Distribution of hazard types in a drainage basin and its relation to geomorphological setting

ELSEVIER

Geomorphology 10 (1994) 95-106

Distribution of hazard types in a drainage basin and its relation to geomorphological setting Hiroo Ohmori a, Hiroshi Shimazu b "Department of Geography, Graduate School of Science, The Universityof Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan bDepartment of Geography, Faculty of Letters, Kanazawa University, Kakumacho, Kanazawa City, Ishikawa Prefecture, 920-11, Japan Received January 1, 1994; revised March 20, 1994; accepted March 30, 1994

Abstract Hazards along a fiver course in a drainage basin are characterized by three types of events: debris flow, turbidity flow and flood. Each has its own channel segment with different sediment transport processes. The sediment transport process is controlled by transportation force: tractive force and slope-direction component of sediment weight, both of which are significantly affected by channel slope. Along large rivers in Japan the boundary between the upstream turbidity flow segment and the downstream flood segment is located at the position with a channel slope of about 1/1000. Along steep, small rivers the boundary between the upstream debris flow segment and the downstream turbidity flow segment is located at the position with a channel slope of about 80 / 1000. The channel slope depends on the shapes of longitudinal profiles of rivers. The longitudinal profiles of Japanese rivers, main rivers and tributaries, can be described by an exponential, power or linear function. The transportation force of the rivers fitted with exponential functions markedly decreases downstream due to the large curvature of the profiles, causing noticeable sediment deposition in the middle courses. The transportation force of the rivers fitted with power or linear functions maintains its strength through the whole river courses due to the small curvature, causing sediment transportation down to the lower courses. The function types are strongly affected by relief in the drainage basins. The rivers flowing in small relief areas are fitted with exponential functions and those flowing in large relief areas are fitted with power or linear functions. Thus, the distribution of hazard types along a river course in a drainage basin is controlled by the distribution of relief in the drainage basin.

1. Introduction Hazards occurring in a drainage basin are classified into three types of events characterized by different transportational and/or depositional processes of sediment. The first type is a debris flow which is defined here as a high-density flow containing numerous gravels of boulder size, the second type is a turbidity flow which is defined as a torrent containing much tractional load of cobble and pebble size, and the third type is a flood which is defined as an overflow and ponding of muddy water without gravel. The debris flow causes 0169-555X/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved

SSDIO169-555X(94)OOO19-N

markedly serious destruction of land by transportation and deposition of boulders, and debris control dams and ground sills are required to prevent the occurrence. The turbidity flow also causes serious destruction by transportation and deposition of gravels, and dykes and spurs are required as defense from the attack. The flood causes widespread damage primarily by ponding of muddy water, and levees and reservoirs are required to prevent flooding. As each requires different control works for protection, distinguishing where and which types of hazard occur along a river course is important for planning land use and flood control projects.

H. Ohmori, H. Shimazu / Geomorphology 10 (1994) 95-106

96

As defined above, hazard types are characterized by the grain size of transported sediment which is controlled by transport processes: debris flow, traction and suspension. The grain size of debris flow sediment depends on the channel slope (Shimazu, 1991) because the transportation force is determined mainly by the slope-direction component of sediment weight itself. The grain size of the sediment transported by traction and suspension depends on the tractive force of stream flow (Hjulstrom, 1935; Plumley, 1948; Iwagaki, 1956; Hack, 1957; Brush, 1961; Egiazaroff, 1965; Bagnold, 1966; Inokuchi and Mezaki, 1974; Knighton, 1975, 1980, 1982; Schumm, 1981; Brierley and Hickin, 1985; Ohmori, 1991; Inoue, 1992). Tractive force is also determined by the channel slope for Japanese rivers (Ohmori, 1991; Inoue, 1992). The channel slope can be evaluated based on the longitudinal profiles of ri~ers. The characteristics of the longitudinal profiles are strongly affected by the distribution of relief in the drainage basins (Ohmori, 1993). This paper examines first the segmentation of a river course based on the hazard types as characterized by sediment transport processes. Second, the sediment transport processes controlled by the shape of longitudinal profile of the river are discussed. Third, the relationship between the shape of the longitudinal profile and the relief in the

drainage basin is examined. And finally, how the distribution of relief in a drainage basin controls the distribution of hazard types is discussed. Forty-five large Japanese rivers with drainage areas of 200 to 14,300 km 2 are examined for the hazards in a large river and 7 steep Japanese small rivers with drainage areas of 50 to 950 km 2 are examined for the hazards in a steep, small river.

