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Accumulation phenomena in fluvial processes and the corresponding stochastic model
Jing Huan (1993–), PhD Candidate, specialized in river mechanics. Email: jingh16@mails.tsinghua.edu.cn 
Received date: 20191203
Accepted date: 20200208
Online published: 20200825
Supported by
National Natural Science Foundation of China(No.91547204)
National Key Research and Development Program of China(No.2016YFC0402500)
National Key Research and Development Program of China(No.2017YFC0404303)
Copyright
Accumulation occurs widely in fluvial processes. Accurately accounting for the effects of previous water and sediment conditions on accumulation is essential for studying riverbed evolution. In this study, to reveal the physical mechanisms of accumulation, various geometric observations of both the upstream and downstream reaches of dams on several typical fluvial channels were analyzed. The changes in water and sediment conditions were defined as external disturbances. Assuming that the probability of an external disturbance conforms to a Poisson distribution, and that the response intensity induced by an individual disturbance decays exponentially over time, a mathematical description of the accumulation of internal responses to external disturbances is given. Furthermore, a corresponding theoretical model for simulating the spatiotemporal readjustments of characteristic river variables is proposed based on stochastic theory. The proposed models are then applied to investigate spatiotemporal readjustment in the upper and lower reaches of dams following their construction. The results indicate that temporally, the vertical, lateral, and overall readjustment rates of the reaches are relatively fast in the early period following dam construction but then decrease rapidly over time. Accumulated riverbed degradation, channel width, and sedimentation continuously increase until a new dynamic equilibrium is reached. These phenomena reflect the representative accumulation characteristics of fluvial processes. Spatially, the erosion intensities in downstream reaches decrease nonlinearly along the channel until eventually diminishing. The unbalanced spatial distribution of erosion intensity arises from the system response characterized by propagation in space but decay over time, which is characteristic of accumulation phenomena after disturbances. The results of the developed model show that the spatiotemporal readjustments of the studied crosssections and channel reaches can be accurately described by the unified theoretical formula derived herein. The model predictions show good agreement with observed field data with determination coefficients of 0.92, 0.93, 0.76, and 0.95 for vertical, lateral, longitudinal, and overall readjustments, respectively. The proposed theoretical models account for both the accumulation characteristics of fluvial processes and their spatial distributions. In demonstrating the proposed approach, this study provides a theoretical basis and new calculation method for quantitatively describing the spatiotemporal readjustments of nonequilibrium fluvial channels following external disturbances.
JING Huan , ZHONG Deyu , ZHANG Hongwu , SHI Xufang , WANG Yanjun . Accumulation phenomena in fluvial processes and the corresponding stochastic model[J]. Journal of Geographical Sciences, 2020 , 30(6) : 1021 1040 . DOI: 10.1007/s114420201768x
Table 1 Characteristic river parameters for the studied crosssections and channel reaches (Williams and Wolman, 1987; Jia, 1992; Peng et al., 2016; Yang et al., 2017) 
Project  River  Average pre dam daily discharge (m^{3}/s)  Average post dam daily discharge (m^{3}/s)  Studied crosssection or reach  Distance (km)  Variable  Survey period  Survey number 

Hoover  Colorado  520  400  CHD1CHD3  1036  Riverbed degradation  19351948  15 
Parker  230  340  CPD1CPD3  3995  19381975  16  
Davis  400  340  CDD1CDD2  19  19481975  28  
Fort Peck  Missouri  200  280  MFP1MFP3  975  Channel width  19361973  8 
Garrison  600  660  MGD1MGD3  3254  19491976  6  
Gavins Point  930  740  MGP1MGP3  748  19551974  5  
Danjiangkou  Hanjiang  1335  1091  HJGHZ  3270  Water level  19601976  6 
Sanmenxia  Yellow  1522  1412  XLDLJ  61678  Accumulated erosion and deposition amount  19611984  21 
SZTG    19651984  20  
Xiaolangdi  Yellow  1266  807  XLDLJ  61678  20002015  16  
Three Gorges  Yangtze  14027  12873  YCHK  30807  20032016  14 
The distance in the sixth column in Table 1 is the distance between each studied crosssection or the middle point of the studied channel reach and the dam site. 
Figure 1 Accumulated riverbed degradation in the studied crosssections downstream of dams on the Colorado River 
Figure 2 Changes in channel width after dam construction in the studied crosssections downstream of dams on the Missouri River 
Figure 3 Longitudinal adjustment of the studied channel reaches downstream of dams 
Figure 4 Accumulated sedimentation in the Sanmenxia Reservoir area and lower reaches of the Yellow River 
Figure 5 Diagram showing the accumulation effects of external disturbances in fluvial processes 
Figure 6 Comparison between the measured and calculated characteristic river variables in the studied crosssections and channel reaches 
Table 2 Parameter values in equation (18) 
Vertical readjustment  α  Lateral readjustment  α  Overall readjustment (entire reach)  α 

CHD1CHD3  0.30, 0.40, 0.30  MGP1MGP3  0.40, 0.45, 0.50  SZTG  0.40 
CPD1CPD3  0.14, 0.22, 0.09  MFP1MFP3  0.18, 0.15, 0.05  LYR (19681975)  0.45 
CDD1CDD2  0.17, 0.16  MGD1MGD3  0.60, 0.25, 0.40  LYR (19761984)  0.40 
LYR in Table 2 represents all lower reaches of the Yellow River. 
Table 3 Parameter values in equation (19) 
Longitudinal readjustment  α/v 

HJGHZ (19651975)  0.0160, 0.0120, 0.0090 
XLDLJ (19611964)  0.0065, 0.0060, 0.0042, 0.0038 
XLDLJ (20032015)  0.0100, 0.0050, 0.0050 
YCHK (20032015)  0.0033, 0.0033, 0.0025 
Figure 7 Changes in characteristic river variables following dam construction 
Figure 8 Relationships between α, α/vand relative variation in peak discharge before and after dam construction (1Q_{post} /Q_{pre}) 
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