The response of salt intrusion to changes in river discharge and tidal mixing during the dry season in the Modaomen Estuary,China

The increase of salt intrusion in recent years in the Modaomen Estuary, one of the estuaries of the Pearl River Delta in China, has threatened the freshwater supply in the surrounding regions, especially the cities of Zhongshan, Zhuhai in Guangdong Province and Macau. A numerical modeling system using nested grids was developed to investigate the salt transport mechanisms and the response of salt intrusion to changes in river discharge and tidal mixing. The steady shear transport induced by estuarine circulation reaches maximum and minimum, respectively, during neap and spring tides, while the tidal oscillatory transport shows an opposite pattern. The net transport is landward during neap tides and seaward during spring tides. The salt intrusion length responding to constant river discharges generally follows a power law of ?0.49. The dependence of salt intrusion on tidal velocity is less than that predicted by theoretical models for exchange flow dominated estuaries. The response of salt intrusion to change in tidal velocity depends largely on river discharge. When river flow increases, the impact of tidal velocity increases and the phase lag of response time decreases. The asymmetries of salt intrusion responding to increasing and decreasing river discharge (tidal velocity) are observed in the estuary.     

Effects of discharge,wind, and tide on sedimentation in a recently restored tidal freshwater wetland

Sediment deposition is one of the key mechanisms to counteract the impact of sea level rise in tidal freshwater wetlands (TFWs). However, information about sediment deposition rates in TFWs is limited, especially for those located in the transition zone between the fluvially dominated and tidally dominated sections of a river delta where sedimentation rates are affected by the combined impact of river discharge, wind, and tides. Using a combined hydrodynamic–morphological model, we examined how hydrometeorological boundary conditions control sedimentation rates and patterns in a TFW located in the Rhine–Meuse estuary in the Netherlands. The modelling results show that net sedimentation rate increases with the magnitude of the river discharge, whereas stronger wind increasingly prevents sedimentation. Sediment trapping efficiency decreases for both increasing river discharge and wind magnitude. The impact of wind storms on the trapping efficiency becomes smaller for higher water discharge. The spatial sedimentation patterns are affected by all controls. Our study illustrates the importance of evaluating both the separate and the joint impact of discharge, wind, and tides when estimating sedimentation rates in a TFW affected by these controls. Such insights are relevant to design measures to reactivate the sedimentation process in these areas.     

A simple approach to estimating freshwater discharge in branched estuarine systems

In tidal estuaries, quantifying freshwater discharge is still a difficult problem that has not yet been overcome due to the inherent difficulty in measuring and analysing the tidal discharge, especially during periods of low river flow. Because observations are often made in the stations further upstream, where the ratio of river to tidal discharge is large, it remains difficult to determine the discharge rate in the saline region. Freshwater discharge estimation is even more difficult in a branched estuary system having multiple diversion channels that connect with each other at a junction. To date, several methods have been developed for estimating freshwater discharge in estuaries. The most widely used are analytical and conceptual models that employ salinity as the principal trace and numerical simulations. However, these methods are very time consuming and costly as they require large sets of observations before the computations can take place. This paper presents a simple approach to investigating the discharge distribution over branched channels by considering the energy loss due to friction. We develop an analytical model that can obtain the discharge rate quantitatively at a junction where the main flow bifurcates into two branches. The model uses the bed roughness, tidal water level, and cross‐sectional profile under tidally averaged conditions as input data. Two selected estuarine systems in the Hiroshima delta in Japan and the Mekong delta in Vietnam have been investigated. Computations of the newly developed model show good agreement with earlier published results computed by sophisticated analytical and numerical models.     

The effect of tide on the hydrology and morphology of a freshwater river

How does river hydrology and morphology change due to tidal influence? We contend that this is a question of particular consequence to many earth surface disciplines, but one that has not been adequately addressed. Previous studies have relied on gradients in channel morphology and stratigraphy to infer energy regime of channels. However, in tidal rivers geomorphology influences the energy regime while the energy regime influences morphology; thus, geomorphic and stratigraphic patterns do not fully resolve the mechanisms which lead to change. We addressed this problem by comparing measurements of hydraulic energy and channel morphology along a tidal gradient to predictions of these characteristics in the absence of tides, and attributed the differences to tidal processes. Measurements of discharge, channel area, and energy dissipation (in kJ day^–1) were made over a 24·8 hour period at four sites spanning the non‐tidal to tidal freshwater Newport River, NC. We then predicted those characteristics under non‐tidal conditions using hydraulic geometry relationships and literature values from coastal plain rivers. Discharge was enhanced more than 10‐fold by tide, and this tidal effect increased from upstream to downstream along the tidal gradient. Cross‐sectional area increased three‐fold due to tide. Energy dissipation measured in the upper tidal river was four‐fold lower than predicted to occur in the absence of tide because tides decreased average velocity and discharge. Energy dissipation measured downstream was similar to that predicted to occur without tides, although there was large uncertainty in predicted values downstream. While this limited dataset does not permit us to make broad generalizations for definitive models, it does provide a proof‐of‐concept for a new approach to addressing a critical problem at the interface of fluvial and coastal morphology. Copyright © 2013 John Wiley & Sons, Ltd.     

