摘要
论文选取我国黄河和美国图特河北汊作为典型案例，以河床演变普遍存在的滞后现象为主线，以描述河床演变过程的滞后响应模型为基础，探讨了不同扰动因素影响下河道的滞后响应特点和调整规律，建立了不同扰动因素协同作用下非平衡态河道复杂演变过程的计算方法，对选取典型案例的长时间河床非平衡态冲淤演变过程进行了模拟。论文成果对于深化对非平衡态河床演变规律的认识，发展非平衡态河床演变学理论和方法具有重要的学术意义和实用价值。
基于河流系统的概念，在分析上游来水来沙条件和下游侵蚀基准面变化对冲积河流系统的不同作用机制基础上，建立了两种扰动因素协同作用下河床冲淤调整的平衡模式和平衡冲淤体的计算方法。
对于受水沙条件和潼关高程共同影响的黄河小北干流和渭河下游的河床演变过程，采用三角形淤积体的平衡态计算模式，利用滞后响应模型计算了1960～2011年潼关高程抬升及水沙变化对黄河小北干流和渭河下游河道冲淤过程的影响，结果表明模型充分考虑了潼关高程和水沙条件对河道冲淤演变过程的协同作用，结果还显示潼关高程对河道冲淤的影响占主导地位，而近期河道的冲淤受水沙条件的影响较大。
对于受水沙条件和河口淤积延伸影响的黄河下游河道的长系列冲淤演变过程，采用梯形淤积体的平衡态计算模式，结合滞后响应模型，建立了黄河下游历年累计淤积量的计算方法，模拟了1952～2010年黄河下游不同河段长时间的河道冲淤过程，计算效果较好，表明模型能够考虑水沙条件引起的沿程冲淤和河口延伸引起的溯源淤积；并且研究表明花园口~利津河段的河床淤积过程与水沙条件的变化密切相关，而孙口以下河段则受河口延伸的影响更为明显。
对于受火山爆发影响的美国图特河北汊的河床演变，分析了河道垂向、横向及纵向的调整过程，研究表明河道的调整速率随时间非线性衰减，河床的调整在空间上呈现上冲下淤的一般趋势；根据平衡比降建立了河床平衡态的计算方法，进而采用滞后响应模型建立了图特河北汊河床深泓高程的计算方法，该方法不仅考虑了当前水沙条件对河床演变的影响，而且考虑了前期水沙条件的作用，用于模拟1980～2011年图特河北汊河床冲淤交替的变化过程，取得了令人满意的结果。
This paper studied the characteristics of the delayed response of the fluvial systemsaffected by different disturbance. A method for simulating non-equilibrium fluvialprocesses was developed based on the delayed response model and the analysis of theequilibrium state of fluvial systems. The long term evolution processes of the YellowRiver reaches and the North Fork Toutle River in the United States were simulatedusing the proposed method. This paper enhances our understanding of non-equilibriumfluvial processes and contributes to the development of the theory and methods withrespect to channel evolution.
Based on the concept of river system, the disturbance of alluvial rivers is dividedinto the runoff and sediment conditions and the base-level change at the downstream.The potential equilibrium state of the fluvial system affected by both the two factorswas studied and a method was developed for calculating the equilibrium value of theaggradation and degradation volume of channel reaches.
Xiaobeiganliu and the lower Weihe River are both affected by water discharge andsediment load and the variation of Tongguan elevation. It's assumed that channelreaches in their potential equilibrium state, compared to the initial boundaries, have adeposition body in the shape of a triangle. Based on the delayed response model and anequation developed for calculating the volume of triangular deposition body, a methodfor simulating the erosion and deposition processes of the river reaches was proposed.The adjustment processes of the river reaches during1960and2011were simulatedusing the proposed method. The results showed that the method takes into account theeffects of both Tongguan elevation and water and sediment conditions. Moreover, it'sshown that Tongguan elevation significantly affected the evolution of the channelreaches, while income water and sediment conditions had greater influence on therecent aggradation and degradation processes of rivers.
