Rainfall Sampling on Rugged Terrain - AgEcon...

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MICROCOpY RESOLUTION TEST CHART MICROCOPY RESOLUTION TEST CHART N~TIONAL BUREAU OF STANOARDSmiddot1963-A NATIONAL BUREAU OF STANDARDSmiddot1963-A

CONTENTS

Introduction _____________________________________________________ _ The problem_______________________________________________________ _

Prior approach to the problem___________________________________ _ Contemporary recommendations for itnprovemenL _________________ _

The studies________________________________________________________ _ Rainfall characteristics study____________________________________ _ Comparative rain gage study_w __________________________ ________ _

Paired rain gage study in Bell watershed __________________ ___ _____ _ Nature of error influencing rainfall samples___ _______________ ________ _ Improving the rainfall sampling networL _____________________________ _ Correcting inaccurate measurements _____ ______ __________________

Method for correction of past rainfall records___ _w _______________ _

Deficiency of vertical gage catchesjn test sample _________________ _ Efficacy of Fourcadee equation in correcting vertical gage sllmples____ _Stuuruary___________________________ __ _ _ _______________________

Literature cited___ __ _______ _ __ _ __ ___ _ _________ __ __

1 5 6 6

11 13 10 24 27 31 36 36 37 38 39

D~cember 1954

Forsale by the Superlntendento( Pocmnents IT S Goernmeot Prrntlng Office 1Yushlngton 25 D C - Peke 20 cents

iRainfaIISanpling

Terrain 1

ByE L HAMILTON forester California Forest anel Ronge Experimenl Slalon foresl Service

INTRODUCTION

~Ieasurement of tbe oltuneof -ater preeipitated on the earths surface is llil imporhlut division of tlie Seiellte of climatology Rllinshyfall measmements provide fundamental knowledge needed in estabshylislullg the climatic type of 11 region and rainfall (lata are essential in many fOlms of land management whether for agric1lJture municshyipal development the production of hydroelectric power or flood control Rainfal] cannot be measured dilrectly like the flow of a river but must be estimated from samples taken at VlUmiddotjOU locations on the watershed For a satisfactory estimll e the individual samples must be as accmate as poisible Hnd elosely 1npresentatlve of thenreas to whichthey are applied The teehnique of precipitation measureshyment in popuJated areas yhieh are usually of minor relief has presented but little difficulty On the other hand precise determinashytions of rainfall in mOllntainous regions pres-eut many ditlicuJties

Sampling tec1miques Uld instrumentation require modification as measurements are e2tended illto the high COtmtry to pro~icle busic hydrologic information for use in water supply problems stream regulation and flood control In this report lire preentecl the results or detaj1ed research jllto the process of how lLnd how much precipitashytion is delivered to ltlotll1tliu wntenhecls and lc(ol1llIclldations for impr(~emel1t in lainfaJl sampling ploeec1me

THE PROBLEM

In 1933 the Clllifomia Forest and RtUlge Experimevt HtlLtion ~tarted a program of llytlrologie research ill southern California CUshyrected toward the development of principles and practices of manageshylllent for chapalTal-(overecl watersheds (19) Tlle tlrea (fig 1) selected lor the investigations included Big Dalton and Sttll Dimas

J Suhmitt(d for 11l1ulicatioll May U)jol bull 1llLintained by the Forlgtllt HprYic~middot U S Department Ilr Agriultul ill coshy

operation with the UniYeJsity of ClllifollIill lIeriele- Hulk numbers in IJllll~nthe8es l(~fer to Literature (i(gttl p m

1

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2 TECIThICAL B1LLElIN 1090 r DEPT OF AGRTCLTLTCRE

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FlCnE 1--1 lilly a nn a lid Jl1 ilf lIlap of 1 IItlJt of ollllHrIl California

canVOll -ituatpd ill till Sail Uabril] ~l()lllllaill within till AIlthmiddot Nat~olla] Foret ClPpla I III i]( nortllPllsl of t 11( (ity oJ GhIHlont Calif This ana tleigIlHtld a- till Sail Diulll- EX]llrillltlltal FOlmiddotPt ill (Olllshymon with lIIost outhpln Cn lifolnia IlI011ntaills is eltaraderiz(c1 by exttmiddot(middotmely ruggtd topoglaphy (fi2middot~) It is slwrpl di-sP(tpd into V-ShHwd canYOllS and kniJplikt ridges host incliyidllal slo]gt(s lllllge hl gradient 10111 W to 1~() jJlJ(Pllt TllP ltl pragp gnuliPllt of thp forest is estilllatpd to bp (iO percellt 111 glIllral the sloJlls (ol1lplising

3 RAIFALL SAnfPLIXG ox RUGGED TERRAIN

these expl1inlPntal atPlhpd Hrp (oll1palublp in ~tPlPI1P~ to pn1tf of tIl 8iPlIt X(yada and the n()d~ r()ulltail~ ill thi (ountn and to th(gt Alps in EHlopemiddot

TIll rppan~h plOgllllll lPllipj m u(tllltp dfII1I1il1atioll of tlw rainfall Ollllloulltaill wntplhpd~ To ltfl([ llli IlWnlInlltl1t Olll or the most intplliw rainfall amplillg y((Il- klloWII 1n dpignNl (31) Thltp llt1l)(1IP(1 a I1d (ight(Pll 11 in gagp of t 11( r - WPtt h(gt1 Blllpan tn - illlhp ill llialllpt~l (1P di(riblltPll OP1 all aLea of

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FlIrItI 2-Ubliqlll yil or a nmiddotli r 111lt11 f t ht ~all Dillin El)(rill 1111 I al FUlIt prtital al i~ xag-~(IIIL

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1 IW)) Hl1l iiIlU U (OIIPIlI rat tOll of I lt (0 PYllT -0 ](11 (Hi l) Thl rain gag- ( pI (lilt ill n HIp(llailinl di-lrihlItioll at InU-llliltmiddot illtlnals alol1 (01110111 (IiI ([H(ially huilt fOI tIl( 11l1jlOP at ~lI(J- 31 011- Jl()(I- Hlle )j(J(Ijool pllutioll alld Oil all Cltlwl anlilshyalgtl(gt traib and lOud TIli 11111111(1 of ditlibul ill Iain al- m cOll-cidplpd tIl(gt IJl()-( pIllt1 icul 0111 1J(lall~p of (lip Jllggp(l tl~IIaill and dln-p IllItih (0(1 Till indiddllal ~n(gt Wlll ill~ta IIrl (r i(lilh in H((oldnlltP ith -pl(iticatioll -lt (p by tIllU -I patitpl BtllPHli (17) T1H( ill-lllltioll- tIPPe (hI dpilHbilil) of hll[lIill thl ragP from till i1l(1 nlld lPOIllIIlPIl(((l tIl( IIP of hlllbIHIY fPIlll- alld walb for (lip jIlIlIH)- Sillcp 1(llIP aile lIlb PIl lIkill itt thi ullillhnhitpd wi ldp rill il H hOjlPd lllll 1l11ililllt plottmiddot(middot[ ion agaillt Iillt llI()PlllllIt wCJltld h( alronlpd I)) Ic(ul illg tIll Ilun gagps ill opellings withiu [hI ChapHITHI (0(1

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LEGEND I 1

bull FOREST ~l l - BOUNDAR1

-gt1 II 1 -=j WATERSHED BOUNoaRIES 11 lId (r-- ~_I4 ( X INTErI4EDIATE WATERSHED NUMBERS

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-1) CONTOUR TRAILS

1 - ROADS

~tr I IIIn ~~____l-=~edi bull SleNOARO RAIN GAGE ETENSIVE SYSTEM

~ STANDARD RAIN GAGE INTENSIVE SYSTEM

FlllU t-( Jli~illa I flallllllin~ network of fI1S jni II gagN 011 till Sa n Dill1llH EJxpprilllelltnl1ltol(Rt

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Data were collected from the established network of rain gages and

analyzed (31) after 2 years of observation to determine whether the distributionopound samples was statisticaily adequate to give a precise measure middotof rain catch by watersheds The analysis indicated that re~lsonably tllOrongh sampling of rainfall Tariation was being accorrlshypIished but gaye no assurance that the samples tl1emselves were accushyrate Large clivergences in rain catch -ere noted and were assumed to be actual variations in rainfall due to topographic influence (~7) Some of the variations were so extreme however that further knowlshyedge of the behavior of ralnfa]l on terrain of this rugged nature seemed necessary

Prior Approach to the Problem

Determination of total precipitation on au area has il1vHed study by investigators in many lands The important publications on the subject have been smnmtlrized by Horton (14) in lOIn Brooks (6) in 1938 and Wicht (30) in 1944 Universally the infueu(e of wind all the catch of l)recipitation by rain gages has been stressed The effect of wind on the catch of a rain gage had been noted as early as

bull 1841 by Thomas Stevenson (~6) In 1861 Jeyons (1(J) founelelefishyciencies in catches of rain gages elevated some distance above the ground Stlrface as compared with adjacent gages located on the ground He concluded that the dis(reptmcjes were caused by turshybulence in the ail flo about the gage a (ondition hich has been termed the Jevons effect_ As a solutlon Jevons proposed tlmt rainshyfall be sampled by Jarge catchment surfaces on the ground

Nipher (930) in 1878 made an important American (ontribution to improvement in rainfall measurement by designing and experimentshying with a shield for rain gages Behyeen 18(j5 anc1 1872 experishyments conducted at Rotherham Englanel (935) relative to the effect of wind velocjty on the catch of rain gages at varying h~ig1lts above the ground resulted in the adoption of specifieatiolls for tlle exposure of rain gages in the Brjtish Isles The gage ntS to be installed so that its orifice -as horizontal 1 foot aboye grol11lCl level alld surshyrounded by a circular turf wan on n radius of 5 feet (4) This is undoubtecUy an excellent l1lode of placement ill terrain of minor reHef but would be definitely unsuitable for the wnc1 precipitous mountains of southernCajifOlllin

Kosc111nieder (18) in 1933 experimented with a (rage e posed in n pit and surrounded by a honeycomb 01 cellular ~leet lIIetal device to reduce turoulellce This procedure elimiuatec1 wind errol from rainfall samples at a windy mountain location but KosChrniedel rejected the jnstnUation as i IllpracticaJ for extended use because of jhe chance of cloggjng by snow leaves animals et( Pagliuca (931) W110 worked on MOllllt vVashingtOll ill K ew Humpsll ire adyocIlted the use of shields somewhat on the Nipller pattelll for precipitation gages and stated further that more represe1ltative sHmples were obtained jf both gage anclshieIcl were illstallec1nornllt] to the slope Nejther of these two reports was twaHablein published form tU1til after the San Dimas installations were compJeted

s DEPT OF AGRICULTURE

Contemporary Recommendations for Improvement

Shortly after the StUl Dimas rain gage lletwork as put in operation there came to our attention the report of investigations by Robert Pels a French hydrologic engineer on the subject of rainfal1 sa mpling in the French AJps (1 ~93) Pels stated in effect that in the high bullmountains the measure of total precipitation is in error if one multishypEes the horizontal projectional area of the watershed by the total depth of water as given by the conventional yertically placed rain gage Aetua]]y he said storm rainfall must be considered as a vector alld the true rainfall sample can be computed by the elementary theory of vectors on the condition that the magnitude and direction of tlle storm vector in space are known On len] ground 01 on vatersheds where the topography is gentle rainfall samples by (ollYentiona] yertishycal gages are sufliciently accurate In steep mountain regions the conTentional rain gale will not giye a true sample of the rainfall The sample is in error because in mountaillous regions storms are usually accollipanied by strong yinds These winds drive the rain onto the slopes at inclinn6OJ1s from the Yertica1 sometimes approachshying the horizontal Pels gaye sewlmiddota1 illllstrations of c1efi(ient rainshyfall sam)]ing in the Alps and rec-ollllllellded that hydrologistR ho ere working in cOlllparable regions inYestigate the tlecuracy of their measurements

THE STUDIES

Since it appealell flom Persmiddot (lElllonstratiollS both obselntiona1 bullftl1clmathematical that- salllpling lUillfall ill windy mountainous areas required more thall lllere 1y setting out gales the research staff of tlle San DillUlS Experimelltal Forest planlled detaiJed stlldies of raillfall behavior and sampling methods Two types of experiments -ere deshysip-ned One was to determine how physieal iadors such as yind speed and direction might affect lllin (atehes The other ms to (ompare rainfall sall1ples from gages having fI Ytlliety of types of placement and different exposures with aetual ground catches of IJrecipitatioll4

The studies -ere c1ireetecl primarily to-ard detelmillinfY t11e effishycacy of gales tilted Jlormal to the giouncl surfaee as Hdy~cated by Pagliuca (Bl) This mode of gage plneemellt (fig 4) -as a simplifishycation of the Hstereomiddotmiddot gage recommended hy Pe] for salll])ling inshyclined rainfaU on steep slopes PelS (J2-J) Ploposecl shapiJl( ~the 1middotni11shygage receiver to simulate that part of the yatershed to b sampled We reasoned that tilting and orienting the gage alConling to the slopl to be sampled would ereate the sanlP pffp(j and Saye the york of taj]Olmiddoting eaeh gage to the topography For self-recordino gages (fig 4) which cannot be tined bllt must be kept plumb the gage 1eshy(eiver could be ~ut so that th~ o1i~ce sloped aeeording to the gnldient of the land surface a style ol reCeI-er employed later by lIayes (1J)_

How a vertical rnin gage may be in error and huY a gage wit]1 receiver orifice parallel to the slope may give a true sample of inclined bull

SpechLl elpdit must 1)(gt gh-en L)lp F H(illllllill and Lowell A Andrews for deyelo[llnent of inHiTlIIl1cntntion Hnd lol](ction 01 reeords

