Reprint frofl IttT SYa? FOUESfPROC NAT SCI F O U M D A D V SCI S E M I M A RPsnn State U n i v 8/29 - 9/10, 1965Pergamon P r e s s - O x f o r d & N . Y. - 1966

FACTORS AFFECTING THE RESPONSE OF SMALL WATERSHEDS TO

PRECIPITATION IN HUMID AREAS

JOHN D. HEWLETT and ALDEN R. HIBBERT

Associate Professor of Forest Hydrology, School of Forestry, University of Georgia, Athens,Georgia, and Research Forester, Coweeta Hydrologic Laboratory, Southeastern Forest Experiment

Station, Forest Service, U.S. Department of Agriculture, Asheville, North Carolina

ABSTRACT

Customary separation of stream hydrographs into overland flow, interflow and base flow has littlemeaning when applied to most small watersheds. A revised description of runoff processes in forestedheadwaters relates quick rises in streamflow to variable source areas and subsurface translatory flow, or therapid displacement of stored water by new rain. Because this makes the classification of hydrograph com-ponents difficult, if not impossible, a numerical rating system, the response factor, was developed fromprecipitation and streamflow records for use in classifying the hydrologic response of small watersheds inhumid areas. A simple uniform hydrograph separation method was necessary to make inter-watershed andinter-regional comparison of response meaningful. Long-term hydrograph records from fifteen forestedwatersheds in eastern United States were separated into quick and delayed flow by computer and rankedaccording to mean precipitation, quick flow, and the response factors quick flow/precipitation and quickflow/total water yield. Similar data from nine agricultural watersheds allowed comparison of responseamong twenty-four small basins, systematically revealing important relationships not usually noted. Theover-riding prevalence of subsurface flow was indicated and exceptions were pinpointed. Possibilities andadvantages of mapping small watersheds or stream networks by a universal response factor were discussed.

STREAMFLOW is generated chiefly by processesoperating beyond perennial stream channels.This truism alone is justification for detailedstudy of the means by which precipitation istransformed into streamflow. Classical hydro-logy has been much concerned with channeland related processes which produce floodvolumes and peak stages at critical locationsdownstream. The main problem on the largerstreams has been to relate flood magnitudeto flood frequency rather than to sourceareas. This downstream focus has feft useven today with a poor understanding ofsource area hydrology, and has contributedto some unnecessary controversy over thesource of floods and alternate methods forcontrolling them.

For example, the statement or assumptionthat all floods are due to surface runoff haspersisted in hydrology papers and even insome hydrology textbooks despite muchevidence to the contrary in forestry andagricultural research. Virtually all techniques

now in general use for estimating flood peaksand volumes, are based on the seldom chal-lenged assumption that a quick rise in stream-flow proves that rainfall is failing to infiltrateand is running over the surface of the groundto stream channels. The term interflow wasproposed, and is in fairly general use, torefer to subsurface flows which contributeflood waters in some cases, but there hasbeen no general agreement as to what inter-flow is or how it works. Hursh (1944)suggested long ago that quick subsurfaceflow was the primary source of stormflowfrom forest land. But only a few hydrologistshave attached any real importance to inter-flow as a flood phenomenon and it hasremained a sort of catch-all term to covermany small watershed processes we do notunderstand. Despite gradual recognition ofthe importance of subsurface processes instreamflow, the traditional concept of storm-flow as a produce of overland flow haslingered on in virtually all hydrologic

275

276 JOHN D. HEWLETT AND ALDEN R. HIBBERT

classification and analysis methods. Thesemethods have become encumbered with aconfusing array of corrections and adjust-ments to force the natural variability amongwatersheds to agree with poorly definedmodels of upstream hydrologic processes.One of the unfortunate results is that westill appear to have no convenient method forclassifying the hydrologic behavior of indi-vidual drainage basins. This paper will bean effort to re-examine some upstreamhydrologic processes, particularly on forestedwatersheds, and to propose the use of aresponse factor for classifying small water-sheds.

HYDROGRAPH SEPARATION

The volume of water represented by thehydrograph at any point in a perennialstream channel is usually divided into fourparts—channel interception, overland flow,interflow and base flow. Definitions varyconsiderably among glossaries of hydrologicterms. Channel interception is usually definedas the amount of flow derived from precipi-tation falling from the clouds or splashing offnearby vegetation directly into the stream.Overland flow is usually defined as anamount of rainfall or snowmelt moving overthe surface of the soil to the stream withoutinfiltrating at any point. Interflow is usually *thought of as the rapid movement of somesubsurface water to the stream during avariably specified period, usually termed thedirect runoff period. However, some hydrol-ogists exclude interflow from direct runoff.Direct runoff is the amount of flow resultingdirectly from a rainfall or snowmelt eventbut arbitrarily limited in duration; it usuallyincludes all three types of flow just defined.Direct runoff" is separated from the fourthtype, base flow, by arbitrary methods referredto as hydrograph separation. Base flow isthought of as flow from ground wateraquifers, or flow that is left after direct runoffhas been separated.

Hydrograph separation is one of the most

desperate analysis techniques in use inhydrology. It must be so, since the definitionsgiven above are discrete in neither space nortime. Channel interception appears easiestto deal with because it can be equated withan amount of water falling in a limited timeon a definable area. However, stream chan-nels tend to grow and shrink in an uncertainway during storms; we usually ignore shrink-ing and expanding channel areas in separatingchannel interception and also in separatingoverland flow from interflow and base flow.Often water will collect on an imperviousarea during a storm but infiltrate before itreaches streams. In other cases, water willinfiltrate but come to the surface in an inter-mittent or ephemeral channel before itflows to the perennial channel. As weapproach the perennial channel spatially, andthe end of direct flow chronologically,interflow becomes hopelessly inseparablefrom base flow. Contrary to popular opinionthese different types of flow rarely arediscernible in the hydrograph trace. It isdoubtful that any graphical technique appliedto a hydrograph is going to put firm defini-tions under such concepts.

