and multiple-regressionmethods - 7O [Krumbeinand Graybill, 1965; Snedecor and Cochran, 1967]. Rainfall To avoidspurious correlations between morphometric varia- IO- blesand discharge,drainage area and thosevariables highly correlatedwith area(e.g., basin length) were eliminated from _50 ¸ the analysisof streamrunoff. FLOOD RESPONSEIN DIVERSEHYDROGEOMORPHIC Flood - 40• •6 Runoff

Central Texas. Central Texas has perhaps the most cata- -30 '- strophicrainfall-runoff regime in the conterminousUnited •4 States. Texas rainfalls between 1- and 24-hour duration ap- - 20rn proachthe world maxima [Baker, 1975]. In addition,it is one of thetwo regionsin theUnited States which have the highest 2 I0 10-yearflood magnitudes for 300-mF'drainage basins [Leopold et al., 1964].Flooding is often the resultof intensethunder- i I I I storms,and thereforethe spatialand temporal distribution of 2000 2200 2400 0200 0400 0600 0800 I000 floodingis extremelyunpredictable. May II, 1972 May 12, 1972 Morphometricdata were collectedfor 13 studybasins Time (Hours) throughoutcentral Texas (Table 2). The drainagebasins were Fig. 6. Rainfalland runoff for ComalRiver at New Braunfels, locatedin diversephysiographic regions on a varietyof rock Texas,flood of May 11-12,1972. Rainfall distribution assumes that the 16-in.recorded maximum was time distributedaccording to a unit types.Basins are locatedon the Precambrianmetamorphic distribution of stormrainfall recorded at CanyonDam [Colwicket al., andigneous rocks of the Llanouplift, on the Paleozoiclime- 1973].Runoff was computed by the U.S. GeologicalSurvey from stoneunits in north centralTexas, on the Cretaceouslimestone visual observationsof water surfaceelevations at regular time inter- of the Edwards Plateau, and on the Cretaceous and younger vals. 946 PATTON AND BAKER: FLOOO POTENTIAL

TABLE 2. Morphometric and Runoff Data for Central Texas

DD, t:,, Q.... Basin A, mi •' S M R, ft BL, mi HD RR mi/mi •' no./mi 2 ttUs

Deep Creek 3 3.42 4 42 270 2.77 0.23 0.018 4.37 12.28 3060 Deep Creek 8 5.41 3 44 270 3.86 0.17 0.013 3.30 8.13 5660 Wilbarger Creek 4.61 3 24 165 3.05 0.10 0.010 3.24 5.20 4279 Rebecca Creek 11.41 6 237 512 4.36 0.61 0.022 6.14 21.27 9300 Dry Creek (BuescherL.) 1.57 4 84 142 1.94 0.27 0.014 10.26 53.50 1870 Mukewater 9 4.02 4 91 135 3.61 0.15 0.007 5.66 22.64 1440 UpshawCreek 4.89 5 105 340 3.72 0.41 0.017 6.20 21.47 4460* Helms Creek 5.92 5 147 505 4.64 0.66 0.021 7.01 24.83 5120' Dry Creek 1.79 4 81 375 1.68 0.64 0.040 8.90 45.25 2145' Burleson Creek 4.16 5 90 437 3.39 0.52 0.024 6.51 21.63 3985* Little Barton Creek 5.95 5 101 442 4.69 0.44 0.018 5.24 16.97 5150' Miller Creek 5.71 6 291 661 3.43 1.19 0.036 9.68 50.96 5010' Bee Creek 3.43 4 145 540 3.34 0.81 0.030 8.10 42.27 3395* Symbolsare as follows: A, drainagebasin area; S, Strahlerbasin order; M, basinmagnitude; R, basin relief; BL, basin length' HD, ruggednessnumber; RR, relief ratio; DD, drainagedensity; F•, first-orderchannel frequency; and Q.... maximumpeak discharge. *Estimated from regionalrunoff equation Qmax= 1403Aø'78 [Patton and Baker, 1975].

