Content uploaded by Robert Ettema

Author content

All content in this area was uploaded by Robert Ettema on Apr 29, 2015

Content may be subject to copyright.

Hans Albert Einstein: Innovation and Compromise

in Formulating Sediment Transport by Rivers

Robert Ettema

1

and Cornelia F. Mutel

2

Abstract: This paper is written to mark the hundredth anniversary of the birth of Hans Albert Einstein 共1904–1973兲. It casts his career

as that of the archetypal researcher protagonist determined to master intellectually the way water ﬂows and conveys alluvial sediment in

rivers. In that effort, Einstein personiﬁed the mix of success and frustration experienced by many researchers who have attempted to

formulate the complicated behavior of alluvial rivers in terms of mechanically based equations. His formulation of the relationship

between rates of bed-sediment transport 共especially bedload transport兲 and water ﬂow comprised an innovative departure from the largely

empirical approach that prevailed at the time. He introduced into that relationship the emerging ﬂuid-mechanic concepts of turbulence and

boundary layers, and concepts of probability theory. Inevitably the numerous complexities attending sediment transport mire formulation

and prompt his use of several approximating compromises in order to make estimating bed-sediment transport practicable. His formula-

tion nonetheless is a milestone in river engineering.

DOI: 10.1061/共ASCE兲0733-9429共2004兲130:6共477兲

CE Database subject headings: Sediment transport; Rivers; Alluvial streams; Fluid mechanics; Turbulence; Boundary layer.

Introduction

Hans Albert Einstein, born in May 1904, might have remained

one of countless civil engineers whose work, although locally

important, had little impact on the world as a whole. However, his

trenchant independence of spirit and famous father, Albert Ein-

stein, launched him into a productive career as a researcher and

educator fascinated with the mechanics of bed-sediment transport

and water ﬂow in alluvial rivers. By virtue of the times in which

he lived 共1904–1973兲, the trans-Atlantic span of his life, and his

name, Hans Albert Einstein’s 共hereinafter called Einstein兲 career

forms a convenient course along which to view the advance of

alluvial-river mechanics as an engineering science. This paper

follows part of his career, viewing his efforts to understand and

formulate two central issues in alluvial-river behavior: the rela-

tionship between bed-sediment transport and water ﬂow, and that

between ﬂow depth and ﬂow rate.

Although Einstein lived most of his youth with his mother

Mileva, who had separated from Albert when Einstein was 10

years old, his career was strongly marked by his father’s inﬂu-

ence. Family correspondence reveals that, though Albert ﬁrst dis-

suaded his son from entering civil engineering, he later fostered

and partly directed that career. Until 1927, Einstein and his

mother resided in Zurich, where he attended school and eventu-

ally earned an undergraduate degree in civil engineering from the

Swiss Federal Institute of Technology 共ETH兲. Albert then encour-

aged his son to come to Germany 共where Albert was a professor

at the University of Berlin兲. Albert facilitated this move by help-

ing him locate a job at the steel construction ﬁrm of August

Klonne, in Dortmund, where Einstein worked as a structural en-

gineer focusing on bridge construction. However, by 1931 Albert

was becoming increasingly apprehensive about the growing Nazi

power in Germany. Understanding well the threat posed to Jews,

and concerned about his son’s safety, Albert encouraged a return

to Switzerland. Seven years later, Albert would again feel the

pressure to ensure his son’s safety, and would facilitate a second

move 共this time to the United States兲 and job change. Thus Ein-

stein’s career was also marked by historic movements; each shift

in its course was induced by a change in the political climate

linked with such movements.

This paper discusses how despite the politically encouraged

moves, or perhaps because of them, Einstein emerged as a leading

expert in alluvial-river mechanics, his expertise being sought

around the world. The paper does so with scant inclusion of equa-

tions. Practically every major textbook on alluvial-river mechan-

ics and sediment transport 关e.g., the books by Einstein’s doctoral

students Graf and Chien 共Graf 1971; Chien and Wan 1999兲兴

present the main equations comprising Einstein’s formulations.

For a broad technical assessment of Einstein’s contributions to

alluvial-river mechanics, the writers defer to the useful synopsis

by Shen 共1975兲, another of his doctoral students. The Proceedings

of a symposium, to honor Einstein on the occasion of his retire-

ment, lists his publications and the graduate students with whom

he worked 共Shen 1972兲.

A theme running through this paper is innovation and compro-

mise. Though springing innovatively from emerging concepts of

turbulent ﬂow and probability theory, concepts that were becom-

ing well established in engineering only during the early decades

of the twentieth century, Einstein’s formulation of sediment trans-

port becomes beleaguered by confounding physical details and

the natural variability of sediment and ﬂow conditions in rivers.

1

IIHR-Hydroscience and Engineering, Dept. of Civil and

Environmental Engineering, College of Engineering, The Univ. of Iowa,

Iowa City, IA. E-mail: robert-ettema@uiowa.edu

2

IIHR-Hydroscience and Engineering, Dept. of Civil and

Environmental Engineering, College of Engineering, The Univ. of Iowa,

Iowa City, IA. E-mail: connie-mutel@uiowa.edu

Note. Discussion open until November 1, 2004. Separate discussions

must be submitted for individual papers. To extend the closing date by

one month, a written request must be ﬁled with the ASCE Managing

Editor. The manuscript for this paper was submitted for review and pos-

sible publication on January 8, 2004; approved on February 6, 2004. This

paper is part of the Journal of Hydraulic Engineering, Vol. 130, No. 6,

June 1, 2004. ©ASCE, ISSN 0733-9429/2004/6-477–487/$18.00.

JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JUNE 2004 / 477

Inevitably, simplifying assumptions, empiricism, and other judi-

cious compromises are needed to prop formulation so that it is of

practical engineering use. It is a theme common to many efforts in

formulating sediment and water movement in alluvial rivers.

Beginnings: Meyer-Peter’s Flume

Professor Eugene Meyer-Peter of the Swiss Federal Institute of

Technology 共ETH兲 in Zurich needed to know how much sediment

moved with water ﬂowing along the Alpine Rhine, especially the

amount of coarser sediment, gravels and sands, that moved along

the river’s bed. This need was to bring the young Einstein from

Germany, where he then worked, back to Switzerland, the country

of his birth.

In the late 1920s, the Swiss federal government and the local

cantonal government of St. Gallen, responding to concerns about

an alarming increase in the frequency with which the river

ﬂooded, had contracted Meyer-Peter to recommend an effective

modiﬁcation to the Alpine Rhine over a 20-km reach extending

from the Alps to the head of Lake Constance. The river, which

wends through the Swiss Alps to Lake Constance 共Fig. 1兲, was

aggrading, and likely would break out of its leveed banks and

disastrously ﬂood its valley. Political considerations gave Meyer-

Peter’s work urgency, as the Alpine Rhine above Lake Constance

formed an international border between Switzerland, Austria, and

Liechtenstein. The key question weighing on Meyer-Peter’s mind

was by how much to narrow the channel so that it deepened

sufﬁciently to convey its loads of water and sediment.

Though many efforts at channel modiﬁcation had been at-

tempted elsewhere in Europe prior to 1930, they had relied on

little more than rules of thumb aided by cut-and-ﬁll adjustments

to arrive eventually at suitably sized, nominally stable channels.

The few formulas purporting to relate ﬂow rate and depth for

water in alluvial channels were so empirically tied to local chan-

nel conditions that they could not reliably help Meyer-Peter.