2. Segments with different sediment transport processes in a large river In relatively large rivers in Japan, the river courses are divided into two segments: the upstream fans (or gravel-bed channels) and the downstream natural levee and delta systems (Yatsu, 1954, 1955; Oya, 1977; Saito, 1988; Ohmori, 1988). The boundary between the segments is clearly recognized at the position where the channel slope is about 1/1000 (Fig. 1; Ohmori, 1991 ). The position indicates the front of the depositional area of gravels and is called the " F D G " (Ohmori, 1991). Using the equation expressing the tractive force, ~-(dyn/cm2): (1)

~'= pgRI

50.0I

:

10.0 5.0 v0- -

..-

.'"i'" .'..

.

.."

......,......../::;::' ...........................

..... .,,..';/:,.,-;.:;.. ...... ::::;::, ........ .,,::::,, ~ ~ : , " :

x

•:

.:°. : ° ~4.

,* •° ....

.." : ...",.~'" : ..' ~:-.

L 1.0

"

t

.,.:%.:-;...,

...r.,~*..:%o ° ° ° ..~ d ° ..'.." . .. , ~ ' -

-

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

.........

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

...." ,°,°,.,.°°.°-* ..... .-" .. ~ , °..° : # : ° . - .°¢" t ° . : . ,

.

.

...... .

.

.

°

.

." .. ..

..'" -9".'"" ,,.....,'~-" .-:s. ...- ..~i,:!.,~ ...'........

......

........ ...

.... ...

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

< ~ "

'

b" O. 0.5

_o

~ S

.

f::c~on:~:;le

&delta

& grave4 t ~

££TL

P 0.1

0.05

/ /I

r/

I

"4

,,near I

100

I

I

........... I

D i s t a n c e f r o m t h e river m o u t h ,

I

I

200

I

I

t

260

xl0 a m

Fig. 1. Segmentation of large rivers in Japan. The boundaries between the gravel bed channels and the natural levee and delta systems are located at the positions with a channel slope of about 1 / 1000 which is evaluated by f ' (x) of the best fit functions (after Ohmori, 1991 ).

H. Ohmori, H. Shimazu / Geomorphology 10 (1994) 95-106 m

"8

the maximum diameter of sediment, d (cm), is given by:

eo

d=RI/O.O5/(o'/p- 1)

f(z)=l. 1329 e 0"0413 x

m

' ~

jeFIDG

i,° 2

a

a

a [3

e -8 N

97

-6

~. -

=

'=

,i, I tOO

I

I

90

i

I

80

J

I

70

i

I

i

60 km

Distance from the river mouth Fig. 2. Example of a part of a longitudinal profile of the River Arakawa, in the Kanto Plain, central Japan, which shows part of a regression line of the best fit function, the observed channel slope, the observed flood stage of a ten-year recurrence interval, the calculated tractive force and the observed grain size. The grain size indicates the mean diameter together with the standard deviation of the tractional sediment. The sediment is divided into groups such as tractional sediment and suspended sediment, each of which shows a log-normal distribution of grain size (based on Inoue, 1992).

and the equation expressing the critical tractive force, ~'c (dyn/cm2):

=O.05(~-p)gd

(2)

(3)

where p is the fluid density (g/cm3), g is the acceleration of gravity (cm/s2), R is the hydraulic radius (cm), which can be substituted by water depth or flood stage, I is channel slope and o- is the sediment density(g/cm3). Because the maximum flood stages frequently observed in Japanese rivers are in the range of 100-500 cm, and cr/p= 2.65, the sediment with a maximum diameter of 1 to 6 cm is transported downstream to the position with a channel slope of about 1/1000. At this position, the sediment changes from gravel to sand, forming FDG (Ohmori, 1991). Based on the relationships between the tractive force and the grain size distribution of sediment observed in 5 large rivers in the Kanto Plain, central Japan, Inoue (1992) showed that the alongstream change in grain size is determined by the tractive force which changes downstream. Gravels larger than cobble size (about 6 cm in diameter or - 6 in ~bscale), which comprise 80% or more of bed material in weight, are transported by traction and most of them are deposited in the reach with a channel slope equal to or larger than 1/1000 (Fig. 2; Inoue, 1992). It means that the downstream end of cobble-size gravel deposition which is equivalent to FDG is located at the position with a channel slope of about 1/ 1000. Because the tractive force markedly decreases downstream due to the abrupt decrease in channel slope, the downstream course gentler than 1/ 1000 is comprised mainly of sandy material. Thus, a large river course is classified into two segments: the upstream turbidity flow segment and the downstream flood segment.