It womd seem, in view of the advancedmathematical and theoretical techniqueswhich ar<e being'applied in synthetic hydrologytoday, that we should be pretty well alongwith the observation and description phasesof hydrology. But despite many records ofrunoff the-description of processes controllingrates of flow from forests, croplands andpastures in, humid areas is by no meansadequate-to* meet the needs of modern water-shed planners. How forests, mountains,croplands, pastures and urban areas con-tribute to floods is still a basis for vigorousargument among agencies and hydrologistswhenever a flood-control program is pro-posed. Furthermore, the movement of agri-cultural chemicals and other pollutantsthrough soils into streams is raising newquestions about the source, timing and turn-over' rates of water from upland areas.

RESPONSE OF SMALL WATERSHEDS TO PRECIPITATION 277

Experiments to control evapotranspirationby chemicals, forest cutting or forest typeconversions force us to consider in detail howand when the water saved will get into streamsand reservoirs. The idea of spreading orspraying extra water on forested slopes toincrease low flows or purify effluents isgrowing; here again attention will be focusedon how this water moves or is detained in theporous mantle. These are old questions whichrequire some new answers.

The concept that streamflow from a smallwatershed is due to a shrinking and expandingsource area—the variable source area concept—grew out of studies of the drainage ofsloping soil models at the Coweeta Hydro-logic Laboratory (Hewlett, 1961). In thenext section, these ideas will be discussed inrelation to the small, forested, uplandwatershed. For purposes of this paper asmall watershed shall generally mean anatural basin large enough to provide flowduring most of the year but not greater than20 square miles. Larger limits might be set;the important restriction is that travel timeand storage in the stream channel duringstorm periods should not be the major factorin determining the volume of direct runoff.

A DESCRIPTION OF FOREST RUNOFF IN RELATIONTO VARIABLE SOURCE AREA

Usually a discussion of the runoff from awatershed begins with the assumption thatdirect runoff,is the product of overland flowand that other types of flow are mereexceptions to the general rule. Perhaps theopposite approach is more logical in the caseof forest land; that is, to begin with theassumption that all flow is subsurface flowuntil there is evidence otherwise. As anyonewho has visited a well-vegetated watershedduring a rainstorm knows, adequate infiltra-tion and subsurface flows predominateduring most storm events. Rainfall and runoffrecords from all kinds of watersheds in thisregion show that only the exceptional storm

produces flow in amounts greater than 25percent of gross rainfall and that the largeststorm flows of record have rarely exceeded50 percent of the rainfall that producedthem. While these figures tend to set anupper limit to the percentage of rainfallwhich might be overland flow, they are notby any means a measure of overland flow;numerous workers have shown that much ofthe direct runoff is subsurface flow also.For example, on one forested Coweetaexperimental watershed, direct runoff as apercentage of rainfall has reached as high as50 percent (6 in. of direct runoff) withvirtually no overland flow involved. As weshall see later these experimental watershedsare not atypical; Sopper and Lull (1965) haverecently provided further evidence thatsimilar experimental watersheds in the north-east represent flow conditions in that regionquite well. If we assume that subsurfaceflows predominate on most wildland soils,how do direct runoff and base flow get tothe channel?

Any effort to model a natural watershedmust fail in some degree. However, it isapparent that the essential features of a smallwatershed as we have defined it are four innumber: a stream channel, a slope, a waterdivide, and a porous mantle of some averagedepth to an impervious layer. Any or all ofthese may be indefinite on a given watershed,but despite the natural variation from place toplace and region to region, most small uplandwatersheds maybe depicted as shown in Fig. 1.The fundamental dimensions are area, channellength, slope percent and porous mantledepth. In this diagram we have assumed thatthe sandy-loam soil mantle to bedrockaverages 6 ft, slope percent is about 30, andthe flood plain is a negligible portion of theslope. Channel length will increase and slopelength will decrease during prolonged rainfall.The basin is entirely forested, or at any ratehas infiltration capacities which will seldombe exceeded by local rainfall intensities. Theseconditions are not unusual in the East,

278 JOHN D. HEWLETT AND ALDEN R. HIBBERT

STORM RAINFALL

Wtwn fh< subsurface flowof water exceeds the capacityof the soil profile to trans- Jml! it, channel length willgrow.

SOURCE OF STORMFLOW

FIG. 1. Diagram showing the source of stormflow (direct runoff) from a forested watershed with auniform soil mantle. The interaction between the factors illustrated constitutes the variable source

area concept of runoffs from small watersheds.

although it would be a misstatement to callthem typical.

A large rainstorm, for example, the 10-yearfrequency storm, is represented in amountand distribution by the blank arrows at thetop, and the total direct runoff by the largeblack arrow at the bottom. Each blank arrowrepresents a unit of rainfall applied to a unitarea beneath it. The smaller black arrowsshown within the soil mantle represent therelative effect of a unit of rainfall upon themagnitude of direct runoff below; the blackarrow over the stream represents channelinterception. Upslope there is no way to

calculate the relative influence of eachrainfall unit on direct flow, but it is apparentthat, unless the entire slope is nearly satura-ted, this influence must decrease fairly rapidly.If it did not then the volume of waterappearing as direct runoff would approachthe volume of net rainfall delivered to theforest floor, an extremely rare occurrence inthis region as records show. Assuming averageantecedent wetness a 4-in. storm wouldrelease about 4 in. of water in and immediatelyadjacent to the stream channel, probably 1 in.one-third up the way upslope, and very littlefrom there on up to the water divide, adding

RESPONSE OF SMALL WATERSHEDS TO PRECIPITATION 279

up to a total of about 1 in. of direct runoff or25 percent of the rainfall. In effect, therefore,the yielding portion of the watershed shrinksand expands, depending on rainfall amountand antecedent wetness of the soil. Areasnear the water divide would detain rainfalllong enough to prevent it from materiallyinfluencing direct runoff, -but would supplymoisture to sustain base flow or evapo-transpiration during the subsequent weeks.

