WATERRESOURCES RESEARCH, VOL. 29,NO. 7, PAGES2287-2297, JULY 1993

PaleofloodEvidence for a NaturalUpper Bound to FloodMagnitudes in the 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 , 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 total number of station years from our analysis, even if they were criticized by other appears impressively large, yet accepting these data as researchers.Most of the palcoflooddischarges (see below/ equivalent to real durations requires an untested assumption usedhere were estimatedat sitesin relativelystable bedrock of validity in space-for-time substitution.The real duration canyonsat reachesspecifically chosen to exhibit simpler of observation at any site in this basin is typically limited to hydraulicsto increasethe accuracyof the calculateddis- less than 70 years, with an average of only 19.8 years. Even charges. the addition of fragmentary historical observationsextends We used the procedureadopted by Costa [1987]to con- individual records to no more than 130 years. The value of structthe envelopecurves. This involvessimply selecting the palcoflooddata lies in the extensionof the real duration the uppermostdata pointsrepresenting the largestpeak of observation [Baker, 1987a, b]. Identifying the maximum dischargesover the entirerange of drainagebasin areas. An floods that have occurred over periods of hundreds to unsmoothedcurve was drawn to encompasseach chosen thousands of years provides a way to test the validity of datapoint, so the resultingenvelope includes some abrupt substitutingspace for time in this region. changesin slope. The purpose of this study was not to The extension of the temporal data base of extreme floods determinean exactrelationship, so equations for theresult- with palcoflooddata will test for consistencywith the upper ing curves were not determined. limit hypothesis as expressed by the regional envelope curves. If this large increase in record length does not raise Assumptions the envelope curves based on modem data, then it is likely that the regional synthesis of modern data is sufficientto In thisapproach it is assumedthat drainagearea is the define the upper limit of flood magnitude that can be ex- most significantfactor affectingmaximum flood discharge pected on a fiver, given its drainage area. Of course, the froma specificbasin [Horton, 1936; Matthai, 1990]. 'I'3fis ENZELET AL. EVIDENCEFOR A NATURALUPPER BOUND TO FILX)DM-XGNIrt DFa

B Es

!Oat•o Wyom•9 Lees

5

F1

Topock O

River

•12• 1 GiI lO

A 26 Liina TM

32 ø 3• 2

Tucson 150 ' km lO ø

Fig. 1. Locationsof extremelylarge flood discharges reported in the paleoflood,historical, or gagerecords in Arizona and southernUtah. The inset map showsthe entire Colon•doRiver basinand ,,e•erai of the main •tem ColoradoRiver gages (solid triangles). Large solid circles denote the location.,, of paleofioodsites (explanation of letters in Table 2). Small solid circlesdenote locationsof the largestsingle flood peak dischargesin the gagedand historical records in Arizona, southernUtah, and southv,.esternCalitbrnia. •,hich affect the envelope curves (explanationof numbersin Table1). TM representsthe location of fivesmall basins in theTortolita Mountains where paleofiood studie,• have been performed (see Table 2).

a.•umption has been criticized because some floods are cannot la5 an egg a .•ard in diameter: it would transcend knownto respondto partial or limited contributingarea nature',scapabilities under the circumstances. [, latthai, 1990].Alternatively, it hasbeen justified by dem- Benson[1964] concluded that drainage area is b.• far the onstratingthat, in specific regions, the largest floods are mostimportant basin characteristic in estimatingflood mag- relatedto and perhapscan be predictedfrom the drainage nitude in •everal states of the ,•outhx•estern United States. areale.g., summaryby Dooge [1986]). Fhisperspective can Roesl,e [1978, p. 33] concluded that lbr estimating the be tracedto classicalstudies in hydrology, includingthe magnitudeand fi-cqucnc5 of fiood•in Arizona,drainage area •ork of Horton [1936, pp. 437-438], who stated is the onl) •,tatisficall.ssignificant variable at the set level in Floodmagnitudes air, ays continue to increasea• therecurrence regressionanal.• sos. Other • ariable,,which .,,lightl.• impro•, e inter•,alincreases, but they increasetoward a definitelimit and the predictionof floodmagnitudes b:• the regres4onequa- notto•,• ard infinity.This is believedto be the morerational form tions tbr Ari,,ona were a•erage basin elevation and mean of expression.No terrestrial .,,treamcan producean infinite flood.A smallstream cannot produce a majorMississippi Ri• er annualprecipitation. For the sameregion, 3Iah'i•'i• [!%o] flood,for muchthe samereason that an ordinarybarnyard fowl identifiedbasin area as a major s,ariable and determinedan 2290 ENZEL ET AL.' EVIDENCE FOR A NATUIL&L UPPER BOUND TO FLOOD MAGNITUDES

lO5

...... I ...... t •,• tiC.,...... t:::,- l ..... ß -: !, / •( p •--'-'"•-F!;=- V 2'1= 22 -.•

...... • ...... '- -4 ' = • ½^ -• ',','• • .- ...... • "7'o 10 3 : ,3.$.q 8.0'o E"' "• •--P--•..z'- ' ....

• o2 ,_. .,'•'-',-,',,-' ',,2/'•••'•- ,' ;••••.'• • •.•.,,, ...... •__.l...... • •- : .•,' -'" C •,•.- '*-• , ½-.,.• •" ' :i••. •- _,.-x-,•.• '• ,, /N2O- AllFlood flood listeddtscharges in Table

I:• ½ •:, ,' ßI • •-g "A}•.•:&•='&• '• "% • I • I EnvelopeCurves: 10 ½.• • •'-•" ?';•..,•*,.•%•., •.• • ...... :;•:'"-• ...... I Ah-Fo tr eentireU..S(Costa, 1987). • ,:" ½•"•--,•=•7•?,'"•' •. -, -•; I B-For paleoflood - [- • -' ",.,••;¾'•.•'•:• :'I, '•' .: ' ] Cga- For gdandhe itsroicdata I- •" "" -"I •. ½,,.., • -• ,, .,." L...... / , ,• ...... ••? ...... •i ...... i ...... t ...... i ...... 1 10 102 103 104 105 10 Area(kin 2)

Fig. 2. Largest modern, historical, and palcoflood peak dischargedata for each station or site in the Colorado River basin and the envelope curves: the entire United States (curve A) the palcoflood data (curve B), and the Colorado River drainage basin (curve C) from U.S. Bureau of Reclamation [1990], which constructedthe curve for drainage basins with areas>250 km2. We extendedthe curve(dashed line) to encompassbasins with smallerdrainage areas. Triangles and circles denote all the data available for the largest flood magnitudesat each gaged or ungaged site; circles denote those data points which can affect the envelope curves (Table 1, Figure 1). Solid squares denote the palcoflood data (Table 2, Figure 1).

