MILITARY HYDROIOGY MANUAL NO, H-7 DETERMINATION O F HYDRAULIC ELEMEWS OF RIVERS

BY INDIRECT METHODS

COMPONENT STUDY NO. 1 CROSSING A RIVER: A PRELIIvDNARY ANALYSE

OF SOME HYDRAULIC ASPECTS

PIEF'ARED I N CONNECTION WITH

BY WATER RESOUFCES D I V I S I O N U, S, GEDLOGICAL SURVEX

DEPARTMEIJT OF THE INTERTOR F O R

RESEAEH AND DEVELOPMmTT PROJECT NO, 8-97-10403

MILITARY HYDFOLOGY R&D BRAI'CH

DEPARTMENT OF THE ARMY WASHINGTON D I S T R I C T , CORPS OF m G I N E E R S

The crossing of a r iver ux-ider assault conditions and the maintenance of l i nes of conmmications across rivers are important problems frequently encountered during mili tary operations, To assure adequate prep- arat ion for a r ive r crossing, accurate knowledge of the depth, width, current veloci t ies , and character of bthtom materials and stream banks i s essent ia l , At positions where direct observatii.)ns or records a r e not f & m & h B b ~ %he estimzte of the sibuation must be constructed upon a knowledge of r ive r character is t ics , photographs a& other remot e observational waterial , A m n u a l which will furnish guidame in the determin- a t ion of river character is t ics for crossing sites devoid of r iver intell igence r d l l equip the f i e l d comander t o prepare a more r e a l i s t i c appraisal of the problem,

For mure than 60 years, systematic s tudies of the water resources of the United States have been m d e by the U, S, Geological Survey Departmenb of the I n t e r i c r , During th i s period a vast amount of informa- t ion pertaining to the flow nf streams has been collect- ed within the scope of the i r a c t i v i t i e s which has m i l i - tary as me11 as c i v i l application, Following a meeting of representatives from the U, S , Geological Survey, the Office Chief of Engineers, Department of the Army and t h e M i l i t a r y Hydrology I)&D Branch, Washington Distr ic t , Corps of Engineers, action was i n i t i a t ed t o assign Sub- project H-7, qetenninat ion of Hydraulic Elements of Rivers by Indirect MethrdsH t o the U, S, Geological Survey, and tcS transfer funds for the conduc t of i n i t i a l studies.

F ross ing a River; A Preliminary Analysis of Some Hydraulic Aspects" i s the f i r s t report prepared by the U. S . Geological Survey fo r the M i l i t a r y Hydrology R&D Branch, Washington Dis t r ic t , in connection With the subproject.

MILITARY HYDROLOGY YUIMUN, NO, H-7 DETEIIMINiTION OF HYDRAULIC ELEM?3MTS OF RIVERS

BY INDIRECT METHODS

CWOMENT STUDY NO, .1 CRDSSING A RIVER: A F'RELIMINAFX ANALYSIS

OF son% HYDRAULIC ASPECTS

T U L E OF CONTENTS

Paragraph

1-01 1-02 1-03

2-01 2-02

3-01

362

4-01 4-02 4-03

4-04

4-05

5-01

601

TABB

S E T I O N I - IIJTRODUCTION

SECTIOM II - RIVER STAGE - FLOOD OR UNf FWf

SECTION 117: - IiyDRAULIC EST?XITES FROM VARIOUS KINDS OF B A S I C DATA

SECTION I V - HYDRAULE EBTIMATES GIVEN PHOTO AND MAP

GENENiL - - - - - - .- - - - - - - - - -. - 10 10

OBTAINED AT RIV-733 SITE - - - - - - - - - - - ll

PODJT, DRAINAGE AREA, AND AERIAL PHOTO - - - I.3 GIVEN: TOPOGRfllsHIC MAP AND AERIAL PHOTO - - - 13

E5TIMATIOI'J aF DISCHARGE - - - - - - - - - - - - CHOICE OF ADDITIONAL INFOFNATION T O BE

GIVEN: DISCiIARGE MEIISU- A T SONIE UPSTFBAM

S E C T I O N V - V N I A B I 1 , I T Y KCTHIN A SHORT REACH OF STREAM

SECTION VI - REDUCING ERRORS IN DEPTH ESTIMATES

MILITARY HYDROLOGY MANUAL NO H-7 DETEIWlINATION OF HYDRAULIC ELENlENTS OF RIVEFE

BY INDWECT NIETHOE

C m m m S m Y NQ, z CROSSING A RIVER: A PRELIMINARY ANALYSIS

OF SOlW HYDRAULE ASPECTS

SECTION I - INTRODITCTION

1-01. FURPOSE

This r epor t i s an i n i t i a l attcinpt t o examine the ways in which hydraulics and hydrology might a s s i s t a military grmp in determining vhether a river can be crossed, by wading or by vehicles, where it should be cnrssed, and whether a bridge is necessary. would pmbably allow the hydraulic parameters t o be related by c k r t s cr nornugrams for ready solution, merely t o examine the re la t ions between the hydraulic factors .

Further vfork

The present repor t i s intended

1-02, STATENEM' OF PROBLEM

Crossing a r ive r is a mmon pmblan i n mi l i ta ry engineering. The prl.blan i s not a t a c t i c a l o r s t r a t e g i c me alone, but it a l so involves hydraulics, hydrology, and physiography. here with these l a t t e r phases,

We a r e ccmcerned

A crcjssing may be made by wading, in vehicles, by ponton or truss bridge, w by boats, deperads on the m t e r i e l a d personnel which must be mcwed, but the decision i s greatly affected by the physical charac te r i s t ics of the river itself, par t icu lar ly i ts midth, depth, and velclcity. and height ,f banks, the size, nature, and posit ion of bars o r riffks, as well as the s t a b i l i t y of these features with respect t o s t ruc tu ra l strength ard roadabili ty, a r e likewise important. graphic or physiognamic cha racter is t ics of the r iver .