As rainfall continues on these fairly deepsoils perhaps half of the area would beinfluencing direct flow. Part of the expansionin the area supplying flow would occur as anextension of the perennial channel intointermittent and ephemeral channels. Itmight be argued at this point that the exten-sion of channels is evidence of overland flow,but most or all of the water may still beentering these channels as subsurface flow.The distinction is important because smalldelays caused by brief infiltration offer largeopportunities for transmission into deeperlayers. A better description of this phase isto say that when the subsurface flow of waterfrom upslope exceeds the capacity of the soilprofile to transmit it, the water will come tothe surface and channel length will grow.This in essence is the variable source areaconcept. Because direct runoff is produced bya watershed whose channel and effective areaare varying rapidly in size, it is little wonderthat techniques such as the unit hydrographwork only on selected storms and tend toyield anomalous results when applied to otherstorms on the same or another small water-shed.

Usually we think of subsurface flow asmoving too slowly to contribute much volumeto direct runoff. Certainly it moves moreslowly than overland flow if we consider onlythe movement of a drop of water from somepoint on the slope to the channel. To under-stand how infiltrated water can produce suchrapid rises in streamflow from forest land, itis helpful to discriminate between two typesof flow which, although not entirely separable,

are more descriptive than the usual interflow,overland flow and base flow. As we proceedupslope in Fig. 1, each unit of rainfallcontributes more to temporary storage andless to direct runoff. However, of the partcontributed to direct runoff, a fraction willbe some of the actual drops that fell duringthe storm—that is, some new rain—and theother fraction will be what we might calltranslatory flow or flow produced by aprocess of displacement. This is a contributionto direct flow of water already stored in thesoil mantle before rainfall began. It will bereleased in large quantities only when the soilis within the field capacity range or wetter.Above the zone of saturation, we may regardsuch movement as due to thickening of thewater films surrounding soil particles and aresulting pulse in water flux as the saturatedzone is approached. The process underrainfall is varying everywhere in a mostcomplex way but such movement can beverified in an elementary manner by allowinga soil column to drain to field capacity in thelaboratory and slowly adding a unit of waterat the top. Some water will flow from thebottom almost immediately, but it will beapparent that it is not the same water addedat the top. Translatory flow as a factor indirect flow will prevail chiefly in the lower andmid-slope portions of our model watershed.Upslope translatory flow may be regarded asa pulse in soil moisture which will migrateslowly downhill.

Fortunately some experimental evidencefor the translatory process is available.Horton and Hawkins (1965) have recentlyperformed tritium experiments on 4-ft soilcolumns which suggest the prevalence oftranslatory movement in natural soil profiles.Referring to the profile diagrams in Fig. 1,Horton's work showed how a 1-in. layer oftritiated water moved through the soil afterit had been drained to equilibrium (fieldcapacity). The first water to flow out con-tained no tritium. Thereafter 1 in. of purewater was added each day to the top of the

280 JOHN D. HEWLETT AND ALDEN R. HIBBERT

column and the effluent was analyzed dailyfor tritium. The tagged inch of water"bumped" its way through the soil pushingahead 87 percent of all the original watercontained by the column before the tritiumwas added. Horton and Hawkins concludedthat infiltered rainwater moves primarilythrough capillary pores, avoiding the largerones, and that each rain tends to displacemost of the water ahead of it. In Fig. 1the profile diagrams indicate how this prin-ciple might apply to flux rates during stormflow.

Up to this point we have not dealt withrainfall variables, overland flow, evapo-transpiration, land use effects, semi-permeablelayers in the soil, or other such factorscontrolling runoff, but have confined attentionto the basic morphological watershed featureswhich will operate to control water yieldregardless of other factors. By sidesteppingthe usual arbitrary classifications of thehydrograph, a fresh look at some upstreamhydrologic processes becomes possible. Forexample, recognition that translatory flow isinvolved reduces the mystery of how forestland can produce large amounts of stormflow without appreciable overland flow. Itwould not be impossible to treat overlandflow as an exceptionally rapid extension ofthe channel system into areas where the soilcannot transmit the water as subsurface flow.This seems more appropriate than treating alldirect runoff as overland flow. A better ideaof how streamflow is actually producedshould allow improvement in syntheticmodels of watershed processes and in theselection of variables for their solution.Some recent work by Snyder (1962) is alreadya step in this direction. Finally, the view of awatershed as a topographic pattern of soilwater storage and availability is already wellestablished in soil survey, site and vegetationstudies, and there will be some advantage inbringing hydrologic theory in line with theseviews.

RESPONSE FACTORS FOR SMALL WATERSHEDS

Although it is virtually impossible toseparate direct runoff from base flow on aphysical basis, we must for practical reasonsclassify flows which run quickly from water-sheds versus flows which are delayed orwell controlled. The main trouble withelaborate hydrograph separation methods isthat an arbitrary classification of the rate offlow is usually added to another arbitraryclassification of the source of flow. That is,we usually decide subjectively which ratesof flow are storm flows and then arbitrarilydivide these rates into direct runoff and baseflow. Since an arbitrary separation must bemade in any case, why not base the classifi-cation on a single arbitrary decision, such as afixed, universal method for separating allhydrographs on all small watersheds? Amethod capable of being applied by acomputer to all hydrographs would meet therequirements.

The simple terms quick and delayed flow,rather than the usual direct runoff and baseflow, will be used to avoid confusion with thevariable definitions and techniques associatedwith the latter terms. Many intricate methodsfor separating quick and delayed flow mightbe programmed for computers but all wouldhave the same basic limitation; they arecompletely arbitrary. We wanted a methodwhich would be simple yet would apply thesame mathematical rule to all hydrographevents. After examining many hydrographevents from about 200 water-years of recordcollected on fifteen small forested watershedsin the Appalachian-Piedmont region, wedecided that a line projected from thebeginning of any stream rise at a slope of0.05 cubic feet per second per square mile(csm) per hour until it intersected the fallingside of the hydrograph would be a simple andsatisfactory method of separating streamflowinto quick and delayed flow. The followingrequirements are met: (1) The computerignores stream rises caused by normal diurnal

RESPONSE OF SMALL WATERSHEDS TO PRECIPITATION 281

PRECIPITATION(p)

THE EVENT

LU5

TIME-

FIG. 2. Diagram of a typical small watershed hydrograph, showing the method used for com-puter separation of hydrograph events into quick and delayed flow. The constant separation slope is

0.05 cfs/mi2/hr.

fluctuation in flow. (2) On the largest single-peaked storm hydrographs of record, quickflow was shut off within a time lapse of 4 or5 days. For watersheds less than 20 squaremiles, experience shows that 5 days willinclude all unusual, damage-producing flows.(3) Large rainfalls separated by a period ofabout 3 days would be calculated as separateevents. (4) All separations examined appearedreasonable and in line with normal practice.

