Purchased by the foraService for t;4-ticial use

Reprinted frominternational Symposium on FOREST HYDROLOGY

Proceedings of a National Science Foundation Advanced Science Seminar held atThe Pennsylvania State University, Pennsylvania

Aug 29 — Sept 10, 1965

PERGA MON PRESS — OXFORD & NEW YORK — 1966

ACCURACY OF MEASUREMENT OF RUNOFF FROMEXPERIMENTAL WATERSHEDS

JACK ROTHACHER and NORMAN MINER

Hydrologist and Associate Hydrologist, Watershed Management Research, Pacific NorthwestForest and Range Experiment Station, Forest Service, U.S. Department of Agriculture,

Portland, Oregon

ABSTRACT

Errors in field measurement of streamflow from experimental watersheds vary with (1) the design ofthe control section, (2) measurement of flowing water (area times velocity) to obtain rating tables andformulas, and (3) with the type and installation of the recorder. Errors in compilation of data are theresults of conversion from a record (trace on a chart or punched tape) of depth of water in a weir tovolume of flowing water for a period of time. Charts can be read both manually and mechanically witherrors of only a few percent. Automated equipment coupled with computers eliminates human errors andminimizes recording and conversion errors. Minimum error obtainable under the best conditions isprobably about 3 to 5 percent.

INTRODUCTION

Measurement of water is critical becausewater is a valuable resource. On experimentalwatersheds, it is even more critical, becauseour understanding of the physical processesaffecting flow and our ability to demonstratethe effect of changed conditions hinge onaccurate measurement. The accuracy mustbe sufficient to enable us to detect changes instreamflow from one period to the next. Thisis tied primarily to the calibration of water-sheds. The question we will try to answer is"How accurate are streamflow measurementsfrom present structures, recorders, andcompilation methods?"

First let us discuss the meaning of thewords "precision", "accuracy", and "error"—three words often used interchangeably.

"Precision" is the degree of refinementwith which an operation is performed or ameasurement is stated. In statistical use,precision is the inverse of variance about themean. A precise measurement is not neces-sarily accurate.

"Accuracy" is the degree of conformity tosome recognized standard (true value).

"Error" is the difference between a

measured or calculated value and a true(standard) value.

Accuracy and error are similar but willbe used in this paper as the complement ofeach other, i.e. an accuracy of 95 percent isequivalent to an error of 5 percent.

Accuracy and precision are not thesame thing. A traditional example is themeasurement of the length of a table witha foot-rule that is only 11.5 in. long. Theanswer of 37.56 in. is quite precise, but theerror is 4 percent if the true length is 36 in.Repeated measurements with the same rulewould confirm the precision, but would giveno hint of the accuracy.

Flowing water can be measured withprecision by repeat measurement, but underfield conditions it is difficult to determineaccuracy of streamflow measurements becausethere is no standard for reference. The bestmethod for estimating accuracy may beindirect, such as the consistency withmeasurements elsewhere or the addition ofparts that make a known total as in a waterbalance. When streamflow from a singlewatershed is related to precipitation or otherfactors, as in a water balance, absolute

705

706 JACK ROTHACHER AND NORMAN MINER

accuracy is required. When streamflows fromseveral watersheds are compared with onekept undisturbed, relative accuracy (pre-cision) is required. Pseudoaccuracy is oftengenerated by neglecting to state knownlimits of error and by carrying extra decimalplaces.

There are two general sources of error inestimating runoff from experimental forests:(1) field measurements and (2) compilation ofdata. For this report, review of accuracy offield measurements is limited to instrumenta-tion at the gaging station: i.e. the controlsection, the rating, and the recorder. Althoughcompilation of records is rapidly passinginto the field of automation, some sourcesof error are common to both old and newtechniques for converting a line, or points,to rates and vol umes of streamflow.

FIELD MEASUREMENTS

Measurement of runoff begins with thecontrol section which may be either naturalor artificial. Reinhart and Pierce (1964)have described the types of installationsgenerally used for research on small water-sheds.

