Downstream Change in Grain Size of River Bed Sediments and

Geographical Review of JapanVol. 65 (Ser. B), No. 2, 75-89,1992

Downstream Change in Grain Size of River Bed Sediments

and Its Geomorphological Implications

in the Kanto Plain, Central Japan

Koichiro INOUE*

Abstract

Longitudinal profiles of most Japanese rivers which are today not at grade can be described

by either exponential or power functions. The differences in fluvial processes should reflect the

differences in best fit function. In order to clarify the downstream changes in fluvial processes

of alluvial river, the downstream changes in the relationships between characteristics of grain

size distribution and tractive force, and between tractive force and channel slope were ex

amined for the five rivers in the Kanto plain, central Japan.

The composition of channel sediment was separated into several log-normally distributed

populations at each sampling point of the river beds. The A-population which is the coarsest size in the separated populations is interpreted to be tractional load, and its size depends on the

tractive force which is strongly affected by the channel slope.

For the river expressed by an exponential function, the A-population having the grain size of -7 to -6 phi disappears abruptly with the decrease in channel slope in the middle reach

. In contrast, for the river expressed by a power function, the A-population having the grain size of -7 to -6 phi is distributed down to near the river mouth

, because the decreases both in the curvature and slope of longitudinal profile are small. The downstream limit of the depositional

area of the A-population having the grain size of -7 to -6 phi corresponds to the position

where the tractive force markedly decreases associated with the decrease in slope along the

course of a river. At these positions, the values of the first derivative of the functions best fitting

the profiles show about 1/000 for five rivers. These positions migrate downstream when the

best fit function type changes from exponential to power due to the difference in their

mathematical characteristics. The distributions of grain size along the middle reach of an

alluvial river show the characteristics peculiar to the best fit function type of river profile

governing the downstream changes in hydraulic conditions. This implies that both the fluvial

processes and the development of the fluvial landforms can be evaluated from the morphological properties of the longitudinal profiles; the best fit function type and the curvature .

Key words: alluvial river, grain size, hydraulic condition, channel slope, mathematical function type of longitudinal profile.

I. INTRODUCTION

According to the grade concept which as

sumes that sediment load is balanced between

inflow and outflow, many Japanese rivers are

not at grade, because a large amount of fluvial

sediment load accumulates in their middle

reaches, forming gravel beds. With a large

amount of tractional load, aggradational pro

cesses in the middle reaches of these rivers

cause the change in shape of the longitudinal

profile, resulting in a change in the mathemat

ical function describing the profile curve

(OHMORI, 1991). The front of the depositional

area of gravels, which is called the FDG

(OHMORI, 1991), is characterized by the channel

slope of 1.0•~10-3 for Japanese rivers. Because

the position of the FDG advances downstream

with the decrease in curvature of the longi-

* Graduate Student , the University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113, Japan

76 K. INOUE

tudinal profile, the FDG of the river described by power function is located downstream rather than that of the river described by exponential function (OHMORI, 1991). In the above study, however, the relationship between the characteristics of longitudinal profile of rivers and the hydraulic regime were not examined based on the field data of channel sediment. Thus, it has not been made clear whether or not the hydraulic condition along a stream course is affected by the characteristics of the shape of longitudinal profile and how it changes with the change in the mathematical function type describing the longitudinal profile.

Concerning the channel sediment, the grain size of bed material decreases downstream, resulting in different fluvial landforms. The grain size reduction has been explained by the decrease in competence of stream flow as the channel slope and/or the discharge change downstream (PLUMLEY, 1948; NAKAYAMA,1952; YATSU, 1955; KNIGHTON, 1975; BRIERLEY and HICKIN, 1985). On the other hand, the grain size reduction has been also explained by the abra

sion and breakage whose influence on bed materials are different with lithologies. It is pointed out that the difference in downstream depos itional destination of the same size particles of channel sediment varies with the difference in their lithologies (IKEDA, 1970; KODAMA, 1992). Although the grain size of channel sediment surely does decrease by abrasion and breakage, it is considered that the downstream distribution of grain size of total channel sediment essentially depends on the hydraulic conditions as it will be proved in this paper.

The hydraulic conditions should be controlled by the morphological properties of river; the curvature and the steepness of longitudinal

profile curve, as proved by OHMORI (1988, 1991). INOKUCHI and SASAKI (1985) and INOKUCHI

(1989) also suggested that the bed material characteristics have a close relation to longitudinal profile. Therefore, it has come to be important to examine totally the relationships between the grain size of sediment, the hydraulic regime, and the longitudinal profile of the river.