Figure 2 shows the relation of terms to thehydrograph. A Fortran IV program waswritten* for the IBM 7094 computer to separ-ate and list various features of each streamrise and depletion period, including v, thequick-flow volume, and a, the delayed-flowvolume, both in inches. The event is definedas the time-rate of flow from the beginningof one stream rise to the beginning of thenext, limited to events where v is at least0.001 in. of flow from the basin. Iffv is lessthan 0.001 in., the computer deletes the

* The authors are indebted to Dr. Jerome Clutter,University of Georgia, for programming this tech-nique, which proved more intricate than its simpleconception indicated. Details on the flow separationprogram may be obtained from the authors onrequest.

"false" event and adds the flow to theconcurrent "true" event. The minimumacceptable volume of v could be made anysize desired. Within the region under dis-cussion, there may be anywhere from about10 to 100 events per year, varying from0.001 to over 7.5 in. of quick flow.

The total amount of quick flow (K)yielded by periods (normally one year) is acharacteristic of natural watersheds, con-trolled chiefly by precipitation and the fourbasic features discussed in the previoussection. Although informative for ratingwatersheds according to the volumes of quickflow they produce, average V alone tells littleabout a watershed's ability to control theprecipitation that falls upon it or its relationto the total yield of water after evaporativelosses are deducted. Using V as the numera-tor, two response factors may be calculated,one expressing the fraction of the totalprecipitation yielded as quick flow, and theother the fraction of total water yield whichis quick flow. We designate these Rp and Ry,respectively, and define them:

(1)

282 JOHN D. HEWLETT AND ALDEN R. HIBBERT

and

Ry =V

P-E (2)

where V is the sum of all quick flow in inchesfrom a basin during a specified period of time(usually a year), P is gross precipitation ininches and E is the actual evapotranspirationin inches. The denominator used to calculateRy is the total amount of water yielded tostreams and groundwater by the watershed,including any that may escape measurementat a stream gage. In both cases, a concreterunway will show a response close to 1 sinceit quickly sheds all the water that falls uponit, whereas a deep, permeable forest soil mightshow a response close to 0. These two methodsfor classifying the response of a watershedwill be compared and evaluated.

It is hypothesized at the beginning that allsmall watersheds, if undisturbed by man, havea long-term mean response factor which maybe determined from records and which reflectsits hydrologic behavior in relation to otherbasins. Thus the performance of basinsmay be compared through a response factoreven though widely separated in distance andrainfall characteristics. Furthermore, theeffect of man's complex activities on water-sheds may be evaluated and classified partlyin terms of changes produced in "natural" •response factors, assuming these may beestimated in some manner.

The simplest response factor is Rp,expressing the fraction of rainfall and snow-melt which flows off as quick flow. Suchcomparisons are not new; direct runoff,separated from base flow by various methods,has often been reported as a fraction ofindividual storm rainfalls. But because of thelack of a universal hydrograph separationmethod, there appears to have been no effortto extend this simple concept to a watershedrating system.

Ry is more difficult to calculate because itrequires either knowledge of actual evapo-transpiration or streamflow records which are

known to include the total yield of the water-shed. If the stream gage catches and measuresall water represented by the term (P—E), thenwe may substitute (V+A), where A is thesum of the delayed flow over the same period.Usually, however, gaging is not that successfuland some delayed flow will pass under thegaging station or leak into or out of thebasin elsewhere. Fortunately small errors inthe denominator of equation (2) will notaffect Ry seriously. If the errors are large, Pmay be estimated from a nearby rain gageand E calculated by one of several theoreticalmethods available.

Either or both of these response factorsmight be used for rating and mapping thehydrologic behavior of small watersheds. Inthis preliminary report, we have chosen todevote most attention to the meaning,variability and predictability of Ry since itmay be calculated entirely from the hydro-graph if good quality records are available.Whenever possible, Rp has also been cal-culated and compared with Ry.

Table 1 identifies fifteen forested watershedsfor which at least 3 years of high-quality,continuous streamflow and precipitationrecords could be secured. These watershedswere expected to show low response factors.We have been unable so far to process suitablerecords from agricultural watersheds. SinceRy is supposed to reflect not so much theland use and cover conditions as the mor-phology of basins and their ability to controlthe water that falls on them, there is someadvantage in limiting the first computationsto basins with little overland flow. Analysisshould provide the original or natural Ryfor these watersheds and provide a testwhether Ry is sensitive to basin morphologyor is merely a reflection of land use, overlandflow and precipitation differences. Somepreliminary estimates of response factors onagricultural watersheds will be introducedfurther on.

Ry is obviously a variable and will fluctuatefrom season to season and year to year. How

RESPONSE OF SMALL WATERSHEDS TO PRECIPITATION 283

TABLE 1Some Physiographic and Other Data from Fifteen Forested Watersheds of Eastern United States

Watershed and location

Coweeta 2, Franklin, N.C.Coweeta 21, Franklin, N.C.Coweeta 18, Franklin, N.C.Coweeta 14, Franklin, N.C.Coweeta 8, Franklin, N.C.Coweeta 28, Franklin, N.C.Coweeta 36, Franklin, N.C.Bent Creek 7, Asheville, N.C.Copper Basin 2, Tenn.Union 3, S.C.Fernow 4, Parsons, W. Va.Leading Ridge 1, Pa.Dilldown Creek, Pa.Burlington Brook, Conn.Hubbard Brook 4, Laconia,

N.H.