7 RAIXFALL SMIPLlXG ox RCGGED TERRAlX

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rail Oil HIl imlilHd -WfllP an -lHlWll ill liI)- ) lilt () HIH] tlw Jol1owiJlI cliI1ioll of tll(OIP( ia 1 (OIIlPpl

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III tIll nle of ltiltll fnlJill mill (ti ) n tnw Illti-UIP j obshy(ailwd l)y pj(lIlJ lilgP nlill fall~ illto tl ~()ltJllall-jl(lI lOulHl oljficp of tll Hltila gg fillillg it (0 a Ih[1t11 of lillill ulIl liillg II Ilea~-1IIPIlIPllt )1 -11 lIlJi ilwhe TIIP Jaill ilP orilicp j (Iw horizontal PlOj((ioll of tIll -loping 1I1tnp Oil ilih lw al talld- ~jn( Iaiufall i- 11[ OIll)JIIlaquomiddotd 1 (pIll ()PI tllP pmip(pd OJ map area (11 nliwp tllP l-illd dppth of wat(1 ill Ihp II j a ()IJPl II I I1l I of t II( Hill JllIJlilig thp IOIIIHI TIll Jilll oj tIll til((d middotgp lJlPPIl(shyall olilip pilip ital ill 1Ilw Oil (h hOljtolllal pIojpdill1l of til lope Tltp hOlizolltal PlojPItiol1ll1 IIpa oftlH olilin i ((Illnl to thp lop tIPI llwitipiP(l by tllP oiIlP of tIll 0ll ltlllg(P Tltp Iopl llltt Ill iO ([l1tI( iIHmiddotIH illdin(pc ill rIll ti1I1P j 1I1Irltiplip(l by nl to gPI IIH (lJoiPllioI1nl Hlltl oj qlltIP illdlP Tlll tilt((IHp (hlll n(li (11)j( illlip of Iaill rlii(lI j pqllal (011 1middotill( (Jppth onl il PIOshyjetiomtl llpa Till altlllli dlptll oj walll ill Ill gHP whplI fl tP b Pi ill llil (lti1 positiol1 is 11 jn]l 111 oldpl to alc-l1lnt(

30aU141) 1middot4- ~

rE~IOAt ~UliLETINI096 U SDEPT OF AGRlCULTURE

I inch of roin I inch of rain

falls through foils through

opening of opening of

50sq in 35 sq in

I bullI I SLOPE AREA

CATCH IS 35 cu in

I I

sectsect Slope area colch

of 50 cu in reaches of 35 cu in reaches depth of I inchon I depth of I inch on projectional area projectional

Slope orpa catch J area

of 50 sq in of 35 sq in

HORIZONTAL PROJECTION OF HILLSIDE (~APAfiEA)

FIGUltE fl-How rain falling verticlill) Oil It slope il -1l1Il1pletl equally w(ill hy II bullmin gnge placed either verticully or normal to the slop(i

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ONRUGG~bD TERRAIN

Sample of same rain V~RTICAL falls through opening RAIN GAGE of 35sqin SLOPE AREA CATCH IS 35 cu in

I I TILTED

I RAIN GAGE SLOPEilREA CATCH IS 50 cu in

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~ S lope area catch Slope area catch of 35 cu in reaches of 50 cu in reaches dpll of 07 inch on depth of 14 inches on projectional area projectiona I area of 50 sq in O of 35 sq in

HORIZONTAL PROJECTION OF HILLSIDE (MAP AREA)

ll)omIE G-Bow inelined Inin fnlling Oil a Iope is iu(olleetly fulllvled by a veriicalrllinage and COITCCtly Illllllled hy II tilted gage

10 TECHNICAL BULLETIN 1096J U S DEPT DF AGRICULIURE

the trne ve16ca1 rainfall the catch of the gage in inches depth measshyured with the gage set ill the yertical position must be dimiddoticled by 07 the cosine of the slope angle Thus YertilllJ rain falli1lg on a slope can be measured equally well by a wltieal gage or by a gage tilted ]101111a1 to the slope provided that this slope area catch is coneeted to equal its horizontally projected or map area catch

In the second case (fig G) the rain is drimiddoten onto the slope at an incljllation of 45 derees from the YelticaJ Assume tlult rain falls throuh the orifice of the tilted age to a depth of 1 inch Tlle gage being normal to the slope a full eirc1e 50 sq1lare inches in area is exshyposed to the fa]] of ra1n The slope area catch of the gage is 50 cubic inches The slope area of the gngeis ronYerted to its projected area 35 square inches as before The 50-cnbie-inell slope area cateh now fills the gage to n deptll of 14 i11(11(s This is th( true l1l(asure of the rain leaehinl the grollnd At the Yeltica1 gage howewl an ellipse is presented to the fall of slnntinl rai1l Henee the same rain that was l11ea~ured as 1-1 inches depth or )0 (lillie 1mmiddothes by the tilted gage iYes the -eriieal ule a en teh of ) eubilt indIes This eatell when applied on the )()-sCjuHre-inch projectional area of the Iae fills it to a depth of 07 inch

It is evident therefore that the w]j-ical gage has not ien a trne measure of the rab reae]li IHmiddot the ground md furthermore tllat the error is serious sincp the veitieal ~ale calllple is onl~ 30 percent of the true sample FOlllCalt1e (rJ) has demonstrated ll1athematiea 11~ that as the storm direction SVillS across the slope this error in sample decreases progressively by a Junction of the eosine of tlle c1iifereJlee hetween gage aspect and siorm direction Hlnce a pair of Iages yertical and tilted on a clue south aspect will be expeetecl to ginmiddot identieal measurements when the storlll is from the east or the west Furthermore if the storm direction is opposite to tlle aspect of the gales the vertiealage catch is greater than the tilted age catch

Thns theoretical eOIl(epts inc1ieate(l fiJmiddotst the inncleCjlltlcy of the conventional verfiea11y installed rll ill gage and se(onlt1 a method for improyement of rainfall sampling teelmique by tiltillg the gale To confirm these concepts a program of researeh inclllding three studies was set up

Rainfall cltamctelmiddoti8tic8-The first stndy was designed to amplify and to localize Pels theorem that true rainfall in countr) of great reshy]ief mnst be determined by sollltion of tIl( ])Jmiddotoblem imoh-jll theshyfluxion of the preeipitatiol vedo] oyer n topographic sllrface To determine the pJmiddotecipitntioll wctOJ it yonld he lleetSsar to measlllmiddotp three components The Yerti(a1 component the north-south eOl1lposhyJient and the east-west (middotoll1lxmenL The yertieal component can be determined by means of an onlillary Yertieally placed rain gage tlleshyother two by means of a clirec-tional rain ~age SineI these (omposhynents of the ndn Yec-to) nre a fllmmiddottioll of wlIld the rainfall eharuetprshyistics study was set Ill) to study wind in its relation to rainfall This would ineJude wind speed and diredion rate of rainfall and the eHp( of wind 011 the direetiOll and inclination of rain (jipn this knowlshyedge of the precipitation v(lttor then a trne ample of rainfall on a rugged mOllntainols slope could be omputed from the eateh of a yertical raiu gage

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RAIlTFALL SAJ1PLING ON RUGGED

001npa1ative rain gages-The second study was carried on in COllshy

jWlCtion with the first study and was designed to determine (1) The possible error in the conventional vertical rain gage by comparingits catch with that of a control catchment surface on the ground (2) methods of increasing the accuracy of rain gages by changing their construction and mode of placement and (3) the relation of wind speed and direction to the catch of the test gages

PaiJedrain gages-In the third study two networks of 22 paired tilted and vertical gages each in a IOO-acre watershed (Ben No2) were compared as to catch This was an extension to the field of techshyniques determined in the second study

These three studies have been reported separately (11 [28 139) but their results have not been dmwn togfther to show their harmonious relation The foDowing review wm indiclLte how they fit together

Rainfall Characteristics Study

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The rainfall chnracteristics study dealt with the behavior of rablfall in relation to wind (11) Rainfall rate wind direction and wind velocity -ere recorded synchronously The vectorial components of rainfull were measured by a directional rain gage 01 Yectopluviometer to use the term aptly applied to it by Pers The San Dimas instrument (fig 7) differeel radically from the one described by Pels (fig 8) but supplied similnr data It consisted of a horizontal and a yertical funshynel mounted on a rotating head -hich was kept pointed into the wind by a vane Rain caught by the fnnnels was directed into separate compartments of the receiver tank one compartment for eilch (luadshyrant of the compass for each funnel

F-34264B

]irmmE 7-Sun DilllnR Yectoplmiometer (right) tipping bucket rain gage (left) and wind measuJmiddoting instrumeuts on Huin Gage Hill

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FIGUltE 8-VectopluYionwtcl dCiig-ned by Professor Hobert Pers Grenoble France

The angle of inclination of the rainfall (i) from any qnadrant was calculated by the fOJlllula

tan i=VH (1) where V is the catch of the funnel ith its rim ill a yeltical plane and H is the catch of the funnel ith its rim in 11 horizontal plane Or theaverage inclination of the storlll could be determined by summing the catch of the vertical lmd horizontal funnels separately and then upp1yipg the formula The instruments were installed on a small hill Rain Gage Hill freely exposed to the prevailing wind

Angles of inclination of the rainfall and average storm directions were computed from data supplied by the vectoplnviometer These angles and directions permitted the determinatjon of rtin yectors for bullmiddot each storm according to the following detinition It precipitation falls at the same inclination and from th(1 same direction throughout a storm then the storm can be represented graphically by a line parshyt11e1 to the path of the raindrops and equal in lellgth to the amount of rainfall as measured by the depth of water caught by a gage with

~RATh-YALL SAJltIPLING ON RUGGED TERRAIN

its axis xgtamllel to the rain Such It line is a vector IHld will give tL clear pIcture of the storm as ~egltrds both (lirectionaudmngnitude Practical use of the ruin vector will be brought out bl t11e section Correcting Inaccurate~IeaslUmiddotements In the present (liscussion the chief use of tlle rain vector is to perlnit the classification of storms

DmjIlg the 7-year course of the study 174 storms occlUTed 1uoshyclueing 251 iuches of rain Of these storms there were (0 over oneshyhaH lllch in flize for which n11 data were complete Analysis of these data showed that southern Californiu storms could be classified as northerly 01 southerly on the bnsis of direction from which the rain Ct1ll1e ald tiUlt these storm classes eouM be related to -wiml speed to the angle of inclination of rainfall [md to rld_nfall intellsity as fo]]ows

Siann C11188 IfortllelJ 801l1Iimiddotfii

StorlllS __________________________________________lIUlllher__ 24 3(1 ~lotal lllUount of rl1ill ______________________________ immiddotlJpf __ 4(1 lli8 Avpragt mlgIe 01 illclilllltiOlL _____________________dp-Ttes__ ln Average wincl spee(L_______________________lllilpf Ill lJ0111__ 4n 114 verngp rainfall intellfltity________________illlllP ]le1 110111-_ O O 044

_-llmlysis of data on hidl this tabulation is based Ahowed that l10rtherly storms usually produce small amounts of precipitation occurring generally at low intensity and at only slight il1e1inations from tll(gt vertical Southerly storms on the other ha11(L Rre the great min producers Theil preeipitation is llSLUtlly of much greater inshytensity than that of i-he northerly storms they are accompanied by higher -i nd speeds than the nOlthelly Atorms and their preeipitatjoll llsually is inelined tl (cmsidentble amount fro111 the yertical An imshyporbult result of this analysis was that measured vahles of the inclinashytion of rain correlated yell with nvprage wind speeds of the storms (fig 9)

The theoretical disCussioll of vertieal and tilted gages showed that yertienl rain falling 011 n slope eould be measllred equally well by either t1- Yeltieal 01 a tilted rain gage 1111lined min which came equally from aU direetions at the saUlI inelination would be caught hY the nrtical gage praeii(ally the same as if it were eltical rain But this study shmwd tlmt Conditions necessary for both gages to be aCCl1rate cl i(] not exist on the experi menta 1 forest Here most of the min Illgt sharply inclined also most of the rain came from the south Since the steep tOpOglRplty had n penerally south aspect these fil1(lings explained why rainfall samples on the experimental fmest were in erlol Thp sizp of the PITOI and a means for obtaining good sllmples were shown by fhl (omparntiYe min gage stndy-

Comparative Rain Gage Study

Three cilculal (Oll(rete eatchment sUrIaees were instal1ed on Rain Gage Hill (fig JO) Thelgte catdunents designed to serVe as controls in the study were set- on sOllth east~ and nortlnvest exposures and were eaeh IO feet in diameter (785 squale feet in area) They were laid flush witll the glollnd surfaec Hnd patmiddotnllel to the slopes whose gradients ranged from 10 to 40 perc~llt Each catchment -was proshyvWed ith a metal bOl(ler strip to prevent loss or gain of water by

bull bull

-1

~ 111

Q ~ ~40 t-------+---~-----+------+---__pound-__l

~ bull ~ Iamp 30

0 bull ~

bull ~ shy~20middott-------t---=~-r~------+------__i

bull~ 1amp 010 lu

~ t

2 4 6 8 10 12 14 16 STORM AVERAGE WIND SPEED (MP Hl

FIGlm )-Helatioll of thc lwernge wind speed of -tOIIIJ to tile angle of inclination of minfal

runoff or splashing Immediately adjacent to each catchmellt eight gages were installed Two sbmdald 8-i11ch Yeathel Bureau gages ewere instaUed Yerticany one with the receiver 40 inches above the ground aud the other in a pit with the receiver at grollnd level Three standarc1~ 8-inch gages were tilted normal to the ground surface with

receivers respeetiyely at 40 inches and 1 foot above the ground and at grolUld level The other tIuee gages included (a) 1m 8-illcll gage of standard height insblJed vertically HJIc1 equipped with a receiver cut on a bias so that the edge of the funnel -as paraJlel to the grollnd surface (this gage was called a stereo-gage as a modification of tlle Pels (23) desigll) (b) a trough type gage 220 square inches in area installed parallel to the ground smface and (c) a 4-inch-c1iametel gage instalJed verticaJly with the l(ceiver 40 inches above the ground