The lower Yellow Rive(rLYR)is affected by the water and sediment conditions aswell as the extension of the river mouth. Assuming the potential equilibrium channelreach has a trapezoidal deposition body, a calculation method for the volume of thetrapezoidal deposition body combined with the delayed response model were used to develop the calculation method for the non-equilibrium fluvial processes of the LYR.The evolution processs of the LYR during1952and2010were simulated using theproposed method and satisfactory results were obtained. The results showed that theproposed method considers the effects of water and sediment variation and estuaryextension on channel evolution. Meanwhile, it's indicated that the aggradation anddegradation processes of the channel reach between Huayuankou and Lijin were closelyrelated to the income water and sediment conditions while the reach downstreamSunkou gaging station was more significantly affected by the rise of base-level causedby estuary extension.
The vertical, lateral and longitudinal variations of channel geometry of the NorthFork Toutle River （NFTR） following volcanic eruption were analyzed. The resultsshowed that NFTR adjusted most rapidly during the first3years after the eruption. Therate of adjustment decayed as time elapsed and the channel gradually tended to a stableor equilibrium state. Moreover, the channel bed of the upper NFTR was severelydegraded while that of the lower reach aggraded. The aggradation and degradationprocesses of the channel bed during1980and2011were simulated by the delayedresponse model. The results showed that different modes of the delayed response modelcan well simulate the relaxation paths of the channel bed of the NFTR. Since thedelayed response model considers the cumulative effects of the water and sedimentconditions on the evolution of the river, it is able to simulate the adjustment processesof the river from a perturbed state after the eruption to a certain steady-state.
引文
Bagnold R A. An empirical correlation of bedload transport rates in flumes and natural rivers.Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences,1980,372（1751）:453-473.
Bracken L J, Wainwright J. Geomorphological equilibrium: myth and metaphor? Transactions of theInstitute of British Geographers,2006,31（2）:167-178.
Bray D. Regime equations for gravel-bed rivers. In: R.D. Hey, B. J.C., C.R. Thorne （Eds.）,Gravel-Bed Rivers. Wiley, Chichester,1982. pp.517-542.
Brunsden D. Applicable models of long term landform evolution. Zeitschrift für Geomorphologie,1980, Supplement36:16-26.
Bull W B. Geomorphic Responses to Climatic Change. New York: Oxford University Press,1991.
Burkham D E. Channel changes of the Gila river in Safford valley, Arizona,1846-1970. U.S.Government Printing Office Washington, DC,1972.
Chang H H. Geometry of gravel streams. Journal of the Hydraulics Division,1980a,106（9）:1443-1456.
Chang H H. Geometry of rivers in regime. Journal of the Hydraulics Division,1979a,105（6）:691-706.
Chang H H. Minimum stream power and river channel patterns. Journal of Hydrology,1979b,41（3）:303-327.
Chang H H. Stable alluvial canal design. Journal of the Hydraulics Division,1980b,106（5）:873-891.
Chen X, Yan Y, Fu R，et al. Sediment transport from the Yangtze River, China, into the sea over thePost-Three Gorge Dam Period: A discussion. Quaternary International,2008,186（1）:55-64.
Chorley R J, Kennedy B A. Physical geography: a systems approach. Prentice-Hall International,London,1971.
Church M. Geomorphic response to river flow regulation: Case studies and time‐scales. RegulatedRivers: Research&Management,1995,11（1）:3-22.
Costa J E. Response and recovery of a Piedmont watershed form tropical storm Agnes, June1972.Water Resources Research,1974,10:106-112.
Davies T R H, Sutherland A J. Extremal hypotheses for river behavior. Water Resources Research,1983,19（1）:141-148.
Einstein H A. The bed-load function for sediment transportation in open channel flows, USDepartment of Agriculture,1950.
Gilbert G K. Report on the geology of the Henry Mountains, United States Geographical andGeological Survey of the Rocky Mountain Region. Washington, D.C.,1877.
