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Some methodological developments in the analysis of sediment transport processes using age distribution of floodplain deposits
GEOHDRPHOIOGY ELSEVIER
Geomorphology 16 (1996) 139-145
Some methodological developments in the analysis of sediment transport processes using age distribution of floodplain deposits Futoshi Nakamura *, Shun-ichi Kikuchi Department of Forest Science, Faculty of Agriculture, Hokkaido University, Sapporo 060, Japan Received 15 March 1995; accepted 13 September 1995
Abstract Floodplain areas are primary storage sites for river sediment. In the Saru River, ages of floodplain surfaces were examined by tree ring analysis, and vertical and horizontal configurations of floodplain deposits were measured by field and aerial-photo surveying. A flood in 1992 provided a good opportunity to examine depositional and erosional processes of floodplain sediment before and after the flood. Predominant disturbances were observed in the unconstrained, wide reaches where floodplains dew,lop. This event indicated that eroded areas of floodplain deposits in each age class linearly increased with sediment volume and that the proportion of the total area eroded decreased exponentially with increase in the age of sediment. We constructed basic equations expressing continuity of age distribution in order to analyze river sedimentation in a time series according to the results of the 1992 flood. The floodplain disturbance rates determined by this analysis showed similar temporal changes with sediment transport rates monitored at the Iwachishi Reservoir. A sharp increase in sediment discharge was seen after 1962 associated with the historical maximum rainfall in the temporal analysis of floodplain sediment. The time se:ries approach presented here is useful for evaluating the speed of sediment waves and the cumulative impact of sedimentation in a river basin.
1. Introduction Sediment originating from hillslopes can be trapped at a number of storage sites such as the foot of hillslopes, alluvial fans, and floodplains (Page et al., 1994; Nakamura et al., 1995). Sediment in storage may be retained for years, decades or centuries. Floodplains such as those discussed in this paper are primary sediment storage areas (reservoirs), especially on wide valley floors (Dietrich et al., 1982; Madej, 1984; Nakamura, 1986; Kelsey et al., 1987). Everitt (1968) used the ages of cottonwood estab-
* Corresponding authc,r. Phone: + 81-11-706-2529. Fax: + 8111-706-4935. E-mail: [email protected]
lished on a floodplain of the Little Missouri River of western North Dakota, to elucidate a recent disturbance history of the valley floor. He constructed a model based on age-area distribution of floodplain sediment and estimated channel migration and sediment transport rates. Dietrich and Dunne (1978) computed residence time of floodplain deposits by dividing sediment volume in a storage by bedload discharge rate. Kelsey et al. (1987) developed a stochastic model for the long-term transport of stored sediment in Redwood Creek, northwestern California. This is a Markov-chain model based on the probability of transition of particles among four different sediment storage reservoirs classified by their stabilities. Nakamura (1986) used age distribution of
0169-555X/96/$15.00 '9 1996 Elsevier Science B.V. All rights reserved
SSDI O169-555X(95)O0139-5
140
F. Nakamura, S. Kikuchi / Geomorphology 16 (1996) 139 145
Niseu
~.
Pacific Ocean
Investigated
-
A
{
-,
,
,'l ,
/
0 I
10
20 km
I
P
Fig. 1. Locationof the Sam River basin and the section studied.
floodplain sediment to calculate residence time and transport distance in Japanese rivers originating in steep terrain. Methods developed previously cannot account for time series changes in sediment transport, although they estimate the average value of sediment transport rates in a given period. Nakamura et al. (1995) developed a means of analyzing floodplain sediment based on a continuity equation of the age distribution and comparing the results with sediment discharge recorded at a reservoir in northern Japan. The continuity equation has the advantage of clarifying a temporal series of floodplain disturbances and sediment transport. However, there are several assumptions which had yet to be verified by field research. In 1992, there was a heavy rainfall on the Saru River where we had previously made a detailed base-map of floodplain landforms before the flood. Comparison of floodplain landforms before and after the flood provided an opportunity to validate those assumptions. Here, we present some methodological
developments in this analysis supported by the results of field investigation.
2. Study site and methods The Saru River is a gravel-bed river, originating at Mount Memuro (1754 m) in the Hidaka Mountain range and flowing to the Pacific Ocean. The watershed area is 1345 km 2. We investigated a 28.9 km section of the river, extending from the confluence with the Nukabira River to the Iwachishi Reservoir located 57 km upstream from the mouth (Fig. 1). The average riverbed gradient in the study section is 0.36-0.52%. The basin is underlain primarily by sedimentary rocks, but also includes metamorphic rocks of Cretaceous age, with Tertiary sedimentary rocks distributed along the lower reaches. Annual precipitation is about 1200 mm. In 1962, the Saru River basin experienced a heavy rainfall (248 mm in two days) triggering numerous landslides over the 20
iO~Ro~ad~ ~.