The choice anmg these poss ib i l i t i e s

The form

Thcse are physio-

1-03, SCOPE

This report is an at tanpt tcl nutline i n preliminary and t en ta t ive form, suine re la t ions ex is t ing in rivers which might be organized, Mith fur ther vsork, i n to handboclk f om t o s erve as a guide f o r the military

t ac t i c i an and engineer in reaching decisions regarding the place at ifhich a crossing should be attempted, and the most advantageous means of accomplishing it. based upon the type and intensitiy of basic information avai lable to the mi l i t a ry engineer, from an i n i t i a l assumption that only a minimal amount of information is available, and the report proceeds with postulates of increasingly adequate information. In each case an at tanpt is m d e to indicate procedures which will maximize the useful in formt ion derivable fron t& given amount of basic information.

The report i s b u i l t around a se t of postulates

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SECTION II - RIUER STAGE -FLOOD OR U R FLOW

2-01. GEI’ERAL

It i s obvious that the re la t ive stage o r hei@t of the water is of The basic f i r s t importance i n judging the f e a s i b i l i t y of a cmssing,

data available t o the engineer may apply to conditions during low flow whereas the operation i n question might have to be accomplished a t t h e of high flow, o r v i c e versa, We a re concerned imnediatcly, therefore, with the description of the r iver a t various stages of flow and the problems of extrapolation f r o m known conditions t o those p r e v a i l k g a t som other t b e .

2-02. RIVER STAm AM) THE BANKFCTLL STAGE

We vKl l . begin,then, with a discussion of changes in stage of a river. stable interrelationships between hydraulic ard physical parameters ’ This s t a b i l i t y provides the base on which the generalizations made in this r q o r t r e s t , One of t hese apparently stable character is t ics of r ivers is the re la t ion betvrem flood frequency a d the banwul l stage.

A s w i l l be noted throughout this report , there a r e numerous

The r ive r c h n n e l is made by the action of the r iver . 1% is genemlly rectangular or e l l i p so ida l in cross section and is usually, though by no means always, branded l a t e ra l ly by f l u v i a l deposits, Rock-defended spurs extending intcj the valley from the adjacent hill slopes seldom comprise more than, l e t us say, one quarter of the t o t a l valley sides and rock outcrops i n the wall of the r iver channel a re even l e s s comon, a l luv ia l i n origin and a r e b u i l t t o a height r e l a t ive t o the channel bed which bears a more o r less de f in i t e re la t ion tV. the frequency with which the va t e r surface a t t a ins various intermediate elevations.

For the most part , t h e walls of the channel a r e

As a broad generalization, it my be said that the water level reaches the bankfull stage on the average, once or *ice each year. This can be determined where gaging s ta t ion records a re available by constructing a flow duration curve of values of dai ly mean flow, Briefly, t h i s consists of counting the number of occurrences of da i ly man discharge of various sizes, and ta l ly ing the data in di f fe ren t categories of size. f r o m the la rges t to the smallest, and each cumulative f igu re i s divided by the t o t a l number of days of record, The resu l tan t quotients represent the percent of time that given discharges a re equalled o r exceeded a t the s t a t i m , frequency graph by means of a stage-discharge relation.

The numbers i n each category a re then accumulated

The dischargefrequencies can be translated into a stage-

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An example of the percent of time a river channel flows a t various stages i s provided in Figure 1, which shms visual ly the area of cross section of flowing water r e l a t ive to bankfull and the corresponding percent o f time each i s equalled o r exceeded,

It can be seen that the flow which just fills the channel t o bank- full capaoity occurs on about two days of each year, mean of the da i ly mean discharge values i n a r ive r 5.3 cquallod or* m c c d e d about 25 percent of t he time, o r exceeded only .an e ~ u ~ ~ ~ m % ~ ~ three mnWm oat f i l l s the channel t o about half the t o t a l depth between dry bed and bankfull, only t h e lowest 10 percen-t, approximately, of t h e channel d e p a .

Recognizing tMt these generalizations a r e both a p p r o b a t e and tentative, they can be summarized i n a graph which is assumed to be more or l e s s applicable to most r ivers , Figure 2 (uppcr) oxpesseS khcrela- t ion of the flow duration (percentage of time equalled or exceeded) to the percentages of the depth between dry bed and bankfull occupied by m.tcmt,

The arithmetic

That is, the average flow is equaued t h e yew and

The median flow, equalled on half the days of the year, f i l l s

In this repor t the problem of forecasting water stage w i l l not be discussed. dependent( on the $ype of precipitation, importance of snm, and the physiographic and hydrologic factors ,

The time of year when flood c re s t s a r e l ike ly t o develop i s

Despite t h e severe shortage of data with which to t e s t the appli- aabi l i ty t o a l l r ivers of t h i s re la t ion between the percentage of the channel which i s f i l l e d by discharges of different frequencies, present information kidlicstca t h a t the r e l a t tun is a s otxnsmt%ve as any o f the o ther generalizations on which t h i s report is based. i s v i t a l l y necessary t o know the frequency of flow in computing other paramters a d 93 t h i s graph becoms of great bportance. FurtPller work should be done and is now in progress t o t e s t the r e l i a b i l i t y of the relation.

It

There remains then, the prac t ica l problem of determining from various kinds of basic information the f l o w frequency, considered coincidentally with the derivation of other desired informa- t ion assuming the ava i l ab i l i t y of various amounts of basic data.

This problem m i l l be

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SETION I11 - HYDRAULIC ESTIMATES FROM VARIOUS KIm OF BASIC DATA

3-01. DETER1IINATION OF DISCHARGE FROM A.J3RIAL PHOTOS

The problem of choosing the location and conditions appertinent t o a r iver crossing my a r i s e i n an area where no strearnflm o r other hydraulic data a re avai lable , It can be assumed, hmever, tha t a t l e a s t an a e r i a l photograph of t he area in question is avai lable , for even if a complete mosaic had not been constructed, a f e w photographs f r o m a reconnaissance a i rp lane can nearly always be obtained. can be determined f r o m a photograph alone?