No.yr

2724272824132155

10113433

Source

USFSUSFSUSFSUSFSUSFSUSFSUSFSUSFSUSFSUSFSUSFSPenn.USGSUSGSUSFS

Area(acres)

316031

1521877360114735882296

30315302637

89

Meanelev.(ft)

280032502700289031303940425031001900570

270012001900900

1965

Mean*slope

%

303432212233472227

7181943

26

Soil material

Granitic sandy-loamGranitic sandy-loamGranitic sandy-loamGranitic sandy-loamGranitic sandy-loamGranitic sandy-loamGranitic sandy-loamGranitic sandy-loamGranitic sandy-loamGranitic sandy-claySandstone silt-loamShale silt-loamSandstone sandy-loamGlacial stony-sandGlacial stony-loam

Foresttypef

O-HO-HO-HO-HM-HM-HM-HO-HO-HPineM-HM-HSc-ON-HN-H

Forestcover

10010010010010010010010010095

10010010085

100

* Calculated by dividing the change in elevationfrom the weir to the highest point by the horizontallength of the watershed.

t Abbreviation key: Oak-hickory (O-H); mixedhardwoods (M-H); scrub oak (Sc-O); northernhardwoods (N-H).

much does it vary and how many years ofrecord are necessary to estimate the long-term mean? Several watersheds from theSoutheast with from 11 to 27 years of recordwere used to estimate the time required toreduce Ry to an acceptable estimate of thetrue mean. It appears that 6 years of recordare required to estimate mean annual Rywithin 15 percent of its true value about 95percent of the time. Although not as good aswas hoped, this variation will not preventan orderly ranking of watersheds. Calculatedfrom 207 years of record on 15 watersheds,the weighted average standard deviation ofRy was 0.04. As might be expected, Rpvaried similarly. The same number of yearsare needed to estimate Rp to similar limits.However, the numerical value of Rp is usuallyabout \Ry. Also, the standard deviation ofRp averages only about 0.02.

To determine how much deviation inannual precipitation from local mean precip-itation affects Ry and Rp, regressions werecalculated and tested for significance. Thepooled regression coefficient in the following

equation was significantly different from 0at the 0.01 level.

(Ry-Ry) = 0.0015 (P-P). (3)

The coefficient is so small that precipitationmust deviate from the mean by 35 in. tochange annual Ry by 0.05 points. Equation (3)may be used to adjust Ry determined onshort records, but fortunately we mayconclude that Ry is fairly stable with respectto local annual precipitation variation.Similar regressions of Rp on annual precipi-tation produced a higher (significant) regres-sion coefficient.

(Rp-Rp) = 0.0020 (P-P). (4)

Because the numerical value of Rp is smallerthan that of Ry, equation (4) represents asubstantial influence on the value of mean Rpdetermined on short records. If the locallong-term mean precipitation is known,adjustment of Rp by equation (4) is recom-mended. Mean Rp then becomes a responsefactor for the watershed at mean precipitation.

284 JOHN D. HEWLETT AND ALDEN R. HIBBERT

TABLE 2Annual and 6-month Values o/Ry on Three Watersheds

Season

May-Oct.Nov.-Apr.Nov.-Oct.

May-Oct.Nov.-Apr.Nov.-Oct.

May-Oct.Nov.-Apr.Nov.-Oct.

Year42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62

COWEETA 210.09 0.07 0.05 0.05 0.06 0.06 0.09 0.09 0.11 0.06 0.04 0.04 0.05 0.08 0.04 0.09 0.05 0.08 0.08 0.08 0.080.09 0.10 0.09 0.08 0.12 0.08 0.09 0.11 0.07 0.06 0.13 0.14 0.12 0.11 0.08 0.11 0.08 0.09 0.06 0.09 0.090.09 0.09 0.08 0.07 0.10 0.07 0.09 0.10 0.08 0.06 0.11 0.11 0.10 0.10 0.07 0.11 0.07 0.09 0.07 0.09 0.09

COWEETA 36— 0.160.100.130.180.190.230.280.330.130.080.100.120.210.080.220.080.250.150.140.14— —' 0.25 0.17 0.26 0.18 0.21 0.26 0.20 0.19 0.27 0.27 0.27 0.27 0.20 0.28 0.22 0.20 0.14 0.19 0.25— — 0.22 0.15 0.24 0.18 0.21 0.27 0.25 0.17 0.24 0.23 0.23 0.25 0.17 0.26 0.19 0.22 0.14 0.17 0.23

FERNOW 4— — — — — — — — — 0.440.240.430.430.390.450.460.440.240.240.190.45_ _ _ _ _ _ _ _ _ _ _ 0.320.220.200.300.350.360.290.250.370.260.35— — — — — — — — — — 0.310.280.300.320.390.370.350.250.350.250.37

Table 2 contains representative values ofannual and 6-month Ry from three water-sheds with fairly long records. Season hassome affect on the numerical value of meanRy but not as much as might be expected.Winter season Ry correlates most closelywith the annual mean. However, means andvariances between seasonal and annual Rywere tested and found non-significantlydifferent in four out of five watersheds;Fernow 4 was the exception. An incompleteanalysis showed that Rp tends to be signifi-cantly higher in winter than in summer, afact to be expected because of the highercontributions of summer rainfall to soil-moisture recharge and evapotranspiratioii.

The major factor causing variation in bothresponse factors from period to period and yearto year appears to be the number and size ofthe larger rain storms occurring within theperiod. Storm rainfalls in excess of 6 in. tendto release about half their volume to quickflow. Two or more such storms in any periodwill tend to elevate the response factor forthat period beyond two standard deviationsfrom the mean response. Fortunately thisseldom happens, and because of the moder-ating influence of watershed morphology on

all storms, both response factors have astrong central tendency.