0
1o
oJo 50
100
Road/ 150
200 m
Fig. 2. An exampleof cross-sectionalview of the floodplain surfaces and riparian forests in the Sam River.
141
F. Nakamura, S. Kikuchi / Geomorphology 16 (1996) 139-145
entire basin and distarbed the valley floor. Another heavy rain (245.5 mm in two days) fell in the basin in August 1992. The age of floodplain sediment was determined from the age of even-aged forests established on the floodplains (Fig. 2). Seeds of pioneer species, such as Salix, Populus and Alnus spp., are readily winddispersed over a broad area and are thus able to establish themselves on floodplain deposits soon after floods. They form even-aged forests which give a good indication of the age of these deposits (Araya, 1971). Partial, weak disturbances and forest succession create heterogeneously structured stands. Therefore, dating of sediment age by tree-rings includes more errors in older deposits, especially those greater than 50 years old, in Japanese riparian forests. The size and distribution of floodplain sediment were measured by field surveys and aerial photographs. The field survey, tree ring counting, and interpretation of aerial photographs were carried out from 1983 to 1985. Sediment accumulation data collected since 1960 in the Iwachishi Reservoir were used to determine annual sediment discharge rate from the upper basin. The watershed area of this reservoir is 567 km 2. The floodplain geomorphic changes after the 1992 flood were examined in the field and by aerial photographs. The base-map of the valley floor geomorphology made in 1984 allowed us to estimate the area of scoured and additional deposited sediment by the 1992 flood. First, we estimated the degree of disturbance based on the valley floor morphology and the conditions of the riparian forests. The floodplain deposits are classified into three categories: completely scoured sediment deposits, partially disturbed deposits, anti new deposits formed by the flood. Estimates were based primarily on comparison of aerial photographs taken in 1985 and 1992. Further, partially disturbed sediment deposits are ranked by degree. The deposits which lost riparian trees but retained sediment were ranked first. Deposits covered by fallen trees were included in the second rank. The third group consists of deposits where no trees were damaged but under-story vegetation was flushed out. These disturbance types of riparian forests were examined at 321 locations in the field, and geomorphic changes were simultaneously measured by tape and hand-level.
Second, the identified scoured and newly deposited areas were delineated on a 1/5000 scale map and their areas were calculated. The areas were multiplied by the aggraded and degraded depths measured in the field to determine the volume of deposits.
3. Basic equations used in analyzing age distribution of floodplain sediment The age distribution of floodplain sediment per unit length was calculated by tree ring analysis of even-aged forests (Everitt, 1968; Nakamura, 1986). The age distribution of floodplain deposits reflects the history of sediment transport. Examples of age distribution, including the Saru River, are shown in Fig. 3. Although each of these rivers exhibits a different pattern, floodplain deposits tend to decrease in area as their ages increase. This indicates that the sediment deposits in floodplains created by past floods are gradually scoured away with time, and that sediment transported from upper reaches replaces this old sediment (Nakamura, 1986). Contrasts in the age distribution of floodplain deposits along each of the three rivers may be attributed to differences in the magnitude of the floods that created them. In other words, if older floodplain deposits still remain and occupy a large area of valley floor, we concluded that the previous flood that created such deposits had a higher magnitude than subsequent floods. Accordingly, the age distribution of each river is shaped by decreasing trends with increasing age and by differences in the magnitude of floods. Here, the continuity equation of age distribution n(x, t) can be expressed as: ~n(x,t)/~t=
-On(x,t)/~x-e(x)
n(x,t)
(1)
where n(x, t) is the area of age x years when the time is t (years), and e(x) represents the percent loss of x-year old sediment per unit area per year. The area initially created for each age class can be expressed as n(O, t - x), because the area aged x years was created at time t - x (years). We can calculate n(O, t - x) by:
142
F. Nakamura, S. Kikuchi / Geomorphology 16 (1996) 139-145
1000 800 600 400 200 0 1 10 11 2021 3031 4041-5051-6061-7071 80 1000[ Furano River
8°°I
600 --~
amount of sediment discharge downstream (Madej, 1984; Nakamura, 1986). The residence time of sediment is very brief in the narrow reaches (Nakamura et al., 1987), which means sediment passes quickly downstream. The sediment transported to the wide sections is often trapped and replaced with old sediment in association with bank erosion caused by the lateral shift of river channels. Thus, distinctive changes in valley floor morphology were observed especially in wide reaches. A wide reach, 22.8 km upstream from the confluence with the Nukabira River, is illustrated in Fig. 4 to show the changes in
400 200
0
1-5
i i iliill sediment ~
6-10 11-1516 2021-2526-3031 3536-40
2500 t 2000'
1500 1000 5OO 0
1-5
6-10 11-1516-2021-2526-3031 3536 40
Age c l a s s
of f l o o d p l a i n
deposits
Before the 1992 flood
(year)
Fig. 3. Age distribution of floodplain geomorphic surfaces. The dashed line in the Nunobe River shows the exponential decreasing curve calculated by regression analysis (redrawn from Nakamura et al., 1995).