Also, the few formulas for estimating bed-sediment transport

were sketchy and, at best, loosely related bed-sediment transport

to water discharge or depth through a particular reach of river.

Schoklitsch 共1930兲, a leading European authority on river-

engineering at the time, wrote in his highly regarded textbook Der

Wasserbau that ‘‘at the present stage of research, a ‘‘calculation’’

of sediment load was out of the question.’’ Meyer-Peter realized

he faced a complicated task, and in 1927 had set about designing

and supervising the construction of ETH’s impressive hydraulics

laboratory with which to undertake it.

A French engineer, Du Boys 共1879兲, had done some simple

ﬂume experiments and proposed the ﬁrst mechanistic formula for

estimating bed sediment transport as bedload, the portion of bed

sediment transport whereby bed particles move on or near the

bed. A difﬁculty with his formula, though, was its basis on a

misconceived notion of bed-particle movement. Du Boys had as-

sumed that bed sediment moves as a series of superimposed

shearing layers, and had arrived at a formula relating rate of bed-

load transport as per unit width of channel to a critical ﬂow con-

dition beyond which ﬂow mobilized bed sediment, and an excess

of average shear stress exerted on the bed. Subsequent ﬂume ex-

periments showed the sliding layer view of bed-sediment move-

ment to be fallacious 共e.g., Schoklitsch 1914; Gilbert 1914兲. Nev-

ertheless, the notion of a critical shear stress 共or ﬂow rate, ﬂow

depth兲 associated with bed-sediment transport was conceptually

appealing. Consequently formulas similar to Du Boys’ were con-

sidered best suited for estimating not only bedload transport but

also the total rate of bed-sediment transport; prior to the 1930s, it

was moot whether engineers actually distinguished between the

two transport terms.

Perhaps the most advanced at sizing alluvial channels were the

British, who had sought an improved design method for irrigation

canals dug through sandy terrain in parts of the Indian subconti-

nent and Egypt. The method, termed the Regime Method 共e.g.,

Lacey 1929兲, relied almost entirely on empirical relationships to

characterize channels under long-term equilibrium or ‘‘regime.’’

The Regime Method was still in development, and its applicabil-

ity to the Alpine Rhine with its gravel bed was uncertain.

The problems with the Alpine Rhine clearly showed that the

few existing formulas were far from being dependable or useful.

More understanding of fundamental processes was needed. Ac-

cordingly, Meyer-Peter implemented a comprehensive plan entail-

ing ﬁeld measurements in the Alpine Rhine, as well as hydraulic

modeling and ﬂume experiments to be conducted in ETH’s new

hydraulics lab.

To recruit research assistants, Meyer-Peter placed an advertise-

ment in a Zurich newspaper. The ad caught the attention of Mil-

eva Einstein, and she contacted Albert. He had brieﬂy thought and

written about aspects of river mechanics 共关Albert兴 Einstein 1926兲,

appreciated the importance of Meyer-Peter’s work, and saw a

promising, safer career opportunity for his and Mileva’s elder son.

In 1931 Einstein joined Meyer-Peter’s research effort and started

working toward the doctoral degree.

At ﬁrst a rather lackadaisical and playful research assistant

共Fig. 2兲, not that well regarded by Meyer-Peter, Einstein eventu-

ally became intrigued by gravel-particle movement along Meyer-

Peter’s ﬂume. After a few years, Einstein and colleagues wrote a

series of papers presenting research ﬁndings stemming from

Meyer-Peter’s plan. The papers were on bedload transport, hy-

draulic radius and ﬂow resistance, measurement of sediment

transport, and hydraulic modeling 共Einstein 1934; Meyer-Peter

et al. 1934; Einstein 1935; Einstein and Mu

¨

ller 1939兲.

New Insight: Railway Schedules and Galton’s Board

While observing particle movement along the ﬂume 共Fig. 3兲, Ein-

stein realized that a distribution describing the rates of travel of

identical particles could be used to determine an ‘‘average travel

velocity’’ for a group of particles. He borrowed this notion from

railway-schedule terminology, implying the total distance traveled

Fig. 1. Alpine Rhine constrained to a single, straightened channel

just upstream of Lake Constance, Switzerland

478 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JUNE 2004

divided by the total time of travel including stops. With such a

velocity determined, it might be possible to formulate the compo-

nent of bed-sediment transport called bedload, the transport of

bed particles in successive contact with the bed of a channel.

Einstein also realized he needed a course in probability theory

if he were to deﬁne distributions and average values of particle

velocity and travel distance. Fortunately, an excellent mathemati-

cian at ETH, Professor George Polya, offered the course Einstein

needed. Polya took keen interest in the problem Einstein wished

to formulate, though he initially was daunted by its complexity.

He guided Einstein through some of the probabilistic aspects of

bed-particle movement. The two men drew closer as Einstein

sought Polya’s advice on the development of the theoretical as-

pects of his doctoral thesis 共George Polya, letter to Albert Ein-

stein, 1935兲.

Einstein viewed gravel particle movement as a succession of

alternating forward leaps and rest pauses. Einstein assumed the

forward leaps to be relatively brief compared to the rest pauses. In

analogy with the movement of a commuter train, the particle is

taken to move over a distance that is long compared to the indi-

vidual distances between stops, and that travel periods were neg-

ligibly brief compared to stop periods. To simplify the formula-

tion he assumed that the forward leaps take no time. Certainly this

would be the case for low rates of gravel transport, for which

water ﬂow dislodges particles from the bed and moves them

downstream until lodging in some momentarily secure seating. At

intense transport rates, however, a blizzard of particles would

bounce along the bed, each particle pausing for the barest of

moments, if pausing at all. The assumption simpliﬁed the proba-

bilistic analysis and lent it symmetry.

Polya suggested that Galton’s board would be a convenient

statistical device for describing and tracking the movement of a

bed particle. Galton, a cousin of Charles Darwin, was a statisti-

cian who developed a board comprising two perpendicular axes,

of which one represents distance traveled, and the other repre-

sents duration of pause 共Fig. 4兲.

To play bed-particle movement on Galton’s board, Einstein

ﬁrst had to deﬁne the board’s properties in terms of movement on

the bed. Since water ﬂow conditions along the ﬂume were con-

stant, he assumed that the likelihood of particle motion was the

same at any point and at any time on the bed. Using Galton’s

board Einstein arrived at a formula giving the travel distribution

of a set of particles along the bed 共or board兲. The formula is

expressed in terms of a probability distribution that describes the

number of particles located a distance increment downstream

from the particle source 共the origin of the board兲 since a given

period had elapsed. From the known characteristic distribution

共and the distribution moments兲, Einstein could determine the av-

erage distance traveled and average resting period of bed particles

moving across the board, and thereby potentially estimate the rate

of sediment transport.

In correspondence with his father, Einstein described his re-

search, explaining its objective, the difﬁculties he faced, and the

approach he was taking. Albert responded with interest and en-

couragement, offering suggestions intended to clarify the process

Einstein was attempting to formulate. Albert gave considerable

thought to his son’s research subject, and took pleasure in sug-

gesting ways to formulate particle motion. For example in one

letter from Princeton in 1936, Albert proposed a way to eliminate

the approximating assumption whereby the periods of particle

motion were taken as negligibly short compared to the periods

that the particles were at rest on the bed. That assumption be-

comes weak at high intensities of bedload transport for which

almost the entire bed is mobilized. Usually Albert’s suggestions,

though probing Einstein’s formulation, were not fruitful. They led

to complicated mathematical equations whose solution then en-

tailed dubious simpliﬁcations.