followed by valuesof drainage density,first-order streamfre- drainagebasins are underlainby the PrecambrianFarmington quency, and ruggednessnumber. Canyon complex composed of metamorphic sedimentary The Wasatchfront. Woolley [1946] noted that in north rocks, metamorphicigneous rocks, and intrusivegneiss [Eard- central Utah between 1847 and 1938 over 500 cloudburst ley, 1944]. The larger basinsare eroding into the Triassic floods were recorded along with reports of extensivecrop clastic sedimentsand, in places,cross narrow belts of Paleo- damageand highway, bridge, and building destruction.Butler zoic clastic and carbonate rocks [Eardley, 1944]. In general, and Marsell [1972] detail the 836 flash floods reported between the drainage basinshave high relief (relief ratio, 0.08-0.27), 1939 and 1969, the majority of which occurred along the high drainagedensity (6.68-10.01 mi/mi ø) and extremelyhigh Wasatch front. These floods are the result of intense rainfalls, ruggednessnumbers (4.60-10.95). up to 4 in. in 12 hours, from severethunderstorms created by SouthernCalifornia. Intenseprecipitation in southernCal- the orographiceffect of the Wasatch front [Butlerand Marsell, ifornia is controlled by extratropical North Pacific cyclones 1972]. Although the volume of flood runoff is considerablyless which move inland, generating storms with recorded in- here than for central Texas, flash floodscommonly cause mud tensitiesof up to 11.5 in. in 1 h 20 m [Anderson,1949]. The and debris flows which greatly increase property damage mountainous regions of southern California are particularly [Woolley, 1946]. Interestingly,the flashflood magnitudeindex affectedby flash flooding, runoff being up to 1260 ft3/s/miø' for this regionis extremelylow, rangingfrom 1.5to 3.5. This is from a 17-mi•' drainage basin [Anderson,1949]. Therefore the becausethe magnitude index is calculated from the distribu- San Dimas experimental on the southern slope of the tion of the annual peak flows, which along the Wasatchfront San Gabriel Mountains near Los Angeles was an excellent are related to events (see U.S. GeologicalSurvey locality for analysis.The regionalflash flood magnitudeindex Water-SupplyPaper 1927). is 0.7. Runoff in the San Dimas region is locally even more Eleven drainage basins along the Wasatch front were se- erratic, the flash flood magnitude index approachingor ex- lected for study (Table 3). The drainagesinvestigated have ceeding 1.0 for many basins. their headwaters east of the Wasatch fault and flow westward, The San Gabriel Mountains are a fault block range bounded eroding steepcanyons into the fault scarp.Where the streams by three major fault zones [Maxwell, 1960]. The mountains exit from the front, broad alluvial fans have formed themselvesare highly faulted and consistof pre-Cretaceous on top of Pleistocenelacustrine . Most of the small schist,gneiss and granitic rocks surroundedby Tertiary and

TABLE 3. Morphometric and Runoff Data for North Central Utah

DD, F•, Qo.5, Q0.,, Q0.0•, Q .... Basin A, mi 2 S M R, ft BL, mi HD RR mi/mV no./mF' ftS/s fta/s fta/s fta/s

City Creek 19.2 5 602 4150 10.23 6.71 0.080 8.54 31.35 64 109 167 163 Hardscrabble Creek. 28.10 5 1028 3230 7.65 4.84 0.080 8.02 36.58 252 416 638 464 CentervilleCanyon 3.15 4 71 3600 3.77 4.60 0.180 6.75 22.54 12 28 62 30 FarmingtonCanyon 10.60 5 276 3170 6.29 4.56 0.095 7.60 26.03 142 300 598 298 Emigration Creek 18.00 5 629 3575 8.33 5.72 0.081 8.65 34.94 25 63 137 156 Mill Creek (Salt City) 21.70 5 785 4540 9.65 7.26 0.089 8.61 36.17 50 91 151 152 Rick Creek 2.35 4 68 4300 3.04 5.67 0.270 6.97 28.94 17 48 130 51 Parrish Creek 2.08 3 55 4255 3.63 5.10 0.220 6.68 26.44 12 31 72 30 Holmes Creek 2.49 4 98 4100 2.84 7.17 0.270 9.23 39.35 17 39 85 36 Dry Creek 9.82 6 354 5785 5.27 10.95 0.210 10.01 36.04 210 385 682 597 Mill Creek (Bountiful) 8.79 5 307 3945 6.07 6.08 0.120 8.15 34.92 40 103 248 140

Symbols are the same as those defined in Table 2 with the addition of Q0.5,discharge with 0.5 exceedenceprobability per 100 events; Q0.a, dischargewith 0.1 exceedenceprobability per 100 events;and Q0.0a,discharge with 0.01 exceedenceprobability per 100 events. PATTON AND BAKER: FLOOD POTENTIAL 947

TABLE 4. Morphometric and Runoff Data for San Dimas Experimental Forest, Southern California

DO, F1, Q0.5, Q0.l, Q0.0•, Q.... Basin A, mi*' S M R, ft BL, mi HD RR mi/mi*' no./mi*' ftS/s ftS/s fta/s fta/s