Nakamura et al. (1995) reconstructed a floodplain disturbance history based on these equations assuming that the erosion rate per unit area per year was constant regardless of the age of sediment. In the following, we examined validity of continuity equations, specifically the estimation of e(x) based on the results of floodplain disturbance before and after the 1992 flood in the Saru River.
~
~
(T~ ,"x
I, i;j{ J O ~
Severe damage Medium d a m a g e
OSlightdamage 100
0 I ....
4. Results and discussion
4.1. Disturbance of floodplain deposits by the 1992 flood The unconstrained, wide reaches of valley floor provide sediment storages that function to vary the
i ....
i
200m I
After the 1992 flood Fig. 4. Changes in riparian trees and floodplain geomorphic surfaces after the 1992 flood. Damage of trees are ranked by degrees. The areas where trees were washed away by the flood are ranked "severe", areas covered by fallen trees are ranked " m e d i u m " , and deposits where no trees were damaged but under-story vegetation was flushed out are ranked "slight".
143
F. Nakamura, S. Kikuchi / Geomorphology 16 (1996) 139-145
Table 1 Degree of riparian forest disturbance after the 1992 flood Age Totaldisturbance Arealpercentage of disturbance area (m2) Severe a Mediuma Slighta 7 11 14 17 21 26 30 40 <
350,000 172,000 27,000 50,000 33,000 98,000 71,000 66,000
55 71 25 34 28 34 19 16
42 21 52 29 15 23 6 0
3 8 23 37 57 43 75 84
200
%
150
100:
,o5 I
0
•
50
I
,
100
I
I
150
200
,
I
250
,
I
i
300
I
350
i
I
400
Floodplain area (x l0 s m2)
a Degree of damage follows the classification in Fig. 4.
Fig. 5. Relationship between eroded area of each age class and the total area. geomorphic surfaces and riparian forests after the 1992 flood. The deposits identified as bare land in the aerial-photos taken in 1985 were dated 7 year-old in 1992. These sediments and 17 year-old sediments were partially scoured and removed. Seven year-old sediments were distributed adjacent to the river channel where frequent fluvial disturbances take place. The trees aged 17 years grow mainly in the abandoned channel siituated on low geomorphic surfaces representing the bottom of the former riverbed. The 1992 flood inundated the entire valley floor and water filled the abandoned channel, knocking down the trees in its path. On the other hand, the older sediments, such as 26 and 45 year-old, were not significantly disturbed by the flood because they were located on high geomorphic surfaces. In 1992, the ages of sediment areas formed frequently on the floodplain are 7, 11, 14, 17, 21, 26, 30, and 45 years. 'The degree of riparian forest disturbance by the 1992 flood varies according to the age of the sediments (Fig. 4). The disturbance area and intensity over the entire section studied is summarized for each age class (Table 1). Riparian forests tend to be more extensively and intensively disturbed as they are y o u n g e r In general, older sediment is located away from the active channel and creates a high geomorphic surface in cross-sectional profile. This geomorphic setting prevents old sediment from being frequently disturbed by floods. Eroded areas, including those completely and partially scoured, were calculated for each age class and compared with its total area (Fig. 5). As previously assumed in Eq. 1, the eroded area is approximately proportional
to the total floodplain area of each age, although there is a considerable variation. This variation can be attributed to the age of the sediment; because older sediment (26, 30 and 45 years) is distributed below the regression line, while newer sediment (7, 11, 14, 17, 21 years) is found on or above this line. This means that erodibility of floodplain sediment decreases with age. In general, floods start to scour sediment deposited at erosion-prone sites such as adjacent to active channels and leave sediment locating at margins of the valley floor. Thus, the older sediment avoiding repeated floods can be situated at sites safe from fluvial disturbances. Accordingly, areal percentage of eroded sediment correlates inversely with age (Fig. 6). The percent losses of new sediment, such as for 7 and 11 year-old
6O
~50
o
o
~ 40
20
o
o
10 0 20 30 40 Age of sediment (years)
50
Fig. 6. Areal percentage of eroded sediment with respect to the age.
144
F. Nakamura, S. Kikuchi / Geomorphology 16 (1996) 139-145
sediment, were greater than 50%, while that of 45 year-old sediment was less than 10%. This correlation can be expressed by the following equation: e92 (x)
=
o/exp(
- fix)
(3)
w h e r e e92(x) is the percent loss of floodplain sedi-
1000 g" g
500
4.a
ment aged x by the 1992 flood, and constants a and /3 are 77.36 and -0.057, respectively.