Einstein approached the probabilistic formulation of the bed-

load transport of bed particles from two standpoints. One stand-

point aimed at determining the distribution of particle travel dis-

Fig. 2. A playful Einstein amidst a pile of fellow Swiss Federal

Institute of Technology students

Fig. 3. Observation, by Einstein, of 22-mm-diameter gravel from the

Alpine Rhine moving in Meyer-Peter’s new ﬂume at Swiss Federal

Institute of Technology

Fig. 4. Galton’s board

JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JUNE 2004 / 479

tances in the ﬂume, whence Einstein could attempt to relate

average particle velocity to the water ﬂow parameters. The second

one sought to simulate the capture of bedload particles by a bed-

load basket, such as he had tested in the ETH ﬂume. His experi-

ments with the ﬂume led to data curves, like those in Fig. 5,

relating bedload transport rate per unit width of channel versus an

average speed of particle travel, with particle shape as a third

variable.

A major step in his formulation required relating the average

characteristics of particle travel to turbulent ﬂow behavior. This

step also required that Einstein deal with the experimental difﬁ-

culty of particles departing the end of the ﬂume during an experi-

ment. As big as it was, the ETH ﬂume was too short. Without

information on the distances traveled by those lost particles it was

difﬁcult to deﬁne the average characteristics of particle move-

ment. Einstein earned Polya’s commendation by working around

this conundrum statistically.

Einstein attained the doctorate degree from ETH in 1937 共Ein-

stein 1937兲, submitting a thesis in which he novelly applied prob-

ability theory to describe bed-particle movement in turbulent

ﬂow. Though the scope of his thesis research did not include

formulation of a method for estimating rates of bed sediment

transport under given water ﬂow and channel conditions, Ein-

stein’s insights into individual motion of bed particles formed the

basis for his new approach to formulating bedload transport. In a

letter to Einstein, Meyer-Peter described Einstein’s doctoral study

as producing ‘‘some intriguing ideas, but not exactly useful for

my Alpine Rhine study.’’

Formulation: Enoree-River Flume

Albert, who had moved to the United States in 1934 because of

his concern about political movements in Germany, persuaded

Einstein to come to the United States in 1938. His arrival coin-

cided with the recent establishment of the U.S. Soil Conservation

Service 共SCS兲, reﬂecting a great national concern about soil ero-

sion and the condition of many rivers. Albert assisted his son in

securing a position as a cooperative agent with SCS’s newly es-

tablished ﬁeld laboratory on the Enoree River 共Fig. 6兲, near

Greenville, S.C. The lab was established for measuring sediment

loads in the Enoree River in order to better understand the rela-

tionships between sediment transport and water ﬂow. It was lo-

cated in a region of South Carolina that had experienced severe

soil erosion problems incurred with intensive farming. Einstein

worked with colleagues Joe Johnson and Alvin Anderson on ways

to measure sediment transport. They quickly realized the need to

distinguish two distinct populations of sediment conveyed by

water in the river. In one paper 共Einstein et al. 1940兲 they coined

the term ‘‘washload’’ to describe the river’s load of suspended

ﬁne silt and clay-size particles derived from soil erosion and usu-

ally not comprising the river’s bed, the source of bed-sediment

load.

Einstein continued trying to translate the ﬁndings from his

thesis research into a practical method for describing and predict-

ing bedload transport of sediment in rivers and streams. He was

unconvinced by the critical-shear-stress approach used by several

prior formulations 共e.g., Du Boys 1879; Shields 1936兲.Inhis

opinion, bedload movement was better related to ﬂow turbulence

near the bed. Accordingly he took the principal conclusions from

his thesis and used them as a basis for a new approach that

equated the volumetric rate of bedload transport to the total num-

ber and volume of particles likely to be in motion. In turn, the

number and volume of moving particles depended on the prob-

ability that water ﬂow would lift or eject an individual particle

from its seating on the bed and move it downstream in a given

period. Einstein viewed that probability as reﬂecting the stochas-

tic nature of water velocities close to the bed.

The difﬁculty lay in determining the probability that the hy-

drodynamic lift on any particle on the bed is about to exceed the

particle’s weight within a given period of time. From a different

perspective, the probability could be viewed as the part of the bed

for which hydrodynamic lift force exceeds particle weight. The

probability problem is comprised of two parts. One part con-

cerned the need for an equation for hydrodynamic lift; particle

weight is relatively easy to formulate. The other part concerned

ﬁnding a meaningful expression of time; transport rate implies

movement per unit time. Einstein adapted a well-known and stan-

dard formula for hydrodynamic lift, writing it in terms of a local

velocity of water ﬂow at a level near the bed. Here, though, as-

sumptions were needed regarding estimation of the velocity and

lift coefﬁcient.

The trickier problem concerned the inclusion of a time period.

The most reasonable period to use was the average time required

for the water to remove one particle from the bed. Unfortunately

there is no way to express the time required for hydrodynamic lift

to pick up a particle. Einstein assumed that lift involves some

characteristic dynamic feature of the ﬂow ﬁeld around a particle

Fig. 5. Sample of data from Einstein’s work with Meyer-Peter’s

ﬂume at Swiss Federal Institute of Technology

Fig. 6. U.S. Soil Conservation Service’s Enoree-River Flume, South

Carolina, 1939. The ﬂume was designed for measuring sediment

loads and ﬂow in an actual river

480 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JUNE 2004

falling in still water. Particle diameter divided by particle fall

velocity expresses a characteristic time. Up to this stage, his for-

mulation was reasonably rigorous, once the under-girding as-

sumptions about average particle step length were accepted. But

the subjective use of fall velocity for particles in a description of

particles rolling and bouncing along the bed was unsettling.

By combining formulas for the weight rate of bed particles

moving as bedload, hydrodynamic lift on a bed particle, bed par-

ticle weight, and characteristic time based on bed particle fall

velocity, Einstein arrived at a seemingly simple relationship be-

tween intensity of sediment discharge and the probability of par-

ticle entrainment from the channel bed. In terms of a more de-

tailed formulation 共repeated in most textbooks兲, Einstein

expressed this relationship as

A⌽⫽ f

共

B⌿

兲

(1)

The two parameters, ⌽ and ⌿, were central to Einstein’s charac-

terization of bedload transport; ⌽⫽ dimensionless expression for

intensity of sediment transport; and ⌿⫽ dimensionless expression

for ﬂow intensity or gross shear force exerted on the bed. A and

B⫽ constants incorporating awkward details about particle shape

and step length, as well as water velocity distribution.

Einstein could not derive the exact form of the relationship

between ⌽ and ⌿. Too many variables were unknown. He instead

had to ﬁnd the relationship from plots of bedload data interpreted

as ⌽ versus ⌿. If his formulations were correct conceptually, the

data would lie systematically along a single curve signifying a

single general relationship, or ‘‘law,’’ for bedload transport.

Validation Test: Gilbert’s Data

Obtaining reliable data from which to determine the relationship,

however, was not straightforward. Einstein used the only two

comprehensive sets of lab ﬂume data readily available to him at

the time: his from ETH 共Meyer-Peter et al. 1934兲, and those pub-

lished by Karl Grove Gilbert about 20 years earlier 共Gilbert

1914兲. Gilbert, a prote

´

ge

´

of John Wesley Powell, had conducted

novel and comprehensive ﬂume experiments at the University of

California-Berkeley. The great river surveys of the 1800s 关notably

Humphreys and Abbot 共1861兲, Powell 共1875兲兴 were accompanied

by engineering and scientiﬁc desire to know more about the me-

chanics of rivers in the United States Gilbert’s data encompassed

a greater range of sediment and ﬂow conditions than did Ein-

stein’s ETH data. Incidentally, Gilbert too had used a railway

analogy to characterize water and ﬂow and sediment transport in

rivers; the term ‘‘grade,’’ meaning channel slope, was borrowed

from the grade of railway tracks, which commonly were laid

along the relatively level ground of ﬂood plains alongside rivers

and streams 共Pyne 1980兲.