Wolfskill Canyon 2.49 5 409 2695 2.56 9.83 0.199 19.26 164.25 24 202 1311 1010 Watershed 1 Fern Canyon 2.20 5 465 2900 2.46 10.16 0.223 18.50 211.36 19 149 1040 215 Watershed 2 Upper East Fork 2.18 5 347 2560 2.56 8.63 0.189 17.81 159.17 13 118 905 160 Watershed 3 Bell Canyon 2.01 5 386 1520 2.21 7.02 0.130 24.40 192.03 15 165 1710 217 Watershed 8 Wolfe Canyon 1.18 5 344 1610 1.86 7.59 0.163 24.91 291.52 2 83 1862 145 Watershed 9 Subwatershed 2-1 0.054 3 19 727 0.41 2.51 0.337 18.27 351.85 1 11 95 22 Subwatershed 2-2 0.065 3 22 647 0.48 2.28 0.252 18.61 338.46 2 20 190 22 Subwatershed 2-3 0.085 2 13 990 0.55 2.53 0.337 13.50 152.94 1 19 233 51 Subwatershed 8-1 0.122 4 55 992 0.68 5.52 0.277 29.38 450.81 0.5 14 827 22 Subwatershed 8-2 0.061 5 75 719 0.38 4.48 0.360 32.94 1229.5 0.7 26 862 33 Subwatershed 8-3 0.10 4 39 1031 0.54 5.62 0.358 28.81 390.0 0.6 10 150 18 Subwatershed 8-4 0.061 3 13 921 0.45 3.14 0.390 18.02 213.1 0.4 8 139 10

Symbolsare the sameas thosedefined in Tables 2 and 3. Morphometric data are from Maxwell [1960].

Quaternary alluvial deposits[Maxwell, 1960]. Morphometric be as high as valuesin the Wasatch front and are generally data measuredby Maxwell [1960] were used from 12 basins comparable to values for central Texas. This can in part be (Table 4) within the San Dimas experimentalforest. Relief is attributed to the easily eroded impermeabletill underlying high (relief ratio, 0.130-0.390), and drainage density is ex- most of the drainagebasins (data from Indiana StateGeologi- tremely high (13.50-32.94 mi/mi2). As a result,the ruggedness cal Survey regional maps 1-8). The ruggednessnumber is number is high again (1.85-10.16), indicatingextremely high slightly lower for Indiana than for the previously discussed relief fine-textureddrainage basins.The fine texture of the regionsof high flash flood potential. drainagenetwork is demonstratedby the frequencyof first- The AppalachianPlateau. Eleven basins (Table 6) were order streamswhich exceed3600 per squaremile in one basin. chosenfor studywithin the AlleghenyMountain, unglaciated This demonstratesthat as drainagedensity increases,the in- Allegheny Plateau, and Cumberland Plateau divisionsof the creasein total channel length is createdas the result of a far Appalachian Plateau [Morisa•4a,1962]. The region contains greater increasein first-order streamsand not as the result of Paleozoicrocks, gently folded in the Allegheny Mountain an increasein the lengthof higher-orderchannels. region, becoming more horizontal westward and southward Indiana. Regionaland at-stationflash flood magnitudein- onto the unglaciatedAllegheny Plateau and the Cumberland dicesfor Indiana are quite low, rangingfrom 0.2 to 0.3. In this Plateau. In this region, basin relief rangesfrom low to inter- area of relativelylow flood potential,10 basins[Lee and Del- ! mediatevalues (relief ratio, 0.005-0.067),but drainagedensity leur, 1972] were selectedfor study (Table 5). With the ex- is consistentlylow (2.58-5.75 mi/mi2), and as a result,rugged- ceptionof southcentral Indiana, the entire state is coveredby nessnumbers have intermediate values (0.17-1.11). The low a thicknessof more than 50 ft of glacial ground and end drainagedensity values in basinswith intermediaterelief prob- moraine (data from Indiana State GeologicalSurvey regional ably indicate the greater infiltration capacity of thicker soils maps 1-8). Of the basinsinvestigated, only one crossessignifi- and the increasedvegetative cover prohibitingferosion. For cant outcropsof Mississippianshale, siltstone, and sandstone; example, several Texas streams have lower values of relief the othersare underlainby Wisconsinanand Illinoisanglacial ratio but greater valuesof drainagedensity. Ruggedness num- material (data from Indiana State GeologicalSurvey regional bers, however, are nearly identical for the two regions. maps 1-8). Basin relief is extremelylow in Indiana (relief ratio, Correlationanalysis. M orphometric data from each of the 0.0008-0.016), but drainagedensities (2.17-11.80 mi/mi :) can five study regions were compared (1) to stream discharge