What

An important and, fortunately, a conservative hydraulic element can be measured from a photograph, r i ve r width, a t a r i v e r cross section does not change w i t h increasing r ive r Stage nearly as f a s t as depth ard velocily . the mater surface often i s not mch less than the width of bankfull stage, This implies t h a t the r iver width determined from an a e r i a l photograph is prirrarily a function of drainage area upstream from the cross sect ion i n question rather than a function of stage, providing the r iver i s flowing less than bankfull. bankfull width may be indistinguishable from the ac tua l width of flow- ing water if the photograph is of mll sca le , A corollary of this f a c t i s t h a t the stage of the r iver cannot be judged w i t h necessary accuracy d i r ec t ly from an a e r i a l photograph alone.

The vidth of flowing water

Even a t lour flovr, the width af

A s a mtter of fao t , t he

The matter of where the width is t o be measured is of no l i t t l e knpnrtance, One of the charac te r i s t ics of na tura l r iver channels i s a universal var iabi l i ty , p r e s m b l y random in nature, Therefore, 5n measuring width, the mean of several individual measurements should be obtained, There is some non-random variation in width related t o the occurrence of a l t e rna te pools and riffles along the s t r e m ; width should be measured a t the foot of the pools which i s a l so j u s t ups trem f r o m r iffles.

Rjffles and pools along the r ive r usually shaw up nicely on an a e r i a l photograph, the pools showing up as r e l a t ive ly uniform dark areas in contrast t o t h e li&ter zones of white water or coruscations from which the l igh t sparkles, than one-third the length of pools, a s j d g e d by the r e l a t i v e surface m n i f es ta t ions ,

On the average, r i f f les a r e no more

Using the re lat ionship betrvem c h n n e l width and bankfull discharge shom in Figure 3, it is possible t o derive a p p m x b t e l y the discharge frorn a measurement of width. 1% can be seen fromFigure 3, however,

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+ahat given a width value alone, the discharge of bankfull stage cannot be specified any more closely than 2 5 times; that is, the discharge read df the graph correspollding to a specified width may actual ly be as much a s f i v e times as large as the actual discharge or only one-fifth as large, r a t e r i a l l y reduced by adding certain additional basic information.

A s Will now b e discussed, these limits of error can be

If pools and r i f f les a r e discernible on an a e r i a l photograph they may be used as an indepmdent check of r ive r w i d t h because the distance hetween successive r i f f l e s in a r i v e r c b n n e l appears to be re la ted t o the disoharge corresponding to the bankfull stage. phctograph, it m y be eas i e r t o measure the dis tance between successive 15 f f l e s than t o measure stream width, the discharge corresponding t o the bankfull stage may be estimated f r o m Figure 4 which was derived from a sample of r ivers studied i n the eastern United States,

This e s t i m t e of bankfull discharge should be checked against the

On a S m a l l scale

Using this relationship then,

value derived from the re la t ion of w i d t h against discharge provided ?'in Figure 3 ,

If the a e r i a l photograph shows that the stream i s meandering, finspection of Figure 3 indicates tha t the choice of possible bankfull discharge values is r e s t r i c t ed by about half, and thus the e s tkmte of discharge is inrpmved, having limits of error of approxlmately 2,5 times. The independent e s t%te of bankfull discharge derived from Figure 4 still i s possible by using one-half t he meander wave length r a t h e r than the distance between successive riffles, :Length shduld be the mean of t h e s t ra ight l i n e distances between Sua- cessive points of inf lect ion of the meander curves, and the mean value should be derived from not l e s s than f ive such discrete measuremts .

The estimate of wave

It should be added t h a t i n s tudies mde t o date, a stream is sa id to meander Ff it has discerniblo pmmsals of curvature similar t o a sine curve, and if the r a t i o of thalweg distance t o s t ra ight down-valley distance exceeds 1.5.

If the r iver channel i s multiple ra ther than single, t ha t is, if ' he re a re several channels s q a r a t e d by islands, then the Value of the bankfull discharge should be determined by masuring the width of t he stream a t a place where a l l of t h e water flows i n a single channel, t ha t is, Figure 3 appl ies to the undivided channel of a braided river. 'In a braided stream, again the limits of e r ro r of bankfull discharge derived from width a r e reduced t o + 2.5 times a s i n the instance of a meand erin g r iver .

-..

- 6 -

However, if a r iver is neither braided, tha t i s , separated by successive islands, nor meandering i n recognizable loops o r sinusoidal curves, then the f u l l l imit of e r r w of discharge equal t o 2 5 times is applicable. Streams apparently s t r a igh t may have width-discharge chanicter is t ics a imi la r t o those in meandering or braided streams.

Some reductior? of this error i s possible by u t i l i z ing the f a c t t h a t

Thus, if i n slmi-arid or plains areas, width f o r a given discharge is usually greater than f o r streams of equal discharge i n a humid area. a stream i s i n a plains o r plateau area having an annual r a i n f a l l of %20 inches, the portion of Figure 3 applying t o braided streams should be used, If the r iver i n question i s i n an area having an annual rain- f a l l of 20-50 inches, the ffmeanderingff portion of Figure 3 should be used.