1980-1984 0
100
4.2. Analysis on sediment transport process
50
Nakamura et al. (1995) took the percent loss of sediment as constant. However, we found that it varies with age. Thus the percent loss should be expressed as a function of sediment age as indicated by Eq. (1). The problem is what function can be applied to evaluate the annual percent loss of sediment. Obviously, it should be expressed as an exponential function as shown in Fig. 6. The constants c~ and /3 in Eq. 3 must be altered because they represent a single event that occurred in 1992. However, the relative trend of this curve may not greatly vary with flood events, thus the exponent of Eq. 3 can be applied: e ( x ) --- ce' exp( - / 3 x )
(4)
Assuming that the decreasing trend (exponent of the curve) of floodplain sediment with age in the Sam River (Fig. 3) is equivalent to the mean of e(x) in Eq. 4, a ' can be calculated by the following equation: ," Xma x
Ot'=mXmax/lo
exp( --/3y) dy
(5)
where m is the exponent of age distribution of sediment and Xmax is the maximum age of floodplain sediment.
Table 2 Summary of estimated loss of sediment Age (x)
Annual loss of floodplain sediment [ e(x)]
1-5 6-10 11-15 16-20 21-25
0.062 0.047 0.035 0.026 0.020
I
I
I
5000
10000
Floodplain disturbance rate
(#Am/year)
Fig. 7. Comparison between the sediment transport rate recorded at the Iwachishi Reservoir and the floodplain disturbance rate estimated by the time series analysis.
The evaluated e(x) by substituting Eq. (5) into Eq. (4) is shown in Table 2. These values were substituted to Eq. 2 and n(0, t - x) was calculated. Sediment volume was estimated by multiplying n(0, t - x) by the average depth of floodplain deposits aged x. Sediment deposited since 1960 was analyzed for comparison with the sediment transport rate monitored at the Iwachishi Reservoir (Fig. 7). The sediment volume and transport rate were averaged over five years. Both values are closely related although their dimensions are different. Numerous landslides and subsequent sediment transport by fiver channels in 1962 are responsible for a surge in the sediment discharge rate from 1960 to 1964. This widespread, intensive disturbance can be seen in the floodplain disturbance rate estimated by the analysis.
5. Conclusion
In previous studies (Everitt, 1968; Nakamura et al., 1995) percent loss of floodplain sediment has been considered as constant regardless of its age. However, this study indicates an exponential decrease in the percent loss with age. Precise estimation of these values is needed to clarify historical processes of river sedimentation using continuity of age distribution. We could not physically explain percent loss of floodplain sediment. This erosion rate should be
F. Nakamura, S. Kikuehi / Geomorphology 16 (1996) 139-145
related to geological,, geomorphological and hydrological characteristics of the river basin, such as subsurface and surface geologies, flood discharge, pattern of the drainage network, and longitudinal and cross-sectional river morphologies. These approaches allows the prediction of future processes of sediment movement in a given watershed. A time series approach is useful for analyzing and assessing the cumulative effects of natural and manmade disturbances in a fiver basin (Dickert and Tuttle, 1985). The basic equations presented in this paper are applicable for analyzing sediment transport processes in a time series such as estimating the speed of a sediment wave (Ozaki, 1991; Nakamura et al., 1995).
Acknowledgements We would like to thank Professor Araya for his kind advice throughout this study. This research was supported in part by Grant-in-Aid for Scientific Research (05660152, 07308066) from the Ministry of Education, Science and Culture, and a grant from the Japanese Society of Erosion Control Engineering.
References Araya, T., 1971. Morphological study of bed load movement in torrential rivers. Res. Bull. Exp. For. Hokkaido Univ., 28: 193-258 (in Japanese with English abstract).