3. Segments with different sediment transport processes in a steep small river Viewed in the drainage basin, steep small rivers are equivalent to the upper courses and tributaries of the large rivers examined above. They are frequently attacked by debris flows occurring in their uppermost steep channels and tributaries. Based on the grain size distribution along the channels of main courses and tributaries of steep small rivers in Japan, Shimazu (1990, 1991) pointed out that the mean diameter of

98

H. Ohmori, H. Shimazu / Geomorphology 10 (1994) 95-106

D A 0 0

200

E E

g

,eg~ O

~100 t-

0

I

I

1 [llJll

5

[

10

I

, IJl,tl

50

I

100

,

, It

500

between 200 and 400 m upstream from the junction with its main river, tributaries are classified into two categories: the debris flow tributary which has a lowerend channel slope larger than 80/1000 and the turbidity flow tributary which has a lower-end channel slope less than 80/1000. In the debris flow tributary, debris flows run down through the whole course into the main river, whereas in the turbidity flow tributary, debris flows, even if they occur, cannot reach into the main river because they are deposited in the middle course, and turbidity flows are dominant in the lower course.

Channel slope, xlO~ Fig. 3. Relationship between channel slope and mean diameter of sediment in steep small rivers and tributaries. Different symbols indicate different drainage basins (after Shimazu, 1991 ).

sediment increases with the increase in channel slope for the lower courses gentler than about 80/1000, whereas the mean diameter decreases with the increase in channel slope for the steeper upper courses (Fig. 3; Shimazu, 1991). Along the river courses steeper than 200/1000, bedrock is often exposed continuously and a marked sedimentation is not recognized. Sediment deposition becomes conspicuous downstream, forming clearly shaped debris flow lobes in the courses with a channel slope of 200/1000 to 80/1000. The debris flow lobes contain a number of boulders with a maximum diameter larger than 100 cm. There are no huge boulders in the downstream courses gentler than 80/1000 where the sediment diameter decreases with the decrease in channel slope. In such gentle gradients, gravels are transported by turbidity flows and the upstream huge boulders are also moved into the gentle courses by turbidity flows after they are diminished in size due to weathering (Schumm and Stevens, 1973; Benda, 1990). The values of the critical slopes agree well with those for debris flows observed in Japan: 11-15 ° ( 195/1000270/1000) for the upstream end of the debris flow deposition and 3-4 ° (50/1000-70/1000) for the downstream end of the deposition (Takahashi and Yoshida, 1979; Kobashi et al., 1980). Thus, a steep small river course is divided into two segments: the debris flow segment which is steeper than 80/1000 and the turbidity flow segment which is gentler than 80/ 1000. Using the channel slope at the lower end of a tributary, represented by the mean slope of the channel

4. Longitudinal profiles of rivers controlling sediment transport processes Based on regression analysis, the longitudinal profile of a large river in Japan can be described by one of three mathematical functions: exponential, power and linear functions (Ohmori, 1988, 1991; Inoue, 1992; Ohmori and Saito, 1993). It was noted that the tractive force, which is calculated by Eq. (1), significantly decreases downstream in the rivers fitted with exponential functions due to the large curvature (Fig. 4a), even if flood stage increases downstream (Ohmori, 1991; Inoue, 1992; Fig. 2). Downstream decrease in tractive force is small along the river courses fitted with power functions due to the relatively small curvature, and the tractive force in the rivers fitted with linear functions maintains the same strength through the whole river courses because the change in channel gradient is negligible (Fig. 4a). As the channel slope is estimated by the first derivative of the best fit functions, the location of FDG is also estimated based on the best fit functions. The locations of FDG estimated by the first derivative of the best fit functions, f '(x) = 1/1000, are not different from the locations of FDG observed in Japanese rivers, as shown in Fig. 1, where the observed FDG is indicated by the boundary between the alluvial fan and gravel bed and the natural levee and delta (Ohmori, 1991). Thus, it can be said that the degree of development of the upstream turbidity flow segment and/or the downstream flood segment depends on the function type. Utilizing linear, power, exponential and logarithmic functions, regression analysis between altitude and distance was performed for the longitudinal profiles of

H. Ohmori,14.Shimazu/ Geomorphology10 (1994)95-106 - -

1.0

power f .

exponential f.