Since it hac1 been concluded in the original report (28) that the COllshy

ventional 1Yeather Burean type rain gage was the most practical we shall consider iu this discllssion OIl]Y the data from the contlo] surfaces and the stlludardrain gages installed with their receivers at the cusshytomary 40 jnches ahove grouud Furthermore since the datil 1btained at the llorthwest aspect iustaUatiol) were judged unreliable becanse of interference by ac1)acent vegetation only the south and east aspect illstallatjons will be discussed

The results of this study ean be SUmUHllized for )4 storms on the south aspect tndi7 on the east as follows

Rainll callglltO-Il~t1~IIJlc(njfi~lii8i((t bull

(illccs) (il1cIC6)OOntrol surfnce on glmiddotOI111(1-________________________________ 1423 1210 Verticnl gnge ____________________________________________ 11921~~33

Tilted gnge____ bull_________________________________________ 1437 1208

15 RAnFALL SAMPLIXG OX RLGGED TERRAIX

bull

bull

shy F 173IJu

VII HI III middotRail (a~ Hij 11 Ill -111 IlillJlh EtriltlUI1l 11111- t oIIOi1l1- ilt~laJillljIlIJ~ i11 ill tl nlinfatl hlrjfmiddotl rht~ and Ibmiddot IIIU]ln)Ulh till Ul --t ntlimiddot ~IJHI J lsJlP(middot

bull Thpp IPldh ~III)Id IIwl Ill Il i1l agl Illt tIll (l1lth np(middott did Ilol in a t I1( ~nlIpll or t IH railt lIIWItill tIll IIJIIIIlI (jilt 101 lIlfn(p Ill Htlll)I(- aPlagpc 1 II(I(Pllt 1lmiddotIiitlIt 01 J() illlItt Ip-bullbullt tIlt U1H t i nll t hI HgP tilt pel lollilal t () Ill JOIIlH I Iopl h jh Ollplld 11 iJwlJp- llloll lllp H JIIIIIIL 1lIltp lIlIlpl( tIppillg Iith till g(Jlllld

303lH ~I-

TECETh-rCAL BUlLETIN 1096 U S DEPT OF AGRICULTURE 1 bull -

catch within 11)ercent At he east aspect there was little diff~rence 1SalldO2 inches 01 15 Jl11d 02 percent respectiYely between the cateh of either the ertical or the tilted tge md the catch of the control surface These fincfulgS were significant beeanse the raillfdl characshyteristics study indicated that the ~rreatest proportion of rainfall came from the south Installing a standard gage at or nellr ground level increased its accuracy but not enough to warrant the arnOtmt of effort required to dig pits and to provide for the necessary splash-eliminating screen Furthermore pit gages are inadequate for snow measureshymentsas pointed out by Kosdulliecler (18) lmc1 they are SLUe to be interfered with by lllinmls and to be choked by windbloHlleaTes ulld other material

10rmiddot~-----------r-------~----~----r---~----~--~

~ ~ 8~--------~---------+--------~-------------~~--~

~ -Ishy

~ CL ~ 6r---------_r----------~--------~~~------+_--------_4

~ gt Cl III

r~

~ ~ 4r---------_r--------~~~------~----------+_--------_4 ~

~ -l

y= 0032 + 0900 x~ ~ 2~--------~~~------~--------_r----------+_--------~ [E

2 4 6 8 10 CONTROL SURFACE CATCH SOUTH ASPECT (INCHES)

FIGL~ItE 11-Rplnliol ()fyertlcul ruin gllge catch to the cateh of 1111 ndjllclnt lontlol l1ltehment sluface at ground len

The illadeq~mcy of the south vertjcal gllge In obtlliJl1ng an JlCCllmte sample of the cttchof the south control catc11illcnt surface is indishycated in the regression graph of figure 11 Likewise figure 12 shows theconiollllity of the tilted gage stunpJes with the catch of the control

17 RAThFALL SAMPLING ON RUGGED TERRAIN

bull catchment surface The least squares equation for the vertjcal gage regression is

Y=O02+0)OOX (2)

and for the tilted gage legrlssioll is

y= -O018+1027X (3)

The regression eoetHcients of 0900 and 1027 for the yertical and tlll tilted gages respectiwly differ from the 011es published by Storey and Hmnilton (98) 1Hunelr ODil50 and1025G The differellce is explained by the fact that three mOle yeats of data yere ayailable fo the c1eriashyton of eqlmtiolls (2) allclmiddot(3) These additional data strengthened the relatiolls indicntld by the le~1Ission It is noteoOlthy tlwt tlw II1Or of the ycrtic-al gage increased appreciably while the tilted gage Ir101 1IIllH iIlld a1111os1 the same

Thl JesuHs obtailwd at both the south and the enst aspects confirm c1is(usioJ)s by Hodon (1415) Oil poundadols inHllenc-ing the estimation of prpcipitation on U llminuge basin HortoJ stated that if tl rainshy

l I I I I - 10 1

Pl- shy

() ie lu

~

i58

Vlt - ~ ~ shy

lt6

~ gt E

~ 0 Ll - ~ -l- ~ ~ ~

(34 Vshylu ltl

~ I- shysect y= -0018 + 1027)(V~2

V -

I I I 2 4 6 8 10

CONTROL SURFACE CATCH SOUTH ASPECT (INCHES)

FWUllt 12-U(llltion of uin Clu~ht in n lllill ~ng( iltp~lllll(l mifntp(1 n((or(lill~ to the slopr anti IISJl(Ct of (he grIIlIHI to lhat tlllIglt lJy 1111 adjacPIl( control cnt(hmPlIt slILfllCc at ground I(middotpl

1096 USDEPTOF AGRICULTURE

bearing wind blows against a mountain slope then the amount of Tain falling on the mountain slope will generaHy be greater than the amount which would fallon an equal horizontal projected area and greater than the amount caught or measllred by a horizontal (rim of Teceiver) rain gage Horton derived an equation to show the extent of the error taking into account the iucliIUltion of the rain the slope of the watershed and the difference in angle between the aspect of the watershed tlml the direction of the storm The term for direction of storm in Hortons equation tells why there is no significant difference between gage samples and grOll11d catch at the east aspect The error hI the rainfall sample is greatest when storm direction is 110r))1a1 to the slope there is no e11or when the d ilectioll is across the slope The cosine of the angle between storm diredionand slope aspect is a relatiye measure of the errol the cosine being greatest (uJlity) for a direction norma] to the slope and zero for a direction across it A more complete mathematical discussion of this subject YaS made by FOlllcade (9) in 1042 and has sened as a useful text durillg later lesearch on lail1faII sampIi ng

In the present study the percent differences behyeell tilted and veltishyea] gages were related to tlit angle of incli natiou of the Ia ill IIlramrecl chuing th( rainfall charaeiPlistics study (fig 13) The iollowing equation s delind by the Illtthod oJ least squares

T= -lHl-+O((lOi (-t)

Y is the perceJlt difflIlJ1(( IJPtW(lIl the c(ltieal amI the tilted gages bull ancl i is the angle of inelinatioll of the rain in d(glpes as meaSLIred by the adjacent YfctopluyiometeL When th( minis bot slightly inclined

40

00

tmiddot

-

-

V middot middot Y-3394+0660 lt middot middot I

m ~ ~ ~ W 60 ANGLE OF INCLINATION OF RAINFALL (I) (OEGREES)

FLGnu l~-nelutioll o( J)lI((lIt (lillprPII(e heiw((l1 Yerti(nl and tUt(( ~IIg-e cutcite) soul h lHJlllt to lht llllgll uf illlliulltiOll of raiufall

~7ALL SAMPLLNG ON RUGGED TER~ 19

there is no difference between the two gages 1mt as the inclination passes 15 degrees the percent difference becomes more and more i11)shy

preeiable Since rainfall lnclination is clilectly related to wind speed (fig 9) the vertical gage error is a function of wind

Thus errors aYCragil1g () percent of true rainfn)] were found to be middotassociated with nse of wrtical gages in these moulltahlOus areas Gages tj]tec1normal to the slope on the other hanel had errors of only 1 percent Tilting the gage anel orienting it to the slope aspect then promised to pr(wide a good means of sampling rainfall in steep mountajns The remaining questjoll waS whether tilted gages gave more accllrate estimates of rainfall 011 a watershed

Paired RainGage Study in Bell Watershed

The third study (~9) begun in 1935 ltompared a network of tilted gages with an already established network of yertical gages in estimntshying the meun prfCipitution on a small Yfttersllec1 Tlle study was set up j11 a 100-acre clraiJluge No2 of the Bell small watersheds (fig 14) whjc11 had beenequippecl for intensie hydrologic studies The topography of Bell watelshedXo 2 is (middotharadelized by sharp ridges and slopes ranging from 40 to 105 percent gradient and by exposures ranging from west through south to 1I0rtheast with south southeast and south west exposures pledol1lina ting-

Twenty-ho rain gtleS had been jJ1stltlled onr the nltelshed in the conventional vertical HlIllUer Oll -foul (ontolll truils at elevations of 25002800 3100 und3400 feet For this study a gage tilted normal to the ground surface waS illstallecl (lose to ealth existing vertical gage (fig- 15) The orientation and tilt of each tilted g-uge was estabshylished hy the lalld slope and aspect in a cilde of 50-foot rtldius about

FIGntE 14-B1l WII tlJslwd No2

20 TECHXICAL Bl-LLETL 1096 U S DEPT OF AGRICt-LTURE

bull

bull

III (Itl(al gaglgt TIl(gt~llIly a--(lIIip(1 (III 11 ~ pal- llllillg Irhitlt lillI( data fol 11 -tOIlII-- I(jp ll(()Idll

AJlllJH11Imiddotj~()ftllllgtdatn h-i(OllltIlld -jllli uri) illdilatld Ihatshy1 Tilpcl gugl ltt-I1l-- (gtl 1IlIaily IligIHI thall till PJlieul gagl

(a tdlP~ lind (Ill I 1lIHgt d i 1llIlI Hl ill (a( l1 dill 10 I j I(i Ilg I itp gag 1It eJP(j dld Iy glPIIt lI tltlll 011 It 1)( lXPPl(Pl Ily (It l(l

~ Tltl IliI(ioll IJPIIlpII (01111 (al((- of tIll 10 1Ii- of glltS (oulcllw IxJlI(--ld by I Ill lx]lollll1tial pjuHtioll

(5) bullill whi(h E is I Ill (slilllal(d apragl aIel 111 (lll tihpd gagl- orl(shyspoJldillg to (it uPIag( (atcit P(J SlW111 (X) ill tIl nlti(al gag

a Till (lllldald PJJOJ of E rHrild fJ()JIl ~) (I) hD 1)([((111

21 RAINFALL SAMPLING ON RUGGED TERRAIN

4 Because of this rather large standard error other factors perhaps including wind direction probably limited the accuracy of the predjctshy

bull ingequation

5 Tiltedgages facing into the prevailing incl showed the greatest excesses in eaten tilted gages fucillg away from tJ1C wind generall) caught less than the vertjcal gages and tilted gages nOlmal to the preYailing wind showed 110 significant differences in catch from vertical gages ~

ThisH11a]ysis~yluch hlml)ed all the obserylttions into a singJe regresshysion did not take into consicle1lltion variations in exposllre of gages directjon of stOlms or effect of wind Y(locity on the inclination of rainfall Storey and vnm at this time did not have the results of the rainfall chalactelis6cs stndyol the ltpplication of thoe results to the comparative rain gage studY To tie these two studitgts more c]osely in with tl1e dah1- col1cctecl in Btgtll watershed No2 anothtgtr ana]ysis was conducted by thtgt wliter Htgtltgt only ID gagtS w~le ustgtd insteucl of the original 22 beeanstgt clI]tgtful checking of the origillal1tgtcolds indishycated thnt data cleliwcl from tlutgte of the gages were enoneousin one case becauie of persistent leakage and in the other two beCatlse the tilted gages were not jnstnlltgtd so illHt theh aspects or directions of tilt were representative of the aspects of the sites

Precipitation estinlHtes fo) the wntershtgtd difleltgtd Considerably btgtshytween the vertical and the tilted gage networks (ta ble 1) The per-

TARLE 1-Mean amma17JJecipitaHon in Bell Icate8ltecl No 9 aB (srishymatNl 7)11 flip (at(l1 of pamhi JtIlOllmiddots of l(ItiNtl and tilted rain gagcN by hydro7ogic ]NU1 1JS-3J

STOltMS 1158 llUl 1 Ixclr IX A~IOllT

E( iumtcd meall ILlll1l1aJ pr(eipitatioll J)ifT(rrlltP in pitimatc

HtorJll~ Itil(ltCI-- prtical)YprUral Tilled

galC gacos

YUIil)( llchs [ I(lcs [wh(~ fgtIrCflll 1pound)3536 tl a (j a n 03 +83 1931imiddot37 1 I a G a x 2 +56 J 9a3S ]2 ii 5 (j 2 +37 1938middot 3n s a S 3 H ~ 1 +26

Total I(ibull 172 + bulllt + 4 9

RT()ltMS ~IOltB JHAX 1 INIII tN A~I()NJ

bull ]935middot31i 5 1S (i 21 5 ~ 2 n 156 HJ36middotmiddota7 J2 a70 -12 (i bull 5 (j +J51 1937-38__ ~ _ It 352 125 i a +207 1938-39 _ _ _ ____ (i 160 1 1il middott 19 middot11 )

TOLal _ __ bullbull __ aI 106 X 12-1 5 -l 165-~~~J 1 By(roopic rear iflthe J2-lIJonth p(riod from October 1 uf 11 gien yellr through