Graf W L. The rate law in fluvial geomorphology. American Journal of Science,1977,277（2）:178-191.
Gupta A, Fox H. Effects of high-magnitude floods on channel form: a case study in MarylandPiedmont. Water Resources Research,1974,10（3）:499-509.
Hack J T, Goodlett J C. Geomorphology and forest ecology of a mountain region in the centralAppalachians, US Government Printing Office Washington, DC,1960.
Hey R D, Thorne C R. Stable channels with mobile gravel beds. Journal of Hydraulic Engineering,1986,112（8）:671-689.
Hooke J. River channel adjustment to meander cutoffs on the River Bollin and River Dane,northwest England. Geomorphology,1995,14（3）:235-253.
Howard A D. Equilibrium and time scales in geomorphology: Application to sand‐bed alluvialstreams. Earth Surface Processes and Landforms,1982,7（4）:303-325.
Huang H Q and Chang H H. Scale independent linear behavior of alluvial channel flow. Journal ofHydraulic Engineering,2006,132(7):722-730.
Huang H Q, Nanson G C. A stability criterion inherent in laws governing alluvial channel flow.Earth Surface Processes and Landforms,2002,27（9）:929-944.
Janda R J, Meyer D F, Childers D. Sedimentation and geomorphic changes during and following the1980-1983eruptions of Mount St. Helens, Washington （1）. Shin-Sabo,1984,37（2）:10-23.
Jia Y. Minimum Froude number and the equilibrium of alluvial sand rivers. Earth Surface Processesand Landforms,1990,15（3）:199-209.
Kirkby M J. Maximum sediment efficiency as a criterion for alluvial channels. In: K J Gregory（Ed.）, River Channel Changes. Chichester: Wiley-Interscience,1977, pp.429-442.
Knighton D. Fluvial forms and processes: a new perspective. ed.2. Arnold, Hodder Headline,PLC,1998.
Lacey G. Flow in alluvial channels with sandy mobile beds, Proceedings of the Institute of CivilEngineering, London,1958, pp.259-292.
Lane E W. The importance of fluvial morphology in hydraulic engineering. Proceedings ofAmerican Society of Civil Engineers,1955,81（795）:1-17.
Langbein W B. Geometry of river channels. Journal of the Hydraulics Division, ASCE,1964,90（HY2）:301-312.
Leon C, Julien P Y, Baird D C. Case study: equivalent widths of the Middle Rio Grande, NewMexico. Journal of Hydraulic Engineering, ASCE,2009,135（4）:306-315.
Leopold L B, Langbein W B. The concept of entropy in landscape evolution. Geological SurveyProfessional Paper500-A. U.S. Government Printing Office Washington, DC,1962.
Li R-M, Simons D B. Geomorphological and hydraulic analysis of mountain streams. In: R D Hey,C R Thorne （Eds.）, Gravel Bed Rivers. John Wiley and Sons,1977, pp.338.
Mackin J H. Concept of the graded river. Geological Society of America Bulletin,1948,59（5）:463-512.
Meyer D F, Martinson H A. Rates and processes of channel development and recovery following the1980eruption of Mount St. Helens, Washington, Workshop （HW6b） on Erosion andSediment Transport Resulting from Volcanic Eruption Vancouver, British Colombia,Canada,1987.
Miao C, Ni J, Borthwick A G L，et al. A preliminary estimate of human and natural contributions tothe changes in water discharge and sediment load in the Yellow River. Global and PlanetaryChange,2011,76（3）:196-205.
Nanson G C, Huang H Q. Least action principle, equilibrium states, iterative adjustment and thestability of alluvial channels. Earth Surface Processes and Landforms,2008,33（6）:923-942.
Nielsen, A. Theory of electrolyte crystal growth. The parabolic rate law. Pure and AppliedChemistry,1981,53(11):2025-2039.
Petts G E, Gurnell A M. Dams and geomorphology: research progress and future directions.Geomorphology,2005,71（1）:27-47.