I n s m r y , considwing the instance where only an a e r i a l photograph i s available as basic da ta , it i s possible t o estimate the bankfull dis- charge mith a m a x i m error af general r a i n f a l l conditions o r if the photograph shms ei ther meandering o r braiding, the possible error i n estimating bankfull discharge is re- dmed t o approximitely t 2.5 times,

5 times. By u t i l i z ing information on

3-02. ESTIMATION OF WEAN VELOCITY AND FlrEAN DEPTH

Raving determined the bankfull discharge, it becomes possible to estimate roughly mean velocity ard mean depth for any givm aznoUnt of water i n the channel. which sumnlarizes the relat ion between depth, velrxi-ty, and discharge,

Such esti imtes a re pqssible by the use of Figure 5

The explanation af Figure 5 might best be given by an example, Assiune that from an a e r i a l photograph the bankfull width was masured to he 300 fee t , and t h a t t h e stream i s located i n a subhumid area, no f'urther information available, t h e bankfull discharge read from Figure 3 i s found t o l i e midvay between the error limit l ines for meandering s t ream. discharge may be between 4,800 and l 4 , O O O cfs, h g values a r e obtained:

With

T h e value of discharge is 8,000 cfs, but the ac tua l From Figure 5, the follow-

Bankfull Bankfull M.ean veloc it y discharge depth a t bankfull

4 , go0 f ram( 8.6 ( 2.6

8,000 frm( 10.0 ( 3 .1

u, 000 f r o m ( 12-5 ( 3.8

6.6

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The large possible error i n depth stems from t h e f a c t t h a t the ra te of change of depth with discharge a t a given r iver cross section i s very nearly the sane as is the r a t e of change of depth with increasing dis- charge i n the downstream direction a t the bankfull stage, l i m i t is indicated-on the velocity-discharge graph for a given bankfull discharge. It is belicvcd khat t h e error in oskhatSim d * e corresponding velocity i s not more than less than that.

No er ror

30 percent, and i s usually

Continuingwith the example, l e t us assume that a r iver crcssing i s to be made during law flow, but it i s not known exactly how "low" the f l o w W i l l be, Figure 2 indicates that the median flow is considerably less than the mean annual f lat , believes that a 50-50 chance is a reasonable one i n estimating the dis- charge a t t h e of crossing, t ha t is, the f low will be less than that assumed on 50 percent of the days of the year, it can be seen t h a t corresponding t o a 50 percent duration (point A ) the observed discharge should b e -06 or 6 percent of the bankfull iiischarge, Figure 2 a l s o shows tha t this w i l l mean a depth equal t o 30 percent of bankfull depth (point B ) ,

Let us assume t h a t the engineer of f icer

Then, from Figure 2

The e s t b t e d depth a t t i m e of crossing, therefore, Will be 30 percent of the estimated bankfull depth a s foUutvs, (from upper graph in Figure 5)s

Discharge f o r Range Bankfull 50% of time of discharge L6% of bankfull) depth

4,800 290

84.0

Thus, from an a e r i a l photograph alone, it can be ascertained t h a t 50 percent of t h e time, t h i s stream having a width of 300 f e e t mi@t lave a mean depth between 0,9 and 4.7 fee t .

The mean velocity, on the othm hand, can be estimated from Figure 5 by koving down and l e f t , parallel t o the at-a-station curves, from points A and B on the bankfull discharge l i ne to A 1 and Bl:

L i m i t s of Bankfull . Discharge velocity d is char Re 50% af t i m e f .p . s . (+30%1

4,800 290 (1.40 es t i m t e d (0.98 lower l i m i t

u, 000 840 (1,60 esti3llated ( 2.08 upper limit

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Thus the mean velocity will l i e between 1.0 and 2.1 f e e t per second,

Stream gaging experience has shown that a r iver can be waded by a man if the product d velocity and depth is Less than eight, There- fore, if t h e velocity wepe as much a s 2.1 f e e t per second, a man could negotiate a depth of 3.8 f ee t , per second, a man could theoret ical ly negotiate a depth of 5.7 f ee t , In actual i ty he cannot safely negotiate depths greater than 1.5 f ee t a b u e the crotch, or for a 6-foot man, say 4.5 f ee t , In any event, the a e r i a l photogrzph alone will indicate i n the example ci.ted t h a t the mear veloci ty and depth probably wi l l allow men to wade the stream 50 percent of the days in a year, i s Traded a t the head of a r i f f l e (foot of a pool) as it should be, the la rges t values of man depth and mean velocity indicated in the graphs a r e not l ike ly t o be exceeded a t any point in the cross section.

If the velocity were as low a s 1.4 f e e t

Considering further, if t h e stream

T!k authors have no data or experience which w i l l allow a close estimate of perniss ible depths an3 ve loc i t ies negotiable by d i f fe ren t rni1:itary vehicles. the most favorable place t o cross under various conditions.

However, r iver experience gives some clue a s t o

'liver beds composed of m t e r i a l of heteorogeneous s i ze tend t o s o r t out the f ine material on the r i f f l e sections and leave the bed more or les 3 paved with coarser f r agmat s . be zhhosen f o r vehicle crossing because the depth w i l l be re la t ive ly small and the bed mre firm than i n the pools.

The upper par t of a r i f f l e should

Rivers carrying sand of uniform s ize , however, present a different The bed of r i f f l e s w i l l be composed of essent ia l ly the same problem,

material a s any other pa r t of the stream, ova? sandy r iver beds w i l l tend to scour the bed m e d i a t e l y downstream from each wheel ard the vehicle w i l l tend t o s i n k into the bed. TO avoid t h i s , crossing by automotive equipment i n r ivers of medium o r f ir .e sand should be made in as deep a section as the vehicle cElll traverse, because t h e de2p sections w i l l have low water veloci t ies a d , thereff.Trre, t he undermining of the wheels

Moreover, high velocitJies

wil l be minimized,

A t normal o r low flow, pools w i l l tend t o be about three %hies as deep as r i f f l e s , with consequent velocity of about one-third t h a t Of the r i f f l e .

For pmtcxl bridges, obvi.ously the deepest reach and lowest velocity should be chosen which means a pa- bridge should be located in a pool and about ha l f way. b e h e m an upstream an3 domstream r i f f l e .