Natural Control SectionsNatural control sections in a stream are

generally chosen where depth, width, andvelocity measurements can be made con-veniently, and where the channel is suffici-ently stable to permit determination of arating curve that remains relatively un-changed with time. They generally are usedfor large streams where artificial controlsections are impractical. It is often difficultto obtain a satisfactory rating for extremehigh flows because of the short time involvedand the difficulties caused by debris. At best,error might be controlled to +5 percent. Inmost cases, estimates of streamflow made atnatural sections would not be this good.Eschner (1965), studying the effects of forestprotection on streamflow in an Adirondack

watershed, states that the 50-year streamflowrecord was considered good. Daily error wasestimated to be less than 10 percent andmonthly and yearly, "more nearly accurate".

The U.S. Geological Survey (1963) statesthat:

The accuracy of streamflow data depends prim-arily on (1) the stability of the stage-dischargerelation or, if the control is unstable, the frequencyof discharge measurements, and (2) the accuracy ofobservations of stage, measurement of discharge,and interpretation of records. "Excellent"indicates that, in general, the error in the dailyrecords is believed to be less than 5 percent ;"good", less than 10 percent ; "fair", less than 15percent ; and "poor", probably more than 15percent. The records of monthly and yearly meandischarge and runoff are, in general, more nearlyaccurate than the daily records.

Artificial Control StructuresMost experimental watersheds are small

enough that some design of artificial controlsection can be used efficiently. Artificialcontrols have several general advantages overnatural sections and, if properly maintained,give a more accurate measurement of stream-flow. Rating of the structure may be deter-mined in the hydraulic laboratory or it maybe field rated. Once determined, this ratingusually remains unchanged with time, pro-vided the installation is carefully maintained.Leakage due to loss of water throughimproper tie-in of artificial structures tobedrock is an obvious source of inaccuracy.Control structures which pond water aremore subject to this error than those thatcause little or no change in the stream profile.Although a faulty structure may not give anaccurate estimate of the true volume of waterpassing the measuring point, it is customaryto assume that small leaks are unchangingand do not affect before—after comparisons.Flow through the structure can be meas-ured with a precision characteristic of thedesign.

Flumes are most satisfactory where sedi-ment and debris are problems which mightdestroy the accuracy of sharp-crested weirs.

ACCURACY OF MEASUREMENT OF RUNOFF FROM WATERSHEDS 707

They are often designed for higher capacitiesbut are less accurate at low flows than somesharp-crested weirs. Laboratory tests (Robin-son, 1960; Brock and Krammes, 1964)indicate that flumes may be subject to con-siderable error when approach conditionschange markedly. Brock and Krammes,testing four velocity-of-approach conditions,found that, based on average rating curves,the error of discharge varied from 14 to 20percent for small flumes and 11 to 20 percentfor large flumes. This indicates the range oferrors due to deviation of field installationsfrom the laboratory design. Field rating ofeach flume should considerably improve theaccuracy. Another source of error resultsfrom a gradual change in the coefficient offriction. Algae growth may gradually decreaseflow velocity, thereby raising the stage. Theresulting overestimate is particularly signifi-cant during warm seasons when streamflow islow.

Sharp-crested weirs are generally consi-dered the most accurate design for measuringstreamflow. While they are generally consi-dered to have a limited capacity they can besuccessfully used up to a height of 5 ft. Sincetheir geometry is well defined and fieldconstruction, if carefully done, can duplicatelaboratory installations, they are often ratedin the laboratory. If properly maintained,they can give measurements accurate towithin 1 or 2 percent.

It is often difficult to maintain installationsto laboratory specifications. King (1954, pp.4-11) points out that ". . . standard condi-tions for accurate measurements have notbeen determined . . . and even so would bedifficult to maintain . . . there are influencesnot clearly understood which affect the dis-charge over weirs and that in the presentstate of the art the weir cannot be called aprecise instrument for measuring water." Heshows that various formulas developed in thelaboratory vary by 1 to 5 percent. Dischargeis increased by slight rounding of the edge ofthe weir blade and rusting of the upstream

face. Barr (1910, see King 1954, pp. 4-14)found he could increase discharge over apolished brass weir plate by about 2 percentby roughening the upstream face withvarnish and emery dust. Distribution of velo-cities in the channel of approach and ventila-tion below the nappe are other factorsinfluencing discharge over a sharp-crestedweir. In the case of a rectangular weir, adepressed nappe, caused by wear on theblade, algae growth, etc., can result in a 6percent increase in flow at low heads. Thiserror is particularly troublesome at very lowflows. At the Fernow Experimental Forest, avolumetric check of a number of 120° V-notch weirs showed that on some installationscheck measurements were considerably diffe-rent from flow based on a standard formula(Hornbeck, 1965). One of nine weirs checkedshowed appreciable error (over 5 percent)up to 0.58-ft head, several required adjust-ment for stages up to 0.25 ft, and on onlytwo of the nine did checks indicate that theformulas could be used without adjustment.To minimize this error, it is generally recom-mended that the head of water over a sharp-crested weir should not be less than 0.2 ftunless careful rating measurements are madeon the specific weir being used.