For a river, the fluvial processes should be studied through a feedback system between

characteristics of landforms, hydraulic condi

tion and sediment. This viewpoint is required

not only when we make clear the development

of the fluvial landforms in alluvial plains; fans,

natural levees, and deltas, but also when we

predict the geomorphic change in rivers

throughout the whole course from mountain to

sea, based on analyses of the morphological

properties of rivers. As the first step to clarify

the fluvial processes through the above feed

back system, the parameters which express the

characteristics of the longitudinal profile of

rivers are used. This paper discusses the gravel

transport process and the downstream distribu

tion of grain size of river sediment through

alluvial river course; how the grain size of chan

nel sediment changes along the alluvial river

course with the change in hydraulic conditions,

and which relationship is established between

the hydraulic conditions and the characteristics

of the longitudinal profiles of rivers.

II. STUDY AREA

The Kanto plain, central Japan, is the largest

plain in Japan (Figure 1), through which many rivers flow, forming various fluvial landforms. Five alluvial rivers; the Ara, Tama, Tone, Watarase and Kinu Rivers (Table 1), were examined, because hydrological data have been observed over a long period. Concerning the Watarase River for which the abrasion and breakage of gravels were discussed by KODAMA

(1992), the grain size distribution was analyzed for the total channel sediment at each sampling

site based on data most of which are the same as those of KODAMA (1992). These rivers come down from the mountains higher than 2000m above sea level to the Kanto plain where alluvial fans, natural levees, and deltas are well developed along the river courses. Each river basin is comprised of various rocks (Table 1). The river bed materials are composed of various litholo

gies corresponding to bedrock lithologies of the source area. The study reaches for sediment samples are set up in the middle to the lower reaches where the effect of gravel supply from tributaries is negligible.

Downstream Change in Grain Size of River Bed Sediments 77

Figure 1. Location of the rivers examined.

Table 1. Geomorphic features of the rivers examined

A: basin area (km2) l: river length (km) L: basin length (km) B: mean basin width (=A/L) (km) F: form ratio (=A/L) H: maximum altitude in the basin (m) h: minimum altitude in the basin (m) R: relief ratio G: geology in the basin (GR: granitic rocks, PS: Pre-Neogene sedimentary rocks , NS

: Neogene sedimentary rocks, MR: metamorphic rocks, QV: Quaternary volcanic rocks)

III. GRAIN SIZE DISTRIBUTION

1. Separation of component populations of

bed material

For the examination of grain size composi

tion, 42 sampling sites were selected on bars

developed on the river beds along the middle to

the lower reaches for the above five rivers

(Figure 1). The grain size distributions were analyzed using sieves at 1/4 phi interval. The bed materials are composed mainly of gravel of

pebble and cobble size along the upper reaches, and of sand along the lower reaches. As it had been noted that the grain size distribution of sediment is composed of some log-normally distributed populations (SPENCER, 1963; VISHER, 1969; INOKUCHI and MEZAKI, 1974; and others), each sediment sample was separated into sever-

78 K. INOUE

Figure 2. An example of separation of populations comprising the grain size distribution of river bed material (at the Tone River No. 5).Solid circles show the original grain size distribution and the lines of A-, B1- and c are the separated log-normally distributed populations. Dashed line is resultant of the three best fit lines of A-, Bl and c-populations, showing a good agreement with the original distribution.

al log-normally distributed populations following the procedure of INOKUCHI and MEZAKI

(1974). An example of the original grain size distribution plotted on probability paper is shown by Figure 2, for the sample No.5 of Tone River.

The separated log-normally distributed populations are called A-, B-, C-, and D-populations in order of coarseness (INOKUCHI and MEZAKI, 1974; INOKUCHI, 1977). The population which has the

grain size corresponding to the B-population of INOKUCHI and MEZAKI (1974) can be further

divided into two populations; B1-, and B2

- populations. Both the mean diameter and the standard deviation of each separated lognormally distributed population are shown in

Table 2.