Slptlllllwr 30 of the SlICC()(cling your

22TEltJHlIICAL BULLETLV 1096 U S DEPTOF AGRICULTURE

cent differences were much smaller for storms of Jess than 1 inch than for the Jarger storms AJso the percent differences ill precipitation estimates varied from year to year The difference in the two estimates for all 71 storms during the l)erioc1 of observation was 185 inches or 15 percent

Of the 40 storms less than 1 111lth in amount 10 gaTeeqllal rainfall averages fOl the two types of gages and 8 gave a higher average for the veltjcal gnges T])eBe storms wep Jenelal1y from east west and north quadrants The greater part ox the difference between the vertical and tilted gages came in the 22 southerly storms Of the 31 storms greater thaJ) 1 i]lCh in amoant only 1 storm was 11ortherly and for this 1 the precipitation average by Tlrtical gages was 6 percent greatet than by the tilted gages In the llmaining 30 storms greater than 1 inch in amount the HVelllge eatel) of the tilted gages was Hl5 percent greater than that of the conventional Ylltieal gages Yearshyto-year vtlliati011s evident1yyp)l asociated with diifellIlCeS in the mclination of rainfall These differences resulted from varia60ns ill the direction and windiness of torms

The explanation of tlw Yniatiolls behnen the two rail1faU estishymates from year to year i rOllnel in the (omparatiw rain gage study A good correlatiON had been obtainld for the perlent differences in catch bet-een a yertiea1 and a tilted ruin ~age and the nngle of inshy-clination of rainfall (Jig 13) ~ince BeH yatershed No 2 and Rai)] Garre Hill are only 1 mile HI)art n ttst was made to dltermine if the angles Jl1tHsuJed at Rain Gage Hill would be applicabJe in the watershyshed AVllage annual yalneB of al1~le of inclination i were sumshymarized for Rain Gage Hi11 allCl compared with tlle average annual percent ditfell]wes in rainfall lstiI1late in thl watershed as rol10s

A 11111111 (I-CraII Differr1lce in c8ii11llltesrullaquo oj i lill(rI-I-Iul fIUfIS

Hydrologil ymiddotnrmiddot I(I(I-(t~) (perc1 J193l-3G_______________________________ fi +1fi GJ936-n_ _____________ __ ______ 14 +Uil1937-3k ___ bull_______ __ __________ __ bull _ 41 +OSIfl38-3L____________ _______ ____ 2r +118 I H~drl)llJ~ic ~pal is fIJI l-JlI1l1th lPIiot fllllll Odolll 1 oj 1 iYPIi )par t Iir()l~h

SeI)el1lbpl O of tile IHt(((etlillg r(middotII

This comparison indicated thnt a relation (0111d be (gtslnbJished to provide a better metllS of lstimatin] wntelshld rainfnll 110111 yertical gage catches thll1 could be accomplished by tlw expolllntialequatlon (5) T1)euro p~rcel1tditeleJ1ces IJetween the a era~(s of the 10 verticaJ and tilted gages in Bell middotwatershed ~o 2 for sonther]y St0ll11S were vlottecl againBt the illlgle of inclination of rainfall as measured at Rain Gage Hill (Jig Hi) and the foJ]owing )inear least squares reshygressioneqnatjon Was deliyed

y= -465+064i (6)

in which Y is the percent difference between the Yeltical and the tilted gages and i is the tmgJe of ine]inatlon of the rainfal15 The equation

~ ]tOOl K n A 1tJJIOJ) 01 (f)illmCTISO ~IIIJCl (MGt ~nSI-lIl~nSTS TO TrWlm JAm BASIS Calif If()INt amp Hnll~p Exp Rtu l)rO~r(gtss I(middotport- Jl-I(j ITYI)writshyten]

bull

bull

-shy

J

bull bull

bull

bull

v

bull

v u o Y= -465+ 064i bull bull

bull r =OBB

I 10 20 30 40

ANGLE OF INCLINATION OF RAIN (il (DEGREES)

FIGURE 16-Relation of the angle of inclination of rain from the ~ertical (at Rain Gage Hill) to the difference in catch by Yertical and by tilted rain gages distributed oyer the watelshell

has a correlation coefficient (r) of +088 inrucating a good degree of precision as a predicting equation Equation (6) is very similar to equation (4) for RaiD Gage Hill gages By substituting angles of jnclhlation into equation (6) the percent corrections fo) the vertical gages were obtained These percent corrections applied against the vertical gage averages give the required watershed estimate on a tilted gage basIs

The standard e11or of estimate of tilted gage values obtaiJled through use of equation (6) was 3 percent when cOlllpared with the measured quantities This memlS that in approximately two-thirds of the cases the calculated quanti6es Were no more than) percent in er1Ol when compared with the measured tilted-gage values To test the equation stlll further estimates were made for 10 storms not included in the computation of the equation but for 1rhich tilted gage readings were available In these 10 storms the standard error for calculated yersus measured tilted gage values was 41 percent which is consistent with the base period standard error of 3 percent Comparing these standard errors wjth the standard errors of 85 and 89 percent obtained by Storey and Wilm (f39) it appeared that equation (6) based on obshyserved storm characteristics was a marked improvement over the exponential equation (5) which was based 011 differences between rain gage catches It mllst be emphasized that both equations (5) and (6) are limited in their use to this Ptllticl1lar watershed This limitation followsbecallse equations (5)nnd (6) were derjyed through the

50

shy

TECHNICAJ BULLETIN 1096 U S DEPT OF AGRICULTURE

interrelations of a relatively large block of rain gages located yithill a small topographical segment of the experimental forest Relations of slope gage aspect a11CI wind yelocity in other watersheds would be different from those in t11e Be]] mltershed

NATURE OF ERROR INFLUENCING RAINFALL SAMPLES

The foregoing studies confirmed tIle hypotheses set forth by Horton (14)Pers (53pound) allCI Fourcade UJ) iJ1legllrd to the questionable accushyracy of rainfall measurement in country of great relief These studshyies suggested that our oJiginal rain gage 110h01k whi]e stntistical]y adequate as to number and distribution of raill gages (oJl) fa iled to provide a Correct measure of rainfall h1 some places The sallle studshyies hmmiddoteyer had snpp]ied a meallS of impJoYing the qlla]ito of miJ1shyfall measurelllent The studies that showed the YCrtieal rain gage to be in error proYed 111(gt ellicacy of thC tilted gage The i11clinatjon of fu1ling raill caused by ind in this area of rough topography and low vegetation aceollnted for the fai]ule of the Yertical gagE to giye an accuratC IlHaSlllmiddote of lailllCaching thC ground

The nlation of wind action to the cnteh of rain gageH has been disshycussed at ]en~rth by nUlllY inYestigntoJs (24514 HJ 18 gO 24 26) A1most without exception they attliblli((] deficielleie ill rainfa11 measshyurelllent to tllrbulenee in the ail stJtalll call sed by the rain gage In efforts to 1Clt1uce this tUlbulencC many experimeJlts ere (oJlc1uctd with shields designed and placed to smooth the airflow owr the gagt o]ifiee (gbullJ lO 34) IWstad czn in 19~4 algUlcl tha tmiddot thCHdioll of the shield would be improvCd by inclining it parallel to the ground surface Hncl Pagliuca (21) in 193-1 recolllmelJded ti]Ung both gage and shield normal to the ground surface Thus recognitioll of SOIllC kind of willd Iffect on rain gage Ca t(hCs lesllHed in changes in min gage design and type of placement Pels (52) howewl in] H32 made )10 It](gtntion of any tUlbll]Cnt action of wind hilt obC1e([ that wind iDclined the rain md modified 11is rain gage to take car( of ihis effect

The experiments at 1he San Dimas Expelin](gtJlta] Forest dCsCribed thus far wCle (ontlllcte(1 without an y lt1i ff(gtentin tioll as to wllPtlwl wind ]uld a smooth 01 a turbulent flow 0111 stll(lies showed that ClUcal gages cl id not gin tCClllate meaHl1lCmcnt of Jai nfa 11 )lllehillg the ground am1 thatmiddot tiliH int((IUuty was dlle to 111(gt eonsidCJHbll inclinashytion of OIl rainfall (allsed by wiud The stuclips showed immiddotthe) that tilted gages indiell1Cd nle quantity of rain rea(hing the glOlIlld yith an errol of 1 ]WJ(ClIt or less In order 10 make -lIlC that nothing

had beCn oyelJooked in ou il1VPstigatioll of Jt1infall IIleasulClllent a siwple shuI of mill gage shielding was (oIHlud(ltl Shields of the Mt Vilshington type dpB(ribed by Blooks (t) ~ were COI1StllIchc1 and bhjelclecl and unshielded rain gages WHe compared in two nearby locatiolls

LY8imet(1 OJ(1(l 81udy-IYinlin several lIlIIH]ICd ytrds of Rai Gage Hi]] is aninstallaHon of soil-filled tanks (JSilfletelmiddots) desigrl(d for the determination ofenlpo-tlHnspiratiou losses 110111 ehapal]l Oegetation (8) The lysimeter alea is fiat and about ~ aCIe5 in size SeYen yeltishy(al rain gages installed there for seYeral realS hac1 shown that rainfa11 did not yary appreciably hom one part of the area to another Gage

bull

bull

bull

RAINFALL SAMPLINGONRUGGED TERRAL~

No L-7 one of these was equipped with a shield after 2 years of obsershyyatiol1 and observed for 2 more years Data from L-7 are compared with those from a nearby unshie1ded gage L-1 in figure 17 In the double mass plotting used for the cOl1lptlrison~ a decided change in the behttyior of the shielded gage would be indicated by an abrupt change ill the slope of the double mass line Before shielding gafre 1-7 caught 08 percent more min than L-1 lll insignificant difference After shielding the accumulated catch of 1-7 exceeded that of L-1 by only 18 percent In vie of such close correspondence in the eatches of the shielded and unshielded gages it is evident that the effect of the thield on the catch of L-7 was very slight

Rain Gage Hillsltielded gage study-The foregoing study was COllshy

cluctecl 011 a lenl area where either yeJtical or inclilled rainfall can be measllred equally yell by a vertical gage To determine how the catch of a rail) gage located on l slope 11i(11 might have 11l01e turbushylent air flo than a fiat area ould be affedp(] bY shielding the gage l second study wm made on Hain Gage Hill Hple two vertical gages V-I and V-2 had been jl1stnJled close to the control catchment surface

I I

V 120

Vbull - ~ is 100 lt =shy -II) 0 Vlt 80Iu

V)

ltt -

fshy J

lu 60 Il

V -SHIELD INSTALLED ~ ON Lmiddot7 r-I ~ 40

V~ i lt

S ~ 20

V()

20 40 60 80 100 120bull CUMULATIVE CATCH GAGE L-I 4 YEARS (iNCHES)

Fwll~ 17--HelaliOl of till n((uIIJlllatpd (tc-h of a Y(rtiltnl rain gage on a lewl area to tlll aCtullmlatPlI ateh of n )(01111 gag Iwior lIltl after sili(lding the l(gt(ofld gagt

U ~DEPT OF AGRICULTURE

After 2 years of measurement one gage was equipped with a Mt Washshyington type of shield and the other was tilted llormal to the ground surface 1feastlremento vere then continued for 2 more years

Data from each of the gages both before and after their modificashytion were compared ith data from the adjacent control catchment surface by double mass plotting Accumulated rainfall in gages V-I and V-2 ms plotted against the accllmulnted catch of the control surshyface 011 the ground (figs 18 and 19) Vertical gage V-I diyerged from the line of eqnality with a slope of 091 (fig 18) for the first 2 years of observation showing 107 percent less rain catch than the control For the second 2 years after th is gage as shielded the curve continued to deyiate from the line of equality this time with 1 slope of 088 and again intlicated 107 pereem ]rss entch than the control

100r--------------~--_r--_----~--_r--_--~

CI) lu 80x ~ ~

~ 60lu

~

~ 4 0

x ~ 40 ~

~ SHIELD INSTALLED i= ON V-I I

5 ~ gt ~

20

20 40 60 80 100 CUMULATIVE CATCH CONTROL CATCHMENT SURFACE (INCHES)

FIGlRllt lB-Relation of Ih( aerulllulated cah-b llf a yertil-al rain gae on a slope to the acculIlulated eateh of a second gage before nnt after shielding

On the other hand the catch of ga~e V-2 diyerged from the line of equality at about the same angle (hg 19) as that of V-1 in the first 2 years but after the gage was tilted it caught yirtually the same amount of rain as the eontrol surface The accumulated cntch of the tilted gage differed from the control by only 02 perc nt In this study

_

bull

bull

~ 80 u ~

=

~ ~

60 ~ l )

k 0

13 jo 40 ~

~ j l

5 ~ 20 u

40 60ao 100 CUMULATIVE CATCH CONTROL CATCHMENT SURFACE (INCHES)

FIGURE 19-Relation of the acclUnulated catch of a vertical rain gage on a slope to the accumulated catch of a second gage installed first vertically thentilted

it was clear that shielding the gage did not improve its efficacy whereas tilting it normal to the slope changed it to an excellent samplingmedium

From this stildy it appeals that in mountainous country of the kind under investigation the major error in rainfall measurement results from the use of vertical lain gages and that shielding does not take the place of tilting The Sun Dimas studies have been concerned with r~in rather than snow The effective sampling of snowfall hy gages is another matter and so far its technique has not been satisfactorily developedmiddot Snow fOlms a minor Plopoltion of the precipitation on the San Dl l llaS Experimental Forest undno reselLrch has been conshyducted 1181e ~~lutive to its measurement

