WATERRESOURCES RESEARCH, VOL. 29,NO. 7, PAGES2287-2297, JULY 1993 PaleofloodEvidence for a NaturalUpper Bound to FloodMagnitudes in the Colorado River Basin YEHOUDA ENZEL Departmentof PhysicalGeography, Institute of EarthSciences, Hebrew University, Jerusalem LiSA L. ELY, P. KYLE HOUSE,AND VICTOR R. BAKER ArizonaLaborators, for Paleohydrologicaland Hydroclimatological Analysis, Department of Geosciences,Universi.ty of Arizona, Tucson ROBERT H. WEBB U.S. GeologicalSurvey, Tucson,Arizona The existenceof an upperlimit to the magnitudeof floodsin a regionis a long-standingand controversialhypothesis in floodhydrology. Regional envelope curves encompassing maximum flood magnitudesstabilize with progressiveincreases in the areal coverageand period of observation (Wolmanand Costa, 1984). However, the short lengths of conventionalgaging records limit substantial advancesin testingwhether this stabilization is evidenceof an upperlimit. In the ColoradoRiver basin there are 32,120 stationyears of gagedata, but the averageperiod at a gagingstation is only 20 years, with most stationshaving less than 70 years of observation.Paleoflood magnitudes derived from sedimentsof large prehistoricfloods from 25 siteson riversin Arizonaand Utah provideadditional data to extend the records of the largestfloods. The paleoflooddata identify the maximum flood dischargesthat have occurred on individual rivers over the last several hundred to several thousand years. Even with this increasein the observationalperiod, the largest paleofiooddischarges do not exceedthe upper boundof maximumpeak dischargesdelineated by the envelopecurve derivedfrom the availablegaged and historicalrecords. This resultaccords with the hypothesisof an upper physical limit for flood magnitudesand suggeststhat, for the ColoradoRiver basin, the upper limit can be approximatedby existingsystematic and historical data for large floods.Similar relationshipsalso hold when paleofloodsand gagedrecords are presentedfor the subregionof southernArizona. INTRODUCTION crease in flood magnitudeas recurrence interval increases beyond 10,000 years and are consideredbounded distribu- Envelopecurves encompassingthe maximumflood peaks tions [Boughton, 1980]. These fundamental differencesbe- experiencedin a region have often served as guides in tween the deterministic and the stochastic approachesto seekingrules to aid prediction in flood hydrology[Creager, flood hydrology center around the existence of and the 1939;Crippen and Bue, 1977; Georgiadi, 1979; Crippen, ability to determine a hydroclimatologicalupper limit to 1982;Wolman and Costa, 1984; Dooge, 1986]. Like other flood magnitudein a specificbasin or a region [e.g., Horton, regionalizationtechniques, this graphicaland empiricalap- 1936; Yevjevich, 1968; Dooge, 1986; Klemeg, 1987]. proachis basedon the assumptionthat the maximumflood There are three basic approachesin estimatingthe magni- perunit drainagearea in one basinis likely to be experienced tude of extreme floods: (1) statistical methods including ina nearbybasin which is subjectedto similarhydroclimatic fitting a frequency distribution to a short series of flood controls[Mutreja, 1986,p. 676]. The conceptualbasis for the measurementsand extrapolating to rare (usually unmea- constructionof envelopecurves is essentiallydeterministic sured) event magnitudesand regional flood frequency anal- andrelies on the ergodicprinciple of space-for-timesubsti- yses,which have been shown to be superiorto the fittingof tution.Implicit in the approachare the assumptionsthat a distribution to short flood series [Potter, 1987; National thereare physicallimits to the supplyof precipitationto a ResearchCouncil, 1988], (2) deriving flood magnitudesfrom basinand to the watershed responseduring a flood- the estimationof hydrologic parameters for rainfall-runoff producingstorm [Yevjevichand Harmancioglu,1987]. In models,and (3) applyingempirically derived relationships contrast,a purelystochastic perspective on thehydrology of betweenflood dischargesand drainagebasin characteristics extremefloods implicitly assumes that the upperbound of a and/orregional climatic characteristics. According to Dooge fitteddistribution cannot be determinedin most caseswith [1986, p. 53S] none of the three approacheshas proven sufficientaccuracy; thus in the most commonlyused un- markedlysuperior to the other. Additionaldata from paleo- boundeddistributions there is an implicitassumption that floodstudies (see below) can contributeto improvingeach of thereis a nonzeroprobability that a largerflood will occur in theseapproaches [National Research Council, 1988]. a given basin. Several distributionsindicate a gradual in- Usually, the statisticalapproach assumes either no bound Copyright1993 by the AmericanGeophysical Union. or an indeterminate bound to flood magnitude so that the Papernumber 93WR00411. uppertail of the frequencydistribution includes discharges 0043-! 