By and large the two sets of data fell along a curve in accor-

dance with his formulation, except for a range of conditions re-

ﬂecting high intensities of sand transport. Those data veered sub-

stantially away from Einstein’s postulated curve, and clustered

along their own curve 共Fig. 7兲. The deviant data suggested that

bedload transport, or rather bed-sediment transport, could not be

fully described using his method. What disconcerted him was the

realization that the deviant data were not merely a batch of results

from a set of extreme hydraulic conditions, but in fact were rep-

resentative of ﬂow and sediment transport in the sand-bed chan-

nels representative of most rivers in the United States.

The deviation caused Einstein to review the formulation of his

method, and to question the accuracy of Gilbert’s data for sand

bed channels. He queried his own assumption that all bedload

particles moved in steps of constant length proportional to particle

diameter, unaffected by ﬂow conditions. His work at ETH had

suggested this to be the case for the gravel beds at fairly low

intensities of transport for which the probability of particle en-

trainment was moderate or low. He conjectured that, with increas-

ing intensity of transport, the probability of entrainment is high

and the step lengths increase from the constant length at low

intensities. As step length increases, the area and number of par-

ticles starting movement together increases, and consequently so

does the rate of bedload transport. This reﬁnement of his theory

modiﬁed the relationship between ⌽ and ⌿, and led to a second

curve with a common stem as the original curve, but which

veered away in almost the same manner as the cluster of Gilbert’s

sand-bed data. The new curve, though, still did not run through

those data. Einstein wondered if Gilbert’s data were tainted with

measurement error.

By 1941, Einstein had sufﬁciently ordered his thoughts on a

method for describing and predicting bedload transport that he

was able to get them published as an ASCE Proceedings paper

共Einstein 1942兲. As was the practice of the ASCE Transactions

Journal, which subsequently published his paper, his paper was

accompanied by discussions by researchers interested in alluvial

sediment transport. It drew praise for its attempt to relate sedi-

ment movement and ﬂow mechanics, but it raised questions about

the main assumptions spanning the gap between formulation con-

cepts and presentation of a practical predictive method. In par-

ticular, it was criticized for purporting to be on greater rational

basis than were the current formulations based on the concept that

a critical value of bed shear stress or rate of water ﬂow be ex-

ceeded before bed particles could move. Difﬁcult questions in-

cluded: Why base the formulation on lift force alone? Why should

settling velocity be included in a formulation of bedload trans-

port? One discusser, Anton Kalinske, remarked that Einstein evi-

dently had ‘‘stepped over into the realm of abstract dimensional

analysis’’ when he used particle settling velocity as a convenient

parameter to put the probability of particle motion in a time con-

text. Kalinske had attempted to include turbulence in formulating

the movement of bed particles 共Kalinske 1942兲, and provided

insightful comments that Einstein eventually would have to con-

sider in advancing his formulation.

Another discusser, Samuel Shulits, who in the early 1930s had

prepared an English translation of Schoklitsch’s book Der Wass-

erbau, wrote that Einstein’s ‘‘scholarly probe into the universal

Fig. 7. Relationship between and ; modiﬁed from Einstein

共1942兲

JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JUNE 2004 / 481

law for the transportation of bed load is inspiring.’’ Shulits then

quickly tempered his praise by comparing Einstein’s formula, Eq.

共1兲, with bedload formulas based on the notion of a critical ﬂow

condition beyond which bed particles of a characteristic size

began moving. He thought the latter formulas more directly ex-

pressed the relationship between ﬂow and sediment transport,

whereas Eq. 共1兲, notwithstanding all the interesting background to

its formulation, essentially devises a functional relationship be-

tween two dimensionless parameters. In his closure to the discus-

sions, Einstein 共1942兲 stoutly defended his approach and dispar-

aged the notion of a critical ﬂow condition, calling it ‘‘a condition

that does not exist in nature.’’The signiﬁcance of his approach, he

argued, was not so much its immediate outcome, Eq. 共1兲 and Fig.

7, but rather its grappling with the problem of formulating bed-

sediment transport in terms of actual turbulent-ﬂow behavior. He

acknowledged that ‘‘the problem is far from solved.’’

Mountain Creek: A Little River

In contrast with the Alpine Rhine and the Enoree, Mountain

Creek in South Carolina was a mere ditch 共Fig. 8兲. Yet, to Ein-

stein, Mountain Creek was an ideal little river. The creek pos-

sessed most of the characteristics of alluvial rivers that Einstein

sought to understand and formulate. Moreover, it was conve-

niently small so that Einstein could measure its water and sedi-

ment loads. The Enoree River ﬁeld station had proven disappoint-

ing for obtaining ﬁeld data on bedload because of insufﬁciently

frequent large ﬂows.

Mountain Creek could help in calibrating or linking his

laboratory-ﬂume insights and equations to the behavior of a sand-

bed river. He had learned from his Alpine-Rhine work at ETH

that laboratory results, and formulations based only on the results

of laboratory idealizations of rivers, usually are regarded skepti-

cally by practical engineers dealing with real rivers. If he could

show that his ideas worked for sediment movement in Mountain

Creek as well as in his ETH ﬂume, then showing that they worked

for a river would be a matter of simple geometry.

As perverse luck would have it, the summer and autumn of

1941 were relatively dry in South Carolina. Flows in the creek

barely moved any sediment. Only a few inches of rain fell, though

a single storm did drop an inch-and-a-half of rain during the

evening of almost the last day Einstein intended to monitor the

creek. He and technicians were out at the enlivened creek imme-

diately the next morning, recording its discharges of water and

sediment. The equipment worked well and the measurements

proved, at least to Einstein’s satisfaction, that his concepts were

valid for a little river like Mountain Creek 共Einstein 1944兲.He

subsequently obtained further data from another little river, West

Goose Creek in Mississippi.

Method Extended: Caltech Flume

With the entry of the United States into World War II, and after

the modest yield of results from the Enoree River, the SCS wound

down its work at Enoree Field Station and reassigned the station’s

personnel. In 1943 Einstein was transferred to SCS’s laboratory at

the California Institute of Technology, Pasadena. Albert was en-

thused about the move and encouraged his son to contact The-

odore von Ka

´

rman, a renowned Caltech ﬂuid mechanician. Von

Ka

´

rman, however, was busy with war-related matters, and he

never developed Albert’s hoped-for relationship with Einstein.

As his part of the war effort, Einstein was seconded to

Caltech’s Hydrodynamics Laboratory to work on shock waves

produced by explosives and projectiles breaking the sound barrier.

However, he still had opportunities to continue developing his

bedload method and to investigate several pressing problems

emerging in the wake of dam building and other engineering ac-

tivities along rivers, in particular along the Rio Grande River. As

Einstein saw things, accurate estimation of bed-sediment load, not

just bedload, was the most important problem in alluvial-bed river

engineering. The ability to predict bed-sediment load in a river

would enable engineers to predict the river’s response to changes

in its water and sediment loads, thereby reducing the uncertainty

associated with utilizing the river as a resource for water and

hydropower.