There are many specially designed sharp-crested and broad-crested weirs and flumeswhich meet the needs of special situations.Review of limited data available indicatesthat the average field installation probablyhas an error of ±2 to 10 or more percent.Holtan et al. (1962), discussing the use ofexisting structures such as culverts, con-servation structures, spillways, etc., state thatunder good conditions field structures,similar to models used in the hydraulic study,can give an accuracy to 90 percent. Aug-mented by field measurements, error can bereduced to 5 percent. When conditionsdeviate from those under which the structurewas designed, errors may approach 30 per-cent. They warn against economizing onstructures in long-term studies, as the cost

708 JACK ROTHACHER AND NORMAN MINER

of the structures may be small compared withthe total cost of the study.

Other methods of measuring flowing waterin streams have been attempted. Probablyone of the more interesting ones, which iscurrently being intensively studied. employsthe use of fluorescent dye (Rhodamine B).Volume of flow is related to the dye concen-tration after thorough mixing in the stream.A continuous record might be obtained on aclock-fed absorbent paper strip. A fluorometeris used to analyze concentrations. No estimateof accuracy is currently available.

Measurements at the Control Section.Basically, flowing water is measured in cubicfeet per second (c.f.s.), or cubic meters persecond, as the product of velocity and area(width x depth):

Q = AV

where Q = c.f.s.,A = area (depth and width in feet),V = velocity in feet per second.

(i) Area. Because the geometry of the con-trol section remains relatively constant (exceptpossibly at times in natural sections), only

one measurement, depth, is required fordetermining area. With suitable hook gagesand other devices such as the bubble gage,depth can be measured with a precision of±0.001 ft. Whether accuracy is also to thisdegree depends on the care with which theinstallation was made, the type of controlsection, and the operational procedures used.

The influence of an error in gage height oninstantaneous measurement of flow can becalculated for any given installation. It is, ofcourse, greater for weirs or flumes that havewide bases than for those with narrow bases.For V-notch weirs, a small increase in flowduring low flow will produce a relativelylarge increase in head and good sensitivity.In spite of this, for a triangular weir the errordecreases with increasing depth (or discharge),although not as much as for rectangular weirs.Excerpts from a table by King (1954, table 46)show that for a 90° V-notch weir and a 2-ftrectangular weir the error is larger at lowflows, smaller at high flows (Table I).

(ii) Velocity. The speed of water flowingthrough a control section may be moredifficult to measure than depth (or area).

TABLE 1Errors in Weir Discharge Resulting from Errors in Measurement of Head

Flow Error in headV-notch 2-ft rectangular weir

Head Error in discharge Head I Error in discharge

c.f.s. ft ft c.f.s. percent ft c.f.s. percent0.05 0.001 0.20 0.0006 1.2 0.04 0.002 4.0

0.005 0.003 6.1 0.011 21.20.010 0.006 12.2 0.022 43.6

0.10 0.001 0.27 0.0009 0.9 0.06 0.003 2.60.005 0.005 4.6 0.013 13.20.010 0.009 9.1 0.027 26.6

1.00 0.001 0.69 0.004 0.4 0.27 0.001 0.50.005 0.018 1.8 0.027 2.70.010 0.036 3.6 0.055 5.5

5.00 0.001 1.32 0.010 0.2 0.82 0.010 0.20.005 0.045 0.9 0.045 0.90.010 0.095 1.9 0.090 1.8

25.00 0.001 2.53 0.025 0.1 2.45 0.025 0.10.005 0.125 0.5 0.075 0.30.010 0.250 1.0 0.150 0.6

* Excerpts from table 46 (King, 1954).