99

linear f.

. . . . . . . . .

a

..go,:......" "~ 0.5

0.0

0.0

0.5

0.0

1.0

0.5

1.0

Distance ratio Fig. 4. Examples of the longitudinal profiles of rivers described by different functions. (a) For large rivers, (b) for small, steep rivers. Distance and altitude are expressed by ratios, where both the horizontal distance and relative altitude between the lowest and highest points of a measured river course are 1.0. o e x p o n e n t i a l f. 1.00

• p o w e r f.

a linear f.

•. o . ~a _,..~

5_o

adj, aaT,..-.filacCb,~°

~oo

D ae~

,a ,.c~c9o"

•

!~

[]

0.95

0

[]

~

°c

OD ~0 O0 00~

~"

0

0

_~o.

0

O'"

O

/

0.90

I

,

0.85

,

I

I

I "/,

0.90

,

=

I

I

,

I

,

0.95

1.00

Correlation coefficient for exponential function Fig. 5. Distribution of correlation coefficients of exponential and power regression functions; for steep, small rivers and tributaries. The function types are determined based on the least mean error among the utilized exponential, power, linear and logarithmic functions.

main courses and tributaries of steep small rivers in Japan. The longitudinal profiles also show a good fit to both exponential and power functions. The correlation coefficients of individual rivers are larger than 0.85 for both functions and larger than 0.95 for either of the functions (Fig. 5). Based on the mean error of estimate, some of them, which have also large correlation coefficients larger than 0.95 for linear function as well for exponential and power functions, are best described by a linear function. Thus, the longitudinal profiles of steep small rivers in Japan are expressed by an exponential,

power or linear function, as also noted by Shepherd (1985) for bedrock rivers in Texas, USA. Based on the frequency of the function type for each class of the lower-end channel slope (Fig. 6), tributaries with an exponential function type profile are limited to those with a lower-end channel slope less than about 200/ 1000 (about 1023x10-3). Tributaries with a power function type profile increase in number with the increase in slope and the increment is remarkable for a channel slope larger than about 60/1000 (about 101~xl0-3). Tributaries with a linear function type

100

H. Ohmori, H. Shimazu / Geomorphology 10 (1994) 95-106

250~- D e x p °nential f.

oo1- m owe,,. ~5

.~ 1 5 0 t

llinear

I.

.

.

.

I

.

.

10°s 10 10 = 1 j 4 1 0 " ' 10 " 100 102=10241#" 1# 81000 Lower-end channel slope,

x10 -3

Fig. 6. Frequency distribution of function types for each class of the lower-end channel slope of tributaries. The lower-end channel slope indicates the mean slope of the 200 m long channel just above the junction with its main river.

profile are limited to those with a gardient larger than about 100/1000. As noted previously, using the lower-end channel slope of 80/1000, tributaries are classified into either a turbidity or debris flow tributary. Most of the tributaries fitted with exponential functions are classified as turbidity flow tributaries. The transportation force of debris flows, which is principally caused by the slopedirection component of weight of the debris, markedly decreases downstream due to the large curvature (Fig. 4b), causing the deposition of boulders in the middle courses, with the lower courses dominated by turbidity flows. The tributaries fitted with power or linear functions are classified as debris flow tributaries where the downstream decrease in transportation force is small due to the small curvature (Fig. 4b) and debris flows run through the whole courses. Because the above characteristics are representative of steep, small rivers, hazard types of a steep, small river also depend on the function type.

the relationship between function types and relief. Both indicators represent the relief condition of a drainage basin by a single value. As suggested by the relationship between the hypsometric integral and the relief ratio (Fig. 7), small hypsometric integrals indicate small-reliefdrainage basins and large hypsometric inte0.5

i

function type o : exponential

_.

0.4

• : power a : linear D

ml~ *" C "- 0.3 ,~

•

0

•

•

•

.

[]

•

•

,.

cl 1¢ 0.2 O la, >, 'I- 0.1--

o

~8o o

dP

o •0

5. Relief controlling the function types for large rivers The relief condition in a drainage basin is expressed by many indicators. For large rivers, the relief ratio defined by Schumm (1956) and the hypsometric integral defined by Strahler (1952) are used for examining

0.0 0.001

I

I

I

I I a~lL 0.005 0.01

I

I

I

J I 0.05

Relief ratio Fig. 7. Distribution of function types of large rivers in relation to the relief in drainage basins (after Ohmori, 1993).