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SECTION I V - HYDRAULIC ESTIMATES GIVEN AERIAL FHOTOGRAPHS AND PLANIIVETRIC MAP OF DMINAGE BASIN

(NO TOPOGRAPHY)

4-01, GENERclL

Maps without oontour l ines are so c m o n that i n most areas in the world, a , m p shawing drainage l ines would be avai lable , ab.&, to suppose then, t ha t f o r a river crossing these two items might be available, The min purpose of the planimetric map i n the present problem i s t o determine approximately the drainage area of the r i v e r basin above the point i n question. The following section demonstrates haw th i s one additional piece of basic da t a may be used to improve the estimates previously made from a e r i a l photographs alone.

It i s reason-

4-020 ESTIVATION OF DISCHARGE

Figure 6 presents the re la t ion of bankfull median and mean annual discharge t o drainage area far an area having about 18 inches annual runoff ( l ike e a s t c m t r a l U . S o ) .

This re la t ion holds f a i r l y we l l f o r sub-humid areas, but elselvhere the annual d i s c h r g e can be e s t i m t e d by a s imilar graph based on a wei&ted annual runoff. "he problan of estimating annual discharge for drainage areas of various s i z e s i s one on which considerable information ex i s t s ard w i l l not be discussed i n d e t a i l h r e .

Vith the drainage area known, the discharge expected a t any specif ic frequency can be estimated b e t t e r from the dischargedrainage area relat ionship than fmm the discharge-width relat ion. data m y be used i n a d i f fe ren t way, and the a e r i a l photograph of a stream i n a humid region provided an estimate of drainage area of 1000 square miles and a w i d t h of 180 feet . F r m the drainage area, the bankfull discharge can be estimated as 16,000 cfs, Entering Figure 5 on the discharge sca le of 16,000 cfs, the velocity corresponding t o bankfull discharge can be read a s 7,2 f e e t per second (point C ) ,

The width Assume t h a t the planimetric map

To estimite the man depth,

d = A = 16000 I L2,3 ft, 'FB v 180 (7.2)

In an actua2 f ie ld problem, because bankcull discharge occurs only once or twice each year, the bankfull depth i s so unlikely to occur that i t s value lower discharge.

is of less +ortance than the depth a t some more frequent and The man annual discharge occurs on the average of

-10-

a b u t 30 percent of the time, that is, 3 days out of every 10 have a daily mean flaw equal t o o r i n excess of mean annual flow, A t l e a s t i n spring-freshet time, discharges equal t o mean annual a r e l ike ly t o occur on a g o d many days and, therefore, t h e problem becomes of sore prac t ica l important e,

To e s t M t e the mean depth for such a re la t ively frequent d i sch rge , the value of discharge might bes t be read from a graph l ike Figure 6 (which appl ies t o an area of 18 inches annual runoff), using the rtlean annual discharge l i ne , Width should be obtained from the a e r i a l phoM- graph, a d velocity m y be estimated from the lowest l i n e in Figure 5. Then depth a t a discharge equal to the m a n annual can be computed from the equation

d = A w v

Because more data a r e available on r iver character is t ics a t mean annual discharge than , a t other discharge frequmcy, actual r i ve r data provide some indication of the r e l i a b i l i t y of estimates of depth made by the methods givm abave, The e s t i m t e d discharge, velocity, and depth a r e compared,with the actual values in Table 1 placed near the end of t h i s report , Correlation charts of estimated versus ac tua l values of depth and velocity a re given i n Figure 7 f o r the t r i a l sta- t ions of Table 1, Looking f i rs t a t the velocity data, it can be seen that Figure 5 gives a smaller range of velocity than is ac tua l ly experienced i n the l i s t of s ta t ions used as a t e s t , The correlation chart appears to M i c a t e t h a t low veliicit ies tend t o be o v e r e s t d t e d by Figure 5 . U n t i l more data a r e available, however, it is not la?c,Wn whether t h i s wvuld always be true, from Figure 5 appears tm be l e s s than 100 percent i n 23 cases out of 30.

The er ror i n e s t imt ing veloci ty

Inspecting the correlation curves pertaining t o depth, note first the points designated by cmsses , Estimates of d e p ~ a re i n error less than 100 percent in 26 cases out of 30 and on the average, the error is less than 50 percmt, These may appear a t f i r s t to be large errors, but one is reminded tha t ou r problem is to e s t i m t e the mean depth of a r iver a t any place i n any humid region, given nothing more than an a e r i a l photograph a d a map showing s i ze of drainage a rea , "his e s t i w t e then, can be m d e without ever going t~ the r i v e r ,

What would be the most important piece of additional information which might be obtained by v i s i t i n g the r iver? mihen one looks a t a river from the shore the hardest parameter t o estirrate i s water deptlI; and in the r iver crossing p m b l a , depth is the most important factor t o determine,

- 11 -

From the shore of any stream, a very sa t i s fac tory estimate of mean velocity can be obtained by a f l o a t , s t ra ight s t ick and attached wei&t, is ample i n length, A rock should be t i ed t o one erpd of the s t ick , of such a s i ze that the s t i c k f l o a t s upright w i t h only a few inches stick- ing out of t h e watw, The rock can be t i ed t o the s t i c k with s t r ing , but e lectr ic ians f r i c t i o n tape has proven to be eas ies t ard bes t , fo r it retains som adhesive property even when wet , If adhesive is not available, the s t i c k can be s p l i t and the rock wedged in the clevis,

A f l o a t should be timd over a reach suf f ic ien t ly long that a t l ea s t one r i f f l e aril one pool a r e traversed, and the beginning and end of t he timed reach should be analogous with respect t o the pools and riffles. For example, if the upstream point of the timing reaah is a t t he head of a r i f f le , the downstream end should also be a t the head of a riffle downstream.

The f l o a t m y be made of a Even i n a deep river, a &foot s t i c k

The mean velocitg of the whole stream, defined as the quotient &/A can be approxirnzted closely by multiplying t h e f l o a t velocity by the fac tor 0.8, appears t o b e reasonably consistent, of one foo t o r less on a rocky bottom, a f ac to r of 0.6 gives a some- what more accurate value.