TABLE 5. Morphometric and Runoff Data for Indiana

DD, F•, Qo.5, Qo.•, QO.01, Omax, Basin A, mi" S M R BL, mi HD RR mi/mi*' no./mi • fta/s fta/s ftUs ftUs

Little Indian Creek 33.43 6 129 77 8.82 0.031 0.0016 2.17 3.85 343 500 726 500 Lawrence Creek .2.64 4 97 120 2.17 0.139 0.010 6.10 36.74 527 1350 3,247 2,650 Bear Creek 5.80 5 259 310 3.66 0.575 0.016 9.80 44.65 603 1573 3,792 1,830 BeanBlossom CreekJ 13.40 6 785 373 5.22 0.833 0.013 11.80 58.58 1792 4651 11,108 8,140 169.70 6 3066 240 26.39 0.222 0.0017 4.88 18.07 4265 8807 17,006 12,900 Hinkle Creek 18.20 6 624 110 4.83 0.138 0.0043 6.62 34.28 1346 4206 12,291 4,920 Cicero Creek 205.7 7 3066 200 18.40 0.163 0.0020 4.30 14.90 3311 7548 15,942 9,800 Buck Creek 33.84 6 817 45 9.72 0.048 0.0008 5.69 24.14 810 1792 3,760 1,780 80.55 7 2159 182 12.03 0.200 0.0028 5.82 26.80 2155 3803 6,686 3,460 Little Cicero Creek 42.06 6 1003 110 9.68 0.096 0.0021 4.64 23.85 1242 2960 6,701 3,980

Symbolsare the sameas thosedefined in Tables 2 and 3. Morphometricdata are from Lee and Delleur [1972]. 948 PATTONAND BAKER:FLOOD POTENTIAL

TABLE 6. Morphometricand RunoffData for the AppalachianPlateau

DD, F•, Qo.5, Qo.•, Qo.o•, Q.... Basin A, mi2 S M R BL,mi HD RR mi/m? no./mi• ftS/s ftS/s fta/s fta/s Tar HollowCreek 1.5 4 74 330 3.2 0.17 0.048 2.79 49.33 127 337 803 957 HomeCreek 1.6 5 70 210 3.4 0.23 0.035 5.75 43.75 123 293 618 378 Mill Creek " 2.7 4 104 400 4.3 0.44 0.030 5.66 38.52 GreenLick Run 3.1 4 79 860 2.2 0.59 0.067 3.65 25.48 263 607 1,244 1,400 BeechCreek 18.7 5 186 550 14.8 0.29 0.007 2.84 9.95 1062 2,083 4,124 2,210 PineyCreek 24.5 5 271 1650 14.9 0.95 0.021 3.04 11.06 1093 2,685 5,834 6,850 CasselmanRiver 62.5 6 653 1700 25.1 1.07 0.013 3.34 10.45 2320 4,442 8,034 8,400 EmoryRiver 83.2 7 1936 540 25.8 0.57 0.004 5.57 23.27 7233 13,759 24,095 18,700 YoughloghenyRiver 134.0 6 1798 1590 25.1 1.11 0.012 3.68 13.41 4375 8,535 15,447 11,800 DaddysCreek 93.5 6 1181 730 27.8 0.40 0.005 2.87 12.63 4612 9,346 17,430 11,600 Little M ahoning Creek 87.4 6 1058 1500 25.8 0.73 0.011 2.58 12.10 3059 5,056 7,849 5,300 AlleghenyRiver 55.0 7 5966 1010 27.4 0.56 0.007 2.92 10.84 7562 5,708 29,182 55,000 Symbols are the same as those defined in Tables 2 and 3. Morphometricdata are from Morisawa[1962]. valueshaving an exceedenceprobability per 100events of 0.1, ally,the best results were provided by equationsinvolving the 0.5, and0.01 and (2) to the maximumdischarge of record.For basin magnitude,the ruggednessnumber, and the first-order thecentral Texas watersheds it was feasible to includeonly the streamfrequency. For watershedshaving low flashflood - maximum dischargeof record. The correlation matricesare tential(Indiana and the AppalachianPlateau), morphometric presentedin Tables 7, 8, 9, 10, and 11. parameters were better estimators of the mean annual flood Basinmagnitude, the total numberof first-orderstreams, (Q0.5)than the maximumdischarge of record(Qmax). This correlatesbest with infrequentrunoff eventsin the San Dimas againsuggests that drainagenetworks adjust to andreflect the andWasatch watersheds, whereas in the Indianaand Appala- magnitudeand frequencyof the dominant runoff events, chian Plateau watersheds the correlation coefficientsbetween whichin turn reflectthe intensity,duration, areal extent, and basinmagnitude and dischargeincrease with increasingfre- frequencyof the rainfallinputs. Although this morphometric quencyof runoff.This suggeststhat regionscharacterized by adjustmentis probablyto a rangeof discharges,the valuesof infrequenthigh-intensity storms adjust their drainagenet to Qmaxand Q0.5can be thought of as end membersof the the infrequenthigh-magnitude runoff events. Regions charac- dischargespectrum. terizedby morefrequent less intense regional storms adjust theirdrainage nets to theresulting more frequent lower-mag- DISCUSSION nitude floods such as the mean annual flood. The result is not Severalgeneral trends are apparent from the morphometric completelyindependent of drainagearea, as is shownby the data.With the exception of centralTexas, basin relief is higher highcorrelation of areato basinmagnitude in severalregions. for the flashflood prone regions than for the low-potential Basinmagnitude was used in the regressionanalysis because regions. Furthermore the north central Utah and southern recent studies have shown that it is a more sensitive measure of Californiadrainage basins have the highestdrainage density drainagebasin response than is area [Blyth and Rodda, 1973]. values.High basin relief combined with highdrainage density Floodformulas. Equationswere developed for floodpre- createssteep short hillslopes, minimizing the lengthof over- dictionin eachof the five regionsby stepwiseleast squares land flowand againmore rapidly concentrating runoff. Cen- regressionstatistics (Table 12). Basin magnitudewas em- tral Texashas intermediate values of basinrelief and drainage ployed along with drainagedensity, first-order stream fre- densitybut perhapsthe greatestflood discharges. The coarser quency,relief ratio, and ruggedness number. Drainage density drainagetexture and lower basin relief is probably offset by the was not employed in the equationswith first-order stream moreextreme rainfall events and the thin imperviouslithosols frequency,as they are highly correlated [Melton, 1957]. Gener- developed on the Edwards Plateau. In contrast, the