H. Ohmori, H. Shimazu / Geomorphology 10 (1994) 95-106

grals the large-relief drainage basins for Japanese rivers (Ohmori, 1993). From Fig. 7, the distribution of a function type is limited in a range of hypsometric integral. Most rivers fitted with exponential functions have integrals less than 0.25, those fitted with power functions have integrals ranging from 0.20 to 0.35, and those fitted with linear functions have integrals larger than 0.30. Thus, the function types describing the longitudinal profiles of rivers are strongly affected by the relief in the drainage basins and it can be said that long flood segments are developed in the drainage basins with integrals less than 0.25, and long turbidity flow segments are developed in the drainage basins with integrals larger than 0.25.

101

gests that the turbidity flow tributaries occur in small relief areas and the debris flow tributaries in large relief areas. When a drainage basin of a main river is covered with a grid system and divided into unit squares in which several lattice points are included, we can calculate the mean altitude and the standard deviation for each unit square based on the altitudinal data of the lattice points. Mean altitude and the standard deviation of a unit square are given by: n

and:

(5)

D= i=I

6. Relief controlling the function types for steep small rivers

where Yis the mean altitude, D is the standard deviation, xi is the altitude of the lattice point i, and n is the number of lattice points in a unit square. The standard deviation, which is called the "dispersion of altitude" (Ohmori, 1978), is, statistically, an absolute measure of the dispersion of surface altitude, and indicates physically the dispersion of potential energy of surface material. It has been noted that the dispersion of altitude is proportional to both relief energy and surface gradient (Ohmori, 1978, 1981; Ohmori and Sohma, 1983; Ohmori and Hirano, 1984), and is in a functional relation with erosion rate (Ohmori, 1978, 1981, 1983). Using a grid system with intervals of 250 m on 1:50,000 scale top-

Because the distribution of tributaries with different hazard types in a drainage basin affects the distribution of hazard types along their main river courses, a more detailed examination was performed for the steep, small rivers. Fig. 8 shows the relationship between the relief ratio and the lower-end channel slope of tributaries. Channel slope increases with the increase in relief ratio. Based on Fig. 8, where each function type is expressed by a different symbol, exponential functions generally show small relief ratios, and power and linear functions usually show larger relief ratios. This sug1000 i X

5oo

o" exponential f. A"

~ ~oq[]

power f.

r.t g

o : l i n e a r f.

d o.. _o -o

100

~c-

50 o

?

A

o

~

-'~

:,~o olff:x~oE ~( o

0

J

~

[]

o "o e-

o

z

o

5

^~

~

Oo Ooo8

~

A

0

0

o A

t

Ol

l 0.05

Iol

i~l

= 0.1

I

t

l 0.5

Relief

;

,,,1 1.0

ratio

Fig. 8. Relationship between the relief ratio and the lower-end channel slope of tributaries for different function types.

H. Ohmori, H. Shimazu / Geomorphology 10 (1994) 95-106

102

...... iii~i i~iiii!

i!i!iii!~~ ~ ~iili~::~ ~:::

~i

........

ii~ili ii~

'~:'

'

@~

.....

~ii

"

"

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

: ; E Lr

...... ~ -

. . . . . . . . . .

~ :~ <~ ~

,,

~=::::: .-.,..,

.-...- . . . .

:::::: ......

, ........

~ ::: ii~

~ ~ ~ ~S ~ ~iiii~i~i~t

~

::.:: ~:i ~:.:.,~ • -.-.I~

.--

.....-

:::::i~igii

"'""•

..... ,:.:.:

......

;:;::::

--..

..

i£yj=== t:=ifli= i=~i !iy.:~lii=::.i:¢~i~-;I I ::::i I :::::n~il!:u:~s~:liiiii /

!iiiiil

,:

[

;~ ::iiiill

:~

iii

,iii,.ii, • :;;;:q.;-:::;',

',.

"-:-;.:l:.:.:-:'

l k m

[ ] N-type [ ] M-type [ ] T-type

[ ] D-type

0 [ ] 30 [ ] 50 [ ] 70 [ ] 90 [ ~ 1 1 0 [ ] 1 3 0 [ ]

Type of square

Dispersion of altitude, m

Fig 9. Example of the distribution of square types and the dispersion of altitude for a drainage basin of a steep, small river: the Fujikoto River with a drainage area of 285 k m2, in northeast Japan.