upper envelope curve for the gaged record of floods, which Palet:ttoods Hydrology also encompasses all estimated historical floods in the re- In appropriate settings, fine-grained flood depositsand gion. Malvick claimed that the addition of average elevation other paleostage indicators (e.g., silt lines and scour line•,• and mean annual precipitation does not significantly change provide a long record of large floods. During large floodsin the results. stable bedrock canyons, fine-grained sand and silt fall rap- The principal limiting factors controlling the magnitude of idly out of suspension in areas of markedly reduced flo• extreme floods are the amount, intensity, duration, and velocity, such as back-flooded tributary mouths and eddies distribution of precipitation over the entire drainage basin. It at channel irregularities [Baker, 1975; Patton et al., 1979; can be assumed that during all the largest flood-producing Kochel and Baker, 1982; Kochel et al., 1982: Baker, 1987a: storms the contributing areas from a specific basin will be Baker and Kochel, 1988]. At some sites, stratigraphic similar or, alternatively, that the basin produces large floods recordsof multiple floods span several centuriesor millen- in a similar manner (e.g., high elevation area within the basin nia, and the individual flood depositscan be distinguished contributes to the runoff or integration of flood peaks from several tributaries). For example, integration of runoff oc- through sedimentologicalcriteria. Evidence of the largest curs in arid drainage basins mainly during extremely rare and floodsis selectivelypreserved; deposits from smallerfloods lie closer to the active river channel and are more likely to be intense rainfall events [Wolrnan and Gerson, 1978]. These assumptionsunderlie both the envelope curve construction removedby subsequenterosion [E/y and Baker, 1990].A and the determination of a design flood by modeling basin close distancebetween paleoflood study sites and gaging hydrology. stationsis desirableto calibrateand comparebetween the A related assumptionunderlying these approachesis that two types of data. Unfortunately, such coincidencei• rare the largest recorded floods resulted from precipitationpat- andonly a smallnumber of the paleoflooddata are from the terns that were optimal for runoff generation in a particular same sites as the historical and modern floods. In this .•tud.•, basin and that the preferred precipitation patternsfor gener- only the largestflood recorded at a site by flooddeposits ating floods are therefore included in the data. This implies and/orother paleostage indicators is considered.The ages of that the data that define the envelope curve are from basins the floodswere determined for mostpaleoflood studie, b.• that produce the lai'gestfloods because their shape,orienta- radiocarbondating of associatedorganic or archeological tion, elevation, and vegetation distribution are optimal for material.These dates establish the floodchronology and aid flood generation. It should be emphasized that the limiting in determiningthe totallength of the recordchronicled b) flood hypothesisdoes not imply that all drainagebasins in the paleoflood deposits. the selectedregion have the potential to producea discharge Paleoflooddischarge estimates are calculatedby compar- at the level of the regional envelope curve, but rather it ing the heightsof flood paleostageindicators with •,tter indicates that they will not naturally produce floods that surfaceprofiles calculated by the step-backwatermethod exceed the curve. [O'Conno• and Webb, 1988]. The elevation of a g•ven ENZELET AL.: EVIDENCEFOR A NATURALUPPER BOUND TO FLOODMAGNITLtDES 2291

TABLE 1. FloodsThat Control the Positionof the EnvelopeCurve of Arid and SemiaridParts of the ColoradoRiver Basin

Number Peak in Drainage, Discharge, Station Name Figure2 Area,km' m3 s-• Year

Copper Hill Wash at Globe, Arizonaa I 4.1 91 1904 San Pedro Tributary near Pomerene, Arizona': 2 9.7 !87.9 1948 9487100 Little , Arizonaa 3 30 390 1962 BroncoCreek near Wikieup, Arizona a't' 4 49.2 2080 1971 Eldorado Canyon at Nelson Landing, Nevadac 5 59.3 2152 1974 DragoonWash at St. David,Arizona "'b 6 86 1530 1975 TontoCreek Below Kohl's Ranch, Arizona a'a 7 62 521 1970 BlackCanyon Wash near Wickenburg, Arizona '•'t' 8 73.8 905 1964 9484570 near Pantano, Arizona a 9 99.4 765 1958 Picacho Wash at All American Canal, California e'a 10 107.4 1050 1939 '9498870 RyeCreek near Gisela, Arizona d'a 11 315 1255 1970 9478500 QueenCreek at WhitlowDamsite near Superior, Arizona 1;a 12 375 1215 1957 9515500 HassayampaRiver at Box Damsite near Wickenburg,Arizona a 13 1080 1645 1970 9473000 AravaipaCreek near Mammoth, Arizona h 14 1390 2005 1983 9512800 near Rock Springs,Arizona 15 2875 2405 1919 9471000 SanPedro River at Charleston,Arizona a'i 16 3195 2775 1926 AguaFria River at LakePleasant, Arizona aJ't 17 3780 2975 1916 9473100 San Pedro River below near Mammoth, Arizona 18 11,240 3910 1983 9426000 Bill WilliamsRiver belowAlamo Dam, Arizonaa'l 19 11,995 5665 1891 9508500 below Tangle Creek, Arizona 20 15,175 4250 !891 0512170 at Arizona Dam near present Granite Reef Dama'm 21 34,240 8500 1891 9519500 below Gillespie Dam, Arizona 22 128,540 7080 1891 9380000 Colorado River at Lees Ferry, Arizona 23 289,440 8500 1884 9402500 Colorado River near Grand Canyon, Arizona 24 366,590 8500 1884 9424C•30 Colorado River Near Topock, Arizona 25 456,420 11,330 1862 9521000 Colorado River at Yuma, Arizona 26 628,840 7080 1916

Data have been provided by U.S. GeologicalSurvey gRecentfield work and step-backwatercalculations indicated WATSTORE data base, except when specified. that the peak is overestimated(G. Benito-Ferrandez,L. L. Ely, "Discussedin detail by Carmody [1980]. Y. Enzel, unpublisheddata, 1990). bAldridge[ 1972] and/or Aidridge [1978]. hRoberts[1987] estimated the peak of thisflood to be muchlower. CGlano,and Harmsen [1975]. /SeeU.S. Geologicalsurvey microfilm, reel 151. dSeeU.S. GeologicalSurvey Water Supply Paper 2052. JFromSmith and Heckler[ 1955]. eSeeU.S. GeologicalSurvey Water SupplyPaper 967-A. •U.S. GeologicalSurvey microfilm, reel 198; fU.S.Geological Survey microfilm, reel 454. {Seealso U.S. GeologicalSurvey Water Supply Paper 1049. mU.S. GeologicalSurvey microfilm, reel 392.

