河流过程的累积现象和随机模型

doi:10.11821/dlxb202005014

摘要/Abstract

摘要：

累积现象普遍存在于河流过程中,准确考虑前期水沙条件的累积影响对冲积河流河床演变规律的研究至关重要。为揭示累积现象的物理实质,本文对国内外多条典型冲积河流上枢纽修建后其上下游河道冲淤实测资料进行了分析。定义水沙条件变化为外部扰动,并假定其发生概率符合泊松分布及单个扰动引发的系统反馈强度随时间呈指数衰减。本文运用统计力学中的随机理论给出了冲积河流外部扰动诱发的内部反馈随时间的累积过程及其时空间演进的数学描述和理论模型,并将其应用于枢纽修建后其上下游河道形态时空调整过程的模拟。结果发现,从时间上看,断面垂向、横向及全河段的冲淤调整速率早期较快,之后迅速减缓,河床累积冲刷深度、河宽及河段累积淤积量随时间不断增大直至平衡,表现出典型的累积特性;从空间上看,坝下河段冲刷强度沿程非线性衰减直至消失,这种空间分布上的不平衡是外部扰动引发的系统反馈在空间传播的同时随时间衰减的综合结果,是河流过程累积特性的另一外在表现。模型应用结果表明,河道垂向、横向、纵向及全河段的时空冲淤调整过程均可用归一化公式来描述,计算值与实测值符合较好,相关系数R ²达0.92、0.93、0.76和0.95。本文模型同时考虑了河流过程的累积特性和系统反馈的空间传播特性,可为定量描述扰动后非平衡态河道的时空调整过程提供理论依据和新的计算方法。

关键词: 累积现象, 河流过程, 累积冲淤量, 累积冲刷深度, 河宽

Abstract:

The accumulation phenomenon commonly occurs in fluvial processes. Accurately considering the accumulation effects of previous water and sediment conditions is essential for the study of riverbed evolution. To reveal the physical dynamics of the accumulation phenomenon, herein various geometry observations upstream and downstream of dam on several domestic and overseas typical fluvial rivers were analyzed. To do this, the changes in water and sediment conditions were defined as external disturbances, based on assumptions that the probability of an external disturbance conforms to the Poisson distribution and the feedback intensity induced by an individual disturbance decays exponentially with time. In this paper, a mathematical description of the accumulation processes of internal feedback induced by external disturbances is given, and a corresponding theoretical model is proposed for simulating the spatio-temporal adjustment processes of river characteristic variables on the basis of the stochastic theory in statistical mechanics. Further, the above models were then applied to investigate the spatio-temporal adjustment processes of the upper and lower reaches of dams after their construction. Results revealed two key findings. (i) Temporally, the vertical, lateral, and whole reaches' adjustment rates over time are relatively fast in the early period following disturbances but then slow down rapidly, while the accumulated bed degradation, river width and accumulated sedimentation continuously increase until a new dynamic equilibrium state is attained; these phenomena reflect the representative accumulation characteristics of fluvial processes. (ii) Spatially, the erosion intensity downstream of dams decreases nonlinearly along the channel until it eventually diminishes. In fact, the unbalanced distribution of erosion intensity across space arises from the system feedback caused by external disturbances propagating in space yet decaying over time, which is another external manifestation of an accumulation characteristic in fluvial processes. Model applications indicate that the spatio-temporal adjustment processes of cross sections and channel reaches can be accurately described by the unified theoretical formula derived from equation deforming, since the model predictions show good agreement with observed field data: coefficient of determination (R ²) between them attained values of 0.92, 0.93, 0.76, and 0.95. The proposed theoretical models take both the accumulative characteristics of fluvial processes and the spatial propagation characteristics of system feedback into account synthetically. In demonstrating this approach, this study provides the theoretical basis and new calculation method for quantitatively describing the spatio-temporal adjustment processes of non-equilibrium fluvial channels following disturbances.

Key words: accumulation phenomenon, fluvial process, accumulated erosion and sedimentation, accumulated riverbed degradation, channel width

景唤, 钟德钰, 张红武, 石旭芳, 王彦君. 河流过程的累积现象和随机模型[J]. 地理学报, 2020, 75(5): 1079-1094.

JING Huan, ZHONG Deyu, ZHANG Hongwu, SHI Xufang, WANG Yanjun. The accumulation phenomenon and stochastic model in fluvial processes[J]. Acta Geographica Sinica, 2020, 75(5): 1079-1094.

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枢纽名称	所在河流	年平均流量(m³/s)		断面(河段) 编号	距坝里程 (km)	河流特征量	测试时段(a)	测量次数
枢纽名称	所在河流	建库前	建库后	断面(河段) 编号	距坝里程 (km)	河流特征量	测试时段(a)	测量次数
胡佛大坝	科罗拉多河	520	400	CHD-1—CHD-3	10~36	累积冲刷深度	1935—1948	15
帕克大坝		230	340	CPD-1—CPD-3	39~95		1938—1975	16
戴维斯大坝		400	340	CDD-1—CDD-2	1~9		1948—1975	28
佩克堡大坝	密苏里河	200	280	MFP-1—MFP-3	9~75	河宽	1936—1973	8
加里森大坝		600	660	MGD-1—MGD-3	32~54		1949—1976	6
加文斯角大坝		930	740	MGP-1—MGP-3	7~48		1955—1974	5
丹江口水库	汉江	1335	1091	黄家港—皇庄	3~270	枯水位降低值	1960—1976	6
三门峡水库	黄河	1522	1412	小浪底—利津	61~678	冲淤量	1961—1984	21
三门峡水库	黄河	1522	1412	四站—潼关(库区)	-		1965—1984	20
小浪底水库	黄河	1266	807	小浪底—利津	61~678		2000—2015	16
三峡水库	长江	14027	12873	宜昌—湖口	30~807		2003—2016	14

垂向调整	衰减系数α	横向调整	衰减系数α	全河段调整	衰减系数α
CHD-1—CHD-3	0.30, 0.40, 0.30	MGP-1—MGP-3	0.40, 0.45, 0.50	三门峡库区四站—潼关	0.40
CPD-1—CPD-3	0.14, 0.22, 0.09	MFP-1—MFP-3	0.18, 0.15, 0.05	黄河全下游(1968—1975年)	0.45
CDD-1—CDD-2	0.17, 0.16	MGD-1—MGD-3	0.60, 0.25, 0.40	黄河全下游(1976—1984年)	0.40

纵向调整	综合衰减系数α/v
黄家港—皇庄段(1965—1975)	0.0160, 0.0120, 0.0090
小浪底—利津段(1961—1964)	0.0065, 0.0060, 0.0042, 0.0038
小浪底—利津段(2003—2015)	0.0100, 0.0050, 0.0050
宜昌—湖口段(2003—2015)	0.0033, 0.0033, 0.0025