There is no question that the slopeseparation coefficient used to compute quickflow will influence the numerical value ofresponse factors. In order to determinewhether a range in slopes would change theranking of watersheds and thus defeat thewhole purpose of the response factor concept,slopes of 0.03, 0.07 and 0.09 were added inthe separation program and response factorswere computed again. Table 3 shows that

TABLE 3Changes in the Uncorrected Annual ResponseFactor Ry as the Separation Slope is Increasedfrom 0.03 to 0.09, Averaged from One Wet and

One Dry Year of Record

Watershed

Coweeta 2Coweeta 14Coweeta 8Coweeta 36Fernow 4Hubbard Brook 4

Slope coefficient0.03

0.130.130.160.290.410.43

0.05* 0.07

Ry0.11 0.100.12 0.100.15 0.130.25 0.230.35 0.320.37 0.34

0.09

0.090.100.120.210290.32

* Slope 0.05 used as the standard in this paper

RESPONSE OF SMALL WATERSHEDS TO PRECIPITATION 285

increasing the slope sharply reduces thenumerical value of Ry. The effect on Rp wassimilar. However, the ranking of watershedsremains virtually unchanged throughout therange of slope tested. An increase of 0.01 unitin slope produces about 5 percent decreasein Ry. Some justification for selecting astandard slope of 0.05 was obtained fromcalculations of the standard deviation of theindividual event Ry for several years of datafrom six watersheds. This analysis showed atendency toward minimum variation at slope0.05, indicating that higher or lower slopesmight cause additional variation in mean Ryby periods. While more study of the influenceof the separation slope is needed, particularlyin relation to variation in response factorswith watershed size, we feel that a slope of0.05 will prove to be a satisfactory standardfor small watersheds.

WATERSHEDS COMPARED BY RESPONSE FACTOR

The second column in Table 4 showsuncorrected Ry for fifteen forested watersheds

of the Appalachian and Piedmont region.Watersheds are ranked and grouped accord-ing to the corrected Ry, calculated byequation (2) from precipitation and evapo-transpiration estimates listed as P and E.The standard deviation of uncorrected Ryand the mean annual quick flow in inches arealso shown. The estimate of E is admittedlycrude; we merely used maps of the easternUnited States prepared by Thornthwaite,Mather and Carter (1958), showing estimatedaverage potential evapotranspiration (Ep) andaverage annual water deficit (D) in inches, andassumed that Ep minus D is equal to actualevapotranspiration E. The only justificationfor such a crude method is the limited effectof rather large errors in (P—£) on Ry. Onlythree response factors were significantlychanged. In the case of the Union 3 andFernow 4 watersheds, Ry calculated directlyfrom the hydrograph was probably too highbecause some of the total water yield escapesmeasurement by the gaging station. BentCreek 7 was corrected to a higher Ry,indicating perhaps that some water may be

TABLE 4Uncorrected and Corrected Mean Ry for Fifteen Forested Watersheds, Ranked and Grouped According to

the Corrected Ry

Watershed

Coweeta 2Coweeta 21Coweeta 18Coweeta 14

Coweeta 8Bent Creek, N.C.Coweeta 28

Coweeta 36Copper Basin, Term.Dilldown, Penn.Fernow, W. Va.Union, S.C.

Leading Ridge, Pa.Burlington Brook, Conn.Hubbard Brook, N.H.

UncorrectedRy S.D.t V P Ep D E

CorrectedRy

inches

0.090.090.090.10

0.120.090.15

0.210.220.200.320.44

0.280.270.33

0.030.020.020.03

0.030.050.03

0.040.070.090.050.10

0.040.120.10

2.84.53.43.7

5.42.78.5

13.96.26.07.93.7

4.47.58.4

72787272

774888

9060505847

404746

32323232

313129

2833252534

252322

0000

010

01112

111

32323232

313029

2832242432

242221

0.070.090.090.09

0.120.15*0.15

0.220.220.230.23*0.25*

0.280.300.33

* Correction in Ry significant at the 0.05 level. t S.D. stands for standard deviation.

286

added to the basin from adjacent areas. Theseare fairly small basins; on watersheds ofseveral square miles, water exchange by under-flow, deep seepage or lateral movement shouldnot usually be large enough to influence thenumerical value of Ry. Turning to Rp, it isapparent that failure to measure evapo-transpiration plays no part in this responsefactor; only gross error in estimating precipi-tation and quick flow are involved in Rp.

Both Coweeta 2 and 36 are contained withinthe larger watershed Coweeta 8, demonstrat-ing the fact that subwatersheds may haveresponse factors both larger and smaller thanthe main basin. The moderating effect of sizeon response makes possible both internal andexternal comparisons of hydrologic behavior,area by area or basin by basin.

An outstanding feature of the responsefactors listed in Table 4 is that none of theseforested catchments yield more than one-thirdof their total yield as quick flow. HubbardBrook 4, Burlington Brook and LeadingRidge 1 group together as quickest yielders offlow, probably due chiefly to shallow soilmantles. Coweeta 2, a steep but deep-soiledcatchment, empties only 7 percent of its totalyield as quick flow, while Coweeta 36, onlya mile away, dumps 22 percent. At the same

JOHN D. HEWLETT AND ALDEN R. HIBBERT

time, Coweeta 36, the steepest and highestwatershed in the set, yields an average of13.9 in. of quick flow per year, five times asmuch as Coweeta 2, which yielded only 2.8 in.In Coweeta 36 we have an example of acompletely forested catchment which, althoughdemonstrating no appreciable overland flow,produces much larger volumes of potentialflood waters than most pastures and culti-vated areas.

Although the records of most agriculturalwatersheds are not yet in shape to run throughthe separation program, we have selected nineexperimental watersheds from those listedand described by the Agricultural ResearchService (1965) and made a rough estimate ofRy and Rp for comparison with the fifteenforested catchments (Table 5). Records wereselected which showed only negligibleamounts of delayed flow—that is, runoffceased within a day or two after rainfallceased—and thus all measured flow wasassumed to be quick flow. If anything, theresponse factor so calculated should be biasedupward slightly because the separation slopewas not applied to flow during the runoffperiod. Most of these small basins are undersome form of improved management. Thestartling exceptions are the Beaver Creek,

TABLE 5Estimated Response Factors for several Agricultural Watersheds, derived chiefly from "Hydrologic Data forExperimental Agricultural Watersheds in the United States", ARS, U.S. Department of Agriculture, May 1965

i i ~Watershed

Coshocton 135, OhioCollege Pk. W-6, Md.Blacksburg W-III, Va.Watkinsville W-l, Ga.Coshocton 185, OhioCoshocton 127, OhioOxford W-10, Miss.Beaver Crk., Mo.fOxford WC-1, Miss.