depositprovides a minimumestimate for the peak stageof Hydrauliccomplications can arisefrom the natureof a the associatedflood. However, in several cases, the heights specificfiver reach.The expandingalluvial reach of the Salt of the depositsclosely approximate the actual stageof the River, near Phoenix, Arizona posedthe largestproblem for floodpeak. This has been demonstratedby flume studies thehydraulic modeling of the paleoflooddischarges {Table 2) [Kochel and Ritter, 1987: Baker and Kochel, 1988], obser- [Fuller, 1987].This reach was studiedin part to extendthe vationsof modern and historical flood deposits,comparison paleoftoodmethodology described above to moreproblem- withgaged discharges, and field observationsof the close atic settings.Other than this one study, the paleoflood relationshipbetween flood depositsand diagnostichigh- methodologyused for data reported herein corresponds water marks such as scour lines and silt lines plastered on strictlyto the"slackwater deposit and paleostage indicator" channelwalls [Ely andBaker, 1985;Baker, 1987a;Partridge (SWD-PSI) technique[Baker, 1987a] appliedeither to sta- andBaker, 1987; O'Connor et al., 1986a, b; R. H. Webb, ble-boundaryreaches or to reacheswith well-knowngeom- unpublisheddata, 1992]. Kochel [1980] estimatedthat de- etry. Dataobtained through other paleoflood reconstruction positheight was 10%less than actual water surface elevation techniques,including regime-based procedures and paleo- andR. H. Webb (unpublisheddata, 1992)has documented competencestudies, are not includedin the maximumpeak silt lines {high water marks) 50 to 90 cm higher than paleoflooddischarge data base{Table 2). associateddeposits. In severalof thepaleoftood studies cited In Table 2 the dischargesare listedaccording to the ranges in Table 2, the resultsare based on silt lines, scourlines, or reportedby theoriginal researchers, and they are the largest debristhat indicatemaximum flood stage.Thus the quoted paleoflooddischarges in eachof the studiedbasins in Utah dischargesare directlyassociated with the largestflood that and Arizona {Figure !). All of these paleoflood studies hasoccurred at the site over the periodof the paleoflood involvedpast and present researchers at the ArizonaLabo- record.While we stressthat the paleoflooddischarges based ratoryfor Paleohydrologicaland HydroclimatologicalAnal- ,solelyon the height of flooddeposits are minimum estimates ysis(ALPHA) in the Departmentof Geosciencesat the ofthe peak discharge, considerable experience demonstrates University of Arizona.Because no evidencewas cited by the that:discharge underestimation is probably 20% or less[e.g., originalauthors to suggestcauses of floodsother than Kochelet al., !982].Baker [1987a] reviewsthe field obser- precipitation,we assumethat all thelisted paleofloods were vationsthat justifies this conclusion. formedthrough rainfall-runoff processes {i.e., no natural 2292 ENZEL ET AL.' EVIDENCE FOR A NATURAL UPPER BOUND TO FLOOD MAGNITUDES

TABLE 2. Summary of Estimated Paleoflood Magnitudes

Maximum Peak Code in Dischargeof Largest Figures Drainage Paieoflood, Flood, in River/Site a 2 and3 Area,km2 m3 s- • years Data Source

Colorado River, Arizona C 279,350 13,600-14,200 -•4000 Ely et al. [1991]J. O'Connor,L. Ely, E. Wohland others (unpublished data, 1993) Verde River, Arizona V 14,240 5000-5000 2000 Ely andBaker [1985]' O'Connor et al. [1986a] Salt River, Arizona S 11,150 4100-4600 2000 Partridge and Baker [1987]and O'Connoret al. [1986a] Salt River, Arizonab P 33,650 8500-9900 1000+ Fuller [ 1987] 11,300-12,700 , Arizona T 1630 800-1000 •500 O'Connoret al. [1986a]and Ely et al. [1988]. Aravaipa Creek, Arizona A 3160 970 •900 Roberts [ 1987] Redfield Creek, Arizona R 285 350-400 •1000 Wohl [ 1989] Oak Creek, Arizona O 1213 1350 >)100 Melis [1990] and T. S. Melis (personal communication, !991) East Fork, Utah E 840 800-850 1000 + Y. Enzel, L. L. Ely, and R. H. Webb (unpublished data, 1990) Virgin River, Arizona Vi 10,306 1700-1900 1000+ Enzel et al. [1993] , Utah K 5370 400-600 c --500 Smith [1990] and S.S. Smith (personal communication, 1991) EscalanteRiver a, Utah Es 820 700-750 1000+ Webb [1985]; Webb and Baker [1987]; and Webbet al. [ 1988] Es 1990 1250-1550 Es 3290 1850-2100 Es 4430 860-940 Boulder Creek, Utah B 450 350-450 500+ O'Connor et al. [1986b] Tortolita Mountains, TM House [1991]' P. K. House (unpublisheddata, Arizona 1992) Cochie C1 9.8 60-80 "' Wild Burro WB 11.1 120-150 "' WB 18.1 200-300 "' House et al. [1991] Ruelas RU 6.0 80-100 --' Prospect Pr 9.6 40-50 600+ Cafiada Agua Ca 4.7 30-50 White Tank Mountains WT 14.6 57-142 --' P. K. House (unpublished data, 1992), CH2MHilt Arizona and French [1992] Tiger Wash., Arizona TW 220 283-382 P. K. House (unpublished data, 1992), CH2MHill and French [1992] Sierra Estrella, Arizona SE 2.8 21-29 P. K. House (unpublished data, 1992), CH2MHill and French [1992]

aSee Figure 1 for locations. The paleofloodsare plotted in Figures1, 2, and 3 accordingto site code except for the Tortolita Mountains paleoflood estimates which are represented in Figure 1 as TM. bSaltRiver downstream of theconfluence of theVerde River; Explanding flow can cause large overestimation. CTheactual largest flood was largerthan reportedby Smith [ 1990].He identifiedfield evidencefor a largerflood locatedin a channelreach which is difficult to model (S.S. Smith, personal communication, 1991) aDifferent sites on the fiver.