Convinced of the essential correctness of his bedload method,

Einstein set about extending it by addressing several complicated

aspects of bed-sediment transport: bedform development, trans-

port of nonuniform bed sediment, and combined bedload and

suspended-load transport of bed sediment 共i.e., total bed-sediment

load兲.

SCS researchers at Caltech, Arthur Ippen and notably Hunter

Rouse, had formulated an equation for the vertical distribution of

suspended bed sediment over the depth of ﬂow. The equation, and

lab data supporting it, were written up by Rouse 共1939兲, and

subsequently elaborated by another SCS researcher, Vito Vanoni

共1946兲. Commonly called the Rouse equation, it is one of the

more successful formulations of sediment transport. However, it

gives only the distribution of suspended-sediment concentration

relative to some reference elevation near the bed, showing that the

concentration decreases rapidly with higher elevation in a ﬂow. A

practical difﬁculty was that the equation does not give the abso-

lute suspended-sediment load. To get that, the relative distribution

has to be tied to a known, or estimated, sediment load concentra-

tion at some level near the bed. Here, Einstein saw an opportunity

to link the Rouse equation with his formulation of bedload and, in

his words, to produce ‘‘a uniﬁed method for calculating the part

of the sediment load in an alluvial river that is responsible for

maintaining the channel in equilibrium’’ 共Einstein 1950兲.

Einstein surmised that the suspended-load distribution as de-

scribed by Rouse’s equation could be spliced to the top of the

bedload layer as described by the bedload formulation. The con-

centration of particles moving at the top of the bedload layer

would serve as a convenient and reasonable reference concentra-

Fig. 8. Mountain Creek, Miss., 1941. The creek was ﬁtted with a

size-reduced version of the sediment-measurement apparatus used for

the Enoree River 共Fig. 6兲.

482 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JUNE 2004

tion with which to set the maximum concentration at the bottom

of the suspended load distribution. However, the splicing of bed-

load and suspended load is easier said than accurately done. It

meant also that Einstein needed to strengthen the rigor of his

bedload formulation. His statistical observations on particle mo-

tion would have to be modiﬁed, including his earlier assumption;

the average step of a certain particle is the same even if the

hydraulic conditions or the composition of the bed changes. Gil-

bert’s data and the data from Mountain Creek showed that this

assumption did not hold at the intense rates of sediment transport

occurring for sandy rivers.

To see how particles move under conditions of intense rates of

sediment transport, and to get adequately detailed data on bed-

sediment transport at high intensity rates for which bed sediment

would be transported in suspension as well as along the bed,

Einstein needed more ﬂume experiments. During the period

1944–1946, while others at Caltech were largely occupied by

defense-related research, Einstein used his spare time to churn

water and sediment through a small recirculating ﬂume in the

SCS lab.

Recognition: Rio Grande River

While concerns about soil conservation and sediment transport

had been set aside during World War II, these concerns returned

urgently right after the war, at which time Einstein was well po-

sitioned to play a leading role in addressing them. In May 1947

the various federal agencies concerned with rivers and their wa-

tersheds convened at the Denver headquarters of the U.S. Bureau

of Reclamation to hold the nation’s ﬁrst meeting focused on the

sedimentation troubles facing engineers and soil conservationists

in the United States. All the federal agencies sent representatives.

Also in attendance were engineers and scientists from diverse

state agencies, universities, and a number of overseas organiza-

tions. The conference placed Einstein center-stage as one of the

nation’s leading authorities on sediment transport at a time when

the full implications of the nation’s sediment troubles were be-

coming pressing.

The need for the conference had arisen from a growing na-

tional recognition of the widespread, adverse consequences that

sediment troubles were posing for river-basin development and

for the conservation of land and water resources. The national

scope of the troubles had become increasingly worrisome during

the mid-1930s, shortly after the federal government had initiated

numerous programs to enhance irrigation, hydropower, naviga-

tion, ﬂood control, and soil conservation. Severely eroded water-

sheds, river-channel aggradation or degradation, reservoir sedi-

mentation, and the adverse environmental effects of muddied

waters all indicated that much more needed to be learned about

watershed and river behavior. Prominent among the sediment

troubles discussed were those along the Rio Grande River.

SCS colleague Vito Vanoni 共1948兲 outlined for conference par-

ticipants a history of the development of predictive relationships

for sediment-transport and water ﬂow in alluvial rivers. He laid

out the big questions to be addressed in order to better understand

how rivers move sediment, and ended his presentation by lament-

ing the lack of scientiﬁc and engineering attention given in the

United States to sediment-transport problems, problems whose

national importance he ranked with the more popular contempo-

rary problems of atomic energy and rocket propulsion. Fewer than

10 professionals in the United States, he estimated, were devoting

the major part of their time to the study of sediment transport.

Prominent among the 10 was Einstein, whose new approach to

bedload transport estimation Vanoni described as ‘‘a radical de-

parture from all previous bed-load formulas.’’

Einstein addressed the participants on two issues of keen in-

terest with regard to the sediment troubles along the Rio Grande:

measuring and predicting the rate at which rivers move sediment

along their bed 共Einstein 1948兲. He likened the middle Rio

Grande to Mountain Creek, asserting that it behaved essentially

like the creek. Unlike the other speakers, Einstein could draw on

and describe European as well as U.S. experience. Moreover, for

many participants the name Einstein held beguiling promise of

major breakthroughs in understanding and formulating the me-

chanical laws of sediment transport by rivers. Within several

months of the Interagency Sedimentation Conference, former

SCS colleague Joe Johnson facilitated Einstein joining the engi-

neering faculty of the University of California at Berkeley.

Over the following 2 years, Einstein completed a detailed

write-up of his bed-sediment transport method and published it as

U.S. Department of Agriculture Report 1026 共Einstein 1950兲, now

widely recognized as a milestone in alluvial-river mechanics. His

method became widely known thereafter as the Einstein method,

and was used extensively by the Bureau, the U.S. Corps of Engi-

neers 共USACE兲, the U.S. Geological Survey, and many others.

Report 1026 elaborated and better explained Einstein’s probabil-

ity approach to bed-sediment transport. Moreover, it presented an

elegant splicing of the bedload and suspended-load components

of bed-sediment transport, and it introduced new concepts aimed

at reducing some of the empiricism in the ⌽ versus ⌿ relationship

introduced by Einstein 共1942兲.

The concepts included modifying the ﬂow intensity parameter

⌿ so that it could be used for estimating the transport rates of

particle-size fractions comprising a bed of nonuniform sediment.