IMPROVING THE RAINFALL SAMPLING NETWORK

Having determined that om riLinfall measurements were in error and having found a means of leducing the error ill the individual samples our 11ext move was to devise a sampling hetwork which would provide amiddot better determination of watershed precipitation At

shy

28 TECHNICAL BULLETL~ 1096 U S DEPT OF AGRICULTURE

the same time it was desiraLle to reduce the number of rain gages ill order to lessen the effort required to make the fildmeasurements aIld to process the data Accordingly a llew network was established utilizing fewer gages all but six of whiell wele tiltd Ille gages of this network were to be located according to topographic facets (J92) of uniform slope~ exposure and Ieyation in each of the 12 intermedishyate watersheds comprising the lxperimentnl forest

Tentatively it was decided that there should be at least one gage fol each topographiC fate To mak this prblilllinary assignment of gages a map was prepald indi(ttting tlw altitudinal zones by 1OnOshyfoot interval (lasses Next eadl altitudinal zone of ea(h watlrshcl was subdivided nto at least two areas boundd usually by the stnanl (hannel and tlw diricling ridge laeh of which had a relatiwly unishyform llIajor aSlw(t If the subdiision was laq and its (onfigurashytion included more than one major aspect it was further subdi-i(pcl TlliR proceclule l(stll l-pel ina patte1l1 of Hi-) topog1aphic facets (fig ~O) The assigllllllllt of onl ain gage Pll facet 110- appealld to bl an unbahlllcld distJibution be(ause tltl faclts (1( llIHqual in alpa Hence additional gages blin~ingthe total numbel to 72 wele assigned to the network all(1 careful (onsidemtion of accessibility loutes of tltlel for field ObSPIWlS and raillfall pattlJJ~s jlOlll till original ertieal rain ga~e Ipeolds

This was a (onsidelabll reduction in tlw lllllltlW1 of aes whilh had originally bePIl cOI1Ric1Plld neClsstllT to obtain an adeqllHte SHIll pI 01 -atelshed prleipitaJion TIll 1eduction howlver appeared to be justified OUI 1)1I-ious idea tll1lJ (onsic1lIable variations in rainfall resulted fronl topogmplli( illflLHnc(s -illlill a lilllitpc1 area was in erlor as ca n Iw shown by to exam pIps

Storey had prepalPll a tnulSPlt 0 I topogla ph) alld rainfall (fig 21 11) as a result of his study in the Bpll Canyon t1l(I511(lt1s (27) This study was 1l1ac1( beforp our Iesearch 011 the efree-t of lainfall inClillashytionOll raill gagecttlllPs nlS cOlllplltl ViTl11l the o1iginal ([ttht uSld in the Collstluetion oi Ih Iainfall tTanspd- was COIIedld by (laquouation similar to eqtUttiOIl (6) but derived fOI the inc1iviclua1 gagps 01 the J)(tolk a llew 11101( a(cUlah millialJ pIOfiII (fig 21 B) was (onshystructed for the Same area and StOJlll This cOlected plofile showed little varia tioll of Ia i1Ilal lin Ipsponsp to topoglaphy

Vertical gages No 5] and No F-l both tlt the StnH (Ilmtion (5100 I(lt) in t11l hpnd of Fe1n Canyon hae ahout t-he Stl11( aspect and are less than 1~ milp apnrt Both gal~S U( 111 Pry willcly situations During 1() natS (ff obsPlntfion (1)H-4) ) No in (alight 1(i5 i lIellPs 01 rain No F-l -101 fhp SillllP 1)(1iolt1 ctulht ~Oli inelHs 01 lHii pcreent less The cl ifltIPIIe was origi nnl Iy as(li IJtd to topoglaphie differences between tltl 10 gagl loCations Titpd gales were inshystalled in 1)+7 at boOI rage 10(H tiolls and ObRIve(i for +years Duri ng this period gage lIT (aught 102 inches of rain ancllagl F-]T (aught 100 inehes 01gt IW1(pnt less Thus again it was shown that variations in ritin gage (uteh a( reflections of tltl i na((u la(Y i n the operation of the rain Iagps lalhe than llflections of extenal ptlpets bull

From thesl (OIIlIHlisons it was evident tllHt the allJount of rainfall YariatioTl within the ttlIslwcls 01 the San DinwR Experimental Forest waS J111leh hss tha n had fOllnerly b((11 thOlllht

bull bull a ~

SAN DIMAS EXPERIMENTAL FOREST

~

i ~

~ c

~ ~ g

I ~

bull RAIN GAGE

PATTERNS iNDICATE FACETS OF ASPECT AND ELEVATIOK

SCAlt IH MIIU

) LJ1a

]~10llI1 20-DistlihUIiOIl Ilf tntIll uIn guges In n nelw()jk pstuhIlsllcd uccordlng to flll(la nr IIlIlfC)II1I Rlo)e 111111 uspect hy ~ ultlllllll wit hili illlilllllllll lItlmiddotllilPI1H ec

30 TECHNICALBULJt~TL~ 1096 U S DEPT OF AGRICULTURE

STORM OF APRIL 7 1935

Rainfall profile from originalverlical gage data RAINFALL ELEVATION INCHES) (FEET)

5

A 3

2

o 00==-

Rainfall profile from vertical gage data corrected to a tilted gage basis

5 4

3

2

o

o 1000 2000 3000

FEET

FrorltE 21-HolY iUi((unttI Iainfall IllIpl (lin hlIlt1 to lllon(oul eOu(lufioll bull lS to the etIp(i of lopogrnllll~ on ]1Ilipitation A Profile of 11(11 sllIall water- h(ds frolll lit1r( U slorm of April 7 l)~j in TClpOgTII)lhit Infhllnees 011 11(shy(illitatioll by E C ~lOI4r lJ llnfill 1lltIralYlI using (ollpdld ltlata

The distribution of gages by elEntioll follop(1 (lm(l~v the proshyportion of total area in (Hch altitudinal zone

AImiddottO Ra JfllX-Ititu(lillll ZUlli r fllt) UIII) rlelCclIl)

1(iOO-2iiOO_____ ______ bull _~__________ ____ 27 S 2-OO-JOO _____ ________ ___________ middot1-1 4ii aiiOl-1iiorL__ _______________ ~___ ~___ __ ___ 10 lS 400--00______ _____ ____ __--______ -_________ _ 10 )

In indhiclual wai(lhl(ls Ih(gt distribution of gng(s waRgelHImiddotlly within fgt IWI((gtnt of tll( jl(Jccnt 01 uca in (1(11 ZOIl (]08e scrutiny of figure 20 will r(Yeal tlmt some faceis do not (Olltain a rain gage These laeet W(Ie too difficult 01 aetess to p1aee It gage and lainfall for these J11ust bc interpolated 110111 a(ljacpnt gages Otllll faCeis seem to ha ( mol( gages HUln a1( wa )lanted Herp t(CCss is easy and extm gages l)(rlllit c1ltE)minltion of rainfall pattcll1s that can be ada ptpc1 fOI lise in Iupns heIe tccess is llorp clinic-lilt

Rain gages ill Illp Ill Iwtwolk wele plaeed as nen I the center of Hie facets as possibll ELCb gage was tilted normal to the avela~( gradient of tbe -fnCpt and olilnlwl ac(orc1inl to the HYelalC facet itsped Reelal ex(lptioJ1s Ie the pmdi(l oJ tilting the gages Illustbe noted Bceanse of inueessibl( tlITain it lIS llecpssary to locate bull fiv( gag(s in V-Rhqwd (anYOll bottoms a Ild OIW on It ridge top in shyorder to insull adl(juate lleal (oV(Iage by the min gage network

The original and the new 11(tOIl(S were OI)Jatpd togeth(l fol a years A comparison of the results of sampling during this time

RAIKFALL SAlfPLING O RUGGED TERRAIN 31

iucHcated that (1) average watershed precipitation as calculated from the tilted gage DbYork was higher than irom the original Yeltical

-gage nebYork and (2) isohyetn1 maps dJu Yll from tilted gage data ~yeieenerally less (omp1icatecl tluu) maps ltlJl1l flom Pltitu1 gage data The 1att showed ilnndi tlollgh and Ii(lges clue to the variashytions hidl 1utye bp(1l shown to be caused by P1ToneOllS yertical gagecate-hes middot

It sbou1d be kpt in mind that the recoI1l1l1eIH1p(lue of tilt-pcl gages is not based upon the faet that nuse gages gellPlally lnteh more rain than ertiCHI gages on tlll -llll Dimas ExpPIilllellta1 FOlest Gages tilted opposite to tht gtle11 i1 ing d ilPctioll of shlllw show ]ower catches than Y(ltica1 gages On the ~a n Di IIIas Fo]pst tlll ptp(]omishylIating gape aspC(t is souHllJly and l1lost of tlw stOlIllS (OI1lP hom thp sOllth hence 11I0st tiltCd gagls (atch larg(gtl alllounts of rain thun veltienl gages In nOlthprly StOlllli the tiltN1 gagES eat(h less rain than the PLtieal gages Tlw elTOI in rain eateh 1lonl HJti(n1 gages Jlltl bp pihpl positin 01 Iltsectnhyp but is (gtlilllillattd ill pither cnse when thp gnges art tilted

CORRECTING INACCURATE MEASUREMENTS

Ulllinsect til( (OllISP of IPs~al(h on til(gt Jphaiol o IHillfnll anlt1 the

ue(llIluy of min gages Iaillfall data fOIll tl1l oli~6nal llti(al gagt netwolk had b(~n u((ullIuln tillg Olniously t Ilese lln tn IOllld IN]llile eOLTPttioll before they (ould hp a ppl iedi 11 hylt1Iologic ana ~rses A means fol (oJTEdion of elti(al gage data had bepn lh~elopl(l and is providNl ill equation (()) ~I though t-hi eq untioll was a ppl ieab1p ollly in or neal the Bell Iatels]lPds tllP [llilleiples pstab1islwcl there (0111lt1 bl applied e1sp11poundgtI( ii t1w 1(lnJi()ll~ 11(IePII Pltieal and tiltpd gagps and illdination of Iainfall PIp known III ant-ilipation 01 the tak of (olTeding elti(nl gagp data additional illstllllllpntation IU insttlllec1 througliolLt the -lnl)illlls txjlPlilllPlltal FolPst Thirshyteen tiltpd ruin gagps wele paired with exist-illg YPItilal gages at loeations whtre s(Illtiny of tl( Pltic-nl gagl dahl incliluted the need -fol fUlther inquiry int-o 1llatiol1s IJl(WlPII StOll1l behayiOl and rain agl catelles To ddpIII1 i 11( StOlill lltt OIS edop III jollw(-PI mcaslIreshyjn(llts (Il (XtllIdtd thloughout rbl alPH

111( Iotatillg type of pdoplll-iol1lptpl dpscrihed early in this paper Was Ilplac(d hy a diifPI(lIt tPt of iIlStllllllCJlt OUI original dile(shytional Iaill )age hnd I)((n dtsigned to imploP UpOIl nIl (lIll ltlpS(libld hy Pels (B) but 1)1(Jpd lomplient(gt(1 to build alld to liSP simplel ([liee was desigll((1 (fig ~~) It lllS nil assllllbly 0[ fOlll oldinal gal nmizet1-i lOn 1IC1Itl I pi pt plboYs illstlad of Pels fOlll Illll i1 bOXtR ]llislllatil in shape Thp plbows H indws in dian1(t(I W(Ip attadwd by i1011 SII ps to H (pnilal soektt clesignp(I to f-it Oil a 4- by -t-i neh postshyand wel( spueec1 no clpglP(s armli- so that tIlt (ltitn I openi ngs faeed the (HIdina1 points of the (onlpass A (oni(n1 (ontailler ployidecl with a dmin coek at tllP IOWll ell(1 WliS aita(hed to (aell of thp 10(gt1 op(gtlIings of tIll elbols Thl min (atlll of tllCh oplnillg was drained 101 IlpaSUI(IIIPII( into a (y1in(]pl (a1iblatEltl to thr eai(h of Ull H-illeh lin gagt This dilC(tioilal gage hrll oli(n(lt1 ploperl) slIpp1ie(1 IlIPaHlIIes of th(gt hOlizoninl (oll1pc)]wnts of Ininfall Thl eLtieul lt0I11-POIWnt- of t-he eu i IIfn II Im oI)t iItd hy a l)Ii ita1gagt

32 TECHXICAL BrLLETIX 109(1 U S DEPT OF AGRICCLTURE

I l E

bull

-4

FIGItE - (11111111111(111 It li)lIt 11 1IHIIIIln) hrillIl)I 11111111(111 I rainfall ~hilldl(l 111 i111 middotiJlIhmiddotdilIl1lIPr II( III ht in IIII prlit-I1 bull ullipollni (II n1illlall

I-f tIl( lOIlIPiWllt of Illill an knowlI Iain P(tOI fol lulllb of (illl(I lI11ifollll 01 nllrill dill(tion and in(linltiol1 (In )( dllPIshyllIimd H1Hl (llll )l lIpd tl ((I1I]gtllt( trill Iainfall rlOlll a (I(i(lll a~l (alch If tllp pl(ipitatioll fall itll (Onstnllt Ill(inatioll Ind conshy

stallt dllplIIOl1 tit tOI1I1 (11 ill lppn-lItld hy I lill pIndhl to till path of nil I[lindmps alit Iqual III PlIgth t til( laillfal1 H IIlPH