145
Dickert, T.G. and Tuttle, A.E., 1985. Cumulative impact assessment in environment in environmental planning - - a coastal wetland watershed example. Environ. Impact Assess. Rev., 5: 37-64. Dietrich, W.E. and Dunne, T., 1978. Sediment budget for a small catchment in mountainous terrain. Z. Geomorphol. Suppl., 29: 191-206. Dietrich, W.E., Dunne, T., Humphrey, N.F. and Reid, L.M., 1982. Construction of sediment budgets for drainage basins. In: Sediment Budgets and Routing in Forested Drainage Basins. USDA Forest Service General Tech. Rep. PNW-141, pp. 5-23. Everitt, B.L., 1968. Use of the cottonwood in an investigation of the recent history of a flood plain. Am. J. Sci., 266: 417-439. Kelsey, H.M., Lamberson, R. and Madej, M. A., 1987. Stochastic model for the longterm transport of stored sediment in a fiver channel. Water Resour. Res., 23: 1738-1750. Madej, M.A., 1984. Recent changes in channel-stored sediment Redwood Creek, California. Redwood Natl. Park Tech. Rep., No. 11, 54 pp. Nakamura, F., 1986. Analysis of storage and transport processes based on age distribution of sediment. Trans. Jpn. Geomorph. Union, 7: 165-184. Nakamura, F., Araya, T., and Higashi, S., 1987. Influence of river channel morphology and sediment production on residence time and transport distance. Erosion and Sedimentation in the Pacific Rim (Proc. of the Corvallis Symp. in 1987), IAHS Publ. No. 165, pp. 355-364. Nakamura, F., Malta, H., and Araya, T., 1995. Sediment routing analyses based on chronological changes in hillslope and riverbed morphologies. Earth Surf. Process. Landforms, 20: 333-346. Ozaki, V.L., 1991. Long term monitoring of channel stability on Redwood Creek, California. 1991 Progress Report, Redwood National Park, 18 pp. Page, M.J.,Trustrum, N.A. and Dymond, J.R., 1994. Sediment budget to assess the geomorphic effect of a cyclonic storm, New Zealand. Geomorphology, 9: 169-188.
Geomorphology 16 (1996) 139-145
Some methodological developments in the analysis of sediment transport processes using age distribution of floodplain deposits Futoshi Nakamura *, Shun-ichi Kikuchi Department of Forest Science, Faculty of Agriculture, Hokkaido University, Sapporo 060, Japan Received 15 March 1995; accepted 13 September 1995
Abstract Floodplain areas are primary storage sites for river sediment. In the Saru River, ages of floodplain surfaces were examined by tree ring analysis, and vertical and horizontal configurations of floodplain deposits were measured by field and aerial-photo surveying. A flood in 1992 provided a good opportunity to examine depositional and erosional processes of floodplain sediment before and after the flood. Predominant disturbances were observed in the unconstrained, wide reaches where floodplains dew,lop. This event indicated that eroded areas of floodplain deposits in each age class linearly increased with sediment volume and that the proportion of the total area eroded decreased exponentially with increase in the age of sediment. We constructed basic equations expressing continuity of age distribution in order to analyze river sedimentation in a time series according to the results of the 1992 flood. The floodplain disturbance rates determined by this analysis showed similar temporal changes with sediment transport rates monitored at the Iwachishi Reservoir. A sharp increase in sediment discharge was seen after 1962 associated with the historical maximum rainfall in the temporal analysis of floodplain sediment. The time se:ries approach presented here is useful for evaluating the speed of sediment waves and the cumulative impact of sedimentation in a river basin.
1. Introduction Sediment originating from hillslopes can be trapped at a number of storage sites such as the foot of hillslopes, alluvial fans, and floodplains (Page et al., 1994; Nakamura et al., 1995). Sediment in storage may be retained for years, decades or centuries. Floodplains such as those discussed in this paper are primary sediment storage areas (reservoirs), especially on wide valley floors (Dietrich et al., 1982; Madej, 1984; Nakamura, 1986; Kelsey et al., 1987). Everitt (1968) used the ages of cottonwood estab-
* Corresponding authc,r. Phone: + 81-11-706-2529. Fax: + 8111-706-4935. E-mail: [email protected]
lished on a floodplain of the Little Missouri River of western North Dakota, to elucidate a recent disturbance history of the valley floor. He constructed a model based on age-area distribution of floodplain sediment and estimated channel migration and sediment transport rates. Dietrich and Dunne (1978) computed residence time of floodplain deposits by dividing sediment volume in a storage by bedload discharge rate. Kelsey et al. (1987) developed a stochastic model for the long-term transport of stored sediment in Redwood Creek, northwestern California. This is a Markov-chain model based on the probability of transition of particles among four different sediment storage reservoirs classified by their stabilities. Nakamura (1986) used age distribution of
0169-555X/96/$15.00 '9 1996 Elsevier Science B.V. All rights reserved
SSDI O169-555X(95)O0139-5
140
F. Nakamura, S. Kikuchi / Geomorphology 16 (1996) 139 145
Niseu
~.
Pacific Ocean
Investigated
-
A
{
-,
,
,'l ,
/
0 I
10
20 km
I
P
Fig. 1. Locationof the Sam River basin and the section studied.
floodplain sediment to calculate residence time and transport distance in Japanese rivers originating in steep terrain. Methods developed previously cannot account for time series changes in sediment transport, although they estimate the average value of sediment transport rates in a given period. Nakamura et al. (1995) developed a means of analyzing floodplain sediment based on a continuity equation of the age distribution and comparing the results with sediment discharge recorded at a reservoir in northern Japan. The continuity equation has the advantage of clarifying a temporal series of floodplain disturbances and sediment transport. However, there are several assumptions which had yet to be verified by field research. In 1992, there was a heavy rainfall on the Saru River where we had previously made a detailed base-map of floodplain landforms before the flood. Comparison of floodplain landforms before and after the flood provided an opportunity to validate those assumptions. Here, we present some methodological
developments in this analysis supported by the results of field investigation.