Phillips J D. Emergence and pseudo-equilibrium in geomorphology. Geomorphology,2011,132（3）:319-326.
Phillips J D. The end of equilibrium? Geomorphology,1992,5（3）:195-201.
Phillips J D. The job of the river. Earth Surface Processes and Landforms,2010,35（3）:305-313.
Powell D M. Dryland rivers: processes and forms. In: A J Parsons, A D Abrahams （Eds.）,Geomorphology of Desert Environments. Springer Science and Business Media,2009, pp.350.
Richard G A. Quantification and Prediction of Lateral Channel Adjustments Downstream fromCochiti Dam, Rio Grande, NM.PhD Thesis, Colorado State University,2001.
Savageau, M A. Biochemical systems analysis: I. Some mathematical properties of the rate law forthe component enzymatic reactions. Journal of theoretical biology,1969,25(3):365-369.
Schumm S A. River metamorphosis. Journal of the Hydraulics Division,1969,95:255-273.
Schumm S A. The Fluvial System. John Wiley and Sons,1982.
Schumm S. River response to baselevel change: implications for sequence stratigraphy. The Journalof Geology,1993:279-294.
Shuttle, C G, ORegan B, Ballantyne, A M, et al. Experimental determination of the rate law forcharge carrier decay in a polythiophene: Fullerene solar cell. Applied Physics Letters,2008,92(9):093311-093311-093313.
Simon A, Klimetz D. Empirical Analysis of Long-term Sediment Loadings from the Upper NorthFork Toutle River System, Mount St. Helens, Washington. Department of Agriculture,Agricultural Research Service National Sedimentation Laboratory,2013.（unpublished）.
Simon A, Rinaldi M. Disturbance, stream incision, and channel evolution: The roles of excesstransport capacity and boundary materials in controlling channel response. Geomorphology,2006,79（3）:361-383.
Simon A, Robbins C H. Man-Induced gradient adjustment of the South Fork Forked Deer River,West Tennessee. Environmental Geology and Water Science,1987,9（2）:109-118.
Simon A, Thorne C R. Channel adjustment of an unstable coarse‐grained stream: opposing trendsof boundary and critical shear stress, and the applicability of extremal hypotheses. EarthSurface Processes and Landforms,1996,21（2）:155-180.
Simon A. Adjustment and recovery of unstable alluvial channels: identification and approaches forengineering management. Earth Surface Processes and Landforms,1995,20（7）:611-628.
Simon A. Channel and Drainage-basin Response of the Toutle River System in the Aftermath of the1980Eruption of Mount St. Helens, Washington. Open-file Report96-633. US Department ofthe Interior, US Geological Survey,1999.
Simon A. Energy, time, and channel evolution in catastrophically disturbed fluvial systems.Geomorphology,1992,5（3）:345-372.
Soufi M. Processes and trend of gully development in a forest environment in Australia,2th ISCOConference,（2）, Beijing, China,2002, pp.487-493.
Starkel L. The reflection of hydrologic changes in the fluvial environment of the temperate zoneduring the last15,000years. In: K J Gregory （Ed.）, Background to palaeohydrology. Wiley,Chichester, UK. Chichester: Wiley,1983, pp.213-235.
Surian N, Rinaldi M. Morphological response to river engineering and management in alluvialchannels in Italy. Geomorphology,2003,50（4）:307-326.
Thorn C E, Welford M R. The equilibrium concept in geomorphology. Annals of the Association ofAmerican Geographers,1994,84（4）:666-696.
U. S. Army Corps of Engineers. Cowlitz River Basin Water Year2002Hydrologic Summary:Mount St. Helens, Washington, Toutle River and North Fork Toutle River.2003.
Voight B, Glicken H, Janda R J，et al. Catastrophic rockslide avalanche of May18. In: P W Lipman,D R Mullineaux （Eds.）, The1980Eruptions of Mount St. Helens, Washington. USGeological Survey Professional Paper1250,1981, pp.347-377.