1I1pd by ill dlplh or wa(ll llIt( hy II gag with it lXIS pltlrallll to tIll I1till (Iig ~~) If tit axi of tl1( gag( is not palalll 10 th Iaill rillIlHlIt it (It(h (iUI lw (OllIP1tld f101l1 t hp (atlll or a ga~l hidl would 11lt1Ip It axi palnlll to illl Ialll hill hosl pflpdi( (01 (ntdlshyIIIPIlt) llJP(l is tllP PIcJj(dioll of till ~llgP olili(l Ollto I plailP pqHnshydi(ltlUI to Ill( dil(lttioll of Ihp Inill H Ihp lIHdl h(llwlpn till Ilin lnd the gHgP lxi j (3 (IIPI) til( Hltll Ip(11 til( plalH of (hI ltTl(tin 11 Ipa lind I IH llP oli ri(l j II10 3 alld [Ip dll(t in IInn is I(s (ltn n 11]( unll of t 11( glg( wi fil hy 11 iad III of (0 3 Tit I 111( cll1 It 11 nd I Itl OltUliP of 111( rHg (atlh Hlp abo 1-- thall thnl or a lik ugP lHncling

in 10 (1)( Ill j 11 by t Itl fadm (o 3 Jf~ is t IlP IpIIgI It 0 r Illi st () 1111 p(loJ

t IHII diP clpt It of I ]( gng( (Ikh i (0 f3 111 If ttltl of IIt 11111)1 rliolIII till stortll ( IJI 111 tltl mil yaye 11Ii~

If tl( SjOllI1 do lIot linn Iollslalll dilp(ioll lIlHI illlinlltioll i[ (In II( lokpll into pIII (ctllll to II( nllllliJll of its pha-p- llainfal ill bull (H(h phl (n II 1 hl1I hI IPPIP~(lIt pd hy 1 (dol n lid t I)(-l Y(([OJS (n II Ill ltI(pltI to gi( til( Sllilllllttioll (dOl IP]I 1(11 I ill Ih whol stOllll

Th( SlIlll of p(lns i Ihp H((Olr (Iig ) joinillg Ill( initial [Joint

RAThFALL SAYPLIXGON RUGGEDTERRAIN 33

CC PARISOi OF tFr[CTIVE AREA AGAINST ACT UAL AREA OF lAIN GAGE

SHOWING DIRECTJON or VECTO~S

FnlCIIE ~3-V(ct(Iill] J1]IIPlIIltlitiOIl (If II tUIIll

of the first Yectol to the termina I point of tJH last when they are joined consecutiyely as are 1 J~ and r The projection of the sum of vectors is then equal to the SUlll of the projections of the vectors This means that whether tl)e storlll i~ constant in (lirectjol1 or not the Jength AD of the plojedion of the storm vector onto the 1aill gne axis is equal to the catch of the gage ~

Computation of i the angle of jnclination of ltdnfall and Il the storm diledion was made by means of equu60ns derived by Foulcadei (9 10) FOlllCades publication fo]]owing Pels JetHl appeared

bull JAlIES RomIt1 C flU 8101111 middotECTon llS II ~~ASrllloIImiddotS1 ASH AIII~ICAIlOI1 10 ItAINPALl MEASCIlEMENf Culif FOrest amp RuugeExp SttlprogresS report 1)45 LTypewrittenJ

34 rJECH1TICAL BULLETIN 1096) u SbullDEPTOF AGRICULTURE

while the author middotas~Ulalyzing these data and served as a useful text Computations of i and W are made as follows

R=cRtch of standard velticallain gnge=verticnl component of the storm

middot~i=(atches of YIrtiral apertUles of directional rain gage (recto-W pluYJOmeteJ fig ~~)

i=allgle of inClinatioll of rain (flom the yertical) to =directioll of storlll N-S=RII ]1 f 1E-W=Rc = 1OIlZonta COlllpOJlents 0 t 1e storm

To find tlte (lelage 8t01111 direction

tan i ll =RR anc11ikeise tall ir=RR then tan w=RjRII and Eubstitutillg the abow

I tall 1I=lan itall in (8)

To fil1d 111( ((1(f((f( illril1atio1 of tlte min

tan i=RR cos U and since RIIR=tan in tan ill

tan z=--shy (0) cos~o

Ot

tall if t an =--- (10)

1-1n U

Elenn vectopltnriometels ill addition to the original instnullent on ampdn Gage Hill were installed within the experimental forest They were located so as to determine the components of rainfall illclinatiol and direction at different eleYations at yariolls aspects and under conditiOlls of topography sHeh as (Lllyon bottom ridge top ald side slope

Observations frol11 the vectopuvjollletelS takeJl fOl perlolls of 1jime rangiJlg from 3 to 7 years gave nt]ues of i ill many parts of the experimental fOlest and showed that the inclination of rain varied from ije pJace to another jnresponse to topography and exposure A pattell1 of thent1ues of W was also establIshed These plenliling storm wind directions and angles of inclination of rain are shown in the form of term averages infigurI24

The wind patiellls at V-iallCl V-4 high locations relatively free fromlccaJ topographiC interference indicate that the prevlljJjng flow of ail over the Ixperinlental forest is from south to north Average storm willd directions at the other vectopluviometer locations reflect the drninage pattern of the area Drainages bearing east of JlOrtJI characteristica1ly haye southwester]y storm directions and those bearshying west of north June southeasterly storIn directions It appears as jftJle nllrJOW steep-walled canyon mouths act as nozzles direding the ruJl1ow in the predominant directions of the drainage pattern

bull

~

bull bull ~ ~c~

SAN DIMAS ) bull EX~ERIMENTAL FOREST ~ J l t fi_~ I ( ~-

~_Y )) i --($)J ( --7 lt - A ji ( I f ) t L 1(bVO-- rshy ~V15J ~13~--- lt I ____ - I I I 1 - I --- ~ j lt~Jv

II I 00 - -- r -- ---

7 I -I ( - j -~) ) gt-- I- 1 -- 1- - i V J -1 --shy---- shy ~ J ) ---- - l -- -( ___ ___ 1I r rJ~ j_--- ------f N o

J 1 1--- V12middot- l2l ij) + ~ V7 __-1- ( bull---bullbull g

) ( shy _l tj

-- -VECTOPLUVIOMETER ~

126 I-_-J AND NUMBER PIo ~

(pound) r

~ PREVAILING STORM l2l WINO DIRECTION

SCALE IN 11[$

~ ~ ~ AVERAGE ANGLE OF== ImiddotI~middot INCLINATION OF RAIN

FlllUilE 24-Pntterll of UVlIugP siollll dllllt jon nud II 1(Ingl IIngh~s of illelilllltioll of lujnfnIl ohlnincd OYCI n pciio(( Of yenrs CI ilOIll C(tollluviolllellIS lit iOlIIUons jndicntcll AIIOW8 fly with the wind Ot

i TECTh1(AL BULLETIN 1096 U S DEPTbull OF AGRICULTURE

Method forCorrecfion of Past Rainfall Records

The task middotof correcting rainfall records collected over a period of 14 years was more laborious than intricate The means were at hand ill Fourcades equation through which the quantity of rain falling on a slope could be computed ampom vertical raill gage dahl by means of storm vectors (9)

The equation as dedyed by Fomc de is stnt-ed as follows

1=R+Rtan 1I tan i cos (B-W) (11) where

1= true rainIal1 sample~ R=sample from vertical gnge a= gladientof slope beillg sampled i= angle of inclination of rain (flol1l vertical)

B= aspect of the slope being sampled w= average storm direction

Theadaptability of equatjol1 (11) for use in all (onditions of terrain becomes immediately apparent The elements of the equation a]Jow for varying derees of watershed slope and tonditions of aspect and fmther it is as usnble for storms IHlving many phases of direction change as for ulli-direetioIHLl storms ([ lind B were measured at the rain gage site and i twd 10 -were determined from data on 1ind speed nnd direc60n recorded at the six climatic stations distributed over the Experimental Forest ~-1ld from vectophlyiometer data

The efficacy of equation (11) was tested by nn analysis designed to bring out the possible need for additional elements as for 11l1stallce storm size Data from 13 vertical Iages paired with tnted gages ColJected oyer a period of 3 to 5 years were applied in equa601l c (11) This gave a sample of about 300 observations reprecentiug varyiul conditions of gage exposure and many types and sizes of storms The analysis was designed to show

1 Extent of the c1eficieuey ill the test sample of the vertical gale catches as COlnpnrec1 to the tilted gale catches

2 Emcacy of Fourcades equation for com puti II the true rainfall from ertical gage catches

Deficiency of Vertical Gage Catches in Test Sample

The differences in catch bebeen pairs of vertical and tilted gages were plotted as plus or minus deviations from the measured catch of the tilted Oages (fig 25) The points with very few exceptions fell below the jine showing that the vertical gages 11early always caught less raiJlpoundan than the tilted gages In small storms (1 inch or less) the error of the vertical aLres waS ou]v 2 percent md these storn~ produced on]yabout 10 pelceJlt ofthe rain in the test sample (hible 2)

_In the laleI storms the error increased to differences of 16 25 and 22 percent between the tilted and vertical gage catches

bull

__________ _

37 R~TFALLSAMPL~G ON RUGGED TERRAIN

bull ~

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o z 4 6 a 10 12 14 OBSERVED VALUE OF TILTED GAGE CATCH (INCHES)

jilGgm 2iJ-lrllId of the (1I0r In yertienl rnin uge (middotIt(middotllt ill Ill llIal~middottielil sam)leuro rEjweurosentin vary-in tonllitions of at (xIltllun 111111 lHr(reuront types and liz(s of ltOIlIlS

TABLE 2-0bisel~middoted and (ommted Iainall cattl(8 by 8tOlIIl 8ize elMs

(omshy DiffereIlceVertical TilLed puted IStorllI izc (inchcs) gage catch gagc catch tilted gage I(R) (Tl cltch (r) R- T r-T

llches I Illll ell Inches Perc(111 j)er((ni0-1 ______________ 61 58 -2 -41-5________________

31960 I 381 370 - 10 -35-9_____________ bull __ ]32 177 175 -middot25 -19-16 __________ __ 165 2]2 217 22 +2 ~rotal 676 83J 320 ]9 -1

1 By mcans of CltllJatioll (1])

Efficacy of Fourcades Equation in Correcting Vertical Gage Samples

-ben plotted as in fjgure 25 the diliereJl(es between observed Hlues of the tilted guge cHiches alld those computed by llleallS of Foul(ades ~qlllltioll gaye an altogether different patteIll (fig 26) The general icatter of the poiJJts a bout the holizonta I axis throughout the range of stor1l1 sizesshos that the equatioll as it stands is workable through il wide range of stolmconditions

The computed values of tilted gage catches cOlresponded closely with observed yalues in the test Humple (table 2) For storms of the 0- to I-jl1ch class hich aCtounted for Jess than 10 percent of the totu rainiaH the computation resulted ill a 4 peltent cliiielence twice that between ouselTed catches of vertical and tilted rages Thus we call conclude that eitlleJ Yeltical 01 tilted gages lTlay be used to sample

2 4 6 a 10 12 14 OBSERVED VALUE OF TILTED GAGE CATCH (INCHES)

bull FIGURE 26-Efficiener of Fourcades equation in computiug tbe rainfall indicated by the tilted gat(s frum etica I gage (I t(ws found lleticiPllt ill ligule 2i

rainfall in small storms and that no gain is lealized by trying to correct vertjeuJ gage obselYutiollS for sman storms

Correcting obsenatiol1S fol hnger storms howeyer results hl better estimates of imiddotninfal The 1- to 5-inch storms produced almost half of the rainfall jn the test sample llllc1 the diffeleJJ(e of 16 percent between vertlcal and tilted gages is appreciable III this class corrected vertica1 gage catches were Yithin 3 pelcent of the tilted gage catch In the lext larger storm c1t1sses~ correction js een more yorthwJlile because the cliflclences drop to 1 pelCeJlt for the 5- to 9-1]1(h class and to 2 pelshycent for the 9- to 16-inch class StorJlls in the 5- to 9-U1Ch class are proshyclncels of comddpJabJe luDoll and those jn the 9- to 1G-jJleh class frequently thlpaten floods Thus estimates of waterhed rainfall catch for fiood (olltro] and WHtpl supply purposes can be sadly defishycient if bnsed upon uncollected samples from yc)middottical rain gages bull

bull SUMMARY

Arcllrnte measurement of rainfaJl 1sn primary consideration in wntershed l1laJJa~eJl1ent leseaJchin the rU~I(c1 San Gabriel ~fountahls of sonthelll California Consequently wlle]) the 8m) Dimas Experishymental Forest was established1 lin extensive network of rain gages was set up in accoldallce with the best avajlable knowledge Several inshyvestigators however had cast doubt on the accuracyof watershed Iuinfal] estimates obtained by sampling with conventional vertically pJaced rain gnges A series of studies was made to iJwestigaie the subject of rainfall sampling These experjments showed that (1) A vertkal rajn gage dic1 not give an accurate sample of the rainfall actually Ieaching tile glonndon an adjacent control catchment surshyface whereas It gage tilted lmd oriented normal to the slope and aspect

bull of the contlol surface ~aye a very good sample and (2) the disb-ibushy bull tion of 11) vertical ruin gages in a 100-acre watershed caught 15 pershy cent less rain than did a parallel network of 19 gages tilted normal to tJle slope The inadeqllacy of the Yeltical ~age us related to the speed of wlnd which cnuses ldn to be greatly mc1ined liS it falls