ACCURACY OF MEASUREMENT OF RUNOFF FROM WATERSHEDS 709

A good velocity meter may be accuratelycalibrated. However, in rough channels,characteristic of most mountainous streams,vertical and horizontal components of flowand other instrumental conditions occurwhich differ from conditions of calibration.Addison (1941) comments that observersclaim the error is +1-2 percent; critics claimthe error is ±3-5 percent. Velocity measure-ment at 0.6 depth gives maximum error of 3percent of the mean in the vertical and anaverage error of 1 percent. Measured at 0.2and 0.8 depth, estimates should be within amaximum of 1 percent of mean verticalvelocity and an average error of 0 percent(King, 1954). Velocity measurements innatural control sections are generally takenat a number of points across the channel sothat no more than 5 percent of the flow is inany one section.

The velocity head-rod has been tested andfound to give velocity measurements withinan accuracy of ±2 percent at tranquil flow(Goodell, 1957). If, however, flow is super-critical, errors may approach or even exceed12 percent (Robinson, 1959).

Most weirs rely on stilling ponds ofsufficient dimensions to reduce velocity to anegligible value (less than 0.5 ft/sec). Ifrequirements of depth and width of pond aremet, velocity of approach correction can beignored. Use of the relationships given byKing (1954) shows that for a 120° V-notchweir with recommended width and depth ofstilling basin, the correction for velocity ofapproach is less than 1 percent. When sedi-ment is allowed to accumulate in the stillingpond so that it approaches H (head of waterin notch) rather than the recommended I H,velocity of approach correction will doubleto approximately 1.4 percent for a head of2.5 ft. With this same elevation of sediment,velocity of approach correction would benegligible for a small head of water.

(iii) Rating tables and formulas. Measure-ments in streams are reduced to rating tablesor formulas requiring only one measurement—

depth. Laboratory calibration of designedweirs, flumes, etc., give reasonably accuraterating tables, i.e. they are based on standar-dized measurements. We have already dis-cussed errors that result when laboratorydesigns are transferred to the field.

Many installations are field rated. Whilethis helps to control errors resulting fromvariations from design dimensions, accuracyof rating tables depends on the accuracyof area and velocity measurements made.Precision can be determined, but in mostcases it is difficult to determine the accuracyof field-rated installations.

RecordersAt the typical research installation, depth

in the stream is recorded on some type ofrecorder which gives a continuous trace of aperiodic punch or signal. Most of theseinstruments can be read to the nearest 0.001ft. But recorders are subject to a variety oferrors, including time, gage height, and chartexpansion.

Many chart corrections are compensatingas streamflow rises and falls. Althoughgenerally unimportant on an annual basis,they are much more serious on a day orstorm basis. Errors as high as 8 to 29 percentmay occur on a daily basis but from less thanI to 4.2 percent on a monthly basis (Hart,1962).

Hart (1962) recommends that time cor-rections be ignored if less than I hr and thatchart expansion be considered negligible ifpaper expansion is less than 0.007 ft. Paperexpansion can be controlled by use of desic-cants and can be determined by use of doublebaseline markers.

Gage height seems to be the chief sourceof error and the principal correction needed.Stevens (n.d.) points out that float-operateddevices are subject to error due to float lagand line shift.

Float lag is related to the diameter of thefloat and the resistance of the instrument.

710 JACK ROTHACHER AND NORMAN MINER

Stevens shows that the error can he appreci-able with small floats:

Diameter Error in feet due to float lag, byof float force to move instrument

(in.)

1 oz. 3 oz. 5 oz.8 0.006 0.017 0.029

12 0.003 0.007 0.01516 0.001 0.004 0.00724 0.001 0.002 0.003

metric pressure does affect the instrument, itis not believed to influence appreciably thestage height measurements. Telemetering ofdata has all the advantages of punched tapebut accuracy is still subject to those errorscharacteristic of the basic measuring device.

COMPILATION OF RECORDS

We should note that this is a compensatingerror.

Errors due to line shift, or the shift of theweight of line (or tape) from one side of thefloat pulley to the other, are much smaller.They range from 0 to 0.002 ft for a 5-ftchange in stage when a beaded line is used(6 oz per 100 ft) to 0 to 0.004 when a metaltape (14 oz per 100 ft) is used. Correction forline shift can probably be ignored for mostresearch installations, as changes in gageheight seldom exceed 2 or 3 ft and errors arecompensating.