2. The movement manner of separated popu

lation

Using the transport stage diagram of BAG

NoLD (1966), the movement mannerr of each sep

arated population was examined. Figure 3 is

the transport stage diagram proposed by BAG

NOLD (1966); the abscissa is the mean diameter

of each population in millimeter, and the ordi

nate is dimensionless tractive force (ƒÆ), which

indicates the magnitude of the ratio of tractive

force to the critical tractive force. ƒÆ is given by

ƒÆ(=ƒÑ/(ƒÐ-p)gd), where ƒÑ is the tractive force (=

ƒÏ gRI), ƒÏ is fluid density (g/cm3), ƒÐ is sediment

density (g/cm3), g is the acceleration of gravity

(cm/s2), d is the sediment diameter (cm), and I is

the channel slope. The channel slope was calcu

lated as the average slope of the channel seg

ment from each sampling point to the upstream

reach of 5km on 1/25000 scale topographic

maps with contour intervals of 5 or 10m. R is

the hydraulic radius (cm), which can be sub

stituted by the mean depths at high water level.

The water depths are calculated from the data

of OHKUMA (1981) for the Tone River, Watarase

River and Kinu River, of Saitama Prefecture

(1987) for the Ara River, and of Keihin Work

Office of Ministry of Construction (1986) for the

Tama River.

An equation for the suspension criterion was

proposed by BAGNOLD (1966) as:

ƒÆ =0 .4V2/gd,

where V is the settling velocity of sediment

particles. Based on Figure 3, A- and a part of

B1-populations are derived from tractional

load, and C-population is derived from the sus

pended load. A large part of B1- and most of B2-populations are distributed around the suspen

sion criterion, suggesting that they are from

both tractional and suspended loads. According

to the calculation by INOKUCHI (1977), however,

the curve of 0.4V2/gd should be drawn some

what upward of that proposed by BAGNOLD

(1966). Therefore, B1- and B2-populations

should be also regarded as tractional loads as

well as A-population. D-population, which has

not been plotted on Figure 3 and is not shown

in Table 2, has a mean grain size of about 2 in


Table 2. Component populations of channel sediment

ƒÓ: mean diameter in phi scale. ƒÐƒÓ: standard deviation in phi scale. W%: weight percentage of proportion. L km: Distance from the river mouth

to each sampling site.

* Samples No . 1-9 of Watarase River are from KODAMA (1992), and samples No. 1 and 2 of Tama River are from SHIMAZU (unpublished data) .

phi scale (=0.25mm), so it is considered to be derived from the wash load (EINSTEIN, 1950). 3. The characteristics of downstream changes

in grain size of each population

The alongstream changes in both the mean

diameters and the standard deviations of sepa-

80 K. INOUE

Figure 3. Distribution of the populations on the diagram proposed by BACNOLD (1966).

rated populations are shown in Figure 4. Con

cerning the same population group, the mean

diameters show a little fluctuation along the

stream courses. The separated populations can

be classified into three groups based on the

distribution of mean diameter: the groups with

diameters of about -7 to -6, -4 to -2, and 0

to 1 in phi scale. Based on the classification of

grain size distribution, the most conspicuous

characteristic is the marked decrease in diame

ter of the largest group along the middle to

lower reaches. A-population which is the lar

gest group for diameter consists mainly of pop

ulations with mean diameter along the up

stream reaches, but they abruptly diminish in

diameter along the middle to lower reaches

except for the Tama River. This fact suggests

that the coarser size grain of -7 to -6 phi is

transported only along the upstream reach of a

river.

4. Relationships between transport compe

tence and grain size

As the tractive force equation is expressed as

follows;

ƒÑ=ƒÏgRIƒÑ

is a function of both the channel slope and

hydraulic radius when the hydraulic radius is

substituted by water depth at high water level.

On the other hand, the critical tractive force (ƒÑc)

of the sediment with a given diameter (d, cm) is

given by ƒÑc=ƒÊ(ƒÐ-ƒÏ)gd, where ƒÊ is a constant

varying with the diameter. The critical tractive

force equation was proposed by IWACAKI (1956)

as;

ƒÑc =sa9a d•†0 .303cm

=134 .6d31/21 0.118 •…d•…0.303cm

=55 .0d 0.0565•…d•…0.118cm

=8 .41d11/32 0.0065•…d•…0.0565cm


Figure 4. Alongstream change in grain size of the separated populations.

Here, to examine the alongstream changes in

the ratios of ƒÑ/ƒÑc for each river, ƒÑ/ƒÑc at each

sampling site is shown in Figure 5. The values

of ƒÑ/ƒÑc, for some sampling sites were not plotted

on Figure 5 because the tractive force cannot be

calculated precisely due to the unmeasured

channel slope by the construction of reservoirs.