¢h

400

[ ] N-type

.= ill

[]

I~"

-~"

~

M-type

[ ] T-type

!iiiiiliiii

DD,,

' =

1=9 0

T

0

I

n I

30

i!i!~i iii~ii: !i!i!~! i

I

50

I

i

70

I

I

90

i

~ i

110

I

i

130

i

I

150

I

I

170

I

I

190

Dispersion of altitude, m Fig. 10. Frequency distribution of square types for each class of the dispersion of altitude for 7 steep, small rivers.

14. Ohmori, H. Shimazu / Geomorphology 10 (1994) 95-106

ographic maps whose contour interval is 20 m, each drainage basin of 7 steep small rivers in Japan was divided into squares of 1 km 2 with 25 lattice points and the dispersion was calculated by Eq. (5) for individual squares. Then, using the channel slope measured on 1:25,000 scale topographic maps with a contour interval of 10 m, channels of 7 main rivers and their tributaries with a drainage basin larger than 0.1 km 2 were divided into turbidity flow segments and/or debris flow segments. Because the critical channel slope is 80/1000, the boundary between the two segments is located on the channel where the distance between two neighbouring contour lines is 5 mm on the maps. Based on the segment types dominantly distributed in each square, all squares in the drainage basins examined were classified into the following four square types: N-type square is a square where turbidity flow segments are dominant together with wide flood plains and/or river terraces over half of the square. M-type square is a square with poor development of river channels themselves where landslide blocks and smooth soil-creep slopes are well developed. Excluding N-type squares, the residual squares dominated by turbidity flow segments are classified as T-type square. D-type squares are occupied mainly with debris flow segments. An example of the distribution of square types in a drainage basin is shown in Fig. 9a. The distribution of the dispersion of altitude for the same drainage basin is shown in Fig. 9b. These figures suggest that N-type squares correspond to a small dispersion and D-type squares to a large dispersion. The frequency distribution of square types for each class of the dispersion is shown in Fig. 10 for all squares totalling 2079 squares of the 7 steep small rivers examined. N-type squares are limited to an altitudinal dispersion less than about 50 m, where most tributaries have no debris flow segment. M-type squares have a low frequency and a wide range from 40 to 160 m. Dtype squares are dominant for dispersions larger than about 70 m. T-type squares which are dominated by turbidity flow tributaries also have a wide range. All of the turbidity flow tributaries have turbidity flow segments at least in their lower courses, but they are classified into two categories: a tributary with a debris flow segment in its upper course and a tributary without a debris flow segment. For T-type squares, the squares occupied with

103

turbidity flow tributaries with upstream debris flow segments have a large dispersion, larger than 100 m, whereas the squares occupied with turbidity flow tributaries without a debris flow segment have a small dispersion, less than about 60 m. Based on the above relationship between the dispersion and the square types, the squares with a dispersion larger than about 100 m are occupied with rivers which are often attacked by debris flows. Although the squares with a dispersion of 60-100 m cannot be clearly divided into either of the two categories, the squares with a dispersion less than about 60 m are occupied with rivers where turbidity flows are dominant. Especially, most squares with a dispersion less than 40 m are occupied with rivers without a debris flow segment. Thus, the distribution of hazard types along a river course is controlled by the distribution of relief in the drainage basin.

7. Conclusions Each of the hazard types; debris flow, turbidity flow or flood, occupies its own segment with a different channel slope in a river course. Along a large river in Japan, gravels of cobble size are transported down to a position with a channel slope of about 1/1000. The position indicates the boundary between the upstream turbidity flow segment and the downstream flood segment. Along a steep small river, debris flows move down to the position with a channel slope of about 80/ 1000. This position is a boundary between the upstream debris flow segment and the downstream turbidity flow segment. Based on the relationships between function types and segment types, between segment types and square types and between square types and relief, the distribution of hazard types along a river course is summarized in Fig. l 1. A river course flowing through an area with an altitudinal dispersion larger than about 100 m is attacked by debris flows occurring in the tributaries whose longitudinal profiles are fitted with power or linear functions (Fig. 1 la). Due to the small curvature of the longitudinal profile, the transportation force maintains the same strength through the whole course and boulders are transported into the main river (Fig. 1lb). The river course flowing through an area with a dispersion less than about 60 m is attacked, not by debris flows, but by turbidity flows occurring in the tributaries whose

a: T r i b u t a r i e s

~

^o~"~ ~ ~ec~" ~

.,,---_i turbidityflow segment b: Steep

Oeb.s flow Iribulary~ (power-linearf.) ~

/ "

r~'

Turbidityflow tributary., smallrelief (exponentialf . ) < ~ ] (dispersion<6Om)

slope: 80/1000

_~.