Further, it involved estimation of the ﬂow energy expended on

bed-particle roughness, not on the entire bed; introduction of two

adjustments to account for the velocity of ﬂow locally around a

particle; and pressure distributions at a bed surface of nonuniform

sized sediment. The modiﬁed parameter is

⌿

*

⫽ Y

共

2

/

x

2

兲

⌿

⬘

(2)

in which ⫽ factor intended to account for the sheltering of

smaller particles amidst larger particles in a bed of nonuniform

sediment; Y⫽ pressure-correction factor, which together with

2

/

x

2

, is intended to account for the inﬂuence of particle size

nonuniformity on hydrodynamic lift; and ⌿

⬘

⫽ ⌿ modiﬁed in an

effort to account for bed sediment development of bedforms on

channel beds. Though quite readily conceived, near-bed com-

plexities in ﬂow and particle disposition meant that and Y have

to be determined empirically from ﬂume data. Textbooks on sedi-

ment transport 共e.g., Chien and Wan 1999兲 explain the details

associated with the terms in Eq. 共2兲, and elaborate on the subse-

quent work examining and Y. Using Gilbert’s data and his own

ETH data, Einstein arrived at the following relationship between

probability for motion, p, the parameter ⌿

*

, and the intensity of

bedload transport for particles in the particle-size fraction, ⌽

*

i

⫽ (i

B

/i

b

)⌽, where i

b

and i

B

⫽ fractions are the fractions of a

given particle size in the bed and the bedload, respectively:

p⫽ 1⫺

1

1.2

冕

⫺ (1/7)⌿

*

i

⫺ 2

(1/7)⌿

*

i

⫺ 2

e

⫺ t

2

⫽

43.5⌽

*

i

1⫹ 43.5⌽

*

i

(3)

This equation is commonly referred to as the Einstein bedload

function 共e.g., Chien and Wan 1999兲. Fig. 9 shows a data curve

relating ⌿

*

and ⌽

*

i

. Though the Einstein method in Report

JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JUNE 2004 / 483

1026 was comprehensive, it was somewhat cumbersome to apply,

and some of its components were found to need adjustment.

Application: Missouri River

For 2 months during the summer of 1948, about 4 months after

his ﬁrst meeting as a board member for the Missouri River Divi-

sion’s Sedimentation Studies program, Einstein was in North Da-

kota and Montana, at the headquarters of the USACE’s Garrison

District. Over the remainder of his career he maintained a produc-

tive relationship with USACE, assisting it with sediment concerns

along the Missouri, the Arkansas, and other rivers, and working to

better formulate sediment transport and water ﬂow in rivers.

USACE’s Missouri River Division was charged to oversee a

vast watershed that covered about one-ﬁfth of the continental U.S.

In 1948, the Division’s efforts were concentrated largely on

implementing the Pick-Sloan Act, which prescribed a plan to con-

trol and regulate the river’s ﬂow for the purposes of ﬂood control,

hydropower generation, and navigation. However, the Division

found implementing Pick-Sloan to be fraught with more difﬁcul-

ties than the plan had envisioned. All of the dam projects called

for were facing difﬁculties and setbacks attributable to the river’s

sediment 共Fig. 10兲.

By September 1948, the technical problems facing the division

were clear to Einstein. He summarized them in a brief report to

the division, stating ‘‘every attempt must be made to study the

questions in the Missouri itself and in its tributaries. This is the

only way to ﬁnd the relative importance of the various inﬂu-

ences’’ 共Einstein, unpublished report to Missouri River Division,

U.S. Army Corps of Engineers, Omaha, 1948兲. He realized that

the efﬁcacy of the predictive methods would have to be checked

by the simultaneous measurement of sediment transport and the

ﬂow variables of the river itself.

One immediate matter was a little delicate. The method se-

lected for estimating the rates of bed-sediment transport through

the river was the bedload equation proposed by Professor Lorenz

Straub, a prominent hydraulics engineer who had been a USACE

engineer in the 1930s. Straub 共1935兲 had proposed the method

while working on House Document 238 共Missouri River Report兲,

a detailed assessment of the ﬂow and sediment problems posed to

engineering use of the Missouri River. As Straub was the senior,

and initially the most vocal, board member, and since his method

had been developed expressly with the Missouri River in mind,

his was the method that the division had decided to adopt. Ein-

stein was uncomfortable with the method. In a long letter report

to the division, he outlined the steps that needed to be taken to

gauge the sediment load conveyed by the river, and he went

through the shortcomings of Straub’s method. Besides being es-

sentially an extension of the shear-stress 共or discharge兲 excess

approach proposed earlier by Du Boys and others 共e.g., Schokl-

itsch 1934兲, Straub’s method assumed that the river kept its cross-

sectional shape and its roughness for the full range of water ﬂow

and while the river’s bed degraded or aggraded. These assump-

tions seemed unreasonable to Einstein, and they were not sup-

ported by measurements of ﬂow depth and ﬂow rate for selected

reaches of the river.

Einstein together with the division’s engineers had examined

data on the Missouri River and several of its tributaries in an

effort to better understand the relationship between ﬂow depth

and ﬂow rate for these rivers. An explanation ventured in terms of

changing channel shape failed because channel shapes were

found not to change appreciably as ﬂow varied. A more promising

explanation related ﬂow energy loss to the intensity of bed-

sediment transport 共and thereby Einstein’s modiﬁed ﬂow-intensity

parameter

⬘

), and variations in bedforms and thereby bed

roughness.

Both Straub’s and Einstein’s methods were used for estimating

bed-sediment transport, though Straub’s was soon abandoned.

Einstein, though, encountered an unexpected complication: down-

stream of Fort Peck Dam, the river’s degrading bed became ar-

mored with coarser bed sediment. No sediment-transport method

had taken armoring into account.

Further Reﬁnement: Berkeley’s Flumes

The University of California-Berkeley’s ability to attract talented

graduate students, combined with Einstein’s link to USACE, en-

abled him to undertake at Berkeley a sustained research effort

aimed at better understanding and formulating sediment-transport

processes. It was an effort largely undertaken by graduate stu-

dents and USACE engineers working under Einstein’s guidance.

They embarked on a comprehensive series of ﬂume investigations

aimed at illuminating key aspects of sediment and ﬂow behavior.

Moreover, Einstein’s Berkeley appointment enabled him to teach,

something he enjoyed 共Fig. 11兲.

Brieﬂy mentioned here are two examples illustrative of that

effort. An especially important issue, and one that has challenged

formulation of sediment transport in rivers, concerns what hap-

Fig. 9. Relationship between ⌿

IL

and ⌽

*

共from Einstein 1950兲

Fig. 10. Board members 共Einstein, Straub, Vanoni, Lane兲 and Corps

engineers ponder bed degradation of the Missouri River downstream

of Fort Peck Dam, Mont., 1948

484 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JUNE 2004

pens if the bed sediment comprises a wide range of particle sizes.

This situation, of course, is the norm for most riverbeds. A basic

assumption underpinning the Einstein method needed further

work; i.e., that all particle sizes in a river may be equally avail-

able at the bed surface and within the bed. Over about 1 year,

1950 to 1951, graduate student Ning Chien and Einstein carried

out a series of ﬂume experiments and were in a position to pro-

vide detailed descriptions of the processes whereby different sized

bed particles segregate in the upper layer of a river bed, how

armoring occurs, and how a riverbed acts much like a reservoir

for sediment, storing it during periods of reduced water ﬂow, and

releasing it during periods of greater water ﬂow.

With doctoral student Robert Banks, Einstein began investigat-

ing how several factors contribute to ﬂow resistance in rivers.

This effort would provide more insight for his sediment-transport

method, and it would help address a crucial companion issue

concerning the relationship between water discharge and depth in

alluvial rivers. The total resistance opposing the ﬂow consists of

the combined effect of resistance attributable to surface rough-

ness, bedforms 共or bar resistance as he expressed it兲, and vegeta-

tion. Einstein wondered if the total resistance could be expressed

as the sum of these components. This thought was not new. It had

been used successfully in determining ﬂow resistance in ﬂow

around bodies.