Area(acres)

734

191972

55308960

4

Crop

improved past.fertilized past.90% cultivatedgood grass past,grain and meadowcultivated, corn62% idle pasture60% oak, 40% cropcultivated, poor

y*

0.60.90.51.61.23.57.57.1

18.1

P Ep D E(in.)

334136493336483854

25282935252534

34

* Watersheds selected because no delayed flow was f From Whipkeyinvolved; all flow was assumed to be quick flow (V). was determined by .., _._0. ,... __,._ , -

1112111

1

242728332424332533

EstimatedRy

0.060.060.060.100.130.290.500.550.86

Estimated

0.020.020.020.030.060.150.160.190.34

and Fletcher (1959); quick flow

RESPONSE OF SMALL WATERSHEDS TO PRECIPITATION 287

TABLE 6Twenty-four Small Watersheds from Eastern United States ranked according to Mean Annual Precipitation,

Quick Flow and the Response Factors Ry and Rp

Watershed

Coshocton 135Coshocton 185Coshocton 127Blacksburg W-IIIBeaver CreekLeading Ridge 1College Park W-6Oxford W-10Hubbard Brk. 4Burlington Brk.Union 3Bent Creek 7Watkinsville W-lDilldownOxford WC-1Fernow 4Copper Basin 2Coweeta 2Coweeta 18Coweeta 14Coweeta 8Coweeta 21Coweeta 28Coweeta 36

Average

p(in.)

333336363840414346474748495054586072727277788890

54

Watershed

Blacksburg W-IIICoshocton 135College Park W-6Coshocton 185Watkinsville W-lBent Creek 7Coweeta 2Coweeta 18Coshocton 127Coweeta 14Union 3Leading Ridge 1Coweeta 21Coweeta 8DilldownCopper Basin 2Beaver CreekBurlington Brk.Oxford W-10Fernow 4Hubbard Brk. 4Coweeta 28Coweeta 36Oxford WC-1

V(in.)

0.50.60.91.21.62.72.83.43.53.73.74.44.55.46.06.27.17.57.57.98.48.5

13.918.1

5.4

Watershed

Coshocton 135College Prk. W-6Blacksburg W-IIICoweeta 2Coweeta 18Coweeta 14Coweeta 21Watkinsville W-lCoweeta 8Coshocton 185Bent Creek 7Coweeta 28Coweeta 36Copper Basin 2DilldownFernow 4Union 3Leading Ridge 1Coshocton 127Burlington Brk.Hubbard Brk. 4Oxford W-10Beaver CreekOxford WC-1

Ry

0.060.060.060.070.090.090.090.100.120.130.150.150.220.220.230.230.250.280.290.300.330.500.550.86

0.23

Watershed

Coshocton 135College Prk. W-6Blacksburg W-IIIWatkinsville W-lCoweeta 2Coshocton 185Coweeta 18Coweeta 14Coweeta 21Bent Creek 7Coweeta 8Union 3Coweeta 28Coshocton 127Copper Basin 2Leading Ridge 1DilldownFernow 4Coweeta 36Oxford W-10Burlington Brk.Hubbard Brk. 4Beaver CreekOxford WC-1

Rp

0.020.020.020.030.040.040.050.050.060.060.070.080.100.100.100.110.120.140.150.160.170.180.190.34

0.10

Missouri, and the Oxford, Mississippi,watersheds; 18.1 in. of quick flow per yearwas yielded by the Oxford WC-1 cornfield,the highest response we have noted. However,perhaps equally surprising is the relativelylow response on other agricultural watershedswhen compared to the forested watersheds.Table 6 ranks all twenty-four experimentalwatersheds first according to local meanprecipitation P, then according to each of theparameters V, Ry and Rp. No particularrunoff relation is revealed in ranking by Pexcept that some areas receive more rainfallthan others. Ranking by quick flow amountshows which of these watersheds are thegreatest source of potential flood waters.Whether these waters do indeed produce oradd to floods depends on many other factors,not the least of which is the troublesomesubjectivity underlying the usual definition

of a flood. There is some relation betweenaverage precipitation and the amount ofquick flow produced but not as much asmight be expected. This indicates the naturalvariability among watersheds which we seekto index by a response factor. Ry indicateshow the watershed controls its total wateryield, Rp indicates how it controls theprecipitation received. In general, Table 6shows that a similar ranking is achievedby both factors. Watersheds which shiftedranking position significantly between Ryand Rp are in italics; an inadequate periodof record was available to determine whetheror not other shifts were important. Union 3moved up in the ranking by Rp, which mayindicate nothing more than that we haveover-estimated actual evapotranspiration incalculating Ry. In the case of Coweeta 36,however, the similarity between uncorrected

288 JOHN D. HEWLETT AND ALDEN R. HIBBERT

I i

and corrected Ry indicates that the totalwater yield has been fairly well estimated andthat the shift in ranking is probably due togreater influence of precipitation on Coweeta36. The shift downward into the group ofnortheastern forest watersheds indicates thatthis steep catchment, while it moderates mostof its yield quite well, is unable to handle allof the excessive rainfall that occurs upon it.Each inch of rainfall above its average of90 in. produces about an additional | in.of quick flow. The wettest water year (Novem-ber 1 to October 30) of record on Coweeta 36delivered 130 in. of precipitation, producingan Rp of 0.22, equivalent to the average atBeaver Creek, Missouri. Coweeta 36 may befairly representative of watersheds above4000 ft elevation in the southern AppalachianMountains, an area characterized by highrainfall.

Which watershed characteristics affectthese response factors most strongly? Vari-ation in the flow separation criteria does notappear to change relative ranking, and, oncestandardized, appears to play little part invariation among watersheds. While there issome variation among seasonal responsefactors, the difference is not consistent. Suchevidence as available indicates that watershedsize, within the 20-square-mile limit we set,plays little part in response factors. Largerwatersheds will have to be examined todetermine the applicability of responsefactor concept to them. The following factorcomplexes, in the order of their naturalprimacy, largely determine the responsefactor of small watersheds within humidregions.

1. The average soil mantle depth, or depthto a relatively impervious layer, is probablyforemost among watershed factors affectingresponse. Soil physical properties—stoniness,permeability, retention and so forth—may beincluded here as a set of associated factors.