Seasonal,tidal, and geomorphic controls on sediment export to Amazon River tidal floodplains

Mainstem–floodplain material exchange in the tidal freshwater reach of major rivers may lead to significant sequestration of riverine sediment, but this zone remains understudied compared to adjacent fluvial and marine environments. This knowledge gap prompts investigation of floodplain-incising tidal channels found along the banks of tidal rivers and their role in facilitating water and suspended-sediment fluxes between mainstem and floodplain. To evaluate this role, and how it evolves along the tidal river and with time, we measured water level, flow velocity, temperature, and suspended-sediment concentration (SSC) in four tidal channels along the tidal Amazon River, Brazil. Eleven deployments were made during low, rising, high, and falling seasonal Amazon discharge. Generally, channels export high-SSC water from the mainstem to the tidal floodplain on flood tides and transfer low-SSC water back to the mainstem on ebbs. Along the length of the tidal river, the interaction between tidal and seasonal water-level variations and channel–floodplain morphology is a primary control on tidal-channel sediment dynamics. Close to the river mouth, where tides are large, this interaction produces transient flow features and current-induced sediment resuspension, but the importance of these processes decreases with distance upstream. Although the magnitude of the exchange of water and sediment between mainstem and floodplain via tidal channels is a small percentage of the total mainstem discharge in this large tidal-river system, tidal channels are important conduits for material flux between these two environments. This flux is critical to resisting floodplain submergence during times of rising sea level. © 2019 John Wiley & Sons, Ltd.     

A conceptual model of depositional,rather than erosional,tidal channel development in the rapidly prograding Skagit River Delta (Washington,USA)

The origin and growth of blind tidal channels is generally considered to be an erosional process. This paper describes a contrasting depositional model for blind tidal channel origin and development in the Skagit River delta, Washington, USA. Chronological sequences of historical maps and photos spanning the last century show that as sediments accumulated at the river mouth, vegetation colonization created marsh islands that splintered the river into distributaries. The marsh islands coalesced when intervening distributary channels gradually narrowed and finally closed at the upstream end to form a blind tidal channel, or at mid‐length to form two blind tidal channels. Channel closure was probably often mediated through gradient reduction associated with marsh progradation and channel lengthening, coupled with large woody debris blockages. Blind tidal channel evolution from distributaries was common in the Skagit marshes from 1889 to the present, and it can account for the origin of very small modern blind tidal channels. The smallest observed distributary‐derived modern blind tidal channels have mean widths of 0·3 m, at the resolution limit of the modern orthophotographs. While channel initiation and persistence are similar processes in erosional systems, they are different processes in this depositional model. Once a channel is obstructed and isolated from distributary flow, only tidal flow remains and channel persistence becomes a function of tidal prism and tidal or wind/wave erosion. In rapidly prograding systems like the Skagit, blind tidal channel networks are probably inherited from the antecedent distributary network. Examination of large‐scale channel network geometry of such systems should therefore consider distributaries and blind tidal channels part of a common channel network and not entirely distinct elements of the system. Finally, managers of tidal habitat restoration projects generally assume an erosional model of tidal channel development. However, under circumstances conducive to progradation, depositional channel development may prevail instead. Copyright © 2006 John Wiley & Sons, Ltd.     

Hydrological regime,morphological features and natural territorial complexes of the Irrawaddy River Delta (Myanmar)

Hydrological and morphological features of the multiple-branched tidal delta of the Irrawaddy River are discussed. Close attention is given to the impact of the interaction of seasonal variations of the river flow and tides on the delta regime. The results of analysis of the deltaic natural complexes using space photographs are presented. The issues of rational use and conservation of the natural resources of the delta are studied.     