This factor b s been checked by numerous f ie ld tr ials and In shallow water, having depths

If the nean stream velocity is obtained, the question a r i s e s of how much improvement i n the e s t i m t e of depth can b e derived from i t s use, I n Figure 7, the c i rc le points in the depth correlat ion graph represent estivllated versus actual values of mean depth derived from

d a A w v where

dSs charge was determined f rom the d i scharge-drainage area graph ( P i m e 6), w i d t h i s known E r a an a e r i a l photograph, and veloci ty is the actual velocity which could be obtained by f l o a t s , It can be seen tkt the c i r c l e points in Figure 7 a r e not appreciably be t te r than the crosses, insofar as the f i t on the l i ne of no e r ro r i s concerned, From th i s sample one must conclude that a b i l i t y tc, es tPmte discharpe from drainage area is the f ac to r l imiting the accuracy of the f i n a l e s t b t e of depth, These r e s u l t s irdicate t h a t mean velocity is such a conserva- t i ve quanti$r i n r i ve r s t h a t errors i n est'irnating velocity a r e srmll compared w i t h other e r rors ,

The average depfh and velocity of a stream in a sub-humid area, can be appro-ted f r o m the graphs presented here as closely as could be done by going t o th.e river and making measurmmts from the shore. Oboiously, if' the strean i s waded and a cross sect ion i s obtained, then t h e discharge can be computed w i t h considerable accuracy, However, our problem assumes that t h e depth is the desired parameter and that it cannot be obtained by a f i e l d m a s u r a n a t .

- 12 -

,!,,-04.. GIVEN: DISCHARGE MEASUFEP,ENI’ AT SOlE UPSTREAP! POINT, DRAINAGE AREA, AND AERIAL PHOTOGRAPH

Providing a river basin is reasonably homogeneous, the relative magnitude of flaw being experienced a t one point closely approxin?ates the r e l a t i v e magnitude of flow elsewhere i n tk basin, That is, low flow a t one point i s usual ly associated with low flow throughout the basin, e t c . and it is necessary t o est-te conditions a t a crossing of the main stream, the same elements considered e a r l i e r can be used, Discharge of t he tributary can be obtained by measuring the cross-sectional area of flowing water using any kind of rough rod, o r s t i c k marked off in fee t . Velocity may be obtained by a f l o a t described ea r l i e r , is imnediately obtained fmm Q equals Area times velocity.

If a f i e l d par ty reaches some t r ibu ta ry t o a me.in stream

Depth should be measured i n a t least 20 places across the stream, Then discharge

Next the discharge should be entered with corresponding drainage area of xeasured t r ibu tary i n the graph of Figure 6, Tke posit ion of this p lo t ted point is influenced by the duration o r frequency of flow and m a n annual runoff. t o the th ree l i nes of Figure 6 w i l l allow the discharge a t some down- stream point having known drainage area ta be obtained. similar t o those described ea r l i e r may then be used to estimate velocity and depth fmm Figme 5, if width i s obtainable from a e r i a l photographs.

A l i n e drawn through the point and p a r a l l e l

Procedures

This procedure also provides the next log ica l s tep i n estimating depth of a la rge r iver which i s too deep t C J made or is inaccessible. A t r ibutary near t h e crossing may be measured and used t o provide a n impmved e s t i m t e of t h e frequency of d i s c b r g e being experienced the main strem, of greater value i n improving the e s t i m t e of depth in the main r ive r than in measuring the ac tua l velocity of the main r iver i t se l f ,

Thus the measurement of a tr ibutary is considered

4;-0’j, GIVEN: TOPOGRAPHIC NAP Ahill AERIAL PHOTOGRAPH

As i n t h e problem cursidered previously, the stream width may be estiwated from an a e r i a l photograph, in addition, not only can the drainage area be obtained but a l so a measure of tk average slope of the stream i n a given reach, usual topographic rnap has a contour interval of 20 feet or 100 fee t and even where the slope d t he stream i s r c l a t ivc ly smaIP, c.mtaWs Of 100 f c c t o m ski-11 yiekt & mu@ c s t W k of ‘thc s k p c nf t h e stream bcd. Tho slo@ do%em5mck ixt %hb? m m e r %bough vmy q q w x h t e i s neverthe16 of s ign i f icant aid i n estimating t h e mean depth ard thus -the mean velocit

If a topographic map i s avai lable

The

~ contrast. to %he previous examples, we nom ape ab3k to m%iUze b!m equations i n s k a d ofl onlo, $mowid&ng it is possible t o estimate channel roughmss, The f i r s t equation is as before,

Q = v ~ d v

- 13 -

Ilhe secord equation is t h e Manning relationship widely used i n engineer- ing pract ice

where R is hydraulic radius approximtely equal t o mean depth, s i s the slope d the energy grade l i ne appmxiwted by the mean slope of the water parameter; Experieric e has dcmnstrated that the Manning roughness parameter, though decreasing s m w h a t i n the downstream direction, lmds nevertheless to vary less than t h o t h e r p a r w t e r s with which we a r e here concerned, For natural r ivers the value of n ordinar i ly varies between .Ol5 and .04. This is a vapiation of about four times whereas width, depth, and velocity can vary over a considerably larger range, Let us assume tha? tha t the roughness parameter r e m i n s a con- s tant f o r a l l the s trearm considered i n the follovlring approximtions . From the a e r i a l photograph width is determined as before and from the lnown drainage area the discharge nay be determined, viously, because the discharge drainage area relationship can be ad- justed by a rough approximtion a f annual mnoff determined from a general knowledge crf r a i n f a l l ard vegetation, l e t us assume f o r the present computations that discharge can be closely approximated from drainage area weighted by these physiographic f ac to r s , From the tvm ewations above then, velocity can be eliminated and we can solve for *,he depth a s a function of discharge, width, and slope, assuming r*oughness i s constant. we obtain

surface or of the bed, and n is the Manning roughness

As discussed pre-

Solving the two equations above simultaneousQ

where K is a constant.