White W R, Bettess R, Paris E. Analytical approach to river regime. Journal of the HydraulicsDivision,1982,108（10）:1179-1193.
Williams G P, Wolman M G. Downstream Effects of Dams on Alluvial Rivers. U.S. GeologicalSurvey Professional Paper1286. US Government Printing Office, Washington DC,1984.
Wu B S, Wang G Q, Xia J Q，et al. Response of bankfull discharge to discharge and sediment load inthe Lower Yellow River. Geomorphology,2008a,100（3）:366-376.
Wu B S, Xia J Q, Fu X D，et al. Effect of altered flow regime on bankfull area of the lower YellowRiver, Chinar. Earth Surface Processes and Landforms,2008b,33:1585-1601.
Wu B S, Zheng S, Thorne C R. A general framework for using the rate law to simulatemorphological response to disturbance in the fluvial system. Progress in Physical Geography,2012,36（5）:575-597.
Yang C T, Song C. Theory of minimum rate of energy dissipation. Journal of the HydraulicsDivision,1979,105（7）:769-784.
Yang C T. Potential energy and stream morphology. Water Resources Research,1971,7（2）:311-322.
Yang S, Zhao Q, Belkin I M. Temporal variation in the sediment load of the Yangtze River and theinfluences of human activities. Journal of Hydrology,2002,263（1）:56-71.
曹如轩,雷福州,冯普林，等.三门峡水库淤积上延机理的研究.泥沙研究,2001,2:37-40.
陈建国，周文浩，孙高虎,等.黄河小浪底水库初期运用与下游河道冲淤的响应.泥沙研究，2008,5:1-8.
陈文彪.水库淤积上延问题的探讨.泥沙研究,1984,4:80-86.
邓安军,郭庆超,陈建国.黄河小北干流河道冲淤演变规律研究.泥沙研究,2011,（2）:27-32.
杜殿勋，戴明英.三门峡水库修建前后渭河下游河道泥沙问题的研究.泥沙研究，1981,3:1-18.
韩其为,何明民.论长期使用水库的造床过程—兼论三峡水库长期使用的有关参数.泥沙研究,1993,（3）:1-21.
贺莉,夏军强,王光谦.黄河下游高含沙洪水演进及河床冲淤过程的数值模拟.泥沙研究，2009，1:26-32.
侯素珍,林秀芝,田勇,等.桃汛洪水冲刷降低潼关高程关键技术研究.郑州:黄河水利出版社,2010.
侯素珍,王平,吕秀环.黄河小北干流近期河床演变成因分析.人民黄河,2008,30（11）:22-23.
胡春宏,陈建国,郭庆超.三门峡水库淤积与潼关高程.北京:科学出版社,2008.
黄河水利委员会.三门峡库区有关问题初步研究,2001.
黄仁勇.黄河下游河道治理方案数学模拟研究[硕士学位论文],武汉:武汉大学，2008.
黄修山.渭河下游河道淤积萎缩对洪水演进规律的影响研究[硕士学位论文],西安:西安理工大学,2005.
姜乃迁,张翠萍,张隆荣，等.潼关河段清淤关键技术研究，“九五攻关”98-958-02-02-03专题，黄河水利科学研究院,2001.
姜乃森，张启舜，黄霖恩.水库淤积上延问题的分析.水利学报,1997,8:67-72.
焦恩泽,侯素珍,王平.有关潼关高程的几个问题.人民黄河,2003,25（7）:19-20.
李凌云,吴保生,侯素珍.滞后响应模型在黄河内蒙古河段的应用.水力发电学报,2011,30（1）:70-77.
李凌云,吴保生.渭河下游平滩流量的预测.清华大学学报:自然科学版,2010,50（6）:852-856.
李凌云.黄河平滩流量的计算方法与应用研究[博士学位论文],北京:清华大学,2010.
