黄河下游水沙关系模型参数随河段距离变化规律

doi:10.11821/dlxb202203010

摘要/Abstract

摘要：

对于多沙河流或河段,水沙关系模型多表示为考虑来水含沙量的幂律函数形式：Q_s=KS_u^aQ^b,本质反映了河道的不平衡输沙规律,模型参数变化主要受到河道边界条件的影响。河段距离作为反映沿程空间尺度的一个重要指标,对模型系数K与指数a、b具有重要的影响。以黄河下游河道为研究对象,分析研究了模型系数K与指数a、b随河段距离的变化规律与计算方法,并用于黄河下游河道输沙沿程变化模拟。模型参数变化规律分析表明：指数a随河段距离的增大而减小,两者呈指数负相关关系;系数K随河段距离的增大而减小,且与指数a呈指数正相关关系;指数b随河段距离的增大而增大,且与指数a呈线性负相关关系,两者之和约为2.0。通过建立模型系数K与指数a、b随河段距离变化的计算表达式,构成了考虑来水含沙量的水沙关系模型的参数条件补充方程。对黄河下游河道输沙沿程变化模拟结果表明,黄河下游河道沿程含沙量的计算值与实测值变化趋势基本符合,确定性系数R²值可以达到0.96,Nash-Sutcliffe效率系数NSE值在0.93以上,模拟效果良好。研究结果有助于深入认识考虑来水含沙量的水沙关系模型参数的物理意义与探索模型参数的确定方法。

关键词: 黄河下游, 多沙, 水沙关系模型, 模型参数, 距离影响

Abstract:

The discharge-sediment relation model is an important research technique in river dynamics. Previous studies established a statistical relationship between the sediment transport rate and the flow discharge that follows a power-law form, shown as Q_s=AQ ^b. Studies have also shown that how to determine the model parameters is an important question. However, for heavy sediment-laden rivers, the discharge-sediment relation model is often expressed by a modified power-law relationship between the sediment transport rate and flow discharge, as well as an upstream sediment supply function: Q_s=KS_u^aQ^b, where the model parameters become more complex. Essentially, the modified model reflects a non-equilibrium sediment transport law, and model parameters including coefficient K and exponents a and b are mainly influenced by river boundary geomorphologic conditions. As an important index reflecting the spatial scale along the river, distance has an important impact on the modified model parameters, namely, coefficient K and exponents a and b. Taking the Lower Yellow River as the research object, we studied the variation laws of the model coefficient K and indexes a and b with distance. The results showed that the exponent a decreases exponentially with the increase of downstream distance; the coefficient K decreases with the increase of downstream distance and has a positive exponential correlation with the exponent a; the exponent b increases with the increase of downstream distance and has a negative linear correlation with the exponent a; and the sum of exponents a and b is about 2.0. From that, the calculation expressions of model coefficient K and exponents a and b varying with the distance were established. As such, it can be regarded as the parameter supplementary equations for the discharge-sediment relation model. Simulation results of sediment transport along the Lower Yellow River showed that the trend of calculated sediment concentrations are consistent with that of measured sediment concentrations. The values of the determination coefficient and Nash-Sutcliffe efficiency are 0.96 and 0.93, respectively. This study helps us to have a better understanding of the physical meaning and exploration of calculation methods for the discharge-sediment relation model parameters in heavy sediment-laden rivers.

Key words: Lower Yellow River, heavy sediment-laden flow, discharge-sediment relation model, model parameters, distance effect

申红彬, 曹兵, 吴华莉, 乔伟. 黄河下游水沙关系模型参数随河段距离变化规律[J]. 地理学报, 2022, 77(3): 635-649.

SHEN Hongbin, CAO Bing, WU Huali, QIAO Wei. Parameters variation law with distance in the discharge-sediment relation model of the Lower Yellow River[J]. Acta Geographica Sinica, 2022, 77(3): 635-649.