Coupled 1D–3D hydrodynamic modelling,with application to the Pearl River Delta

Within the hydrodynamic modelling community, it is common practice to apply different modelling systems for coastal waters and river systems. Whereas for coastal waters 3D finite difference or finite element grids are commonly used, river systems are generally modelled using 1D networks. Each of these systems is tailored towards specific applications. Three-dimensional coastal water models are designed to model the horizontal and vertical variability in coastal waters and are less well suited for representing the complex geometry and cross-sectional areas of river networks. On the other hand, 1D river network models are designed to accurately represent complex river network geometries and complex structures like weirs, barrages and dams. A disadvantage, however, is that they are unable to resolve complex spatial flow variability. In real life, however, coastal oceans and rivers interact. In deltaic estuaries, both tidal intrusion of seawater into the upstream river network and river discharge into open waters play a role. This is frequently approached by modelling the systems independently, with off-line coupling of the lateral boundary forcing. This implies that the river and the coastal model run sequentially, providing lateral discharge (1D) and water level (3D) forcing to each other without the possibility of direct feedback or interaction between these processes. An additional disadvantage is that due to the time aggregation usually applied to exchanged quantities, mass conservation is difficult to ensure. In this paper, we propose an approach that couples a 3D hydrodynamic modelling system for coastal waters (Delft3D) with a 1D modelling system for river hydraulics (SOBEK) online. This implies that contrary to off-line coupling, the hydrodynamic quantities are exchanged between the 1D and 3D domains during runtime to resolve the real-time exchange and interaction between the coastal waters and river network. This allows for accurate and mass conserving modelling of complex coastal waters and river network systems, whilst the advantages of both systems are maintained and used in an optimal and computationally efficient way. The coupled 1D–3D system is used to model the flows in the Pearl River Delta (Guangdong, China), which are determined by the interaction of the upstream network of the Pearl River and the open waters of the South China Sea. The highly complex upstream river network is modelled in 1D, simulating river discharges for the dry and wet monsoon periods. The 3D coastal model simulates the flow due to the external (ocean) periodic tidal forcing, the salinity distribution for both dry and wet seasons, as well as residual water levels (sea level anomalies) originating from the South China Sea. The model is calibrated and its performance extensively assessed against field measurements, resulting in a mean root mean square (RMS) error of below 6% for water levels over the entire Pearl River Delta. The model also represents both the discharge distribution over the river network and salinity transport processes with good accuracy, resolving the discharge distribution over the main branches of the river network within 5% of reported annual mean values and RMS errors for salinity in the range of 2 ppt (dry season) to 5 ppt (wet season).     

Sediment transport in distributary channels and its export to the pro-deltaic environment in a tidally dominated delta: Fly River, Papua New Guinea

Current metre deployments, suspended sediment measurements and surface sediment samples were collected from three locations within distributary channels of the tidally dominated Fly River delta in southern Papua New Guinea. Net bedload transport vectors and the occurrence of elongate tidal bars indicate that mutually evasive ebb- and flood-dominant transport zones occur in each of the distributary channels. Suspended sediment experiments at two locations show a phase relationship between tidal velocity and sediment concentration such that the net suspended sediment flux is directed seaward. Processes that control the export of fluid muds with concentrations up to 10 g l⁻¹ from the distributary channels across the delta front and onto the pro-delta are assessed in relation to the available data. Peak spring tidal current speeds (measured at 100 cm above the bed) drop off from around 100 cm s⁻¹ within the distributary channels to <50 cm s⁻¹ on the delta front. Gravity-driven, 2-m thick, fluid mud layers generated in the distributary channels are estimated to require at least 35 h to traverse the 20-km-wide, low-gradient (2×10⁻³ degrees) delta front. The velocities of such currents are well below those required for autosuspension. A 1-month time series of suspended sediment concentration and current velocity from the delta front indicates that tidal currents alone are unable to cause significant cross-delta mud transport. Wave-induced resuspension together with tides, storm surge and barotropic return-flow may play a role in maintaining the transport of fine sediment across the delta front, but insufficient data are available at present to make any reliable estimates.     