dam failure). Thirteen of these paleofloods are the largest in paleoflooddata from the ColoradoRiver basin.A compari- at least the last 500 years and eight are the largest during the son between the United States curve and the gagedand last 1000-4000 years (Table 2). Flood frequency analyses historical data from the Colorado River basin indicates that based partly on the inclusion of paleofloodmagnitudes for drainagesin the ColoradoRiver basinproduce systemati- the Salt, Verde, and the Colorado Rivers, have shown that cally smallermaximum flood peaks than drainagebasins in these floods have recurrence intervals of > 1000 years [Ste- other regionsof the United States.The U.S. Bureau dinger et al., 1988; Webb and Rathburn, 1989; Ely et al., Reclamation[1990] envelope curve for the largestfloods in 1991]. the ColoradoRiver basinis alsoplotted in Figure2, andwe useit asthe envelopecurve for gagedand historical floods. RESULTS AND DISCUSSION This curve was originallyconstructed only for drainage Figure 2 shows the magnitudesof the largest maximum basinswith areasgreater than about250 km2, andit• peak dischargesrecorded in each gagingrecord from drain- extensionto the smallerdrainage basins was estimated for age basinswith areasgreater than 1 km2 in the entire the purposeof this study.This extensionis some•hat Colorado River basin. The largest floods, which directly problematic,because it excludesthe threelargest affect the position of the envelope curve, are marked in magnitudeestimations (Bronco Creek near Wikieup. Ari- Figures 1 and 2 and listed in Table 1. Curve A in Figure 2 zona;Eldorado Canyon at NelsonLanding, Nevada: and encompassesall of the largestflood magnitudes in the United DragoonWash at St. David,Arizona; points 4, 5, and6 in Statesas reportedby Costa [1987]. Curve B is definedby the Figure2). Costa [1987] suggested that any flood estimate that ENZELET AL.: EVIDENCE FOR A NATURALUPPER BOUND TO FLOOD MAGNITUDES 2293 fallsabove the envelopeshould be carefullyreexamined, The palcoflooddischarges fall on or below the curvewhich especiallyif it occurredin an areaprone to debrisflows or envelopesthe largestgaged and historicalfloods (Figure 2). hyperconcentratedflows, such as the steep canyons of the Althoughthese palcoflood discharges represent much longer southwesternUnited States.Although Costa referred to the periodsof recordand are usually larger than modernfloods United States curve, we use his suggestionalso for the in the individual rivers where they were studied, they regionalcurves. neverthelessare remarkablysimilar to the magnitudesof the In unpublishedreports, Carmo4, [1980] and MaMck largestmodern or historicalfloods in the region.The relation [1980]reanalyzed the largestreported floods that fall above betweenpaleofiood discharges and the regional envelope the Arizona regional envelope curve and concludedthat curve for the Colorado River basin is consistent with the mostof them were overestimated.Carmo•, [ 1980]evaluated conceptthat there is a physical or hydrometeorologicallimit thetwo Arizona floods(Bronco Creek and DragoonWash) on the magnitudeof the maximum flood that can be expected andconcluded (1) that the hydrauliccharacteristics implied in a given drainagebasin [Costa, 1987]. bythe Bronco Creek estimate were physically untenable, and The existenceof a natural upper limit would raise ques- (2)that the necessaryprecipitation to generatethe Dragoon tionsabout the basicassumption, intrinsic to frequentlyused Washflood did not occur in the regionon July 22, 1975. statisticalflood frequency models, that the upper bound on Thereis a significantdiscrepancy between Carmody's and flood magnitudescannot be determined and that they are theoriginal investigator's [Aidridge, 1978] findings regarding beyondthe rangeof practical concerns.Arguments against this date and the recorded rainfall amounts and intensities. an upper limit, or for infinite-tailed distributions, have been gAdridgeclaims that the Dragoon Wash flood occurredon challengedbefore." ßß ß One can sometimes hear that there July25, 1977,and reportsprecipitation amounts 3 to 4 times is no [upper] limit since there always could be, say, 1 mm greaterthan those reported by Carmody;however, Aidridge more rain than there is in any conceivable rainstorm. This is [1978]provides a descriptionof the studyreach that reveals a fallacious argument following from the inability of the a 2 m discrepancyin the water surfaceelevation on opposite humanmind to stopextrapolating which -- - may easily lead banks and run-up in excess of 3 m on a sloping bank a hypotheticalß ß ß analyst to calculate the "probability" of a perpendicularto flow. These hydraulicconditions make the horse-sizeand even an elephant-size dog" [Klemeg, 1987,p. reach inappropriate for slope area calculations, and the 9]. resultingdischarge estimated is highly suspect. Another important result noted by combiningthese data is In the case of Bronco Creek, Carmody baseshis criticism the potential effect of climatic variations on flood magnitudes on the claim made by Aidridge [1972] that the flow was for the rarest events. The influence of climatic variability on subcriticalupstream of a bridge constriction used in the the occurrences of extreme floods has been recognized at dischargeestimation even though the implied flow condi- several time scales, and mechanismsto explain this associ- tions(depth and velocity) results in a Froude numberof 1.7 ation have been suggested[Knox, 1983; Webb, 1985; Baker, in that reach. This indicates that the hydraulic situation was 1987b; Enzel et al., 1989, Ely and Baker, 1990; E/y, 1992; not characterizedaccurately. Furthermore, Aidridge [1978] Eb' et al., 1992; Enzel, 1992; Webb and Betancourt, 1992]. reportsthat, in order to convey the flow through the con- Climate has also varied over different temporal scalesduring strictionat the depth indicated by high water marks, a mean the late Holocene [e.g., Bradley, 1985], the period for which velocityof about25 m s-• is required.A velocityof this palcoflood data are available. However, not one Colorado magnitudeis highly unlikely if even physically possible. River tributary, where a palcoflood study has been per- Clearly,the dischargeestimate for Bronco Creek is ques- formed, has produced a flood with a magnitude greater than tionable. The Eldorado Canyon flood estimate was not the flood expected from the envelope curve of the modern reviewed by Carmody because the drainage lies outside record. For example, during the last 4000 years in the nearby Arizona, but it was described as "poor" by the original Mojave River basin of southern California, episodesof researchers[Glancy and Harmsen, 1975]. frequent large floods with magnitudescomparable to the We did not changethe extensionof the U.S. Bureauof largestmodern floods were able to produce perenniallakes Reclamation'scurve to include thesefloods (Figure 2) and if [Enzel et al., 1989]. However, a hydrologic model of the themodern and historical envelope curve is raisedto include basinand lakes showedthat floods that producedthese lakes eitherthese flood magnitudesor correctedmagnitudes, it couldnot have been much larger than the largestobserved in will notchange the basicpatterns identified in thisstudy. the modern and historical records [Enzel, 1992]. The in- Althoughwe are concernedabout the accuracyof these creasedfrequency of the large floodswas not associatedwith criticaldischarge estimates, we directedour effortsat iden- increasedmagnitudes as would have been the caseif a flood tifyingthe general position and trend of the upperbound and frequencydistribution had been fitted. Rather, thesetrends itsrelation to thepalcoflood data. Therefore curve C (Figure are consistent with a frequency distribution that has a 2) encompassesall of the floodsexcept those which are truncatedupper tail. obviouslyquestionable. This curvecan be usedas a tool to Data available for the entire Colorado River basin are identifythose floods which warrant a reexamination,similar includedin Figure 2. The maximum floodsthat occurred in to the suggestionof Costa [1987] and the practiceof Car- drainagebasins within arid and semiaridsouthern Arizona mody[1980] and Malvick [1980]. are shownin Figure 3. Excluded from this figure are gaging stations on the main stem of the Gila River, basins that drain to the Gila River from the north and have headwaters in high Palcoflood-RegionalEnvelope Curve Relationships elevations, and one station that is clearly affected by urban- In the ColoradoRiver basin, a substantialincrease in the ization in Tucson, Arizona. The resulting curve for the temporalscale of floodrecords does not changethe position southernArizona subregiondiffers slightlyfrom curve C for ofthe envelope curve based on the gaged and historical data. theentire Colorado River basin. Smaller basins 10.2-1 km2l 2294 ENZEL ET AL.' EVIDENCE FOR A NATURAL UPPER BOUND TO FLOOD MAGNITUDES

