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Better understanding of suspended sediment transport processes allows for better management of both rivers and coasts. Based on field data and sediment transport energy theory, this study presents an analysis on the suspended sediment hysteresis in the Lower Tenryu River of Japan in connection to the channel carrying capacity of suspended sediment and morphological characteristics. The transport of suspended sediment in the river exhibited dual behaviors according to the magnitude of flood. It was transport-limited in a 10-year flood while supply-limited in a 30-year flood. In the supply-limited case, the temporal variation of suspended sediment concentrations followed the hydrograph well. In the transport-limited case, however, there was a time lag between peak discharge and maximum suspended sediment concentration. The mechanism of time lag was further clarified to be different for the 10-year flood and a small flood. The objective of this paper is to shed some new light on the relationship of suspended sediment to flow and channel conditions.

Better understanding on the transport of suspended sediment from rivers to the ocean has remained a challenge for an increasing number of reasons. In Japan, the overall erosion rate of the coastline was 7.2 × 10^{5} m^{2}/year before 1980, but sharply increased to 1.6 × 10^{6} m^{2}/year after 1980 due largely to the reduction of suspended sediment supply. In the United States, Environmental Protection Agency (EPA) identifies suspended sediment as the single most widespread pollutant affecting the beneficial uses of the Nation’s rivers and streams [

The relationship between river discharge and suspended sediment concentration is generally expressed by a rating curve, which is described by a power function (Walling [

in which SSC is the suspended sediment concentration (g/m^{3}), Q is the flow discharge (m^{3}/s) and a, b are empirically determined regression coefficient. However, various studies (Klein [

In this study, the patterns of SSC-Q relation during three floods of different magnitude in a regulated gravel river were studied. It is aimed to better understand the hysteresis in relation to flow and channel cross-sectional characteristics and from the perspective of channel sediment carrying capacity.

The Tenryu River (^{th} longest river in Japan. There are five dams along the mainstream; Yasuoka Dam, Hiraoka Dam, Sakuma Dam, Akiha Dam and Funagira Dam. The Lower Tenryu River is the part from the Kashima site to the river mouth, approximately 25 km long. Due to dam constructions in the upstream of the river, particularly after the completion of the Sakuma Dam in 1956, the

sediment supply from the upstream was very much reduced, resulting in significant morphological change in the downstream reaches and beach erosion in the Enshunada Coast as well (Nagashima [^{8} m^{3}. Thus, the annual sediment trapping rate by the Sakuma Dam was estimated to be about 2.6 × 10^{6} m^{3}/yr, which virtually prevented all bed material sediment loads from transporting to downstream reaches. As a result, the active remaining source of beach-forming sediment supply to the coast after the dam construction is the Keta River, which is a tributary of the Tenryu River and located downstream of all sediment-trapping dams but upstream of the Kashima site.

Two large floods occurred in the river in 2006 and 2007, respectively. Hamamatsu River Office conducted fieldobservation of SSC and flow discharge during the two floods. The depth-averaged SSC data, supplied to authors from the river administration office, were used in the analysis of this study. We also collected from the river administration office channel cross-sectional data and continuous water level records for the calculation of flow velocity and depth. In 2008, we installed a back scattering turbidity meter (Compact-HTW) 1m above the river bed at the Kakedsuka gauging station (3.3 km from the river mouth) for continuous monitoring. During the summer of 2008, there was a small flood and the corresponding turbidity data were recorded and converted to SSC according to the calibrated relationship between turbidity and SSC compiled through pre-field lab test.

First of all, flood frequency analysis was conducted for the Lower Tenryu River to determine the return periods of the three floods in consideration. The Log-Pearson Type III distribution was used in the analysis.

To explain the difference among the three cases in terms of carrying capacity, we adopted the energy balance theories of Velikanov [

By dimensional analysis, the difference in energy dissipation rate between clear water and sediment-laden flow could be expressed as

where A = channel cross-sectional area; g, g_{s} = specific weights of water and sediment; w = settling velocity; C_{v}_{ }= suspended sediment concentration by volume, k_{1} and a = coefficients.

By definition,

where J and J_{s} are energy slopes of clear water and sediment-laden flow, respectively. They can be expressed as following

where l and l_{s} are friction coefficient without and with suspended sediment, respectively. Mathematical manipulation of Equations (2-5) led to

Since the difference between l and l_{s} is due to the presence of suspended sediment, (l - ls) in Equation (6) could be assumed to be a function of sediment concentration as

Substitution of Equation (7) into Equation (6) and mathematical manipulation led to

where C_{*} can be considered as the saturation concentration of suspended sediment (kg/m^{3}) under the velocity U; R is the hydraulic radius; K and m are empirical parameters. Following the work of Zhang ([19,20]), which was based on flume experiments and field observation, the values of K and m were assigned to be 0.07 and 1.4 in this study. Then, the transport capacity of suspended load was estimated in the present study as

To make use of this formula, the settling velocity must be determined. In the autumn of 2006, we surveyed surficial sediment size distributions in a vegetated zone on the floodplain 14 km from the river mouth. The type of vegetation was hard tree with an average height of 5 m. After the flood of 2007, we survey surficial sediment size distributions on a vegetated sandbar 5 km from the river mouth.

flood. It can be seen from _{m}) was taken to be 0.3 mm. The settling velocity was then computed according to Dietrich [

(10)

To characterize the three floods in terms of their carrying capacities, the saturation concentrations at the peak discharges of the three floods were computed by Equation (9).

