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The energy based least action principle (LAP) has proven to be very successful for explaining natural phenomena in both classical and modern physics. This paper briefly reviews its historical development and details how, in three ways, it governs the behaviour and stability of alluvial rivers. First, the LAP embodies the special stationary equilibrium state of motion and so its incorporation with the principle of energy conservation explains why so many optimizing hypotheses have been proposed in fluvial geomorphology. Second, the variational approach underlying the LAP provides a more straightforward and simpler fuzzy-object orientated method for solving river regime problems than do the various complex Newtonian formulations. Third, it is shown that in fluvial systems with surplus energy the surplus can be expended with slope and/or channel geometry adjustments, with the degree of channel geometry adjustment quantified by the dimensionless numbers F for depth dominated adjustment and H for width/depth dominated adjustment. Different planforms are preferred at different energy levels, with H providing a quantitative measure of the flow's efficiency for moving sediment. In rivers with insufficient energy, the interactions of endogenous and exogenous factors are shown to be capable, in certain circumstances, of achieving a stationary equilibrium condition which acts as the attractor state. Importantly, this study describes how iterative changes enable systems to achieve such a stable equilibrium.

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Impacts of land use and climate change on runoff were investigated by studying the runoff in the Yarlung Zangbo River basin, China. Trends in precipitation, mean air temperature, and runoff were analysed by non‐parametric Mann‐Kendall tests. Land‐use changes were examined with land‐use transition matrix and geographic information system tools. Land‐use and climate changes showed several characteristics, including increased reforestation, decreased grassland, retreat of glaciers and increased desertification. Human activity caused great impact, especially within densely populated regions and cities. Reforestation and degradation of grasslands were more frequent than deforestation and cultivation of grasslands. Annual mean air temperature, precipitation and runoff showed increasing trends between 1974 and 2000. The impacts of land use and climate change on runoff had different effects depending on region and season. In the season of freezing, climate change clearly affected runoff within regions that experienced precipitation. Altered evapotranspiration accounted for about 80 per cent of runoff changes, whereas land‐use changes appear to have had greatest impact on runoff changes within regions that have inconsistent relationships between runoff and climate change. It was demonstrated that afforestation leads to increased runoff in dry seasons. It was estimated that glacier snow melt has caused annual runoff to increase at least 6·0 mm/10yr, 2·1 mm/10yr and 1·7 mm/10yr in Regions 1, 3 and 4, respectively, whereas evapotranspiration caused annual runoff to decrease at least 7·4 mm/10yr in Region 2. Copyright © 2012 John Wiley & Sons, Ltd.

[1] Although the Bélanger-Böss theorem of critical flow has been widely applied in open channel hydraulics, it was derived from the laws governing ideal frictionless flow. This study explores a more general expression of this theorem and examines its applicability to flow with friction and sediment transport. It demonstrates that the theorem can be more generally presented as the principle of minimum energy (PME), with maximum efficiency of energy use and minimum friction or minimum energy dissipation as its equivalents. Critical flow depth under frictionless conditions, the best hydraulic section where friction is introduced, and the most efficient alluvial channel geometry where both friction and sediment transport apply are all shown to be the products of PME. Because PME in liquids characterizes the stationary state of motion in solid materials, flow tends to rapidly expend excess energy when more than minimally demanded energy is available. This leads to the formation of relatively stable but dynamic energy-consuming meandering and braided channel planforms and explains the existence of various extremal hypotheses.

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Anabranching rivers have been identified globally, but a widely accepted and convincing theoretical explanation for their occurrence has remained elusive. Using basic flow and sediment transport relations, this study analyzes the mechanisms whereby self‐adjusting alluvial channels can anabranch to alter their flow efficiency (sediment transport capacity per unit of stream power). It shows that without adjusting channel slope, an increase in the number of channels can produce a proportional decrease in flow efficiency, a finding particularly relevant to understanding energy consumption in some braided rivers. However, anabranching efficiency can be significantly increased by a reduction in channel width, as occurs when vegetated alluvial islands or between‐channel ridges form. The counteracting effects of width reduction and an increasing number of channels can cause, with no adjustment to slope, an otherwise unstable system (underloaded or overloaded) to achieve stability. As with other river patterns, anabranching can be characterized by stable equilibrium or accreting disequilibrium examples.

The Yellow River in China carries an extremely large sediment load. River channel-form and lateral shifting in a dynamic, partly meandering and partly braided reach of the lower Yellow River, have been significantly influenced by construction of Sanmenxia Dam in 1960, Liujiaxia Dam in 1968, Longyangxia Dam in 1985 and Xiaolangdi Dam in 1997 Using observations from Huayuankou Station, 128 km downstream of Xiaolangdi Dam, this study examines changes in the river before and after construction of the dams. The temporal changes in the mean annual flow discharge and mean annual suspended sediment concentration have been strongly influenced by operation of theses dams. Observations of sediment transport coefficient (ratio of sediment concentration to flow discharge), at-a-station hydraulic geometry and bankfull channel form observed from 1951 to 2006 have shown that, although variations in flow and sediment load correspond to different periods of dam operation, changes in channel form are not entirely synchronous with these. The channel has been subject to substantial deposition due to the flushing of sediment from Sanmenxia Dam, resulting in a marked reduction in bankfull cross-sectional area. Flows below bankfull had a greater impact on channel form than higher flows because of very high sediment load. At-a-station hydraulic geometry shows that the variation of channel cross-sectional area below bankfull in this wide and relatively shallow system largely depends on changes in width. Such at-a-station changes are significantly influenced by (1) events below bankfull and (2) overbank floods. Bankfull depth is the main component of channel adjustment in that depth adjusts synchronously with channel area. The channel adjusts its size by relatively uniform changes in depth and width since 1981. Channel morphology is not the product of single channelforming flow frequency. It is determined by the combination of relatively low flows that play an important role in fine sediment transport and bed configuration as with relatively high flows that are effective at modifying the channel's morphology. The sediment transport coefficient is a useful index for efficiently guiding the operation of the dams in a way that would minimize channel changes downstream. Sedimentation over the nearly 60 years of study period caused the lower Yellow River to aggrade progressively, the only significant exception being the two years following completion of Sanmenxia Dam.