,,.

~'~

. rivers

small

largerelief (dispersion>lOOm)

~

~'~o~"

Z.W

~-

#

~-~7 slope: 80/1000

-,%1 +f= FDG

=~pe: ,/1ooo

,'~.<~.~C~

('~~,¢6~'

,.,~_\...,o'~',;

c~<~,l~.:\ ~ ~ ( ~ t l "~"\-- J~e~e~t~, ~5e9~e~' flooa "~q 4-" t~¢~ l~,t~ ~ \ TM segmenl seg~ne n

c...,,.

>"

,,.,,s

o,

,~\o'."

I ~,~.

--

~"~o)'"

~,~

large relief (hypsometric integral>0.25) 0 Power/linearfunction

"

/ f'~7" •,~'~A,,~'~ ~, (-~

/~.,~'d~ ~r..(~ slope: 1/1000 , , / A ~ FDG ~

..(~ ~ / ',._~" / ~(~/L,W~,,-k

Exponential f. smallr~elief (hypsometric integral<0.25)

Fig. l 1. Schemes expressing the relationships between the segments with different hazard types and relief in drainage basins

H. Ohmori, H. Shimazu / Geomorphology 10 (1994) 95-106

profiles are fitted with exponential functions (Fig. 11 a). Due to the large profile curvature, transportation force markedly decreases downstream, and, even if debris flows occur in the upstream segments, they cannot run down to the downstream gentle slope segments where turbidity flows are dominant (Fig. 1 lb). When a river flows through an area with a dispersion of altitude less than about 40 m, it has a segment with a channel gradient less than 1/1000 and hazards are caused only by floods (Fig. l i b ) . In a large river course, the hazards mentioned above occur through the whole river course, but the development of a turbidity flow segment and/or a flood segment also depends on the relief in the drainage basin (Fig. 1 lc).

Acknowledgements The authors would like to thank Prof. M. Morisawa, State University of New York at Binghamton, for her kind invitation to the 25th Annual Binghamton Geomorphological Symposium on Natural Hazards and Geomorphology, and for her critical comments on the manuscript.

References Bagnold, R.A., 1966. An approach to the sediment transport problem from general physics. U.S. Geol. Surv. Prof. Pap., 422-I: 1-37. Benda, L., 1990. The influence of debris flows on channels and valley floors in the Oregon Coast Range, U.S.A. Earth Surface Process. Landforms, 15: 457-466. Brierley, G.J. and Hickin, E.J., 1985. The downstream gradation of particle sizes in the Squamish River, British Columbia. Earth Surface Process. Landforms, 10: 597-606. Brush, L.M., Jr., 1961. Drainage basins, channels and flow characteristics of selected streams in central Pennsylvania. U.S. Geol. Surv. Prof. Pap., 282-f: 145-181. Egiazaroff, I.V., 1965. Calculation of nonuniform sediment concentrations. Proc. Am. Soc. Civ. Eng., 91 (HY4) : 225-247. Hack, J.T., 1957. Studies of longitudinal profiles in Virginia and Maryland. U.S. Geol. Surv. Prof. Pap., 294-B: 45-97. Hjulstrom, F., 1935. Studies of morphological activity of rivers as illustrated by the River Fyris. Bull. Geol. Inst. Uppsala, 25:221527. Inokuchi, M. and Mezaki, S. 1974. Analysis of the grain size distribution of bed material in alluvial rivers. Geogr. Rev. Jpn., 47: 545-556 (in Japanese, with English abstr.). Inoue, K., 1992. Downstream change in grain size of river bed sediments and its geomorphological implications in the Kanto Plain, central Japan. Geogr. Rev. Jpn., 65B: 75-89.