TABLE 7. CorrelationMatrix of MorphometricData and Runoff Data for CentralTexas

First Order Drainage Strahler Shreve Basin Relief Drainage Channel Maximum Area Order Magnitude Relief Length RuggednessRatio Density Frequency Discharge Drainage area 1.0000 Strahler order 0.4334 1.0000 Shrevemagnitude 0.3442 0.8647 1.0000 Relief 0.4539 0.6729 0.6821 1.0000 Basinlength 0.8934 0.3606 0.3078 0.3852 1.0000 Ruggedness 0.1371 0.7682 0.8494 0.8841 0.0947 1.0000 Relief ratio -0.0659 0.5037 0.5451 0.8256 -0.2019 0.8853 1.0000 Drainagedensity -0.3872 0.5637 0.7163 0.3415 -0.3683 0.7401 0.5980 1.0000 First-order channel frequency -0.3934 0.5302 0.7278 0.3349 -0.3533 0.7306 0.5817 0.9844 1.0000 Maximum discharge 0.8320 0.3788 0.2790 0.6328 0.6676 0.3052 0.2643 -0.2911 -0.3343 1.0000

The transformX • 1og•0X wasperformed. PATTONAND BAKER: FLOOD POTENTIAL 949

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TABLE 12. RegressionFormulas for PredictingFlood MagnitudesFrom Drainage Basin Morphometry in Diverse HydrogeomorphicRegions

Standard Error Region Equation F Ratio R2 Probability .otEstimate

Central Texas Qmax= 17369Mø'4SHDø'•4F•-ø'øe (3, 9) = 16.41 0.85 0.001 0.1000 Qmax= 36650Mø'e4RRø'•4DD- (3, 9) = 8.59 0.74 0.01 0.1295 Southern California Qmax= 155M•'ø'HD-ø'"F•-ø'73 (3, 8) = 14.87 0.85 0.001 0.2746 Qmax= 380Mø'a•DD-•'a7 (2, 9) = 28.56 0.86 0.0001 0.2450 North central Utah Qmax= 23Mø'•øHD•'•F•- •'• (3, 7) = 9.13 0.72 0.005 0.2923 Qmax- 38618M2'aøRRa'•F•-•'• (3, 7) = 11.50 0.83 0.005 0.2286 Indiana Qmax= 424Mø'"HDø'•aFf'• (3, 6) = 4.05 0.67 0.01 0.4200 Qmax= 424Mø'aaRRø'•DD ø'• (3, 6) = 3.90 0.66 0.05 0.4251 Qo.•= 115Mø'•aHDø'• (2, 7) = 8.46 0.71 0.025 0.3372 AppalachianPlateau Qmax= lOOMø'•HDø'•F•-ø'• (3, 7) = 26.14 0.92 0.0001 0.2153 Qmax= 38Mø'a•DD-ø'•ø (2, 8) = 38.79 0.91 0.0001 0.2151 Qo.•= 5Mø'•THDø'e•RR-ø'• (3, 7) = 220.94 0.99 0.0001 0.0818