39 RAINFALL SAMPLlNG Ox RUGGED TERRAIN

These studies led to the deYe]opment of a ne- sampling network of rain gages tilted and oriented normal to the slopes they represented_ Additional data Were obtained on the rain caught by vertjeal and tilted gages located tluoughout the experimental forest in areas of topographic characteristics differing from those of the original study alea_ Likewise much information YlIS assembled cOl1cerning rtOlm_ wind velo~ities and the direction of stOllllS_ MeamYhi1e rainfall sampling in several watersheds by the original nehyolk of vertical rain gages had been Contlmled md a great mass of data had been col1ected_ Correctjon of rainfall estimates from these wltical rain gages waR made possible through the use of FOl1)cailps equation by whkh true rainfall can be computed from u -eltical gage reading on l-teep terrain provided slope and aspect of the il)Jain a)e kllmn1 nlld storm direction and Hnle of inelination of the rainfall call be detershymined A study of paIred vertical and tilted gages showed thtlt the tilted gage catch exceeded the w]ti(al ga~e eatch by 10 Jlercent jn about ROO inehes of rain Rninfal1 caleh compnt(gtd from the Same Yelticalgltle data by the use at FOllrcudef eqnation agreed -ithin 1 lXlcent -jth the tilted ale catch

bull

This researe]l program has supplied infolnlaHon concerning the behavior of rairl storms in sonthllJ1 (alifornia mOlllltai]s 1 t 18

detelniined that the incidence of ruin on tlle experimental watersheds waS southerly and ~enera]ly at a (ol1sic1erable inclination from the vertical lhis iJ)eidenee was n flmetioll of willd It was found that in(]ined rain fa]]in~ on incli)wc1 wntelsheltls conllt1 not be sampled a((luately by a (OIw(gtn60naJ rain [n~e in taned with its axis vertical At the same time the middotdefection of tlw wrticaJ gage a~ lolTe(middotted uytilting und orientjl1~ it llOllna] to the ~radient and aspect of nIt slope to be sampled Th(gt plin(iple~ t1l(1 pradiees jJl this study should lulye application in oth(gtr ltgiol1s

LITERATURE CITED

(11 _AX()iY~rOlmiddotS llt- IA IEBlTF DES lIJ~(JJJTATIO1i ImiddotX HAITE ~1()iTGE HI (11)0 Enux

PI Forets 71 (~) 117-11- [TrHIl]atioll ~o ~3-4 r R Furpst ~ImiddotiltP 13l]

(21 BSTA~iOll K 1 and ITl-iEWITS(H J l)W LES SIIC-T1ms AJ~IOJlYX~IlCS DlS plevJO~rtTltES BuL GpJllh~ii Int

)Ioeow Xr 10 il]Il (H- by Kofieurol in )[pt Ztehr [Braunshy(llwpi~] 44 71 In7)

(8) 1)~~ fitU IES 1110)1 ETUES 1-I(gtteorologip n s S 14-JR il)u

(4) BOXACIi- L C V flOO TIlE E~JCTS OF EXPOSt-IU TO WIXll UPOX THE A~IOlJ O~ ItIX (AtGHT

IIY ltATXOAIOES NU JJJI~ ~11llI()IlS OFIltOTECllG HAIXGAlGES ~IO~1 ~lll KM Brit Hllinflll 27-1

() BUAAK C Ingt(j ~F1XSS li~B WlNDES HEI m(aX~II~SSUNGEX Bpitr GpoplIrik 48

21-2gt illus

bull (0) BROOKS_ CILItlES F

InaR ~E~lJ FOR lXtnItSA1 STAXllAllllS ~Olt ~EASelUXG 11IECUllNrtOX SNOWshyFA]L Olt s~or conm Ililtrllatl Union G(Il(l Gpophr- 80( Rei HdroL Bill 2gt 02 pp illtlR

(7) 1lS WIXIHHIJEIllf FOIt IH~(lIITNlmN (1oS AlIltr (lt0]1IIy Ilion

lralls ii3)-fi42 ilJIlS r11ll((middotld

S DEPT OF AGRICULTURE

(8) CODIAN E A and HAMlLTON E L 1947 THE SAN DDLS LYSDIETERS PART 1 THE IYSnmTER INSlALTATION

AND RESEARCH PROGRAr[ PART 2 THE RELATIVE PERFORI[ANCE OF FOVR TYPES OF LYSBIElERS Calif Forest amp Runge EXPfriment ~ta Res Note 47 33 pp illus [Processfdl bull

(9) FOURCADE H G ~1042 SOlfE NOTES ON TIm EFFFclS OF THE DCHlENCE OF RAIN OX TUE DISTIUBUTION OF lAINFALL oVlm rIm snlFACE OF UN LEVEL GlOCiIl Royal Soc So Africa Cape Town Tram 29 23-254 illus

(10) 1945 A NOlI~ ON MtlTlI1LE HAIN-GAGES AlIlel Gpophyl Union Tram 2(

(II) 267-268 [Processed] (11) aunLToNE L

1944 RAINFAU lfEASUHKIENr AS IXFLDENCED BY STOIL[ CHAHACnIIWIICS IN SOUJHEHN CALIFOHN1A MOlNlTNS Amer Geophys Union Trans Part III 02 fi18 illus

(12) 1949 lHI~ PROllLEU OF SUIPIJXG RAINFALT TS MOlKrlSOUS AlmAS III

Pro( HpJkeley RyrnpoiullI on Mathematic-nl Rtntisties and PJobability 469-475 illus Berkeley (nlif

(13) EXES G L 1041 A )[ETHOn OF ~fEASlHIKG RAINFALL ON WTNIlY SOPI~S U f lInllthJ~

Weather Re 72 111-114 iIIus (14) HORTON R E

]f)]fl THE mASnE~fEXT OF lIAINFAIL AXil SSOW Npw EuglnIl(l lIter Works Asloc JOllImiddot ll (1) 14-WJ iIlnl

(15 ) Ifl82 IlIIAIXAGE BASIX CIfARACT~I1ISlTCS Amer Geophys Union Irnns

30-301 illus (16) TEYONS W S

lR61 ON TUE IJIFHHKCY OF IlATK TN AN ELICAIIm (1UGIC AS CAnEn BY WIND Phil lIng and JO1I Sci 22 421

(17) KADEL BENTufrx C bull1022 fEASUHE)fENT OF lHECIPI)NIION U S Dept Aglmiddot Wpntlwl HilI

Rul 771 (il E Tnltumellt Div 3G pp (18) KOSCIIlIIIEDEH H

]fl34 MICTTIODS ANIl IlESlLIS OF UEFIKITIC IlAINIALr NICASlJIlIOIENI III IlANZIG IlEPOItI U S Uonthly Wpntlllr Hey 02 i-7 ilIUi

(Trunslt hy RT Martin) flfl) KltAEIlEL C J and SINCLUIl J D

1l40 IlU SN IJnfAS En~I1DIICKlAT FOIlEST Allier Geo]Jh~s UIIioIl Tlnns21 84-02 illus

(20) NUlIEIl J~ E 1878 ON IllIC IlETEH)IlNATTON OF IHE nWE IlAIXIALI IIY ELENrElJ OG~S

Amer Assoc Adv Sci Pro( 106-108 (2]) PAGLIUCA S

1)34- TIlE fEASTTm~)mNJ OF IR~CUIJAIIOX ON A WINIlY )IOINJAIX Sr~nlT1 Amel Geophys Pniol) Tram Part II gti-ii-i-fl

(22) Plms It 1032 HEfAITONS ENIIIIC LES IJONN(ESPTTYJO)I(~JJnQP~s 11 IES lltECIII1Ashy

T10KS TOTALJ~S RECUIlfl~ms PAn lN JlASSIN INlIlOIWCTfOX A TEJTJJE IIIEOHlQUE Dm LA SmiddotllREOPIUVJOlIrfTHIE If(t(~orologie 75 101-106 mUSt

(23) 1032 NOTE COllf1IErmNlAlIm SUIt IA RlEH EOPLTV[mIIRI E [gtteolologie

75 100-nit (24) RiiRIAIl A

1024 lBEIt IlIE WInKlXClIlICS NTPnEItSClIEN fraquo(JflTZlUICnnIlS Met Ztsehl [BlallnSehweig] 41 240-243

(25) SuJlEn 11 DE CItLE S 1021 lIlI~ ItAINILI OI lnm JlHIlISJI ISLES 20fi PII iIlllS LOlldon

(26) SrII~XSON Tllo~rAS 1842 ON l~IIE UE~ECTS OJ ItA TN GAUGES wnll UICS(HlllION OF AN DflHOVED bull

FOR Edinb New Phil Tour 33 17

ONRUGGEDTERRAIN

~

(27) STOREY HG 1939 TOPOGRAP1UCINFLUENCES ON PRECIPITATION Sixth Pacific Sci Cong

Proc 4 985-993 iUus (28) --- and HA)ULTON E L

1943 A COMPAllATIVESTUDY OF llAIN GAGES Amer Geollhys Uni(ln Trans 24 133-141 illus [Processed]

(29) --- and WIL~r H G 1944 A CO~IPAmSON OF VEUTICAL AND TILTED UAIN GAGES IN ESTDIATING

PRECUITATION ON ~roFNTAIN WAflmSHEllS Amer Geollhys Union Trans 25 518-gt23 illus [Processed]

(30) VICHf C L 1944 nflUOVEMENTS IN rHE GAUGING OF UAiIXFAIL So African Forestry

Assoc rour 12 19-28 ill us (31) ILU H G NELSON A Z and STOllEY H C

1939 AN ANALYSIS OF IItECIPITATION ~IEASUIIE1(ENJS ON ~roUNTAIN WATERshySHEDS U S Monthly Weather Hemiddot (iT 163-172 illus

Us GGVERUMEtiT PRIfITIIIG OFFICE 1954

II

CONTENTS

Introduction _____________________________________________________ _ The problem_______________________________________________________ _

Prior approach to the problem___________________________________ _ Contemporary recommendations for itnprovemenL _________________ _

The studies________________________________________________________ _ Rainfall characteristics study____________________________________ _ Comparative rain gage study_w __________________________ ________ _

Paired rain gage study in Bell watershed __________________ ___ _____ _ Nature of error influencing rainfall samples___ _______________ ________ _ Improving the rainfall sampling networL _____________________________ _ Correcting inaccurate measurements _____ ______ __________________

Method for correction of past rainfall records___ _w _______________ _

Deficiency of vertical gage catchesjn test sample _________________ _ Efficacy of Fourcadee equation in correcting vertical gage sllmples____ _Stuuruary___________________________ __ _ _ _______________________

Literature cited___ __ _______ _ __ _ __ ___ _ _________ __ __

Page 1 1 5 6 6

11 13 10 24 27 31 36 36 37 38 39

D~cember 1954

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21-2gt illus




































ONRUGGEDTERRAIN

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THE STUDIES






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bull F-474698



bull







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21-2gt illus




































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bull F-474698



bull







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21-2gt illus




































ONRUGGEDTERRAIN

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21-2gt illus




































ONRUGGEDTERRAIN

~










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bullbull

ONRUGG~bD TERRAIN


I I TILTED


I bull I I










bull

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21-2gt illus




































ONRUGGEDTERRAIN

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F-34264B


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21-2gt illus




































ONRUGGEDTERRAIN

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ONRUGGEDTERRAIN

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bull r =OBB

I 10 20 30 40





50

shy









bull

bull

bull





I I

V 120


V)

ltt -

fshy J

lu 60 Il


V~ i lt

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V()






100r--------------~--_r--_----~--_r--_--~

CI) lu 80x ~ ~

~ 60lu

~

~ 4 0

x ~ 40 ~


5 ~ gt ~

20




_

bull

bull

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=

~ ~

60 ~ l )

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13 jo 40 ~

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5 ~ 20 u







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bull bull a ~


~

i ~

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bull RAIN GAGE


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A 3

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5 4

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2

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1-1n U




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bull ~

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bull SUMMARY





bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II


bull

bull

shy F 173IJu



303lH ~I-



10rmiddot~-----------r-------~----~----r---~----~--~

~ ~ 8~--------~---------+--------~-------------~~--~

~ -Ishy

~ CL ~ 6r---------_r----------~--------~~~------+_--------_4

~ gt Cl III

r~

~ ~ 4r---------_r--------~~~------~----------+_--------_4 ~

~ -l

y= 0032 + 0900 x~ ~ 2~--------~~~------~--------_r----------+_--------~ [E






Y=O02+0)OOX (2)


y= -O018+1027X (3)



l I I I I - 10 1

Pl- shy

() ie lu

~

i58

Vlt - ~ ~ shy

lt6

~ gt E

~ 0 Ll - ~ -l- ~ ~ ~

(34 Vshylu ltl

~ I- shysect y= -0018 + 1027)(V~2

V -

I I I 2 4 6 8 10








40

00

tmiddot

-

-













bull

bull









bull ingequation








galC gacos















y= -465+064i (6)



bull

bull

-shy

J

bull bull

bull

bull

v

bull


bull r =OBB

I 10 20 30 40





50

shy









bull

bull

bull





I I

V 120


V)

ltt -

fshy J

lu 60 Il


V~ i lt

S ~ 20

V()






100r--------------~--_r--_----~--_r--_--~

CI) lu 80x ~ ~

~ 60lu

~

~ 4 0

x ~ 40 ~


5 ~ gt ~

20




_

bull

bull

~ 80 u ~

=

~ ~

60 ~ l )

k 0

13 jo 40 ~

~ j l

5 ~ 20 u







shy








bull bull a ~


~

i ~

~ c

~ ~ g

I ~

bull RAIN GAGE


SCAlt IH MIIU

) LJ1a





5

A 3

2

o 00==-


5 4

3

2

o

o 1000 2000 3000

FEET

















I l E

bull

-4



























Ot


1-1n U




bull

~

bull bull ~ ~c~



II I 00 - -- r -- ---



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(pound) r


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bull

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bull ~

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bull SUMMARY





bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II



10rmiddot~-----------r-------~----~----r---~----~--~

~ ~ 8~--------~---------+--------~-------------~~--~

~ -Ishy

~ CL ~ 6r---------_r----------~--------~~~------+_--------_4

~ gt Cl III

r~

~ ~ 4r---------_r--------~~~------~----------+_--------_4 ~

~ -l

y= 0032 + 0900 x~ ~ 2~--------~~~------~--------_r----------+_--------~ [E






Y=O02+0)OOX (2)


y= -O018+1027X (3)



l I I I I - 10 1

Pl- shy

() ie lu

~

i58

Vlt - ~ ~ shy

lt6

~ gt E

~ 0 Ll - ~ -l- ~ ~ ~

(34 Vshylu ltl

~ I- shysect y= -0018 + 1027)(V~2

V -

I I I 2 4 6 8 10








40

00

tmiddot

-

-













bull

bull









bull ingequation








galC gacos















y= -465+064i (6)



bull

bull

-shy

J

bull bull

bull

bull

v

bull


bull r =OBB

I 10 20 30 40





50

shy









bull

bull

bull





I I

V 120


V)

ltt -

fshy J

lu 60 Il


V~ i lt

S ~ 20

V()