105

lwagaki, Y., 1956. Fundamental study on critical tractive force. I. Hydro-dynamical study on critical tractive force. Trans. Jpn. Soc. Civ. Eng., 41:1-21 (in Japanese, with English abstr.). Knighton, A.D., 1975. Channel gradient in relation to discharge and bed material characteristics. Catena, 2: 263-274. Knighton, A.D., 1980. Longitudinal changes in the size and sorting of stream-bed material in four English rivers. Geol. Soc. Am. Bull., 91: 55-62. Knighton, A.D., 1982. Longitudinal changes in the size and shape of stream bed material: evidence of variable transport conditions. Catena, 9: 25-34. Kobashi, S., Nakayama, M. and lmamura, R., 1980. Movement of surface material. In: A. Takei (Editor), Landslides, Slope Collapses and Debris Flows. Kajima Press, Tokyo, pp. 28-64 (in Japanese) Ohmori, H., 1978. Relief structure of the Japanese mountains and their stages in geomorphic development. Bull. Dept. Geogr. Univ. Tokyo, 10:31-85. Ohmori, H., 1981. Simulation of change of landform from a geomorphometric method. Trans. Jpn. Geomorphol. Union, 2: 95100. Ohmori, H., 1983. Characteristics of the erosion rate in the Japanese mountains from the viewpoint of climatic geomorphology. Z. Geomorphol. Suppl., 46: 1-14. Ohmori, H., 1988. The relationship between the mathematical function types describing longitudinal profiles of rivers and the types of alluvial plains in Japan. In: Research for the Formations of Alluvial Plains and Alluvial Deposits, and Their Relations to Natural Environment during the Late Quaternary in Japan. Dept. Geogr., Nagoya Univ., Nagoya, pp. 6-15 (in Japanese ). Ohmori, H., 1991. Change in the mathematical function type describing the longitudinal profile of a river through an evolutionary process. J. Geol., 99:97-110. Ohmori, H., 1993. Changes in the hypsometric curve through mountain building resulting from concurrent tectonics and denudation. Geomorphology, 8: 263-277. Ohmori, H. and Hirano, M., 1984. Mathematical explanation of some characteristics of altitude distribution of landforms in an equilibrium state. Trans. Jpn. Geomorphol. Union, 5: 293-310. Ohmori, H. and Saito, K., 1993. Morphological development of longitudinal profiles of rivers in Japan and Taiwan. Bull. Dept. Geogr. Univ. Tokyo, 25: 29-41. Ohmori, H. and Sohma, H., 1983. Landform classification in mountain region and geomorphic characteristic values. J. Jpn. Cart. Assoc., 21 ( 3 ) : l - 12 ( in Japanese, with English abstr. ). Oya, M., 1977. Comparative study of the fluvial plain based on the geomorphological land classification. Geogr. Rev. Jpn., 50: 131. Plumley. W.J., 1948. Black hills terrace gravels: a study in sediment transport. J. Geol., 56: 526-577. Saito, K., 1988. Alluvial Fans in Japan. Kokon-shoin, Tokyo, 280 pp. (in Japanese). Schumm, S.A., 1956. Evolution of drainage systems and slopes in badlands at Perth Amboy, New Jersey. Geol. Soc. Am. Bull., 67: 597-646. Schumm, S.A., 1981. Evolution and response of the fluvial system, sedimentologic implications. SEPM Spec. Publ., 31: 19-29.

106

H. Ohmori, H. Shimazu / Geomorphology 10 (1994) 95-106

Schumm, S.A. and Stevens, M.A., 1973. Abrasion in place: a mechanism for rounding and size reduction of coarse sediments in rivers. Geology, 1: 37-40. Shepherd, R.G., 1985. Regression analysis of river profiles. J. Geol., 93: 377-384. Shimazu, H., 1990. Segmentation of mountain rivers based on longitudinal change in gravel size of riverbeds in Tohoku District, northeastern Japan. Geogr. Rev. Jpn., 63A: 487-507 (in Japanese, with English abstr. ). Shimazu, H., 1991. Downstream change in gravel size and bed form along tributaries and gravel supply for the main stream in the

Japanese mountains. Geogr. Rev. Jpn., 64A: 569-580 (in Japanese, with English abstr. ). Strahler, A.N., 1952. Hypsometric (area-altitude) analysis of erosional topography. Geol. Soc. Am. Bull., 63:1117-1141. Takahashi, T. and Yoshida, H., 1979. Study on the deposition of debris flows. 1. Deposition due to abrupt change of bed slope. Ann. Disaster Prevention Res. Inst. Kyoto Univ., 22 (B-2): 315328 ( in Japanese, with English abstr. ). Yatsu, E., 1954. On the longitudinal profile of the graded fiver. Res. Inst. Nat. Resour. Jpn. Misc. Rep., 33: 15-24, 34: 14-21, 35: 16 (in Japanese, with English abstr.). Yatsu, E., 1955. On the longitudinal profile of the graded fiver. Am. Geophys. Union Trans., 36: 655~563.