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类型	河段	分河段	距离(km)	平均比降(‰)	主槽河宽(km)
游荡型	桃花峪—高村	桃花峪—花园口	28.6	0.198	0.8~2.5
		花园口—夹河滩	100.8
		夹河滩—高村	77.1
过渡型	高村—陶城铺	高村—孙口	118.2	0.120	0.5~1.6
过渡型	高村—陶城铺	孙口—陶城铺	46.8	0.120	0.5~1.6
弯曲型	陶城铺—利津	陶城铺—艾山	17.1	0.110	0.3~0.8
		艾山—泺口	101.8
		泺口—利津	167.8

河段		距离(km)	模型参数			模型效果指标
河段		距离(km)	系数K	指数a	指数b	R²	NSE
基本河段	花园口—高村	177.9	0.38^*	0.81^*	1.21^*	0.978	0.975
	高村—艾山	182.1	1.05^*	0.84^*	1.06^*	0.978	0.977
	艾山—利津	269.6	0.52^*	0.95^*	1.11^*	0.984	0.980
扩展河段	花园口—艾山	360.0	0.46⁺	0.68⁺	1.24⁺	0.954	0.949
	花园口—利津	629.6	0.25^+*	0.65^+*	1.35^+*	0.919	0.890
	高村—利津	451.7	0.54⁺	0.79⁺	1.17⁺	0.956	0.946

河段	模型参数	刘月兰等^[15] (1987年)		赵业安等^[16] (1989年)			吴保生等^[17] (2007年)			本文 (2021年)	他人研究参数平均值
		汛期		非汛期		汛期	全年	汛期		全年
		不漫滩	漫滩	非汛期		汛期	全年	汛期		全年
花园口—高村	系数K	0.46	5.40	0.39	0.55		0.38	0.44	0.61		1.27
	指数a	0.76	0.76	0.49	0.76		0.81	0.81	0.88		0.73
	指数b	1.21	1.16	1.33	1.18		1.21	1.21	1.12		1.22
高村—艾山	系数K	0.65	0.79	0.15	0.51		1.05	1.13	0.6		0.71
	指数a	0.83	0.81	1.02	0.92		0.84	0.84	0.88		0.88
	指数b	1.08	1.06	1.25	1.12		1.06	1.06	1.12		1.11
艾山—利津	系数K	0.43	0.43	1.23	0.6		0.52	0.57	0.49		0.63
	指数a	1.00	1.00	1.13	0.96		0.95	0.95	0.83		1.00
	指数b	1.09	1.09	1.21	1.09		1.11	1.11	1.17		1.12

距离断面 (km)	方案1(花园口起点)					距离断面 (km)	方案2(高村起点)
距离断面 (km)	水文站	系数K	指数a	指数b	指数c	距离断面 (km)	水文站	系数K	指数a	指数b	指数c
0	花园口	1.00	1.00	1.00	0.00	0	高村	1.00	1.00	1.00	0.00
100	—	0.75	0.93	1.07	0.07	50	—	0.87	0.97	1.03	0.03
100.8	夹河滩	0.75	0.93	1.07	0.07	100	—	0.75	0.93	1.07	0.07
177.9	高村	0.61	0.88	1.12	0.12	118.2	孙口	0.72	0.92	1.08	0.08
200	—	0.58	0.87	1.13	0.13	150	—	0.66	0.90	1.10	0.10
296.1	孙口	0.46	0.81	1.19	0.19	182.1	艾山	0.60	0.88	1.12	0.12
300	—	0.45	0.81	1.19	0.19	200	—	0.58	0.87	1.13	0.13
360	艾山	0.39	0.78	1.22	0.22	250	—	0.51	0.84	1.16	0.16
400	—	0.36	0.76	1.24	0.24	283.9	泺口	0.47	0.82	1.18	0.18
461.8	泺口	0.31	0.72	1.28	0.28	300	—	0.45	0.81	1.19	0.19
500	—	0.29	0.70	1.30	0.30	350	—	0.40	0.78	1.22	0.22
600	—	0.24	0.66	1.34	0.34	400	—	0.36	0.76	1.24	0.24
629.6	利津	0.22	0.64	1.36	0.36	451.7	利津	0.32	0.73	1.27	0.27
700	—	0.20	0.61	1.39	0.39	500	—	0.29	0.70	1.30	0.30