Using th i s relationship the depth has been calculated for some sample l iver data. along the ordinate and the parameter on the right s ide of the equation along the abscissa, The correlatiun coeff ic ient is about 0.95 and the standard e r ro r about 4.0 percent. This correlation i s considerably b e t t e r than t ha t sham previously f o r the computations i n which slope oras not used. It can be concluded then tha t obtaining a value f o r i-iver slope e i the r from a topographic n?ap o r from leveling along a reach of the r iver adds s i g i f i c a n t l y to our a b i l i t y to est i imte the mean depth, and i s more valuable than a measurment of velocity. obtained the estimate of depth i n the manner just described, velocity (:an hncd5ateXy be ob’taincd by Subs -%&Wh t k E €XIat-Msn

Figure 8 presents a correlation between depth plot ted

Having

-u-

SEETION V - VARIABILITY W I T H I N A SHORT REACH OF STREAM

5-01..

'I'here a r e many sources of error i n estiwa,ting the mean depth and velcrcity of a reach of strean. Among the sigpif icant errors thus f a r not considered is the problem of both random and non-random variation within a given reach,

?he non-random variations a r e re la t ive ly specif ic though the magni-

Nearly a l l natural streams and r ivers a r e characterized by tude of the range of such variation from one river t o another i s n o t ye t l.u-~omn, alternating deeps and shallows, non-random i n character. at ions can be described but only inadequately explained.

These vari-

The deeps are referred to as pools and the shallow reaches as rSflles. cross-sectional area and con sequent low velocity. along the stream t h e pools a re about three times a s long a s the h t e r - vening r i f f l e s , velocity would make the pool an advantageous place t o cross, but because i ts depth is often very much greater than it is over the r i f f l e , the r e l i t i v e advantage of depth versus velocity must be weighed.

A pool a t lwr f lw is characterized by relat ively large I n t o t a l length

Tith regard to wading o r boat operation, the lavr

There i s no consistent difference in stream width between pool and r i f f l e . Then, because the same discharge passes through each, the projuct of depth times velocity is equal over pool and r i f f l e , This reans that if the pool is twice a s deep a s the riffle (a reasonable value found i n natural rivers), i t s velocity i s one half a s great, Wadeability depends upon both the absolute depth and the depth- velocity product, the pool sections whereas the r i f f l e s w i l l be passable by both c r i t e r i a , A t higher flows it is l i ke ly that if one cannot wade the r i f f l e , he can neither wade the pool, ani vice versa, depth-velocity product over the r i f f l e which i s the lk-niting facztor,

A t l aw flow depth alone may preclude wading across

In t h i s instance it is the

A s for a boat operation, obviously, the larger depth and m l l e r velocity of the pool would make it the place t o cross.

River slope a t low flaw is generally so small over the pool reach than one can generalize by saying that a l l of the downstream fall of a river i s made up i n the riffle reaches a t low f low, however, t he slope mer the pools increases and over t he r i f f l e s decreases, and a nearly uniform slope i s achieved.

A t flood f l a r ,

These relat ions a r e shorn i n Figure 9 by the typical Pools and r i f f l e s in the longitudinal prof i le .

- 15 -

-- __" can be seen t M t the absolute elevation of the r iver bed actual ly r i s e s downstream a t the lower end of a pool and then f a l l s rapidly over thc riffle, Clearly the bes t combination of depth and velocity f'w wading or vehicle crossing is a t t h e head of a r i f f l e and tail of E. pool where a considerable length of stream reach has a moderate c.epth and thus a moderate velocity.

Similar relationships are shown i n plan in Figure 10, It is h p O r r - tlant t o note that there may be pools and riffles in the s t r a igh t reach a.s wel l a s i n the mander. p r e n t l y straight'reach, the engineer should be cognizant of these variations, a .ppar qui te regularly i n apparently "straight I f chmnels

In choosing a point d crossing an an a p

Deep, mucky pools corresponding t o inside shoals o r eddies

With regard te the non-random variation along a reach of stream,' data a re available a t present only f o r one stream, Brandywine Creek, Pa. These data suggest t ha t random variat ion of width, depth, and velocity amount to about t 20 percent, vr d v is constant in a given reach, the advantages of minimum Values of two of t he factors must be balanced by a possible disadvantageous variation of the third. crossing operation, minimum depth and velocity a r e sought, a rrEmimUn midth w i l l no doubt be advantageous f o r crossings.

Keeping in mind t h a t the product of

For example, if, for a wading or vehicle

SECTION VI - REDUCING ERRORS IN DEPTH ESTIMATES

&OS-.

As a l ine of inquiry f o r the future , the mos t complex and puzzling problem i s the explanation of var ia t ion of stream width i n different r iv tas for a given-discharge, function of sediment concentration a d bed pa r t i c l e s i ze a s well a s the native of the material i n the banks. The nature of bank and bed mater- i a l a f f ec t s d d t h through (a) variation in erodibi l i ty , (b) determining res:istance fac tor , and (c) type of dune o r other bed configuration aC- cmi)aylyhg d i f fe ren t r a t e s of sediment transport. Although the es t i - mates of water depth discussed here could, of course, be improved by be t te r estimates of stream discharge, tha t hydrologic problem is less complex than the river morphologic ones associated with f ac to r s govern- i n g stream cross section, (braided, s t ra ight , o r meandering) is associated with a variation 5n the form of the cross section a t constant discharge, and t h i s alone tends to imsk the possible e f fec t of variation i n bed ard bank material ,

Current vmrk suggests t ha t this is a

Certainly the form or pattern of the stream

It can be said i n summary t l w t improved methods of estimating r i v e r depth and veloci ty depend a t present on improved knowledge of the c ~ S S - sectional form and the factors vhich govern it, rather than i n hydmlogic factors re la ted t o stream flow i t s e l f .

kea a . Mb m~., n.c. ..... huloi BVW a . et I).rl cr .. 1.0. ... W hod 1 . u bwart . hr .... wmtmu~ a . a t m u e u . b. .... Hll i. 1. u BruMmrq . m a ...... ol(u 1 ... P l r * . r -0 ........... B k u W 1. ar Khwbnt. CMo ........ lu Ir .. LturLllb . ab30 ....... **(rrsdw a. P o.wma, I.8.

wm .... CO~N . me ....... 1. .. WC. p.. ... .......

sa&wbaa 1 . .t. Law . u. .......... kiow .. nr Roap.ot, ohto

;)olou 1; .r mu. o u o

mato a. DT @irob*ilb.,.ohio ...... kwe ltq IW Chilliootha . Ohio ...... W l rwd ... Cabart. ........ 0.- .... Y Srmard .............