100r--------------~--_r--_----~--_r--_--~

CI) lu 80x ~ ~

~ 60lu

~

~ 4 0

x ~ 40 ~


5 ~ gt ~

20




_

bull

bull

~ 80 u ~

=

~ ~

60 ~ l )

k 0

13 jo 40 ~

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5 ~ 20 u







shy








bull bull a ~


~

i ~

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~ ~ g

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bull RAIN GAGE


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5

A 3

2

o 00==-


5 4

3

2

o

o 1000 2000 3000

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I l E

bull

-4



























Ot


1-1n U




bull

~

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II I 00 - -- r -- ---



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bull

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bull ~

-















bull SUMMARY





bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II



Y=O02+0)OOX (2)


y= -O018+1027X (3)



l I I I I - 10 1

Pl- shy

() ie lu

~

i58

Vlt - ~ ~ shy

lt6

~ gt E

~ 0 Ll - ~ -l- ~ ~ ~

(34 Vshylu ltl

~ I- shysect y= -0018 + 1027)(V~2

V -

I I I 2 4 6 8 10








40

00

tmiddot

-

-













bull

bull









bull ingequation








galC gacos















y= -465+064i (6)



bull

bull

-shy

J

bull bull

bull

bull

v

bull


bull r =OBB

I 10 20 30 40





50

shy









bull

bull

bull





I I

V 120


V)

ltt -

fshy J

lu 60 Il


V~ i lt

S ~ 20

V()






100r--------------~--_r--_----~--_r--_--~

CI) lu 80x ~ ~

~ 60lu

~

~ 4 0

x ~ 40 ~


5 ~ gt ~

20




_

bull

bull

~ 80 u ~

=

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60 ~ l )

k 0

13 jo 40 ~

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5 ~ 20 u







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bull bull a ~


~

i ~

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bull RAIN GAGE


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5

A 3

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3

2

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o 1000 2000 3000

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bull

-4



























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~

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bull

__________ _


bull ~

-















bull SUMMARY





bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II






40

00

tmiddot

-

-













bull

bull









bull ingequation








galC gacos















y= -465+064i (6)



bull

bull

-shy

J

bull bull

bull

bull

v

bull


bull r =OBB

I 10 20 30 40





50

shy









bull

bull

bull





I I

V 120


V)

ltt -

fshy J

lu 60 Il


V~ i lt

S ~ 20

V()






100r--------------~--_r--_----~--_r--_--~

CI) lu 80x ~ ~

~ 60lu

~

~ 4 0

x ~ 40 ~


5 ~ gt ~

20




_

bull

bull

~ 80 u ~

=

~ ~

60 ~ l )

k 0

13 jo 40 ~

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5 ~ 20 u







shy








bull bull a ~


~

i ~

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~ ~ g

I ~

bull RAIN GAGE


SCAlt IH MIIU

) LJ1a





5

A 3

2

o 00==-


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3

2

o

o 1000 2000 3000

FEET

















I l E

bull

-4



























Ot


1-1n U




bull

~

bull bull ~ ~c~



II I 00 - -- r -- ---



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(pound) r


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bull

__________ _


bull ~

-















bull SUMMARY





bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II










bull

bull









bull ingequation








galC gacos















y= -465+064i (6)



bull

bull

-shy

J

bull bull

bull

bull

v

bull


bull r =OBB

I 10 20 30 40





50

shy









bull

bull

bull





I I

V 120


V)

ltt -

fshy J

lu 60 Il


V~ i lt

S ~ 20

V()






100r--------------~--_r--_----~--_r--_--~

CI) lu 80x ~ ~

~ 60lu

~

~ 4 0

x ~ 40 ~


5 ~ gt ~

20




_

bull

bull

~ 80 u ~

=

~ ~

60 ~ l )

k 0

13 jo 40 ~

~ j l

5 ~ 20 u







shy








bull bull a ~


~

i ~

~ c

~ ~ g

I ~

bull RAIN GAGE


SCAlt IH MIIU

) LJ1a





5

A 3

2

o 00==-


5 4

3

2

o

o 1000 2000 3000

FEET

















I l E

bull

-4



























Ot


1-1n U




bull

~

bull bull ~ ~c~



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) ( shy _l tj



(pound) r


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bull

__________ _


bull ~

-















bull SUMMARY





bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II



bull ingequation








galC gacos















y= -465+064i (6)



bull

bull

-shy

J

bull bull

bull

bull

v

bull


bull r =OBB

I 10 20 30 40





50

shy









bull

bull

bull





I I

V 120


V)

ltt -

fshy J

lu 60 Il


V~ i lt

S ~ 20

V()






100r--------------~--_r--_----~--_r--_--~

CI) lu 80x ~ ~

~ 60lu

~

~ 4 0

x ~ 40 ~


5 ~ gt ~

20




_

bull

bull

~ 80 u ~

=

~ ~

60 ~ l )

k 0

13 jo 40 ~

~ j l

5 ~ 20 u







shy








bull bull a ~


~

i ~

~ c

~ ~ g

I ~

bull RAIN GAGE


SCAlt IH MIIU

) LJ1a





5

A 3

2

o 00==-


5 4

3

2

o

o 1000 2000 3000

FEET

















I l E

bull

-4



























Ot


1-1n U




bull

~

bull bull ~ ~c~



II I 00 - -- r -- ---



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(pound) r


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bull

__________ _


bull ~

-















bull SUMMARY





bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II









y= -465+064i (6)



bull

bull

-shy

J

bull bull

bull

bull

v

bull


bull r =OBB

I 10 20 30 40





50

shy









bull

bull

bull





I I

V 120


V)

ltt -

fshy J

lu 60 Il


V~ i lt

S ~ 20

V()






100r--------------~--_r--_----~--_r--_--~

CI) lu 80x ~ ~

~ 60lu

~

~ 4 0

x ~ 40 ~


5 ~ gt ~

20




_

bull

bull

~ 80 u ~

=

~ ~

60 ~ l )

k 0

13 jo 40 ~

~ j l

5 ~ 20 u







shy








bull bull a ~


~

i ~

~ c

~ ~ g

I ~

bull RAIN GAGE


SCAlt IH MIIU

) LJ1a





5

A 3

2

o 00==-


5 4

3

2

o

o 1000 2000 3000

FEET

















I l E

bull

-4



























Ot


1-1n U




bull

~

bull bull ~ ~c~



II I 00 - -- r -- ---



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(pound) r


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bull

__________ _


bull ~

-















bull SUMMARY





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LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II

-shy

J

bull bull

bull

bull

v

bull


bull r =OBB

I 10 20 30 40





50

shy









bull

bull

bull





I I

V 120


V)

ltt -

fshy J

lu 60 Il


V~ i lt

S ~ 20

V()






100r--------------~--_r--_----~--_r--_--~

CI) lu 80x ~ ~

~ 60lu

~

~ 4 0

x ~ 40 ~


5 ~ gt ~

20




_

bull

bull

~ 80 u ~

=

~ ~

60 ~ l )

k 0

13 jo 40 ~

~ j l

5 ~ 20 u







shy








bull bull a ~


~

i ~

~ c

~ ~ g

I ~

bull RAIN GAGE


SCAlt IH MIIU

) LJ1a





5

A 3

2

o 00==-


5 4

3

2

o

o 1000 2000 3000

FEET

















I l E

bull

-4



























Ot


1-1n U




bull

~

bull bull ~ ~c~



II I 00 - -- r -- ---



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(pound) r


SCALE IN 11[$

















bull

__________ _


bull ~

-















bull SUMMARY





bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II

shy









bull

bull

bull





I I

V 120


V)

ltt -

fshy J

lu 60 Il


V~ i lt

S ~ 20

V()






100r--------------~--_r--_----~--_r--_--~

CI) lu 80x ~ ~

~ 60lu

~

~ 4 0

x ~ 40 ~


5 ~ gt ~

20




_

bull

bull

~ 80 u ~

=

~ ~

60 ~ l )

k 0

13 jo 40 ~

~ j l

5 ~ 20 u







shy








bull bull a ~


~

i ~

~ c

~ ~ g

I ~

bull RAIN GAGE


SCAlt IH MIIU

) LJ1a





5

A 3

2

o 00==-


5 4

3

2

o

o 1000 2000 3000

FEET

















I l E

bull

-4



























Ot


1-1n U




bull

~

bull bull ~ ~c~



II I 00 - -- r -- ---



) ( shy _l tj



(pound) r


SCALE IN 11[$

















bull

__________ _


bull ~

-















bull SUMMARY





bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II





I I

V 120


V)

ltt -

fshy J

lu 60 Il


V~ i lt

S ~ 20

V()






100r--------------~--_r--_----~--_r--_--~

CI) lu 80x ~ ~

~ 60lu

~

~ 4 0

x ~ 40 ~


5 ~ gt ~

20




_

bull

bull

~ 80 u ~

=

~ ~

60 ~ l )

k 0

13 jo 40 ~

~ j l

5 ~ 20 u







shy








bull bull a ~


~

i ~

~ c

~ ~ g

I ~

bull RAIN GAGE


SCAlt IH MIIU

) LJ1a





5

A 3

2

o 00==-


5 4

3

2

o

o 1000 2000 3000

FEET

















I l E

bull

-4



























Ot


1-1n U




bull

~

bull bull ~ ~c~



II I 00 - -- r -- ---



) ( shy _l tj



(pound) r


SCALE IN 11[$

















bull

__________ _


bull ~

-















bull SUMMARY





bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II




100r--------------~--_r--_----~--_r--_--~

CI) lu 80x ~ ~

~ 60lu

~

~ 4 0

x ~ 40 ~


5 ~ gt ~

20




_

bull

bull

~ 80 u ~

=

~ ~

60 ~ l )

k 0

13 jo 40 ~

~ j l

5 ~ 20 u







shy








bull bull a ~


~

i ~

~ c

~ ~ g

I ~

bull RAIN GAGE


SCAlt IH MIIU

) LJ1a





5

A 3

2

o 00==-


5 4

3

2

o

o 1000 2000 3000

FEET

















I l E

bull

-4



























Ot


1-1n U




bull

~

bull bull ~ ~c~



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) ( shy _l tj



(pound) r


SCALE IN 11[$

















bull

__________ _


bull ~

-















bull SUMMARY





bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II

~ 80 u ~

=

~ ~

60 ~ l )

k 0

13 jo 40 ~

~ j l

5 ~ 20 u







shy








bull bull a ~


~

i ~

~ c

~ ~ g

I ~

bull RAIN GAGE


SCAlt IH MIIU

) LJ1a





5

A 3

2

o 00==-


5 4

3

2

o

o 1000 2000 3000

FEET

















I l E

bull

-4



























Ot


1-1n U




bull

~

bull bull ~ ~c~



II I 00 - -- r -- ---



) ( shy _l tj



(pound) r


SCALE IN 11[$

















bull

__________ _


bull ~

-















bull SUMMARY





bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II

shy








bull bull a ~


~

i ~

~ c

~ ~ g

I ~

bull RAIN GAGE


SCAlt IH MIIU

) LJ1a





5

A 3

2

o 00==-


5 4

3

2

o

o 1000 2000 3000

FEET

















I l E

bull

-4



























Ot


1-1n U




bull

~

bull bull ~ ~c~



II I 00 - -- r -- ---



) ( shy _l tj



(pound) r


SCALE IN 11[$

















bull

__________ _


bull ~

-















bull SUMMARY





bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II

bull bull a ~


~

i ~

~ c

~ ~ g

I ~

bull RAIN GAGE


SCAlt IH MIIU

) LJ1a





5

A 3

2

o 00==-


5 4

3

2

o

o 1000 2000 3000

FEET

















I l E

bull

-4



























Ot


1-1n U




bull

~

bull bull ~ ~c~



II I 00 - -- r -- ---



) ( shy _l tj



(pound) r


SCALE IN 11[$

















bull

__________ _


bull ~

-















bull SUMMARY





bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II




5

A 3

2

o 00==-


5 4

3

2

o

o 1000 2000 3000

FEET

















I l E

bull

-4



























Ot


1-1n U




bull

~

bull bull ~ ~c~



II I 00 - -- r -- ---



) ( shy _l tj



(pound) r


SCALE IN 11[$

















bull

__________ _


bull ~

-















bull SUMMARY





bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II










I l E

bull

-4



























Ot


1-1n U




bull

~

bull bull ~ ~c~



II I 00 - -- r -- ---



) ( shy _l tj



(pound) r


SCALE IN 11[$

















bull

__________ _


bull ~

-















bull SUMMARY





bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II



















Ot


1-1n U




bull

~

bull bull ~ ~c~



II I 00 - -- r -- ---



) ( shy _l tj



(pound) r


SCALE IN 11[$

















bull

__________ _


bull ~

-















bull SUMMARY





bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II

bull bull ~ ~c~



II I 00 - -- r -- ---



) ( shy _l tj



(pound) r


SCALE IN 11[$

















bull

__________ _


bull ~

-















bull SUMMARY





bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II















bull

__________ _


bull ~

-















bull SUMMARY





bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II

__________ _


bull ~

-















bull SUMMARY





bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II





bull SUMMARY





bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II



bull



LITERATURE CITED









21-2gt illus




































ONRUGGEDTERRAIN

~










II
































ONRUGGEDTERRAIN

~










II

Rainfall Sampling on Rugged Terrain - AgEcon...

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Transcript of Rainfall Sampling on Rugged Terrain - AgEcon...