The notion of dividing ﬂow resistance into two parts, particle

roughness drag and bedform drag, was new for alluvial-river me-

chanics. Its ﬁrst practical implementation is the Einstein-

Barbarossa method for estimating the relationship between ﬂow

depth and ﬂow rate in alluvial channels. Einstein and Nicholas

Barbarossa, an engineer with the USACE’s Omaha District, used

data from the Missouri, several of its tributaries, and two Califor-

nia rivers to ﬁnd a relationship between Einstein’s parameter ⌿

*

and that part of ﬂow-energy loss attributable to bedforms. Addi-

tionally, they used the Manning-Strickler equation to estimate en-

ergy loss attributable to surface roughness. Publication of their

method 共Einstein and Barbarossa 1952兲 was a further milestone in

formulating alluvial-river mechanics.

Confronting Complexity

The complex mix of processes at play in natural alluvial rivers

has deﬁed 共so far at least兲 reliable prediction of bed-sediment

transport and ﬂow depth; uncertainties of 100% or more are com-

mon for predicting rates of bed-sediment transport. Engineers and

scientists have long recognized that rivers are complex, and ac-

cordingly have used largely empirical as well as analytical ap-

proaches to characterize alluvial-river behavior. Commonly, the

practical design engineer and the scientist in the ﬁeld have found

the empirical approach more practicable and have been skeptical

of sophisticated, predictive methods based on advanced ﬂuid me-

chanics and data from laboratory ﬂumes. Proponents of the more

empirical approach and those of the largely mechanistic approach

are quick to debate each other’s methods, especially when one

claims to be the superior. The following exchange is an example

of the debate, and illustrates Einstein’s conviction about the ulti-

mate truth of the concepts supporting his method for estimating

bed-sediment load. The exchange follows a paper published by

Ning Chien, Einstein’s student.

Shortly before he returned to China where he was to play a

leading role addressing that country’s river problems, Chien in

1954 published two ASCE Proceedings papers that drew a salvo

of criticism from a leading exponent of the 共empirical兲 Regime

method approach to river behavior. One paper 关‘‘The present sta-

tus of research on sediment transport’’ 共see Chien 1956兲兴 ad-

dressed the relationship between water discharge and bed-

sediment load. In it, Chien described the reliance of sediment-

transport formulation on accurate formulation of water ﬂow.

Appended to Chien’s paper was a stern discussion criticizing

Chien’s neglect of the body of understanding collectively termed

the Regime Method. The discusser, Thomas Blench, a very ca-

pable hydraulic engineer and a leading proponent of that method,

argued that Chien’s paper presented knowledge limited only to

ﬁndings from ‘‘laboratory ﬂumes with triﬂing ﬂows.’’ He further

argued that Chien had neglected ‘‘the vast amount of observations

on canals in the ﬁeld, the dynamical aspect of the formulas

evolved there-from, and the fact that these formulas provide a

simple and adequate means of practical design that has been used

widely for many years.’’ The Regime Method’s formulas, Blench

claimed, ‘‘represent what real channels actually do.’’

Einstein, though not a coauthor of Chien’s paper, wrote an

additional closure discussion to that by Chien. He took issue with

the Blench’s claim about the sufﬁciency of the ‘‘superiority of the

‘simple and adequate’ ’’ Regime formulas. Those formulas, he

pointed out, were developed by curve-ﬁtting of data from ‘‘a very

narrow range of bedload conditions.’’ He went on to express,

among other things, his doubt that the Regime formulas would

work for rivers in the United States. In his closure following

Blench’s cutting discussion of another ASCE Proceedings paper

共see Einstein and Chien 1956兲, Einstein presented ﬁgures showing

the inadequate performance of the Regime formulas.

Since Einstein 共1950兲 numerous methods have been developed

for estimating the relationships between water discharge and bed-

sediment transport in alluvial rivers. Some methods have built on

the Einstein method laid out in Report 1026, or modiﬁed the

method for better accuracy and more convenient use 共e.g., Colby

and Hembree 1955; Bishop et al. 1965兲. Others have developed

from improved insights, and still others have remained resignedly

empirical 共e.g., Brownlie 1981兲. Meyer-Peter’s research plan for

the Alpine Rhine led to another quite widely used method for

estimating bedload transport 共Meyer-Peter and Mu

¨

ller 1948兲.

Ironically, Einstein through his early work at ETH 共Meyer-Peter

et al. 1934兲 had a signiﬁcant role in developing that method.

Fig. 11. Einstein at a Berkeley ﬂume explaining ﬂow processes to

students

JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JUNE 2004 / 485

Latter Years

Much of Einstein’s career can be cast as the archetypal story of

the researcher protagonist determined to master intellectually the

way water ﬂows and conveys alluvial sediment in a river. In that

effort, he personiﬁes the mixed success and frustrations experi-

enced by many researchers who have attempted to describe the

complicated behavior of alluvial rivers in terms of rationally

based equations. The effort begins keenly with apparent good

promise of success, based on innovative new insights into com-

ponent processes. Formulation seems within reach and progress is

made, but then judicious assumptions and curve-ﬁtting empiri-

cism have to be invoked as approximating compromises to ac-

commodate the many confounding complexities inevitably faced.

Einstein retained his long fascination with alluvial rivers 共Fig. 12兲

and continued his efforts to understand and formulate how they

convey sediment. During his latter years, his fascination broad-

ened to include sediment transport in coastal waters.

Einstein retired from his active professorship at the University

of California on July 1971, at the age of 67. His retirement earned

him the Berkeley Citation, an award ‘‘for distinguished achieve-

ment and notable service to the university,’’ and a Certiﬁcate of

Merit from the U.S. Department of Agriculture, ‘‘for pioneering

research in developing the bed-load function of sediment trans-

port by streams, and leadership in developing application of ﬂuid

dynamics theory in solving engineering problems in the ﬁeld of

soil and water conservation.’’ Eight months later the American

Society of Mechanical Engineers presented him a certiﬁcate of

recognition for his 20 years of ‘‘devoted and distinguished ser-

vices to applied mechanics reviews.’’

However, none of these accolades seem to have meant as

much to him as the sedimentation symposium that had been held

in his honor a few weeks earlier in June 1971. About 80 profes-

sors, researchers, and former students of Einstein’s had attended,

many of the students ﬂying in with their spouses from distant

locations to honor their former professor. The symposium report-

edly was very moving for Einstein, who greatly enjoyed the oc-

casion. Perhaps foremost among his contributions were the 20

doctoral graduates he guided while at Berkeley. Many of them

became leading ﬁgures in the study of alluvial rivers and hydrau-

lic engineering.

Late June 1973, while a Visiting Scholar at Woods Hole

Oceanographic Institute in Massachusetts, Einstein suffered a

heart attack and shortly thereafter died. At the time of his death,

he and friend Don Bondurant, a retired USACE engineer, had

outlined a book on alluvial rivers. It was not to be the usual

format of textbook, but rather an approach that introduces typical

engineering problems arising between people and alluvial rivers,

then explains the knowledge and methods needed to solve the

problems. The book, like Einstein’s work to formulate sediment

transport, was a task that unfortunately remained unﬁnished.

In 1988, the American Society of Civil Engineers established

the Hans Albert Einstein Award ‘‘to honor Hans Albert Einstein

for his outstanding contributions to the engineering profession

and his advancement in the areas of erosion control, sedimenta-

tion and alluvial waterways.’’

Acknowledgments

The writers thank Professor Daniel Vischer of ETH-Zurich for his

assistance with background material used in preparing this paper.

They also thank the paper’s reviewers and Pierre Julien, JHE

Editor.

References

Bishop, A. A., Simons, D. B., and Richardson, E. V. 共1965兲. ‘‘Total bed-

material transport.’’ J. Hydraul. Eng., 91共2兲, 175–191.