On Figure 5, when the value of ƒÑ/ƒÑc is close to

1.0, the tractive force is balanced with the bed

load. The ratios of ƒÑ/ƒÑc for A-population are

almost 1.0 and constant, despite the difference

in mean grain size of the populations, while the

ratios of ƒÑ/ƒÑc are widely scattered for the other

populations. Thus, the values of ƒÑ are equiva

lent to the tractive force of the sediment diam

eter of A-population, indicating that the along

stream changes in mean grain size of A

- population can be explained by the changes in

tractive force courses. Inversely, it can be said

that the characteristics in the grain size of A-

82 K. INOUE

Figure 5. Alongstream changes in the ratio of ƒÑ/ƒÑc of each separated population at each sampling site.

The square root of the ratio of ƒÑ/ƒÑc is used for the ordinate.

population is important, because it accounts for

the greater part of the tractional load in relation

with the fluvial processes.

The alongstream change in the tractive force

rvaries with rivers (Figure 6). The rivers can be

classified into two types based on their down

stream changes in ƒÑ. Tama River does not show

a clear tendency of decrease in ƒÑ and the value

of rdoes not change so much through the whole

river course, whereas the other four rivers have

segments where ƒÑ decreases downstream.

Although the tractive force is the function of

channel slope and water depth, it is obvious

from Figure 6 that the values of ƒÑdepend on the

channel slope much more than water depth.

This fact indicates that the alongstream

changes in grain size of A- population are con

trolled by the channel slope, and suggests that

the tendency of alongstream change in channel

slope is divided into two types; the Tama River

and the others. This will be examined in the

following chapter.


Figure 6. Alongstream changes in; tractive force, (g/cm2; upper column), channel slope (middle column), and water depth (lower column).Both the channel slope and the water depth are the relative values. Numerals indicate sampling site of channel sediment.

84 K. INOUE

IV. LONGITUDINAL PROFILE OF RIVER

AND ITS IMPLICATIONS FOR CON

TROLLING THE GRAIN SIZE

1. Parameters describing the characteristics

of longitudinal profile

For examining the tendency of downstream

change in channel slope and/or tractive force,

the longitudinal profiles of the five rivers were

constructed from 1/25000 scale topographic

maps. Distance was measured at each 10m alti

tude contour along stream course from the

river mouth. Regression analyses between alti

tude and distance for five rivers were per

formed utilizing linear, power, and exponential

functions. Based on the correlation coefficients,

the best fit function types were determined for

the five rivers (Table 3). This procedure is the

same as that used by OHMORI (1988, 1991).

The Tama River is best expressed by a power

function; y=axb=fp(x), whereas the other four

rivers are best expressed by exponential func

tions; y=ƒ¿eƒÀx=fe(x) where x is the horizontal

distance from the river mouth (m), y is the

altitude of river bed above sea level (m), a, b, a

and ƒÀ are constants.

According to OHMORI (1988), development of

the FDG is clearly classified by two parameters:

curvature and average slope of longitudinal

profile. In a river, coefficient a of equation y=ƒ¿

eƒÀx indicates the steepness of the longitudinal

profile. Similarly, the curvature is evaluated by

the coefficient b of function y=axb expressing

the longitudinal profile, where the function is

not necessarily the best fit of the river. Because

these parameters reflect the characteristics of

downstream changes in hydraulic conditions,

using both the coefficients a and b, the morphol

ogical characteristics of longitudinal profiles of

rivers were examined with reference to the dis

tributions of grain size along the stream course.

2. Function type of longitudinal profiles and

grain size

In order to examine the effects of both the

average slope and curvature of longitudinal

profile on the grain size of sediment of each

sampling point, regression analyses between al-

Table 3. Results of the regression analyses be

tween altitude and distance for the rivers examined

* r is correlation coefficient of regression function. The underlined

value shows the best fit function of the longitudinal profile of

each river.

titude and distance were performed. Here, the distance was measured from the headwaters to the sampling site, meaning that the distance of the examined river segment decreases with the sampling site located upstream. The values of both a and b vary with each sampling site for the same river. Alongstream changes in their values are shown in Figure 7, where the best fit function types are also signed. Figure 7 points

out the following three points. (1) The values of a and b are almost constant along the upper reach of a river, while in the lower reach the values of a decrease and inversely the values of b increase. Because the increase in b indicates morphometrically a marked downstream decrease in slope, this fact implies that the channel slope decreases significantly along the lower reach of a river. (2) The longitudinal

profile in the upper reach is mainly expressed by a power function even if the longitudinal

profile is expressed by an exponential function for the whole river course from the river mouth to the headwaters (Table 3), with exception of the Ara River. Namely, the Tone, Kinu, and Watarase Rivers, which are expressed by an exponential function for their whole river courses, are best described by a power function