Figures 3-5 show flow discharges and SSC for the three target flood events. The peak flows were approximately 8000, 6000 and 1000 m^{3}/s, respectively, while the maximum concentrations of suspended sediment were approximately 1400, 1200 and 110 g/m^{3}, respectively. The hydrograph of the 2007 flood was relatively symmetrical inserting suggesting no hysteresis between discharge and water level within this flood event.

A four parameter Pearson Type-Ill distribution given below has been used as the form of inflow hydrograph for testing flood routing methodologies by various investigators (Ponce and Theurer, [

where I_{b} is the initial steady flow, I_{p} is the peak flow, t is the time to peak, and c is the skewness factor. The symmetry exhibited in the 2007 flood can be generated by

Equation (11) if the value of skewness factor is given less than 1.15.

According to the flood frequency curve (

2007 floods were calculated to be 4.0 m/s and 4.9 m/s, respectively. The maximum velocity at the Kakedsuka station during the small flood of 2008 was 0.8 m/s. Thus, the saturation levels of SSC at monitoring sites for the three floods were estimated by Equation (9) to be approximately 2700 g/m^{3}, 1300 g/m^{3} and 100 g/m^{3}, respectively. It is clear that the observed maximum suspended concentrations of the 10-year flood in 2006 and the small flood in 2008 were around their thresholds. However, during the 30-year flood, SSC was just 55% of the carrying capacity. Following the concept of Julien [

A characteristic of the Kashima site is that there is a point bar on the left side of the channel (

layed arrival of sediment from tributary in the 2006 flood, the hysteresis can be considered as a mechanism by which the peak flow velocity entrained in-channel sediment deposits and the enhanced cross-sectional mixing due to channel configuration sustained the suspended sediment concentration during the falling limb of the flood.

During the 2007 flood, the water level rose quickly through the level of point bar and continued to rise to a depth of 2.8 m over the point bar. Therefore, the time lag between maximum velocity and highest water level was negligible and the lateral momentum exchange was insignificant in the 2007 flood. In other words, the flood in 2007 behaved as like a flood in a single section channel.

According to Equation (9), at the time when the water level reaches its highest, the flow would be able to carry more sediment if the maximum velocity coincided. Therefore, the time lag between maximum velocity and highest water level reduces the flow capacity to transport suspended sediment.

According to the Kleitz-Seddon formula of flood propagation, flood-wave celerity is greater than flow velocity. Then, one may conclude that the peak of suspended sediment concentration should arrive at a gauging station after the flood-wave peak has passed because suspended sediment is transported at stream flow velocity. The small flood in 2008 was just the case. However, the 2006 flood was a different case. The reason is that the quasi-steady assumption used in deriving the Kleitz-Seddon formula did not hold in large floods. When the effect of water surface variation is considered, differentiating the Manning formula of flow velocity with time led to

where I is the water surface slope (–dH/dt). At the time of highest water level, dR/dt = 0; –dH/dt < 0 at upstream and –dH/dt > 0 at downstream, consequently,

This implies that the peak of flow velocity is ahead of highest water level when the variation of water surface slope cannot be neglected.

By comparing flood discharge data with the morphological change of Enshuda Coast, it was found that the river discharge below 6.0 × 10^{3} m^{3}/s supplied little sediment to the coast (Sato [

Since very large floods did not occur frequently in reality, the strategy to increase sediment delivery would have to be placed on enhancing the carrying capacity of median floods through channel manipulation.

In the Lower Tenryu River, suspended sediment was transported in different modes according to the magni-

tudes of flood. In a 30-year flood, the suspended sediment transport was supply-limited. However, during a 10-year flood and a small frequent flood, the mechanism was found to be transport-limited. In the supply-limited case, the variation of SSC followed the hydrograph well. In the transport-limited case, however, there was a time lag between the peak discharge and maximum concentration. It was further clarified that the cause of hysteresis in the 10-year flood was related to a point bar, while the time lag in the small flood can be attributed to the fact that flood celerity is greater than flow velocity. Besides, it was revealed that the symmetry of the 30-year flood hydrograph could be reproduced by a four parameter Pearson Type-Ill distribution with a value of less than 1.15 for skewness.

The findings of the present study indicate that the occurrence of hysteresis in the relationship between sediment concentration and flow discharge is not just a matter of sediment source but related to flood magnitude and affected by channel morphology. It also serves as a general warning that sediment-discharge rating curves must be used with caution; a relation between suspended sediment concentration and flow discharge obtained from one storm event may not be translatable to events of different magnitudes. Since most of the annual sediment transport usually takes place during a few events (Kronvang et al. [

This work is part of the Enshunada project supported by Japan Science and Technology Agency. The authors are grateful to Hamamatsu River and Road Administration Office for the supply of valuable field measurement data.