397/93/93WR-00411 $05.00 greatlyin excessof any observedflood. Use of thisapproach 2287 2288 ENZEL ET AL.: EVIDENCEFOR A NATURAL UPPERBOUND TO FLOOD MAGNITUDES results in assigninga nonzero exceedenceprobability to a conclusionwould have to belimited to theprevailing phys- flood of any magnitude.The rainfall-runoffapproach is iographicand hydroclimatological conditions of theregion exemplified by the derivation of the probable maximum andthe time scale that characterize the data base leading to precipitation (PMP) and probablemaximum flood (PMF). that conclusion.In contrast,if the paleoflooddischarges This procedure uses the deterministic "worst case scenari- exceed the modern curve, then the hypothesiscan be os" and assumesupper boundsto hydroclimatologicalpro- considered false. cesses [Hoyt and Langbein, 1955; Costa, 1987; Yevjevich and Harmancioglu, 1987]. DATA, METHODS, AND ASSUMPTIONS We concentratehere on the seeminglymuch simpler empiricalapproach to the understandingof extremefloods as Our studyfocuses on drainageswithin arid and semiarid expressedin the compilationof regionalenvelope curves of parts of the ColoradoRiver Basin in Arizona and southern maximum flood discharges versus drainage area. Several Utah (Figure 1), where a large numberof paleofloodstudies researchers have noted that incremental increases in the have been conducted. Modern and historical data were temporal and spatial base of the observationalrecord impart obtained from the U.S. Geological Survey WATSTORE progressivelysmaller changesin the form and position of data base. Gaged records were used regardlessof the station envelope curves of peak discharge versus drainage area length of observationor whether the data were from several [e.g., Creager, 1939;Matthai, 1969;Crippen, 1982;Wolman gagingstations within the samesubbasin; consequently, the and Costa, 1984;Costa, 1987]. While this phenomenoncan arealdistribution of thegaging stations may either underrep- be explained by probablisticreasoning [Yevjevich and Har- resent or overrepresent several subregionsin the Colorado mancioglu, 1987], it has also been hypothesized that the River basin. We included publishedpeak dischargeesti. apparent recent stabilization in the curves enveloping the mates for ungagedbasins as well as estimatesfor gaged maximum floods in the United States is indicative of the basinsthat were not part of the regular station records.For existenceof an upper limit to floodmagnitudes [Wolman and the sake of clarity, we included from this last type of data Costa, 1984; Costa, 1987] and is not simply a stochastic only thosedata pointswith magnitudessimilar to or larger phenomenon. It has also been hypothesized[e.g., Wolman than the gaged data. and Costa, 1984; Costa, 1987] that the upper limit of flood magnitudesis dictated by hydroclimatologicalprocesses and Accuracy of SystematicDischarge Estimates and Curve Construction basin characteristics.The hypothesisof an upper limit to floods has been difficult to substantiate because of obvious Accurate dischargemeasurements of the largestfloods are limitations on the rate of accumulation of observational data. critical for proper definition of the envelope curves. Inves- In this study we present a means of overcoming these tigation of each modern flood magnitude that controls the limitations by the addition of results from 25 palcoflood shape of the envelope curve (Figure 2, Table 1) revealedthat hydrology studies in the Colorado River basin to the data all are based either on indirect discharge estimates, on less base previously composed of only modern and historical accurateestimates of historicalfloods, or on extrapolationof data [see Webb et al., 1988]. This augmentationof the flood rating curves derived from much smaller floods. Most of record extends the effective length of observationat individ- these discharge estimates were rated as "poor" when orig- ual sites by hundreds to thousands of years and thereby inally carried out by the U.S. Geological Survey for reasons allows for an independent evaluation of the hypothesisthat suchas the complexityof hydraulic settingsand instabilityof an enveloping curve with a sufficiently broad spatial and flow hydraulics during the flood. Several of these were temporal data base stabilizes at a position approximatinga subsequently evaluated by hydrologists as substantially natural upper bound to flood magnitudesin a given region. overestimated [e.g., Carmody, 1980; Malvick, 1980] (see The combined gaging records in the Colorado River Basin below). We did not eliminate any estimatedflood magnitude total 32,120 station years. This