励强,陆中臣.沿程淤积与溯源淤积对黄河下游演变影响的数值模拟.地理科学,1989,9（4）:336-345.
林秀芝,姜乃迁,梁志勇，等.渭河下游输沙用水量研究.郑州:黄河水利出版社,2005.
陆中臣.三门峡水库淤积末端位置确定和预估的地貌学方法.地理研究,1982,1（3）:43-54.
齐璞,刘月兰,李世滢，等.黄河水沙变化与下游河道减淤措施.郑州:黄河水利出版社,1999.
钱宁,张仁,周志德.河床演变学.北京:科学出版社,1987.
钱宁,周文浩.黄河下游河床演变.北京:科学出版社,1965.
陕西省水利厅.三门峡水库给陕西带来的灾害及治理对策建议,2001, pp.16.
师长兴,叶青超.黄河河口延伸对下游淤积影响的定量研究.科学通报,1996,41（15）:1399-1401.
孙东坡,刘晓平,薛海，等.黄河下游河道“二级悬河”演变趋势的数值模拟研究.水力发电学报，2008，27（6）:136-141.
唐先海,雷文清.渭河下游泥沙淤积情势及其影响分析. In:陕陕西省三门峡库区管理局（Ed.）,陕西省三门峡库区防洪暨治理学术研讨会论文选编.郑州:黄河水利出版社,2000, pp.74-80.
王开荣,茹玉英,王恺忱.黄河口研究及治理.郑州:黄河水利出版社,2007.
王恺忱.黄河河口的演变与治理.郑州:黄河水利出版社,2010.
王恺忱.黄河河口发展影响预估计算方法.泥沙研究,1988,3:39-49.
王恺沈.黄河河口与下游河道的关系及治理问题.泥沙研究,1982,2:1-10.
王兆印,李昌志,王费新.潼关高程对渭河河床演变的影响.水利学报,2004,9,1-8.
吴保生,夏军强,张原锋.黄河下游平滩流量对来水来沙变化的响应.水利学报,2007,38（7）,886-892.
吴保生.冲积河流河床演变的滞后响应模型-Ⅰ模型建立.泥沙研究,2008a,（6）,1-7.
吴保生.冲积河流河床演变的滞后响应模型-Ⅱ模型应用.泥沙研究,2008b,（6）,30-37.
吴保生.三门峡水库运用对潼关高程的影响分析.北京：清华大学水利系,2003.
夏军强,王光谦,吴保生..黄河下游河床纵向与横向变形的数值模拟——Ⅰ二维混合模型的建立.水科学进展,2003a,4:001.
夏军强,王光谦,吴保生.黄河下游河床纵向与横向变形的数值模拟——Ⅱ二维混合模型的应用.水科学进展,2003b,14（4）:396-400.
谢鉴衡.河床演变及整治.北京:中国水利水电出版社,1990.
尹学良,陈金荣.黄河下游河道纵剖面形成概论及持续淤积的原因.人民黄河,1993,2,1-4.
曾庆华，周文浩，杨小庆.渭河淤积发展及其与潼关卡口、黄河洪水倒灌的关系.泥沙研究，
1986,3:13-28.
张根广,林劲松,赵克玉.渭河下游淤积上延分析.泥沙研究,2004,4,39-43.
张仁,谢树楠.废黄河的淤积形态和黄河下游持续淤积的主要成因.泥沙研究,1985,3,24-35.
张原锋,张留柱,梁国亭，等.黄河下游断面法冲淤量分析与评价.郑州:黄河水利出版社,2005.
张原锋.近期渭河下游河道冲淤影响因素分析.人民黄河,2004,26（8）,8-9.
中国科学院地理研究所渭河组.渭河下游河流地貌.北京:科学出版社,1983.
钟德钰,杨明,丁赟.黄河下游河岸横向变形数值模拟研究.人民黄河，2008，30（11）:107-109.
周建军,林秉南.从三门峡水库的运行看潼关高程的变化.水力发电学报,2003,3:59-67.