Brownlie, W. R. 共1981兲. ‘‘Prediction of ﬂow depth and sediment dis-

charge in open channels.’’ Rep. No. KH-R-43A, W. M. Keck Labora-

tory of Hydraulics and Water Resources, California Institute of Tech-

nology, Pasadena, Calif.

Chien, N. 共1956兲. ‘‘The present status of research on sediment transport.’’

Trans. Am. Soc. Civ. Eng., 121, 833–868.

Chien, N., and Wan, Z. 共1999兲. Mechanics of sediment transport, Ameri-

can Society of Civil Engineers, Reston, Va.

Colby, B. R., and Hembree, C. H. 共1955兲. ‘‘Computations of total sedi-

ment discharge, Niobrara River near Cody, Nebraska.’’ Water Supply

Paper 1357, U.S. Geological Survey.

Du Boys, M. P. 共1879兲.‘‘E

´

tudes du re

´

gime du Rho

ˆ

ne et de l’action

exerce

´

e par les eaux sur un lit a

`

fond de graviers inde

´

ﬁniment affouil-

lable.’’ Ann. Ponts Chausse

´

es, Se

´

rie 5, Paris, 8, 141–195 共in French兲.

Einstein, A. 共1926兲.‘‘U

¨

ber die Ursachen der Ma

¨

anderbildung der Flu

¨

sse

und Baersschen Gesetzes.’’ Naturwissenschaften, 14, 223–225 共in

German兲.

Einstein, H. A. 共1934兲. ‘‘Der Hydraulische oder Proﬁl-Radius.’’ Sch-

weizer Bauzeitung, Band 103共8兲, 89–91 共in German兲.

Einstein, H. A. 共1935兲. ‘‘Die Eichung des im Rhein verwendeten Ge-

scheibefangers.’’ Schweizer Bauzeitung, Band 110共12–15兲, 29–32 共in

German兲.

Einstein, H. A. 共1937兲. Der Geschiebetrieb als Wahrscheinlichkeitsprob-

lem. Mitt. Versuchsanst. fur Wasserbau, an der Eidgenossische Tech-

nische Hochschule in Zurich, Zurich, Switzerland.

Einstein, H. A. 共1942兲. ‘‘Formulas for the transport of bed sediment.’’

Trans. Am. Soc. Civ. Eng., 107, 561–574.

Einstein, H. A. 共1944兲. ‘‘Bed-load transport in Mountain Creek.’’ Tech.

Paper SCS-TP-55, U.S Soil Conservation Service.

Einstein, H. A. 共1948兲. ‘‘Determination of rates of bed-load movement.’’

Proc., Federal Interagency Sedimentation Conference, Denver, 75–

90.

Einstein, H. A. 共1950兲. ‘‘The bed-load function for sediment transporta-

tion in open channel ﬂows.’’ Tech. Bulletin No. 1026, U.S. Dept of

Agriculture, Soil Conservation Service, Washington, D.C.

Einstein, H. A., Anderson, A., and Johnson, J. 共1940兲. ‘‘A distinction

between bed load and suspended load.’’ Trans. Am. Geophys. Union,

21, 628–633.

Einstein, H. A., and Barbarossa, N. L. 共1952兲. ‘‘River channel rough-

ness.’’ Trans. Am. Soc. Civ. Eng., 117, 1121–1146.

Einstein, H. A., and Chien, N. 共1956兲. ‘‘Similarity of distorted models.’’

Trans. Am. Soc. Civ. Eng., 121, 440–457.

Fig. 12. Einstein maintained a life-long interest in sediment

movement

486 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JUNE 2004

Einstein, H. A., and Mu

¨

ller, R. 共1939兲.‘‘U

¨

ber die A

¨

hnlichkeit bei

Flussbaulichen Modellversuchen.’’ Schweizer Archive fur Angewandte

Wissenschaft und Technik, Heft 8, Zurich, Switzerland.

Gilbert, G. K. 共1914兲. ‘‘Transportation of debris by running water.’’ Pro-

fessional Paper No. 86, U.S. Geological Survey, Washington, D.C.

Graf, W. H. 共1971兲. Hydraulics of sediment transport, McGraw-Hill, New

York.

Humphreys A. A., and Abbot, H. L. 共1861兲. Upon the physics and hy-

draulics of the Mississippi River, J. B. Lippincott & Co., Philadelphia.

Kalinske, A. 共1942兲. ‘‘Criteria for determining sand transportation by

surface creep and saltation.’’ Trans. Am. Geophys. Union, Part II, 28,

266–279.

Lacey, G. 共1929兲. ‘‘Stable channels in alluvium.’’ Proc., Inst. Civ. Eng.,

27, 259–384.

Meyer-Peter, E., Favre, H., and Einstein, H. A. 共1934兲. ‘‘Neuere Ver-

suchresultate u

¨

ber den Geschiebetrieb.’’ Schweizer Bauzeitung, Band

103共4兲, 89–91 共in German兲.

Meyer-Peter, E., and Mu

¨

ller, R. 共1948兲. ‘‘Formulas for bed-load trans-

port.’’ Proc., Int. Association for Hydraulic Research, 2nd Meeting,

Stockholm, Sweden.

Powell, J. W. 共1875兲. Exploration of the Colorado River of the West and

its tributaries, U.S. Government Printing Ofﬁce, Washington, D.C.

Pyne, S. J. 共1980兲. Grove Karl Gilbert: A great engine of research, Univ.

of Texas Press, Austin, Tex.

Rouse, H. 共1939兲. ‘‘An analysis of sediment transport in the light of

turbulence.’’ Tech. Paper SCS-TP-25, U.S. Soil Conservation Service,

Washington D.C.

Schoklitsch, A. 共1914兲.‘‘U

¨

ber schleppkraft und geschiebebewegung,’’

Englemann, Leipzig, Germany.

Schoklitsch, A. 共1930兲. Der Wasserbau. Springer, Vienna. 关English trans-

lation by Shulits, S. 共1937兲兴. Hydraulic structures, American Society

of Mechanical Engineers, New York.

Schoklitsch, A. 共1934兲. Geschiebetrieb und die Geschiebefracht,

Wasserkraft & Wasserwirtschaft, Jgg. 39, Heft 4 共in German兲.

Shen, H. W., ed. 共1972兲. Sedimentation. A Symposium to Honor Professor

H. A. Einstein, Colorado State Univ., Ft. Collins, Colo.

Shen, H. W. 共1975兲. ‘‘Hans A. Einstein’s contributions in sedimentation.’’

J. Hydraul. Eng., 101共5兲, 469–488.

Shields, A. 共1936兲. Anwendung der A

¨

hnlichkeitsmechanik und der Tur-

bulenzforschung auf die Geschiebebewegung. Mitt. der Preussischen

Versuchanstalt fur Wasserbau und Schiffbau, Heft 26, Berlin 共in Ger-

man兲.

Straub, L. G. 共1935兲. Missouri River Report, House Document 238, Ap-

pendix XV, Corps of Engineers, U.S. Army to 73rd U.S. Congress.

Vanoni, V. 共1946兲. ‘‘Transportation of suspended sediment by water.’’

Trans. Am. Soc. Civ. Eng., 111, 67–133.

Vanoni, V. 共1948兲. ‘‘Development of the mechanics of sediment transpor-

tation.’’ Federal Interagency Sedimentation Conference, Denver,

209–221.

JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JUNE 2004 / 487