Figure 7. Alongstream changes in the values of; a of function: y=ƒ¿eƒÀx (upper column); b of function: y=axb

(middle column), and the tractive force: ƒÑ, g/cm2 (lower column).Numerals indicate sampling sites of bed material.

for their upper reaches. This fact, that the best

fit function changes downstream from a power

function to an exponential function, inevitably

means that the slope markedly decreases down

stream along these rivers due to the mathemat

ical characteristics of the functions. (3) The

changes in both a and b along a river course cor

respond to the changes in ƒÑ for all the rivers

86 K. INOUE

examined. These three points imply that the

change in grain size of A-population along a

river course corresponds to the alongstream

changes in both a and b as well as in t They

also indicated that the grain size of A

- population remains about -7 to -6 phi along

the upper reach of a river where both the aver

age slope and the curvature of longitudinal

profile do not change so much. Therefore, the

position with marked changes in both values of

a and b is regarded as the downstream deposi

tional limit of A-population (Figure 4, Figure 6,

Figure 7).

Based on Figure 7, the values of a are about

10 and the values of b are 2 to 3, at the positions

of the downstream depositional limits of A

- population having the mean grain size of -7 to -6 phi for all study rivers . These values of b

agree well with those of b reported by OHMORI

(1991). The Tama River, whose whole long

itudinal profile is expressed by a power func

tion, shows that the values a and b do not

change so much even near the river mouth. As

noticed by OHMORI (1991), in the river whose

profile is expressed by a power function, the

migrations of the FDG seem to be accomplish

ed so easily that the gravel bed channel ap

proaches the river mouth.

Incidentally, the equation evaluating the

channel slope is given by the first derivative of

the function best fitting the longitudinal profile.

Figure 8(A) shows the value of f'(x) at the posi

tions where the values of a and b change mark

edly along the river course. Further, Figure 8(B)

shows the value of f'(x) at the downstream dep

ositional limit of the A-population having the

mean grain size of -7 to -6 phi for each river.

Both values of f'(x) are about the same; f'(x)=

1.0•~10-3. Thus, the downstream depositional

limit of A-population having the mean grain

size of -7 to -6 phi, which is equivalent to the

position of f'(x)=1.0 x 10-3, can be regarded as

the FDG for the five rivers.

Based on these facts mentioned above, sche

matic illustrations are shown in Figure 9. The

distributions of the grain size along the stream

course show the characteristics peculiar to the

best fit function type of river profile. Along the

river segments characterized by a power func

tion, even if the whole river course is character-

Figure 8. (A) The channel slope at the position where the values of both a and b markedly change downstream.

(B) The channel slope at the position of downstream limit of A-population

with the grain size of about -7 to -6 phi .

As both a and b for Tama River do not change so much downstream, the value of f'(x) at the location of 109.3km from headwaters which is located at the lower end point of the Tama River in Figure 7 is substituted for f'(x) of both a and b in this Figure.

ized by an exponential function, the grain size

of A-population is almost constant about -7 to

-6 phi. These segments have the characteris

tics of alluvial fan reach. The channel slope of

the downstream limit of the gravel bed is about

1.0•~10-3. For the river characterized by an

exponential function, its lower reach has a

channel slope less than 1.0•~10-3, where the

coarser grain of -7 to -6 phi disappears from

the channel sediment and the channel sediment

consists mainly of sand and smaller particles.

These segments have the characteristics of nat

ural levee and/or delta.


Figure 9. Schematic illustrations of the downstream change in grain size based on the characteristics of the longitudinal profile of alluvial rivers.

V. CONCLUSIONS

In order to clarify the downstream changes in

fluvial processes of alluvial rivers, the author studied the relationships between the characteristics of the fluvial deposits and the tractive force, and between the tractive force and the longitudinal profile of river, in the Kanto plain, central Japan. The results are as follows;

(1) The composition of channel sediment at each sampling site was separated into 2 to 5

groups of log-normally distributed populations. The A-population which is the group with the coarsest size among the separated populations is interpreted to be tractional load based on the

downstream changes in the ratio of the tractive force to the critical tractive force.