2. Study site and methods The Saru River is a gravel-bed river, originating at Mount Memuro (1754 m) in the Hidaka Mountain range and flowing to the Pacific Ocean. The watershed area is 1345 km 2. We investigated a 28.9 km section of the river, extending from the confluence with the Nukabira River to the Iwachishi Reservoir located 57 km upstream from the mouth (Fig. 1). The average riverbed gradient in the study section is 0.36-0.52%. The basin is underlain primarily by sedimentary rocks, but also includes metamorphic rocks of Cretaceous age, with Tertiary sedimentary rocks distributed along the lower reaches. Annual precipitation is about 1200 mm. In 1962, the Saru River basin experienced a heavy rainfall (248 mm in two days) triggering numerous landslides over the 20
iO~Ro~ad~ ~.
0
1o
oJo 50
100
Road/ 150
200 m
Fig. 2. An exampleof cross-sectionalview of the floodplain surfaces and riparian forests in the Sam River.
141
F. Nakamura, S. Kikuchi / Geomorphology 16 (1996) 139-145
entire basin and distarbed the valley floor. Another heavy rain (245.5 mm in two days) fell in the basin in August 1992. The age of floodplain sediment was determined from the age of even-aged forests established on the floodplains (Fig. 2). Seeds of pioneer species, such as Salix, Populus and Alnus spp., are readily winddispersed over a broad area and are thus able to establish themselves on floodplain deposits soon after floods. They form even-aged forests which give a good indication of the age of these deposits (Araya, 1971). Partial, weak disturbances and forest succession create heterogeneously structured stands. Therefore, dating of sediment age by tree-rings includes more errors in older deposits, especially those greater than 50 years old, in Japanese riparian forests. The size and distribution of floodplain sediment were measured by field surveys and aerial photographs. The field survey, tree ring counting, and interpretation of aerial photographs were carried out from 1983 to 1985. Sediment accumulation data collected since 1960 in the Iwachishi Reservoir were used to determine annual sediment discharge rate from the upper basin. The watershed area of this reservoir is 567 km 2. The floodplain geomorphic changes after the 1992 flood were examined in the field and by aerial photographs. The base-map of the valley floor geomorphology made in 1984 allowed us to estimate the area of scoured and additional deposited sediment by the 1992 flood. First, we estimated the degree of disturbance based on the valley floor morphology and the conditions of the riparian forests. The floodplain deposits are classified into three categories: completely scoured sediment deposits, partially disturbed deposits, anti new deposits formed by the flood. Estimates were based primarily on comparison of aerial photographs taken in 1985 and 1992. Further, partially disturbed sediment deposits are ranked by degree. The deposits which lost riparian trees but retained sediment were ranked first. Deposits covered by fallen trees were included in the second rank. The third group consists of deposits where no trees were damaged but under-story vegetation was flushed out. These disturbance types of riparian forests were examined at 321 locations in the field, and geomorphic changes were simultaneously measured by tape and hand-level.
Second, the identified scoured and newly deposited areas were delineated on a 1/5000 scale map and their areas were calculated. The areas were multiplied by the aggraded and degraded depths measured in the field to determine the volume of deposits.