low-potential flash flood regionshave either low (the Appala- Figure 7 in terms of modern geomorphic system concepts chian Plateau) or intermediate (Indiana) values of drainage [Chorleyand Kennedy,1971]. The complexityin the systemis density and low to intermediate basin relief. The combined introducedby the great extent to which climate actually con- effect of thesetwo variableswill be greater length of overland trols the basinmorphometry. In a regionwhere intense rainfall flow acrossgently to moderatelysloping interfluves,a condi- is an infrequent and random event, as in central Texas, a tion which will result in more attenuatedflood . feedback mechanismenhancing the rapid drainage response Becauserelief and drainage densityare apparently the two can be visualized.The erratically distributed rainfall does not most distinguishingvariables, the ruggednessnumber, the di- promote vegetationor development,and therefore the mensionlessproduct of relief and drainage density, should resultinggreater overland flow leadsto hillsloperills or gullies adequately summarize their interaction. When ruggednessof (Figure 1), which are eventuallyincorporated into the channel the study basinsis comparedto basin magnitude(Figure 7), it network. These newly formed first-orderchannels further in- is apparent that basinsof high flood potential (southernCali- creasethe responseof the drainagesystem. The reversewould fornia, north central Utah, and central Texas) have a greater occur in a region where rainfall is temporarily and spatially ruggednessat a given basin magnitude than do basinsof low more uniform. On the Appalachian Plateau, for example, the flood potential (Indiana and the Appalachian Plateau). Figure feedbackmechanism would continually work to dampen the 7 effectively summarizesthree important variables related to basin responseby aiding the developmentof thick soils and basin response:relief, drainagetexture, and drainagenetwork densevegetation, thereby increasinginfiltration rates and re- geometry. Becausethese variables are not well correlatedwith tarding surfacerunoff. Regionsof intermediatedissection and each other they probably explain different flood-producing componentsof the drainage basin. The calculation of a linear distance function (Figure 7) _- i i I I I ii il! i i•,l"m'mP IO0 I I I I I•1 quantifiesthe break betweenthe two data groups of different i i,&o ß ß flood potential. However, this discriminantfunction analysis shows that many basins from both high- and low-potential flood regions plot near the boundary separating the two groups. One possibleexplanation of this grouping is that the permanent morphometric controls are only effective in the determination of flood responsefor extremecases of relief and dissection.Thus the California and Utah basins are clearly distinguishable from the Indiana basins by morphometry 1 - N o o alone. In thesebasins the morphology probably enhancesthe - • • • • o o hydrologicresponse. We suggestthat extremelydissected high • o . / • BASINS n• relief drainage basinsmay exhibit a high flood potential even _ / • CALIFORNIA given relativelylow rainfall inputs(as appearsto be the casein - / • 0 UTAHTEXAS