10 4

,.., 10 3 Ru WB•, I•, '",,, ,• ••••• '" • • 10•

tu 10 • o • Pr A 10 o /• & - Paleofloodmagnitudes ,• - Gaged data

10 '• 10 0 10 • 10 2 10 3 10 4 10 s DrainageArea (km2)

Fig. 3. The relationshipbetween the envelopecurve for the singlelargest peak dischargesin each stationin southern Arizona and the paleoflooddata for the same region. See Table 2 for explanation of letters.

were included in the curve for southernArizona, becausethe Althoughinteresting scientifically, key questionsregard. paleoflood data for the smaller sized basins are exclusively ing envelope curves [Wolman and Costa, 1984] are whether from that region. Paleoflood magnitudeswere estimatedfor they can be sufficiently precise, objective, and usefulfor five small drainage basins in the Tortolita Mountains north of engineeringpurposes. We do not attempt to answerthese Tucson, Arizona, for one basin in the White Tank Moun- questions, but we note that agreement between the curves tains, for Tiger Wash near the Harquahala Mountains, and and the paleoflood data for this particular region addsa new for one basin in Sierra Estrella west of Phoenix, Arizona level of confidenceto the method. Almost all reportsrelated (Figure 1, Table 2) [House, 1991; House eta!., 1991; to envelopecurves add a disclaimerthat they are onlyuseful CH2MHill and French, 1992;also P. K. House, unpublished as a first test of expected flood magnitude estimatedby other data, 1992]. Only one radiocarbon date is available for these means. The intent of such statements is to reduce strict paleofloods (Table 2). Even so, field evidence and relative reliance on such curves [e.g., Crippen, 1982]. However, age dating indicate that they are the largest floods to have Costa [19871,who showsmore confidencein the significance occurred in these ungaged basins during at least the last of the information derived from envelope curves, statesthat several hundred years [Baker et al., 1990; House, 1991]. if a computedflood dischargefor a given drainagearea plots All of these paleoflood dischargesplot on or below the well above the curve, the flood needs to be carefully reex- envelope curve constructed from the gaged data from south- amined. In this presentation we do not intend to develop ern Arizona (Figure 3). The relationshipbetween the paleo- maximumflood relations to be used in hydrologicalapplica- flood dischargesand the regional envelope curves is consis- tions but rather to point toward a phenomenonborne out tent in including an upper limit to flood magnitudesin both from the combinationof paleoftoodand gaged data. The the entire Colorado River basin and the southern Arizona results from the Colorado River basin demonstrate that subregion. Initial analysis of other subregions within the muchmore information is presentin the peak dischargesof lower Colorado River basin indicates that they have substan- the largest floodsthan is generally acknowledged. tially different envelope curves. Also, different types of The observationsreported here generallysupport the storms produce the envelope-shapingfloods in each subre- assumptionunderlying the designstorm approach in which gion, indicating that hydroclimatology plays a major role in an extreme storm is determinedfor a given basinand the defining the curves. Although it is assumedby the authors dischargeof the resultingflood is calculatedusing rainfall- that hydroclimatology is the cause for the upper limit of runoff modeling.Nevertheless, specific PMF and 100-year floods claimed by Wolman and Costa [1984]. Additional flood estimates available to us exceed values estimatesfrom research on these issuesis required. theenvelope curve, some by a greatamount. Consequently, they are alsoin excessof the largestpaleoflood discharge Applications of Regional Envelope Curves estimatesfor the correspondingdrainage basins (Table 3}. The largestfloods axe responses to the mostextreme rainfall This inconsistencybetween the PMF estimatesand the conditionsthat have occurredin both the historicaland prehis- actualregional data (gaged,historic, and paleofloodslisa torical periods.They representprobably the bestnatural ana- causefor concern.It mayindicate that, for this hydrologic• log to a watershed hydrologic model that is available for region, either the understandingof extremerainfall events integratedresponse of a drainagebasin to extrememeteorolog- usedin constructingthe PMP and the subsequentbasin ical conditions.The peak dischargesfrom the biggestfloods responsesis deficient, or a failurein themodel construction, that are characteristicof a givenregion axe those controlling the Both physiographicand hydroc!imatologicfactors may shapeand positionof the regionalenvelope curve. Therefore contributeto the results obtainedfor the ColoradoRiver we think that these curves embody critical informationon the basin.It is a regionof immensevariability in reliefand nature of regionalflood magnitudes. climate.The high spatial and temporal variability of rainfall ENZELET AL.: EVIDENCE FOR A NATURAL UPPER BOUND TO FLOOD MAGNITUDES 2295

TABLE3. ComparisonBetween the Magnitudes (incubic meters per second) ofthe Largest Flood Estimated Using Envelope Curve PublishedProbable Maximum Floods, !00-Year Floods, and Gaged, Historical, andPalcoflood Data for Selected Drainages in the ColoradoRiver Basin

Flood Magnitude MaximumPeak Discharge Probable Estimated From Maximum 100-Year Envelol•, DrainageBasin Paieofiood Historical Gaged Flood Flood m3 s-I

ColoradoRiver (Lees Ferry, Arizona) 13,600-14,200 8500 6230 19,700" 5370b •-13,000 Verde River, Arizona 5000-5400 4250 2690 21,640c 4500b 18,970c SaltRiver, Arizona 4100-46(10 4250 3310 19,200c 4670/• 500O 28,320 c VirginRiver (Littlefield, Utah) 1700-1900 ---1000 d 1000 2,950e 1330f 290O AguaFria River (RockSprings, Arizona) '" 2407 1670 515Yr 28ffi TontoCreek (near Roosevelt, Arizona) 800-1000 --- 1747 2860f 23• Oak Creek (near Cornville, Arizona) 1350 '.- 748 --- 1220f 2220 CochieCanyon (near Tucson, Arizona) 60-80 ...... 190ß 2• ProspectCanyon (near Tucson, Arizona) 40-50 ...... 185* 210

, aU.S. Bureau of Reclamation [1990]. bAndersonand White[1979]. cj. Keaneof theSalt River Project (written communication, 1984) provided the PMFs by the U.S. Bureauof Reclamation(top) and the U.S.Army Corps of Engineers(bottom) for theVerde and Salt Rivers. See also Brown [1988]. dltis believed that the 1862 flood was comparable insize to the 1966 flood [Butler and Mundroff, 1970], but it alsomay be larger. eForBloomington, Utah: smaller than the area which drains to theLittlefield, Arizona, station, U.S. Army Corps of Engineers[1973]. œGarrettand Gellenbeck[1991]. *House [1991].