3. Basic equations used in analyzing age distribution of floodplain sediment The age distribution of floodplain sediment per unit length was calculated by tree ring analysis of even-aged forests (Everitt, 1968; Nakamura, 1986). The age distribution of floodplain deposits reflects the history of sediment transport. Examples of age distribution, including the Saru River, are shown in Fig. 3. Although each of these rivers exhibits a different pattern, floodplain deposits tend to decrease in area as their ages increase. This indicates that the sediment deposits in floodplains created by past floods are gradually scoured away with time, and that sediment transported from upper reaches replaces this old sediment (Nakamura, 1986). Contrasts in the age distribution of floodplain deposits along each of the three rivers may be attributed to differences in the magnitude of the floods that created them. In other words, if older floodplain deposits still remain and occupy a large area of valley floor, we concluded that the previous flood that created such deposits had a higher magnitude than subsequent floods. Accordingly, the age distribution of each river is shaped by decreasing trends with increasing age and by differences in the magnitude of floods. Here, the continuity equation of age distribution n(x, t) can be expressed as: ~n(x,t)/~t=
-On(x,t)/~x-e(x)
n(x,t)
(1)
where n(x, t) is the area of age x years when the time is t (years), and e(x) represents the percent loss of x-year old sediment per unit area per year. The area initially created for each age class can be expressed as n(O, t - x), because the area aged x years was created at time t - x (years). We can calculate n(O, t - x) by:
142
F. Nakamura, S. Kikuchi / Geomorphology 16 (1996) 139-145
1000 800 600 400 200 0 1 10 11 2021 3031 4041-5051-6061-7071 80 1000[ Furano River
8°°I
600 --~
amount of sediment discharge downstream (Madej, 1984; Nakamura, 1986). The residence time of sediment is very brief in the narrow reaches (Nakamura et al., 1987), which means sediment passes quickly downstream. The sediment transported to the wide sections is often trapped and replaced with old sediment in association with bank erosion caused by the lateral shift of river channels. Thus, distinctive changes in valley floor morphology were observed especially in wide reaches. A wide reach, 22.8 km upstream from the confluence with the Nukabira River, is illustrated in Fig. 4 to show the changes in
400 200
0
1-5
i i iliill sediment ~
6-10 11-1516 2021-2526-3031 3536-40
2500 t 2000'
1500 1000 5OO 0
1-5
6-10 11-1516-2021-2526-3031 3536 40
Age c l a s s
of f l o o d p l a i n
deposits
Before the 1992 flood
(year)
Fig. 3. Age distribution of floodplain geomorphic surfaces. The dashed line in the Nunobe River shows the exponential decreasing curve calculated by regression analysis (redrawn from Nakamura et al., 1995).
Nakamura et al. (1995) reconstructed a floodplain disturbance history based on these equations assuming that the erosion rate per unit area per year was constant regardless of the age of sediment. In the following, we examined validity of continuity equations, specifically the estimation of e(x) based on the results of floodplain disturbance before and after the 1992 flood in the Saru River.
~
~
(T~ ,"x
I, i;j{ J O ~
Severe damage Medium d a m a g e
OSlightdamage 100
0 I ....
4. Results and discussion
4.1. Disturbance of floodplain deposits by the 1992 flood The unconstrained, wide reaches of valley floor provide sediment storages that function to vary the
i ....
i
200m I
After the 1992 flood Fig. 4. Changes in riparian trees and floodplain geomorphic surfaces after the 1992 flood. Damage of trees are ranked by degrees. The areas where trees were washed away by the flood are ranked "severe", areas covered by fallen trees are ranked " m e d i u m " , and deposits where no trees were damaged but under-story vegetation was flushed out are ranked "slight".
143
F. Nakamura, S. Kikuchi / Geomorphology 16 (1996) 139-145
Table 1 Degree of riparian forest disturbance after the 1992 flood Age Totaldisturbance Arealpercentage of disturbance area (m2) Severe a Mediuma Slighta 7 11 14 17 21 26 30 40 <
350,000 172,000 27,000 50,000 33,000 98,000 71,000 66,000
55 71 25 34 28 34 19 16
42 21 52 29 15 23 6 0
3 8 23 37 57 43 75 84
200
%
150
100:
,o5 I
0
•
50
I
,
100
I
I
150
200
,
I
250
,
I
i
300
I
350
i
I
400
Floodplain area (x l0 s m2)
a Degree of damage follows the classification in Fig. 4.
Fig. 5. Relationship between eroded area of each age class and the total area. geomorphic surfaces and riparian forests after the 1992 flood. The deposits identified as bare land in the aerial-photos taken in 1985 were dated 7 year-old in 1992. These sediments and 17 year-old sediments were partially scoured and removed. Seven year-old sediments were distributed adjacent to the river channel where frequent fluvial disturbances take place. The trees aged 17 years grow mainly in the abandoned channel siituated on low geomorphic surfaces representing the bottom of the former riverbed. The 1992 flood inundated the entire valley floor and water filled the abandoned channel, knocking down the trees in its path. On the other hand, the older sediments, such as 26 and 45 year-old, were not significantly disturbed by the flood because they were located on high geomorphic surfaces. In 1992, the ages of sediment areas formed frequently on the floodplain are 7, 11, 14, 17, 21, 26, 30, and 45 years. 'The degree of riparian forest disturbance by the 1992 flood varies according to the age of the sediments (Fig. 4). The disturbance area and intensity over the entire section studied is summarized for each age class (Table 1). Riparian forests tend to be more extensively and intensively disturbed as they are y o u n g e r In general, older sediment is located away from the active channel and creates a high geomorphic surface in cross-sectional profile. This geomorphic setting prevents old sediment from being frequently disturbed by floods. Eroded areas, including those completely and partially scoured, were calculated for each age class and compared with its total area (Fig. 5). As previously assumed in Eq. 1, the eroded area is approximately proportional
to the total floodplain area of each age, although there is a considerable variation. This variation can be attributed to the age of the sediment; because older sediment (26, 30 and 45 years) is distributed below the regression line, while newer sediment (7, 11, 14, 17, 21 years) is found on or above this line. This means that erodibility of floodplain sediment decreases with age. In general, floods start to scour sediment deposited at erosion-prone sites such as adjacent to active channels and leave sediment locating at margins of the valley floor. Thus, the older sediment avoiding repeated floods can be situated at sites safe from fluvial disturbances. Accordingly, areal percentage of eroded sediment correlates inversely with age (Fig. 6). The percent losses of new sediment, such as for 7 and 11 year-old
6O
~50
o
o
~ 40
20
o
o
10 0 20 30 40 Age of sediment (years)
50
Fig. 6. Areal percentage of eroded sediment with respect to the age.