Utah). Conversely,low relief poorly dissectedbasins may have --/ O • APPALACHIAN a low flood potential even for high-intensityrainfall. We fur- • INDIANA ther suggestthat flood potential in basinswith intermediate - values of dissectionand relief (e.g., the Texas and some Ap- OOl I I I I IIII I I I I IIII •1 I o lOO i,ooo io :300 palachian basins) depends to a considerable degree on the BASIN MAGNITUDE of the storm input. Although the Texas and Appala- Fig. 7. Ruggednessnumber (HD) versusbasin magnitude (M) for chian basinshave many morphologicalsimilarities, their hy- drainage basins in diverse hydrogeomorphicregions. The dot-dash drologic characteristicsare greatly different. The high-in- line depictsthe resultof a discriminantfunction analysis which yielded tensity storms typical of central Texas induce flash floods, D - M-ø'øOOHDø'ø7•' with a MahalanobisD squareof 5.848 and F(2.54) whereasthe low-intensitystorms of the north central Appala- - 38.08 at probability P - 0.0001. The dashed line is drawn per- pendicularto the discriminantline throughthe discriminantindex. It chians cause a slower responsein basinsthat are topograph- graphicallydefines the boundary betweenhigh-flood potential basins ically similar to those in Texas. (California, Utah, and Texas) and low-flood potential basins (the It is tempting to interpret the relationship illustrated in AppalachianPlateau and Indiana). 952 PATTONAND BAKER; FLOOO POTENTIAL relief (Figure 7) apparently have small basins that are most Horton, R. E., Erosionaldevelopment of streamsand their drainage sensitiveto changesin transient, i.e., climatic, controls. basins:Hydrophysical approach to quantitative morphology,Geol. Soc. Amer. Bull., ,56, 275-370, 1945. Acknowledgments.This researchwas supportedin part under Krumbein, W. C., and F. A. Graybill, An Introduction to Statistical contact A-35460 of the National Weather Servicewith the University Models in Geology,McGraw-Hill, New York, 1965. of Texas Center for Researchin .Additional support Langbein, W. B., et al., Topographiccharacteristics of drainageba- was provided by the National Aeronauticsand SpaceAdministration sins, U.S. Geol. Surv. Water Supply Pap. 968-C, 125-157, 1947. under contract NAS 9-13312 and by the Geology Foundation of The Lee, M. T., and J. W. Delleur, A program for estimatingrunoff from University of Texas at Austin. We thank Leo R. Beard, technical Indiana watersheds,3, Analysisof geomorphicdata and a dynamic director of the Center for Researchin Water Resources,for his sup- contributing area model for runoff estimation, report, pp. 1-92, port and guidance in the project. D. Lott aided in compiling and Purdue Univ. Water Resour. Res. Center, Lafayette, Ind., 1972. reducingthe hydrologicdata. E. A. Begle,J. Boone, S. D. Hulke, and Leopold, L. B., and W. B. Langbein,Association and indeterminacy M. M. Penteadoassisted with the quantitative geomorphicstudies of in ,in The Fabricof Geology,pp. 184-192, Freeman, drainagebasins. The manuscriptwas substantiallyimproved by Alan Cooper, , Calif., 1963. D. Howard's review. Leopold, L. B., M. G. Wolman, and J.P. Miller, Fluvial Processesin Geomorphology,W. H. Freeman, San Francisco,Calif., 1964. REFERENCES Mark, D. M., Line intersectionmethod for estimatingdrainage den- sity, Geology,2, 235-237, 1974. American GeologicalInstitute, Glossaryof Geology,American Geo- Maxwell, J. C., Quantitative geomorphologyof the San Dimas experi- logical Institute, Washington, D.C., 1972. mental forest, California, Tech. Rep. 19, pp. 1-95, Office of Nav. Anderson, H. W., Flood frequenciesand sedimentationfrom forest Res., Dep. of Geol., Columbia Univ., New York, 1960. watersheds, Eos Trans. AGU, 30, 567-584, 1949. McCoy, R. M., Rapid measurementof drainage density, Geol. Soc. Baker, V. R., Flood hazardsalong the BalconesEscarpment in central Amer. Bull., 82, 757-762, 1971. Texas: Alternative approachesto'their recognition,mapping and Melton, M. A., An analysisof the relation amongelements of climate, management,Bur. Econ.Geol. Univ. Tex. Circ. 7,5-5,1-22, 1975. surface properties and geomorphology, Tech. Rep. II, 102 pp., Baker, V. R., R. K. Holz, S. D. Hulke, P. C. Patton, and M. M. Office of Nav. Res., Dep. of Geol., Columbia Univ., New York, Penteado, Stream network analysis and geomorphic flood plain 1957. mappingfrom orbital and sub-orbitalimagery: Application to flood Morisawa, M. E., Quantitativegeomorphology of somewatersheds in hazard studiesin central Texas, NASA final project report, contract the Appalachian Plateau, Geol. Soc. Amer. Bull., 73, 1025-1046, NAS 9-13312, pp. 1-187, Nat. Tech. Inform. Serv., Springfield,Va., 1962. 