2. Average land slope and its effect on theaverage length of slope from the channel to

the water divide, influences response bycontrolling hydraulic potentials for flow andby sustaining depletion rates.

3. The average size and number of thelarger storms—or the average annual storm—influence response by the obvious effect onhigh flow and rates of infiltration. Averageannual precipitation and its distribution maybe included here, as it influences responsethrough control of antecedent wetness con-ditions and variable source areas contributingsubsurface flow.

4. Land use is listed last, not because it isminor, but because its effects on the timedistribution of flow are superimposed on theeffects of the other factors. Land-use effectsare obvious but are perhaps best evaluatedin relation to original or natural responsefactors for the area, rather than as a primehydrologic characteristic. The effects of landuse on flow rates are not always as drastic asthey appear and it is perhaps best to deal withthese effects in relation to response in theabsence of land use.

Any one of these factor complexes maydominate the response of a particular water-shed but that fact need not destroy theessential logic of this list of causes. Unfor-tunately, we do not yet have sufficient datato calculate regressions of the responsefactor on soil depth, slopes and storm sizes.In the meantime, this list will serve as a guidefor the selection of variables.

The calculation of Ry is difficult becauseof the lack of precise methods for estimatingtotal water yield, as well as the scarcity ofhigh-quality streamflow records. We canget around the first difficulty by using theore-tical methods and it is to be hoped that theremay be similar short cuts for determining theaverage amount of quick flow. Since Ryseems to be less dependent on precipitationthan Rp, it may be more responsive tomorphological features of watersheds. How-ever, the simpler factor Rp is easier to visualizeand, if corrected to mean precipitation, may

RESPONSE OF SMALL WATERSHEDS TO PRECIPITATION 289

tell about the same story. Either factor wouldmeet an obvious need of researchers andplanners for a convenient numerical handlefor describing the general hydrologic behaviorof a region, basin by basin.

There are about 50,000 small watershedsof 20 square miles in the humid eastern partsof the United States; each of these has acharacteristic response factor which, if evenapproximately known, would aid plannersin the allocation of funds and in designcriteria for water resource development.Experimental results and prediction methodsmight be grouped and extended partly byresponse classes, as well as on the basis ofgeological formations, soil types, vegetalcover and climate. For example, the appli-cation of predictive techniques such as runoffcurve numbers, the unit hydrograph, hydro-logic condition classes and multiple regressionmethods might be improved in accuracy byroutinely including or adjusting for localnumerical response factors. Mapping hydro-logic response by regions would be no smalljob, but it is to be hoped that every streamreach will not have to be gaged to providesuch a map. Regressions of response onmorphological factors will help extend experi-mental data. On smaller management blocks,skeleton diagrams of stream networks mightbe color coded according to response factorclasses, revealing at a glance the responsecharacteristics of working compartments.Such hydrologic response maps would beanalogous to soil type maps, with which theymay prove to have some useful correlations.A scattering of small gaged watersheds withineach physiographic province may be sufficientto rough in preliminary maps; many suchrecords exist but not always in a formamenable to flow separation by computer.

As the preliminary data in Table 6 suggest,some unusual relations may be expected toshow up when hydrologic behavior iscompared by numerical ranking. If furtherdata bear us out, it may surprise many thatsome improved croplands appear to control

the water that falls on them more efficientlythan some forest lands. Also, if the experi-mental units in Table 6 are representative ofthe eastern United States, then in the longrun only 10 percent of the precipitation (23percent of the total water yielded) is releasedas quick flow. Only a fraction of this 10percent can be classed as channel interceptionand overland flow, since much direct runofffrom forested and other well-vegetated landmust be subsurface flow. While it is riskyto place an average figure on channel inter-ception and overland flow in this region, itmust be greater than 1 percent, the approxi-mate percentage of the land occupied bychannels, but is probably less than half theaverage quick flow, or roughly 2 in. out of54 in. of precipitation on these twenty-fourwatersheds. This conceals many importantexceptions, but nevertheless the crude averagetends to put overland flow in some perspectiveas a component of the total hydrologic cyclein the East.

Often it is not averages but the largestprobable event that most concerns thehydrologist. Mean response factors alone willnot define flood peaks or flood frequency in aquantitative sense. But on the average wemay expect that the largest probable event inany area will produce higher peaks, largerflood volumes, and do more damage and beharder to control in basins with high responsefactors. The response factor is a simpleconcept, basically a mapping technique,which should aid the flow of ideas andexperience between watershed managers andresearchers.

LITERATURE CITED

AGRICULTURAL RESEARCH SERVICE (1965) Hydrologicdata for experimental agricultural watersheds in theUnited States. U.S. Dept. Agr., Misc. Pub. 994.496 pp.

HEWLETT, JOHN D. (1961) Soil moisture as a source ofbase flow from steep mountain watersheds. Southeast.Forest Expt. Sta., Paper 132. 11 pp.

HORTON, J. H. and R. H. HAWKINS (1964) Theimportance of capillary pores in rainwater percola-tion to the ground water table. E. I. du Pont de

290 JOHN D. HEWLETT AND ALDEN R. HIBBERT

Nemours and Co., Savannah River Plant, DPSPU64-30-23. 13 pp.

HURSH, CHARLES R. (1944) Report of the subcommit-tee on subsurface flow. Amer. Geophys. UnionTrans., Part V, 743-6.

SNYDER, W. M. (1962) Some possibilities for multi-variate analysis in hydrologic studies. Jour. Geophys.Res. 67, 721-9.

SOPPER, WILLIAM E. and HOWARD W. LULL (1965)Streamflow characteristics of physiographic units inthe Northeast. Water Resources Res. 1, 115-24.

THORNTHWAITE, C. W., JOHN R. MATHER and D. B.CARTER (1958) Three water balance maps of easternNorth America. Resources for the Future, Inc.47pp.

WHIPKEY, R. Z. and P. W. FLETCHER (1959) Precipita-tion and runoff from three small watersheds in theMissouri Ozarks. University of Missouri, Res. Pub692. 26 pp.