Recently, digital recorders have beenaccepted as reliable instruments for auto-mating the measurement of streamflow. Gageheight is punched on a tape at predeterminedintervals, usually twenty-four to ninety-sixreadings per day. Streamflow based on hourlyreadings was found to differ from that basedon 15-min readings by 0.7 percent for a 400-square-mile drainage and by 2.75 percent fora 10-square-mile drainage (Carter et al.,1963). For research purposes, where smallwatersheds are often used, it would bedesirable to use the 5-min punch out, at leastduring periods when streamflow fluctuatesrapidly. Pierce (1962) reports that the digitalrecorder may have time errors as small as5 min in 6 months, and a maximum error ofstage of 0.002 ft. There is no paper expansionerror and no human handling of data butother errors characteristic of float-operatedrecorders are present.

Bubble gages are reported to be accurateto 0.001 ft and do not have the disadvantagesof float lag or line shift, characteristic offloat-operated recorders. Although baro-

The accuracy of the final flow figuresdepends on analysis procedures as well asfield measurements. An error in chartreading has the same effect on discharge as asimilar en or in adjustment of the recorder.An additional error results from conversionfrom a curved line on a chart representingdepth of water in the weir to a volume (orrate) of water.

Strip Chart Analysis by Manual MethodsIf the trace on the strip chart is a true

record of head in the weir and the ratingtable or equation is accurate, we could,theoretically, determine total flow withouterror by taking enough points on the curve.In actual practice, we may use a short-cutmethod, picking points manually so as tobreak the curve into a number of straight-line segments.

The several methods of point picking giveessentially similar results and have beendescribed in detail by Johnson and Dils(1956). They suggest that errors may be keptsmall if time intervals are limited by consi-deration of (1) curvature of stage hydrographand (2) curvature of stage-discharge relations.Error due to curvature of stage hydrographcan be reduced by breaking the hydrographinto segments having no appreciable curva-ture. However, since over 95 percent of thetime a hydrograph is concave upward. theassumption of linearity results in someconsistent overestimate in discharge.

Johnson and Dils suggest breaking thehydrograph into short intervals (determinedby rate of rise) to minimize error due tocurvature of sta ge-discharge. Bethlahmy

ACCURACY OF MEASUREMENT OF RUNOFF FROM WATERSHEDS 711

(1964) carries this principle to its ultimateend by integration, thus eliminating all errordue to curvature of the stage-dischargerelationship. Comparison of discharge deter-mined by the conventional hand method(average-rate) with the integration methodshows that, at a head of 0.4 ft in a 90° V-notchweir, the error of overestimate by theconventional method (assuming trace isbroken at hourly intervals) ranges from 0percent with a rise of 0.001 ft/hr to 4.7 percentfor a rise of 0.2 ft/hr. Since this is not acompensating error, Bethlahmy suggests themore precise method (integration) be usedwhen electronic data-processing machines areavailable.

The curvature of both the stage hydrographand the stage-discharge relation produces acumulative error resulting in an overestimateof discharge.

Strip Chart Reading by Mechanical MethodsA number of mechanical methods have

been developed for chart reading, includingthe discharge integrator developed by theU.S. Geological Survey. The older dischargeintegrator may give results in error by 3 to5 percent and cannot be used below 0.2-fthead. Newer Benson—Lehner or Gerberchart readers are faster, cause less error, andcan be set up to produce cards or tape for usewith electronic data computers. Hibbert(1961), checking the Benson—Lehner OscarModel K oscillogram reader on an artificialhydrograph, found manual point picking andthe chart reader to vary by considerably lessthan 1 percent.

The digital recorder and telemeteringdevices go one step further by providingpunch tape directly from the recorder withoutrequiring the intermediate stages of chartrecording and chart reading. They are presetto take readings at regular intervals. Previousmention has been made of the range of errorsresulting from several recording time intervals.For small experimental watersheds, where weoften have sharp fluctuations in the hydro-

graph, a short time interval between readingsis necessary to record instantaneous peaksand to minimize overestimates due tocurvature of the stage-discharge relationship.In view of the reported performance of theseinstruments, the speeding up of analysis workby electronic data processing, and theelimination of human errors, automatedequipment seems to have considerable ad-vantage over more conventional instrumenta-tion. Its one major disadvantage is lack of agraphical trace which can easily be scanned.The advantages outweigh this disadvantagefor most studies. If urgently needed, anelectronic computer can be commanded toproduce a graphical trace.