(2) Based on the downstream changes in channel slope and hydraulic radius, the tractive force which is expressed by a function of channel slope and hydraulic radius depends on the channel slope much more than on water depth.

(3) The downstream change in tractive force is controlled by the function type best expressing the longitudinal profile. For the river expressed by an exponential function, the A-population having the grain size of -7 to -6

phi disappears abruptly with the decrease in channel slope in the middle reach. The downstream depositional limit of the A-population having the grain size of -7 to -6 in phi corre-

88 K. INOUE

sponds to the position where the channel slope

markedly decreases in the middlereach. At the

positions the values of f'(x) of the best fit func

tions are about 1.0•~10-3 for five study rivers.

This position migrates downstream as the

profile curvature decreases associated with the

change in function type from exponential to

power.

It is concluded that the distributions of grain

size along alluvial river course show the charac

teristics peculiar to the best fit function type of

river profile which influences the downstream

change in hydraulic conditions, resulting in the

different landform regimes along the river.

Acknowledgments

I am grateful to Professor Hiroo OHMORI, the Uni

versity of Tokyo, for many helpful suggestions, to Mr.

Masashi TAKADA and Mr. Toshihiko SUGAI for their

valuable discussion, and to Mr. Yukiya TANAKA, Mr.

Shigehiro KATO, Mr. Kazuhiko SAWAMURA, and Mr.

Yasushi AGATA who assisted in field surveys. Calcula

tions are performed using the computer programs

possessed by Professor Mitsuhisa WATANABE, Toyo University. A part of the data of bed material was

provided by Mr. Hiroshi SHIMAZU. I thank the following organizations which gave me every facility for

the reference of data; Shimodate, Ara River Upstream, and Ara River Downstream Work Offices of Ministry

of Construction.

(Received Apr. 10, 1992)(Accepted Oct. 10, 1992)

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関東地方の沖積河川における礫径の縦断変化とその地形学的意味

井上耕一郎*

河川縦断面曲線は,従来,平衡河川を表すのに適当で

あると考えられてきた関数回帰式によって近似的に表現

されてきた。日本の諸河川は非平衡河川であるが,その

縦断面曲線は,「指数関数」もしくは「べき関数」で表さ

れる。適合関数形の違いは,河川の運搬作用の違いに反

映していると考えられる。本研究では,河川作用の縦断

方向への変化の実態を理解する目的で,「礫径-掃流カ

-縦断面形」の関係を吟味し,河川縦断面曲線の適合関

数形が異なると掃流力や礫径の縦断変化の特徴がどのよ

うに異なるのかを論じた。

関東地方の5つの沖積河川において,「粒度組成・掃

流力・河川勾配」のそれぞれについて,縦断変化を検討

した。河床砂礫は2～5つの対数正規分布集団に分けら

れる。そのうち最大の粒径を持つA集団の運搬形式は

掃流形式と解釈され,その粒径は,河川勾配に強く規定

された流水の掃流力の大きさに対応していることが確か

められた。

「指数関数形タイプ」の河川では,縦断面曲線の曲率が

大きいため,その中流部において,掃流力が著しく減少

し,それにともなって-7～-6φ の大きさを持っA集

団が特徴的に見られなくなる。それに対して,「べき関数

形タイプ」の河川は,河川縦断面曲線の曲率および河川

勾配の縦断変化が小さく, -7～-6φ の大きさを持っA

集団は,「指数関数形タイプ」の河川と異なり,河口付近

まで存在する。その流下限界は,中～下流部で掃流力す

なわち河川勾配が著しく減少する所に相当しており,そ

の地点の河川勾配は,調査対象5河川においては,いず

れも約1/1000を示している。またこの位置は,縦断面

曲線の適合関数形が「指数関数形」河川よりも「べき関

数形」河川の方が,下流側に位置する。

以上の検討から,沖積河川における河床砂礫の大きさ

は,河川縦断面曲線の適合関数形のタイプに特有な縦断

変化を示すと同時に,河川縦断面形状の特徴を反映した

水理状態の縦断変化によく対応していることが明らかに

なった。このことは,河川縦断面形状(適合関数形のタ

イプ,曲率)から河川の運搬作用や堆積物によって形成

される地形が概ね推定できることを意味している。

* 〒113東京都文京区本郷　東京大学大学院地理学専攻

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