144
F. Nakamura, S. Kikuchi / Geomorphology 16 (1996) 139-145
sediment, were greater than 50%, while that of 45 year-old sediment was less than 10%. This correlation can be expressed by the following equation: e92 (x)
=
o/exp(
- fix)
(3)
w h e r e e92(x) is the percent loss of floodplain sedi-
1000 g" g
500
4.a
ment aged x by the 1992 flood, and constants a and /3 are 77.36 and -0.057, respectively.
1980-1984 0
100
4.2. Analysis on sediment transport process
50
Nakamura et al. (1995) took the percent loss of sediment as constant. However, we found that it varies with age. Thus the percent loss should be expressed as a function of sediment age as indicated by Eq. (1). The problem is what function can be applied to evaluate the annual percent loss of sediment. Obviously, it should be expressed as an exponential function as shown in Fig. 6. The constants c~ and /3 in Eq. 3 must be altered because they represent a single event that occurred in 1992. However, the relative trend of this curve may not greatly vary with flood events, thus the exponent of Eq. 3 can be applied: e ( x ) --- ce' exp( - / 3 x )
(4)
Assuming that the decreasing trend (exponent of the curve) of floodplain sediment with age in the Sam River (Fig. 3) is equivalent to the mean of e(x) in Eq. 4, a ' can be calculated by the following equation: ," Xma x
Ot'=mXmax/lo
exp( --/3y) dy
(5)
where m is the exponent of age distribution of sediment and Xmax is the maximum age of floodplain sediment.
Table 2 Summary of estimated loss of sediment Age (x)
Annual loss of floodplain sediment [ e(x)]
1-5 6-10 11-15 16-20 21-25
0.062 0.047 0.035 0.026 0.020
I
I
I
5000
10000
Floodplain disturbance rate
(#Am/year)
Fig. 7. Comparison between the sediment transport rate recorded at the Iwachishi Reservoir and the floodplain disturbance rate estimated by the time series analysis.
The evaluated e(x) by substituting Eq. (5) into Eq. (4) is shown in Table 2. These values were substituted to Eq. 2 and n(0, t - x) was calculated. Sediment volume was estimated by multiplying n(0, t - x) by the average depth of floodplain deposits aged x. Sediment deposited since 1960 was analyzed for comparison with the sediment transport rate monitored at the Iwachishi Reservoir (Fig. 7). The sediment volume and transport rate were averaged over five years. Both values are closely related although their dimensions are different. Numerous landslides and subsequent sediment transport by fiver channels in 1962 are responsible for a surge in the sediment discharge rate from 1960 to 1964. This widespread, intensive disturbance can be seen in the floodplain disturbance rate estimated by the analysis.
5. Conclusion
In previous studies (Everitt, 1968; Nakamura et al., 1995) percent loss of floodplain sediment has been considered as constant regardless of its age. However, this study indicates an exponential decrease in the percent loss with age. Precise estimation of these values is needed to clarify historical processes of river sedimentation using continuity of age distribution. We could not physically explain percent loss of floodplain sediment. This erosion rate should be
F. Nakamura, S. Kikuehi / Geomorphology 16 (1996) 139-145
related to geological,, geomorphological and hydrological characteristics of the river basin, such as subsurface and surface geologies, flood discharge, pattern of the drainage network, and longitudinal and cross-sectional river morphologies. These approaches allows the prediction of future processes of sediment movement in a given watershed. A time series approach is useful for analyzing and assessing the cumulative effects of natural and manmade disturbances in a fiver basin (Dickert and Tuttle, 1985). The basic equations presented in this paper are applicable for analyzing sediment transport processes in a time series such as estimating the speed of a sediment wave (Ozaki, 1991; Nakamura et al., 1995).
Acknowledgements We would like to thank Professor Araya for his kind advice throughout this study. This research was supported in part by Grant-in-Aid for Scientific Research (05660152, 07308066) from the Ministry of Education, Science and Culture, and a grant from the Japanese Society of Erosion Control Engineering.
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