1975. Patton, P. C., and V. R. Baker,•Low frequencyhigh magnitudefloods Beard, L. R., Flood flow frequencytechniques, Rep. CRWW-119, pp. and their relation to the morphology of streamsin central Texas 1-28, Univ. of Tex. Center for Res. in Water Resour., Austin, 1974. (abstract), Geol. Soc. Amer. Abstr. Programs,7(2), 224-225, 1975. Beard, L. R., Generalized evaluation of flash-flood potential, Rep. Rodda, J. C., The flood hydrograph,in Water, Earth, and Man, pp. CRWW-124, pp. 1-27, Univ. of Tex. Center for Res. in Water 405-418, Methuen, London, 1969. Resour., Austin, 1975. Schumm,S. A., Evolution of drainagesystems and slopesin Benson, M. A., Factors influencing the occurrence of floods in a at Perth Amboy, New Jersey,Geol. Soc. Amer. Bull., 67, 597-646, humid regionof diverseterrain, U.S. Geol. Surv. Water SupplyPap. 1956. 1580-B, 1-64, 1962. Sherman, L. K., The relation of hydrographsof runoff to size and Blyth, K., and J. C. Rodda, A stream length study, Water Resour. characterof drainagebasins, Eos Trans. AGU, 13, 332-339, 1932. Res., 9, 1454-1461, 1973. Shreve, R. L., Statistical law of stream numbers, d. Geol., 74, 17-37, Burkham, D. E., of Cornfield Wash area and effectsof 1966. land-treatmentpractices, Sandoval County, New , 1951-60, Shreve, R. L., Infinite topologicallyrandom channel networks,d. U.S. Geol. Surv. Water Supply Pap. 1831, 1-87, 1966. Geol., 75, 178-186, 1967. Butler, E., and R. E. Marsell, Developing a state water plan, Smart, J. S., Topologicalproperties of channelnetworks, Geol. Soc. Cloudburst floods in Utah, 1939-69, U.S. Geol. Surv. Coop.Invest. Amer. Bull., 80, 1757-1774, 1969. Rep. II, pp. 1-103, Utah Div. of Water Resour., Salt Lake City, Snedecor, G. W., and W. G. Cochran, Statistical Methods, Iowa State 1972. University Press,Ames, 1967. Carlston, C. W., Drainage density and streamflow, U.S. Geol. Surv. Stall, J. B., and Y. S. Fok, Dischargeas related to stream system Prof Pap. 422C, 1-8, 1963. morphology, in Symposiumon , pp. 224-235, Carlston, C. W., and W. F. Langbein,Rapid approximationof drain- International Associationof Scienceand Hydrology, Bern, 1967. density: Line intersectionmethod, U.S. Geol. Surv. Water Resour. Strahler, A. N., Quantitativeanalysis of watershedgeomorphology, Div. Bull. I I, 1960. Eos Trans. AGU, 38, 913-920, 1957. Chorley, R. J., Climate and morphometry,J. Geol.,65, 628-668, 1957. Strahler, A. N., Dimensionalanalysis applied to fiuvially erodedland Chorley, R. J., and B. A. Kennedy, Physical Geography.'A Systems forms, Geol. Soc. Amer. Bull., 69, 279-300, 1958. Approach,pp. 1-370, Prentice-Hall, EnglewoodCliffs, N.J., 1971. Tinkler, K. J., Active valley meandersin south-centralTexas and their Colwick, A. B., H. H. McGill, and F. P. Erichsen, Severe floods at wider implications,Geol. Soc. Amer. Bull., 82, 1783-1800, 1971. New Braunfeis,Texas, Amer. Soc. Agr. Eng. Pap. 73-206, 1-8, 1973. Trainer, F. W., Drainage densityas an indicatorof baseflowin part of Eardley, A. J., Geology of north-central Wasatch Mountains, Utah, the , U.S. Geol. Surv. Prof Pap. 650C, 177-183, Geol. Soc. Amer. Bull., ,55, 819-894, 1944. 1969. Gray, D. M. (Ed.), Handbookon the Principlesof Hydrology,Water Webster,N., Webster'sSeventh New CollegiateDictionary, G. and C. Information Center, Port Washington,N.Y., 1970. Merriam Company, Springfield,Mass., 1965. Hack, J. T., Studiesof longitudinal stream profiles in Virginia and Woolley, R. R., Cloudburst floods in Utah, 1850-1938, U.S. Geol. Maryland, U.S. Geol. Surv. Prof Pap. 294-B, 45-97, 1957. Surv. Water Supply Pap. 994, 1-128, 1946. Hadley, R. F., and S. A. Schumm, Hydrology of the upper Cheyenne River basin, U.S. Geol. Surv. Water Supply Pap. 1531-B, 186-198, 1961. (Received September23, 1975; Horton, R. E., Drainage basin characteristics,Eos Trans. AGU, 13, revised March 17, 1976; 350-361, 1932. acceptedMarch 22, 1976.)