andrunoff, the diversityof runoff-producingprocesses, and Arizona indicatesthe high variability of the floods in this othercomplexities pose severe problems in sucha regionfor region. modelparameterization and verification [Pilgrim et al., For floods in the Colorado River basin, the rarer annual 19t•]. Nevertheless,the range of processesalso means that peaks can be immensely larger than the more common subregionswill exhibit those combinationsof factorsthat are peaks, while for Northeastern floods they are only slightly optimum for the concentration of overland flow and the larger. The "barnyard fowl" analogy of Horton [1936] may orientationrelative to storm tracks for generatingfloods of have a corollary that is applicable here. The Northeastern thehighest magnitude characteristic of the region.Thus the fowl with a gradualgrowth curve of eggsize, mightnot easily variabilityinherent in the smaller,more frequent floods does foreseeits egg-layinglimit at a reasonableprobability level; notextrapolate directly to the propertiesof the largestrarest however, the Colorado basin fowl is faced, at least locally, floodsindicated by a very large samplein time andspace. A with a catastrophicgrowth curve. There may be limits both deterministicpattern (Figures 2 and 3) emergesfor the to eggsand floodsbut the ability to foreseethem may vary largestand rarest eventsthat cannotbe predictedthrough considerablyfrom region to region. simpletheoretical extrapolation of trends apparentin the A caveat is in order for those whose interest lies in statisticsof smaller,more frequentfloods. identifyingan upper limit to flood magnitudein a specific Theabove hypothesis may applymore to semiaridregions watershed.The envelope curve, confirmedby palcoflood of high flood variability than to humid regionsof low data from the last few thousands years, is a potential variability.A simplerationale can be foundin Beard's[1975] indicatorof that limit, and in someregions, one that may be flash-floodmagnitude index F, definedas superiorto approachesrelying on extrapolationfrom much shortertemporal records. However, the envelopecurve will not provide the magnitude for the largest flood to be ex- r =k N _ pectedin a specificbasin. Such a determinationis bestmade where by usingsite-specific palcohydrological information. It must be emphasizedthat the deterministicand stochas- X=Xm-M (2) tic approachesare philosophicallydistinct. The envelope andX,n is the annualmaximum flood, M is the meanannual representsaveraged conditions over a region. It showsthe floodof the annual peak series and N isthe number of events habitual natural response of that region in terms of the inthe series (Xm, X, M areall expressedas logarithms).largest, rarest events. The extrapolationof short-termdata Thisindex is simplythe standard deviation of thelogarithms and/or the modelingof parameters idealized to characterize ofthe observed annual flood series, and it is usefulmeasure the regionboth convey the specifictheoretical responseof forcontrasting regional flood frequency characteristics. Val- basinsconsidered to be representativeof individualcases in uesof F in the ColoradoRiver basinrange from 0.2 in the the region. It is hopedby some in science,without testing, ColoradoRockies to 0.9 in the Arizonadeserts. The latterare that thesetwo approacheswill convergeon the sameresults. equivalentto the highestin the UnitedStates [Beard, 1975; For ColoradoRiver basin peak flood data, conventionaland Baker,1977]. Values in the northeasternUnited States, in palcofloodcombined, it seemsthat the convergencehas not contrast,range from 0.2 to 0.3. The valuefor thearid portion of yet been achieved. 2296 ENZEL ET AL.: EVIDENCE FOR A NATURAL UPPER BOUND TO FLOOD MAGNITUDES

