VOL. 12, NO. 5 WATER RESOURCES RESEARCH OCTOBER 1976 Morphometry and Floods in Small Drainage Basins Subjectto Diverse HydrogeomorphicControls PETER C. PATTON AND VICTOR R. BAKER Departmentof GeologicalSciences, University of Texas at Austin, Austin, Texas 78712 Morphometric parameterssuch as drainage density,stream magnitude, and relief ratio are practical measuresof flood 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 channel system but fail to reveal numeroussmall gulliesthat may form portionsof hillslopehydrologic systems. Flood potential in 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-flash flood potential watersheds.For a given number of first-order channels (basin magnitude), flash flood regions 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 streamflows.Because a proper under- by Horton [1945] and Langbein et 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 drainage basin character- capabilitiesof the varioussources of morphometricvariables, istics,meteorological inputs, and flood hydrograph 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 discharge.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 return period 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, infiltration parametersthat are dependentin some way on one another. capacity of the terrain, and resistanceof the land to erosion 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 baseflow [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 stream order 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 streams (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