In streamflow compilation, the number ofsignificant figures required has frequentlybeen discussed. Leonard (1962) pointed outthat the width of the pen trace may beequivalent to 0.001 to 0.002 ft of stage. On anA-35 chart, the smallest division is 0.01 ft butstage height is visually estimated to the nearest0.001 ft. Comparing "relative accuracy" ofreading to 0.001, 0.005, or 0.01 ft, Leonardfound seasonal and annual flows differedonly slightly:

Stage height Growing Dormant(to nearest season season

foot) (in.) (in.)0.001 3.910 41.603 45.5130.005 3.882 41.588 45.4700.010 3.907 41.585 45.492

Even at relatively low summer flows,growing-season precision showed errors lessthan 1 percent. For instantaneous measure-ments, especially at low flows, precision ofmeasurement may introduce important errors.This is illustrated by Table 1.

DISCUSSION

We have quoted a number of figures thatmight seem to indicate that streamflowmeasurements are not highly accurate. Thereare many possible sources of error. Some arecompensating within themselves and othersare not necessarily additive.

Annual(in.)

712 JACK ROTHACHER AND NORMAN MINER

Accuracy need depends in part on the pur-pose of the study. We must consider whetherchanges expected will be large enough todetect with the information and techniquesat our disposal. Or, if a change of 10 percentin streamflow is of no practical value, itwould be difficult to justify expenditure oftime and money necessary to improve accuracyto 5 percent. Reinhart (1962) has found differ-ences of 0.06 in. in monthly streamflow and10 percent in annual flow to be of statisticalimportance on the Fernow ExperimentalForest.

Perhaps our most valuable contributionhas been to alert the researcher to manysources of error in streamflow measurement.We might go one step further by listingpractices recommended to reduce error to aminimum.

Use artificial control, preferably a V-notch sharp-crested weir, if capacity isadequate for the drainage and sedimentand debris are not serious problems. Thesmaller the flow. the more sensitiveinstallation required.

Field construction should accuratelyduplicate design criteria.

Where practical, periodically field checkdata from laboratory design at eachinstallation.

Carefully maintain design characteristicsof the installation.

Perform frequent checks of the installa-tion to minimize errors resulting fromhazards such as clogging of weir blade,accumulation of sediment, clock stop-page, etc., which cannot be completelycontrolled.

Use automated punch or telemeteringrecording equipment to eliminate humanerrors and minimize recording andconversion errors.

With such an installation and standard ofmaintenance, it should be possible to reduceerrors to 5 percent or less. Such an installationcannot, however, be installed and then for-gotten for weeks or even months. There maybe more of a tendency to do this with auto-mated equipment.

It is obvious that considerable care isrequired to obtain an accurate measurementof streamflow from experimental watersheds.Hornbeck (1965) has described requirementsfor accurate streamflow measurements withthe 120' V-notch weirs used at the FernowExperimental Forest and concluded thatvalues obtained are in error by not more than3 to 5 percent. At Coweeta HydrologicLaboratory, they strive for accuracy to thenearest 1 in. or an error of about 3 percent ofannual flow. These examples probably ap-proach the best accuracy obtainable underpractical field conditions.

As one concluding thought, we mightpoint out that streamflow measurements are,in many instances, more accurate than otherhydrologic and climatologic measurementssuch as soil moisture, ground-water changes,rain and snow measurements, and characteri-zations of physical features of the watershed.The relative accuracy of these other measure-ments is especially important where stream-flow is related to other factors (single water-shed analysis) as in predicting yields orattempting a water balance. Good accuracyof all factors is required here with reasonableprecision. Where experimental watersheds arecompared with one another (control water-shed technique), good precision is requiredwith reasonable accuracy. From our dis-cussion and that of others earlier in theprogram, it appears that at this stage in theart of streamflow measurement, it may bewell to rely heavily on the control watershedtechnique.

ACCURACY OF MEASUREMENT OF RUNOFF FROM WATERSHEDS 713

LITERATURE CITED

ADDISON, HERBERT (1941) Hydraulic Measurements, aManual for Engineers. John Wiley & Sons, NewYork. 301 pp.

BARR, JAMES (1910) Experiments upon the flow ofwater over triangular notches. Engin., Apr. 8,Apr. 15.