CONCLUSIONS Southwest,U.S. Geol.Surv. Water Supply Pap., 1580-D, D1- D40, 1964. Discharges reconstructedfrom paleoflood data in the Boughton,W. C., A frequencydistribution for annual floods, Water Colorado River basin do not alter the positionof regional Resour. Res., 16, 347-354, 1980. flood envelopecurves based on gagedand historical records, Bradley,R. S., QuaternaryPaleoclimatology, Allen and Unwin, Winchester, Mass., 1985. despiterecording several thousand years of extreme events Brown,T. A., Safetyof dammodifications for Salt andVerde at multiple sites. The result is best explainedby the exis- Rivers--Overview,in A ReclamationProject: The Changing tence of a physical upper limit to flood magnitudesthat has Times,8th Ann. Lect. Ser., U.S. Committeeon Large Dams, Salt persistedthrough the last severalcenturies to millennia.The River Project, Tempe, Az., 1988. result also indicatesthat extremesin precipitationintensity Butler, E., and J. C. Mundorff,Floods of December1966 'm southwesternUtah, U.S. Geol.Surv. Water Supply Pap., 1870-a, and areal coverageof stormsduring the last severalcenturies A1-A40, 1970. havenot beenlarger than the extremesobserved in the gaged Carmody,T., A critical examinationof the "largest"floods in record. Our primary conclusionis that it is unlikely that any Arizona:A studyto advancethe methodologyof assessingthe drainage in the Colorado River watershedwill producea vulnerabilityof bridgesto floodsfor the ArizonaDepartment of flood that exceedsthe curve. Any preliminaryflood magni- Transportation,Gen. Rep. I, 53pp., Eng. Exp. Stn. Coll. of Eng., Univ. of Ariz., Tucson, 1980. tude estimatesthat appear to exceed this curve shouldbe CH2MHill, and R. H. French, Alluvial fan data collectionand very carefully reviewed for methodologicalproblems in monitoringstudy, final report, 204 pp., Flood ControlDist. of discharge estimation. Maricopa County, Phoenix, Ariz., 1992. Costa, J. E., A comparisonof the largestrainfall-runoff floods in the United Stateswith the People'sRepublic of Chinaand the world, Acknowledgments. We thank Robert McNish and R. D. Jarrett J. Hydrol., 96, 101-115, 1987. (USGS) for providing us with the gageddischarge data. We thank Creager,W. P., Possibleand probablefuture floods,Civ. Eng. the past and present members of ALPHA, who have studied the N.Y., 9, 668-670, 1939. palcoflooddeposits during the last decade and discussedthem with Crippen, J. R., Envelope curves for extreme flood events,J. us (J. Fuller, J. Partridge, T. Melis, J. O'Connor, L. Roberts, S. Hydraul. Eng., 108, 1208-1212, 1982. Smith, and E. Wohl). The constructivereviews by Bob Jarrett, Jim Crippen, J. R., and C. D. Bue, Maximum floodflowsin the conter- O'Connor, John Costa and anonymousreviewers, and discussions minousUnited States, U.S. Geol. Surv. Water SupplyPap., 1887, with K. Hirschboeck were essentialto this manuscript.This re- 52 pp., 1977. search was supportedby the EngineeringDirectorate, Natural and Dooge, J. C. I., Looking for hydrologic laws, Water Resour.Res., Man-made Hazards Mitigation Program, National Science Founda- 22, 46S-58S, 1986. tion, grant BCS-8901430.This publicationis contribution17 of the Ely, L. L., Large floods in the southwestern United Statesin Arizona Laboratory for Palcohydrological and Hydroclimatological relation to late-Holocene climatic variations, Ph.D. dissertation. Analysis (ALPHA), University of Arizona. Dep. of Geosci., Univ. of Ariz., Tucson, 1992. Ely, L. L., and V. R. Baker, Reconstructingpalcoflood hydrology REFEKENCES with slackwaterdeposits, Verde River, Arizona, Phys. Geogr.,6, 103-126, 1985. Aidridge, B. N., Investigations of floodsfrom small drainagebasins Ely, L. L., and V. R. Baker, Large floods and climate changein the in Arizona, paper presented at 21st Annual Arizona Conference southwestern United States, in Hydraulics/Hydrology of Arid on Roads and Streets, Transp. and Traffic Inst., Univ. of Ariz., Lands, edited by R. H. French, pp. 361-366, American Societyof Tucson, 1972. Civil Engineers, New York, 1990. Aidridge, B. N., Unusual hydraulic phenomena of flash floods in Ely, L. L., J. E. O'Connor, and V. R. Baker, Paleofloodhydrotogy Arizona, in Conference on Flash Floods: Hydrometeorological of the Salt and Verde Rivers, central Arizona, paper presentedat Aspects--Los Angeles, California, May 2-3, 1978, pp. 117-121, 8th Annual U.S. Committee on Large Dams Lecture Series, American Meteorological Society, Boston, Mass., 1978. Phoenix, Ariz., 1988. Anderson, T., and N. White, Statistical summaries of Arizona Ely, L. L., Y. Enzel, J. E. O'Connor, and V. R. Baker, Palcoflood stream flow data, U.S. Geol. Surv. Water Resour. Invest., 79-5, recordsand risk assessment:Examples from the ColoradoRiver 1979. basin, in Water Resources and Engineering Risk Assessment, Baker, V. R., Flood hazards along the Balcones Escarpment in editedby J. Ganoulis,pp. 105-110,Springer-Verlag, New York, central Texas--Alternative approachesto their recognition,map- 1991. ping, and management, Publ. Univ. Tex. Bur. Econ. Geol., 75-5, 1-22, 1975. Ely, L. L., Y. Enzel, and D. R. Cayan, Anomalousatmospheric Baker, V. R., Stream-channel response to floods, with examples circulation and large winter floods in six subregionsof tl• from central Texas, Geol. Soc. Am. Bull., 88, 1057-1071, 1977. southwesternUnited States, in Proceedingsof the 8th Annual Baker, V. R., Palcoflood hydrology and extraordinary flood events, Pacific Climate (PACLIM) Workshop, March 10-13, Asilomar, J. Hydrol., 96, 79-99, 1987a. California,edited by K. T. Redmond,Interagency Ecol. Stud. Baker, V. R., Palcoflood hydrology and hydroclimatic change, in Program Tech.Rep. 31, pp. 91-98, Calif. Dep. of Water Resour., The influence of the climate changeand climatic variability on the Sacramento, 1992. hydrologic regime and water resources, IAHS Publ., 168, pp. Enzel,Y., Floodfrequency of the MojaveRiver and the formation 123-!31, 1987b. of late Holocenelakes, southernCalifornia, USA, Holocene,2, Baker, V. R., and R. C. Kochel, Flood sedimentation in bedrock 1 !-18, 1992. fluvial systems,in Flood Geomorphology,edited by V. R. Baker, Enzel, Y., L. L. Ely, J. Martinez-Goytre,and R. G. Vivian• R. C. Kochel, and P. C. Patton, pp. 123-137, John Wiley, New Palcofloodsand a dam-failureflood on the Virgin River, Utah and York, 1988. Arizona, J. Hydrol., in press, 1993. Baker, V. R., K. A. Demsey, L. L. Ely, J. E. Fuller, P. K. House, Enzel, Y., D. R. Cayan, R. Y. Anderson,and S. G. Wells, J. E. O'Connor, J. A. Onken, P. A. Pearthree, and K. R. Vincent, Atmosphericcirculation during Holocene lake standsin the Application of geological information to Arizona flood hazard MojaveDesert: Evidence of regional climate change, Nature, 341, assessment,in Hydraulic/Hydrology of Arid Lands, edited by 44-47, 1989. R. H. French, pp. 621-626, AmericanSociety of Civil Engineers, Fuller, J. E., Palcofloodhydrology of the Alluvial Salt R•ver, New York, 1990. Tempe,Arizona, M. Sc.thesis, 69 pp., Dep. of Geosci., Univ. of Beard, L. R., Generalized evaluation of flash-floodpotential, Rep. Ariz., Tucson, 1987. CRWW-124, pp. 1-27, Centerfor Res. in Water Resour.,Univ. of Garrett,J. M., andD. J. Gellenbeck,Basin characteristics and Tex., Austin, 1975. streamflowstatistics in Arizona as of 1989, U.S. Geol. Xur•' Benson, M. A., Factors affecting the occurrenceof floods in the Water Resour. Invest., 9!-4041, 612 pp., 1991. ENZELET AL.' EVIDENCEFOR A NATURALUPPER BOUND TO FLOOD MAGNITUDES 2297