......... ...........

n.*ma or ... . 1.0. ....... hrsra?na a. at Bot s*np . I.O. L- & .. Sugar O r o n . 1.0. ..... S t . Wnpb .. xi? DWPnlno . Ohlo .... &?mn .... Is** . m a .......... T i m 4 11. .. SS-r. PLio .......... &gU.( .. P lkfl.ao .. ohlo ....... m- ... nr Daf5uma. Ohio .........

. P

UtlIUt.

# # D a h .

2.2

1.9

1.75

2 . u

1-5

1-95

2.2

2.6

2.0

1.8

1.95

2.5

1.0

2.4

267

2.8

1 . 9

2.P

2.3

2.4

1.6

1.7

1.9

2.2

1.6

1.8 . 2.2

1.9

2.3

2.5

. Aetml

. 1.8

1.1

Ob6

1.2

1.5

1.9

1.5

1.0

1.4

1.1

0 7

2.6

0.5

1.8

2.2

2.0

1.5

0.9

0.6

1.8

2.0

1.5

1.4

2.2

1.3

1.1

1.4

Q8

1.5

2.0

. 1C.tiUtl

w 8.6

4.1

2.5

3.5

1.04

1.6

3-15

4.0

6.5

3.3

4.3

3.8

3.8

7.9

12.9

13.6

3.4

4.8

5.0

9.4

1.2

0.6

0 7

5.0

1.6

3.1

4.8

4 7

4.4

5 -8

-

. LD-1

. 11.5

7.0

3.8

3.9

2.e

2.8

5.3

14.b

3.9

1.6

5.4

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13.0

11.9

22.3

26.0

2.4

4.3

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9.2

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0.9

1.6

5.9

1.8

2.8

4.4

4.8

3.7

4.2

-

1-8 DJ .. JhJaLL-

10.6

7.1

7.2

6.2

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3.6

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10.5

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19.0

4.3

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7.5

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-19-

F i m e No,

1

3

IC

5

7

9

Cross-sections of Brandymine Creek a t Chadds Ford, Pa,, Showing the Stage of Water i n the Channel and the Corresponding Duration of Each (frm Data Col- lected by M, G, Volman),

(Above) Flm Duration in Percent as a Function of

(Lower) Amount af Water in Channel (mean d e p t h b k -

the Percentage uf Bankfull Discharge.

f u l l depth) as a Function of Percent of Bankfull Discharge,

Relation of E d t h vs, Bankfull Discharge a t B a n k f u l l Stage, Separating Meandering Streams From Braided Streams.

Y

Distance Between Successive Riffles o r Neander iirave Length as a Function of Bankfull Discharge,

Relation of Velocity to Discharge a t a River Cross- section and Downstream, and Similar Relationships of Depth t o Discharge in the Dovmtrem Direction for Bankfull Discharge Only.

Appmximately 18 Inches Annual Runoff, Such as Much of Eastern United States,

Drainage Area - Discharge Relations for an Area of

Correlat5on Charts of Computed vs, Actual Values of Depth and Velocity, f r o m Data i n Table 1.

Actual Depth Correlated with a Function of Discharge, Vidth, and Slope.

Longitudinal Profiles of a Reach af a Straight Reach of the Middle River, Va, , Shawing Pools and Riffles, and of a Meandering Reach of Pop0 Agie R i v e r , 7lryo.

Plan V i e w of Pop0 Agie River near Lander, 'TTyc *3 and Middle River, Staunton, Va, Longitudinal Profiles of these Sam Reaohes).

(See Figure 9 f o r

- 21 *-

OEPARTIMENT OF THE ARMY CORPS OF ENGI)IE€:RS

I

DISCHARGE

EMlALLED OR EXCEEDED ABOUT TWICE

A YEAR I

EQUALLED OR EXCEEDED ABOUT TWICE

EVERY 3 YEARS

FLOOD PEAK EQUALLED OR EXCEEDED

ABOUT ONCE FEET

EVERY 10 YEARS I

RTIUENTOFTMCLRMV - CORps OF ENGINEERS

IO0

0. I LJhJ / I

R I

-- Of

,

Wave lenqth of meanders, or twice distonce between sucessive riffles, in feet

Mean velocity, in feet per second - v,

I 1

l i ! I / I I

t

L-

I ! j 1 1 j 0 0

1 1 1 " ' 0

~

FIGURE 6

WTMENT OF THE ARMY CORPSOF ENGINEER -

TI - ---- Yo

8 0

FIGURE 7 -

too' 1 l ( l l l 1 I I I

- I 0 SCIOTO RIVER BASIN - x TOMBIGBEE RIVER BASIN

__ 0 KANSAS RIVER BASIN V MISSOURI RIVER BASIN 4 MISSISSIPPI RIVER BASIN - V YELLOWSTONE RIVER BASIN + CONNECTICUT RIVER BASIN

X

7 - 7

I O

3 - v .sr _.

% - 1 - 1

- 1 - 1 I .

c

L

-

/

I I I I I I l l 100 A 1,000 (Qlws'.)'

IO .I I

i 53 w 4 4

80

76 1

Pop0 AaE RIVER. W. 9

FIGURE IO

0- 400 FEET

MIDDLE RIVER, VA: 1 A I //