BETHLAHMY, N EDAVIA (1964) Improved procedure forcalculating stream discharge. U.S. Forest Serv. Res.Paper PNW-10. 6 pp.

BROCK, R ICHARD R. and JAY S. KRAMMES (1964) Astudy of trapezoidal flume models at San Dimas. U.S.Forest Service Res. Note PSW-50. 12 pp., illus.

CARTER, R. W. et al. (1963) Automation of streamflowrecords. U.S. Dept. Int. Geol. Survey Cir. 474.17 pp., illus.

ESCHNER, ARTHUR R. (1965) Forest Protection andStreamflow from an Adirondock Watershed. Ph.D.Thesis, New York State Univ., College of Forestry,Syracuse, New York.

GOODELL, B. C. (1957) Streamflow measurement. U.S.Forest Serv. Watershed Mangmt. Res. 20 pp.

HART, G EORGE (1962) In: Proceedings, watershedmanagement research conference on collection andcompilation of streamflow records. U.S. ForestServ., Northeastern Forest Expt. Sta. 55 pp.

H IBBERT, ALDEN R. (1961) Processing streamflowrecords for machine computation. U.S. Forest Serv.,Southeastern Forest Expt. Sta. 12 pp.

HOLTAN, H. N., N. E. M INSHALL and L. L. H ARROLD(1962) Field manual for research in agriculturalhydrology. U.S. Dept. Agr. Handb. 224. 214 pp.,illus.

HORNBECK, JAMES W. (1965) Accuracy in streamflowmeasurements on the Fernow Experimental Forest.U.S. Forest Serv. Res. Note NE-29. 8 pp., illus.

JOHNSON, EDWARD A. and ROBERT E. D ILS (1956)Outline for compiling precipitation, runoff, and

groundwater data from small watersheds. U.S.Forest Serv. Southeastern Forest Expt. Sta. Paper68. 40 pp., illus.

KING, H ORACE W ILLIAMS (1954) Handbook ofHydraulics. Ed. 4. McGraw-Hill Book Co., NewYork. 556 pp., illus.

LEONARD, RAYMOND E. (1962) In: Proceedings,watershed management research conference oncollection and compilation of streamflow records.U.S. Forest Serv. Northeast. Forest Expt. Sta.55 pp.

P IERCE, R. S. (1962) In: Proceedings, watershedmanagement research conference on collection andcompilation of streamflow records. U.S. ForestServ., Northeastern Forest Expt. Sta. 55 pp.

REINHART, KENNETH G. (1962) In: Proceedings,watershed management research conference oncollection and compilation of streamflow records.U.S. Forest Serv., Northeastern Forest Expt. Sta.55 pp.

REINHART, KENNETH G. and ROBERT S. P IERCE (1964)Stream-gaging stations for research on small water-sheds. U.S. Dept. Agr. Handb. 268. 37 pp., illus.

ROBINSON, A. R. (1959) Report on trapezoidalmeasuring flumes for determining discharges in steepephemeral streams. Colo. State Univ. Res. Found.Civil Engin. Sect., Mimeo CER59ARR1. 9 pp.

ROBINSON, A. R. (1960) Report on model study of atrapezoidal flume for measurement of stream dis-charge. Colo. State Univ. Res. Found. Civil Engin.Sect., Mimeo CER59ARR57. 14 pp.

STEVENS, J. C. (n.d.) Hydraulic Data Book. Leupold& Stevens Instruments, ed. 5. Portland, Oreg. 144pp., illus.

U .S. GEOLOGICAL S URVEY (1963) Surface WaterRecords of Washington. Water Resources Div.451 pp.

DISCUSSION

SHACHORI: If we look at the whole hydrologic balance, runoff measurements are the most accurate determi-nations we can make; more accurate than areal precipitation, evapotranspiration, interception or ground-water recharge. If runoff measurements are between 2 and 5 percent, no other measurement can even getclose to this.

ROTHACHER: You are quite right. I had included a similar comment in the prepared paper, but omitted itfor brevity.

HEWLETT: If we look at streamflow measurements only in terms of what can be measured through the weirblade, it is the most accurate measure that can be made. But if we look at it in terms of whether we are measuringall of the flow from a catchment area, it is quite a different matter. Each small catchment is a sort of law untoitself. Flow is missed or gained either by flow into or leakage out of the watershed and this should be con-sidered part of the error in measuring streamflow.

•