Georgiadi,A. G., Upperlimits of the elementsof the hydrologic Pilgrim,D. H., T. G. Chapman,and D. G. Daran, Problemsof regime,Soy. Hydrol., 18(3), 225-230, 1979. rainfall-runoffmodelling in arid and semiaridregions, Hvdrot. Sci. Glancy,P. A., and L. Harmsen,A hydrologicassessment of the J., 33, 379-400, 1988. September14, 1974flood in EldoradoCanyon, Nevada, U.S. Potter, K. W., Researchon flood frequency analysis: 1983-!986, Geol.Surv., Prof. Pap., 1019, 59 pp., 1975. Rev. Geophys., 25, ! 13-118. 1987. Horton,R. E., Hydrologicconditions as affectingthe resultsof the Roberts, L. K., Paleohydrologicreconstruction, hydraulics, and applicationof methodsof frequencyanalysis to floodrecords, frequency-magnituderelationships of large flood events along U.S. Geol. Surv. Water Supply Pap., 771,433-449, 1936. AravaipaCreek, Arizona, M. Sc. thesis,63 pp., Dep. of Geosci., House,P. K., Palcofloodhydrology of the principalcanyons of the Univ. of Ariz., Tucson, 1987. southernTortolita Mountains, southeasternArizona, Open File Roeske,R. K., Methodsfor estimatingthe magnitudeand frequency Rep.9l-6, 22 pp., Ariz. Geol.Surv. Tucson, 1991. of floodsin Arizona,82 pp., Rep. ADOT-RS-151121IAriz. Dep. of House,P. K., P. A. Pearthree, and K. R. Vincent, Flow patterns, Transp., Phoenix, Ariz., 1978. flowhydraulics, and flood-hazard implications of a recentextreme Smith, S.S., Relationshipof large floodsand rapid entrenchment, alluvial-fan flood in southern Arizona, Geol. Soc. Am. Abstr. Kanab Creek, southern Utah, M. Sc. thesis, Dep. of Geosci., Programs,23(5), A121, 1991. Univ. of Ariz., Tucson, 1990. Hoyt,W. G., and W. B. Langbein,Floods, 469 pp., Princeton Smith,W., and W. L. Heckler, Compilationof flood data in Arizona UniversityPress, Princeton, N.J., 1955. 1862-1953, U.S. Geol. Surv. Open File Rep., 1955. Klemei, V., Hydrological and engineeringrelevance of flood fre- Stedinger,J. R., R. Therivel, and V. R. Baker, The use and value of quencyanalysis, in ttydrologicFrequenc.v Modeling, edited by historicaland paleofioodinformation in floodfrequency analyses, V. P. Singh, pp. 1-!8, D. Reidel, Norwell, Mass., 1987. paper presentedat 8th Annual U.S. Committee on Large Dams Knox, J. C., Responsesof river systemsto Holocene climates,in Lecture Series, Phoenix, Ariz., 1988. Late-Quaternar3'Environments of the United States--TheHolo- U.S. Army Corps of Engineers, Floodplain information--Virgin cene,vol. 2, editedby H. E. Wright, Jr., pp. 26-41, Universityof River and Fort Pierce Wash, vicinity of St. George, Washington MinnesotaPress, Minneapolis, 1983. County, Utah, 31 pp., Los Angeles District, 1973. Kochel,R. C., Interpretation of flood paleohydrologyusing slack- U.S. Bureau of Reclamation, Colorado River basin•Probable max- water deposits, lower Pecos and Devils rivers, southwestern imum floods, Hoover and Glen Canyon dams, 104 pp., U.S. Dep. Texas, Ph.D. dissertation, 364 pp., Univ. of Tex., Austin, 1980. of the Interior, Washington,D.C., 1990. Kochel,R. C., and V. R. Baker, Paleoftoodhydrology, Science, Webb, R. H., Late Holocene floods on the Escalante River, 215,353-361, 1982. south-centralUtah, Ph.D. dissertation,204 pp., Dep. of Geosci., Kochel,R. C., and D. F. Ritter, Implicationsof flume experiments Univ. of Ariz., Tucson, 1985. for the interpretation of slackwater palcoflood sediments, in Webb, R. H., and V. R. Baker, Changesin hydrologicconditions RegionalFlood FrequencyAnalysis, edited by V. P. Singh,pp. relatedto large floodson the Escalante River, south-centralUtah, 371-390, D. Reidel, Norwell, Mass., 1987. in RegionalFlood FrequencyAnalysis, edited by V. P. Singh,pp. Kochel,R. C., V. R. Baker, and P. C. Patton, Paleohydrologyof 309-323, D. Reidel, Norwe!l, Mass., 1987. southwestern Texas, Water Resour. Res., 18, 1165-1183, 1982. Webb, R. H., and J. L. Betancourt, Climatic variability and flood Malvick, A. J., A magnitude-frequency-arearelation for floods in frequencyof the Santa Cruz River, Pima County, Arizona, U.S. Arizona: A study to advance the methodologyof assessingthe Geol. Surv. Water Supply Pap., 2379, 40 pp., I992. vulnerabilityof bridges to floods for the Arizona Department of Webb, R. H., and S. L. Rathburn, Paleofloodhydrologic researchin Transportation,Gen. Rep. 2, 27 pp., Eng. Exp. Sta., Coll. of the southwesternUnited States, Transp. Res. Rec., 1201, 9-2!, Eng., Univ. of Ariz., Tucson, 1980. 1989. Matthai, H. F., Floods of June 1965 in South Platte River basin, Webb, R. H., J. E. O'Connor, and V. R. Baker, Paleohydrologic Colorado, U.S. Geol. Surv. Water Supply Pap., I850-B, B1-B64, reconstructionof flood frequency on the Escalante River, south- 1969. central Utah, in Flood Geomorphology, edited by V. R. Baker, Matthai,H. F., Floods, in Surface Water Hydrology, vol. O-1, The R. C. Kochel, and P. C. Patton, pp. 403-418, John Wiley, New Geologyof North America, edited by M. G. Wolman and H. C. York, 1988. Riggs, pp. 97-120, Geological Society of America, Boulder, WoN, E. E., Large floods in Redfield Canyon, final report, contract Colo., 1990. IGA-89-6125-210-0111, Ariz. Dep. of Water Resour., Phoenix, Melis,T. S., Evaluation of flood hydrologyon twelve drainagesin Ariz., !989. the centralhighlands of Arizona: An integratedapproach, M. Sc. Wolman, M. G., and J. E. Costa, Envelope curvesfor extremeflood thesis,135 pp., Dep. of Geol., Northern Ariz. Univ., Flagstaff, events: Discussion,J. Hydraul. Eng., 110, 77-78, 1984. 1990. Wolman, M. G., and R. Gerson, Relative scales of time and Mutreja,K. N., Applied Hydrology, McGraw-Hill, New York, effectivenessof climatein watershedgeomorphology, Earth Surf. 1986. Processes, 3, 189-208, 1978. NationalResearch Council, Estimating Probabilities of Extreme Yevjevich, V. M., Misconceptionsin hydrologyand their conse- Floods,141 pp., National Academy Press, Washington,D.C., quences,Water Resour. Res., 4, '• " • 1968. 1988. Yevjevich,V. M., andN. B. Harmancioglu,Research needs in flood O'Connor,J. E., and R. H. Webb, Hydraulicmodeling for palco- characteristics,in Application qf Frequency and Risk in Water floodanalysis, in Hood Geomorphology,edited by V. R. Baker, Resources,edited by V. P. Singh, pp. 1-21, D. Reidel, Noraell, R. C. Kochel, and P. C. Patton, pp. 383-402, JohnWiley, New Mass., 1987. York, 1988. O'Connor,•. E., J. E. Fuller, and V. R. Baker, Late Holocene V. R. Baker, L. L. Ely, and P. K. House, Arizona Laboratoryfor floodingwithin the Salt River basin,central Arizona, unpublished Paleohydrologica!and HydroclimatologicalAnalysis, Department reportto the Salt River Project, Tempe, Ariz., 1986a. of Geosciences,University of Arizona, Tucson, AZ 85721: •602)621- O'Connor,J. E., R. H. Webb, and V. R. Baker, Paleohydrologyof 2022, Fax {602)621-2672. pooland riffle patterndevelopment, Boulder Creek, Utah, Geol. Y. Enzel, Departmentof PhysicalGeography, Institute of Earth Soc.Am. Bull., 97, 410-420, 1986b. Sciences, Hebrew University, 9191)4 Jerusalem, Israel; 972-2- Partridge,J. B., andV. R. Baker, Palcofloodhydrology of the Salt 584210, Fax 972-2-662581. River,Arizona, Earth Surf. ProcessesLandj•rms, I2, 109-125, R. H. Webb, U.S. GeologicalSurvey, 1675 West Anklam Road, 1987. Tucson, AZ 85705. Patton,P. C., V. R. Baker,and R. C. Kochel,Slackwater deposits: A geomorphictechnique for the interpretationof fluvialpaleohy- drology,in Adjustmentsof the FluvialSystem, edited by D. P. iReceived July 31, 1992; Rhodesand G. P. Williams,pp. 225-253,Kendall/Hunt, Dubu- revised January 19, 1993; que, Iowa, 1979. acceptedFebruary 12, 1993.)