Bar dynamics and bifurcation evolution in a modelled braided sand‐bed river

Morphodynamics in sand‐bed braided rivers are associated with simultaneous evolution of mid‐channel bars and channels on the braidplain. Bifurcations around mid‐channel bars are key elements that divide discharge and sediment. This, in turn, may control the evolution of connected branches, with effects propagating to both upstream and downstream bifurcations. Recent works on bifurcation stability and development hypothesize major roles of secondary flow and gradient advantage. However, this has not been tested for channel networks within a fully developed dynamic braided river. A reason for this is a lack of detailed measurements with sufficient temporal and spatial length, covering multiple bifurcations. Therefore we used a physics‐based numerical model to generate a dataset of bathymetry, flow and sediment transport of an 80 km river reach with self‐formed braid bars and bifurcations. The study shows that bar dissection due to local transverse water surface gradients is the dominant bifurcation initiation mechanism, although conversion of unit bars into compound bars dominates in the initial stage of a braided river. Several bifurcation closure mechanisms are equally important. Furthermore, the study showed that nodal point relations for bifurcations are unable to predict short‐term bifurcation evolution in a braided river. This is explained by occurrence of nonlinear processes and non‐uniformity within the branches, in particular migrating bars and larger‐scale backwater‐effects, which are not included in the nodal point relations. Planform morphology, on the other hand, has predictive capacity: bifurcation angle asymmetry and bar‐tail limb shape are indicators for near‐future bifurcation evolution. Remote sensing data has predictive value, for which we developed a conceptual model for interactions between bars, bifurcations and channels in the network. We conducted a preliminary test of the conceptual model on satellite images of the Brahmaputra. Copyright © 2015 John Wiley & Sons, Ltd.     

Data reconciliation of an open channel flow network using modal decomposition

This article presents a method to estimate flow variables for an open channel network governed by the linearized Saint-Venant equations and subject to periodic forcing. The discharge at the upstream end of the system and the stage at the downstream end of the system are defined as the model inputs; the flow properties at selected internal locations, as well as the other external boundary conditions, are defined as the outputs. Both inputs and outputs are affected by noise and we use the model to improve the data quality. A spatially dependent transfer matrix in the frequency domain is constructed to relate the model input and output using modal decomposition. A data reconciliation technique is used to incorporate the error in the measured data and results in a set of reconciliated external boundary conditions; subsequently, the flow properties at any location in the system can be accurately estimated from the input measurements. The applicability and effectiveness of the method is demonstrated with a case study of the river flow subject to tidal forcing in the Sacramento-San Joaquin Delta, in California. We used existing USGS sensors in place in the Delta as measurement points, and deployed our own sensors at selected locations to produce data used for the validation. The proposed method gives an accurate estimation of the flow properties at intermediate locations within the channel network.     

武汉台重力潮汐长期观测结果

采用武汉台超导重力仪(SG C032)14年多的长期连续观测资料,研究了固体地球对二阶和三阶引潮力的响应特征,精密测定了重力潮汐参数,系统研究了最新的固体潮模型和海潮模型在中国大陆的有效性.采用最新的8个全球海潮模型计算了海潮负荷效应,从武汉台SG C032的观测中成功分离出63个2阶潮汐波群和15个3阶潮汐波群信号,3阶潮波涵盖了周日、半日和1/3日三个频段.重力潮汐观测的精度非常高,标准偏差达到1.116 nm·s^-2,系统反映了非流体静力平衡、非弹性地球对2阶和3阶引潮力的响应特征.结果表明,现有的武汉国际重力潮汐基准在半日频段非常精确,但在周日频段存在比较明显的偏差,需要进一步精化.对于中国大陆的大地测量观测,固体潮可以采用Dehant等考虑地球内部介质非弹性和非流体静力平衡建立的固体潮理论模型或Xu 等基于全球SG观测建立的重力潮汐全球实验模型作为参考和改正模型,海潮负荷效应应该采用Nao99作为改正模型.     

Two-dimensional modeling of fine sediment transport with mixed sediment and consolidation: Application to the Gironde Estuary,France

In order to optimize ship navigation in the macrotidal Gironde Estuary, a recent project funded by the port of Bordeaux aims at better understand and forecast hydrodynamic and fine sediment transport within the estuary. In the framework of this project, a two-dimensional hydro-sedimentary model is built. The model includes hydrodynamic forcings, mixed-sediment transport, and consolidation processes. The harmonic analysis of the astronomical tides reveals a strong distortion of the tidal wave inducing the growth of overtide constituents and the non-significant effect of tide-surge interactions in annual-scale prediction. Depending on hydrological conditions, river discharge can considerably alter the model accuracy due to the migration of the turbidity maximum zone modifying the bottom roughness. Comparison with measurements shows the ability of the model to reproduce suspended-sediment concentrations in the central Estuary. Sensitivity of the model to sediment features has also been discussed in regard of suspended-sediment concentrations and fluid mud deposits. The model will be further coupled with ship squat predictions and a morphodynamic model.     

Network concepts to describe channel importance and change in multichannel systems: test results for the Jamuna River,Bangladesh

Most of the largest rivers on Earth have multiple active channels connected at bifurcations and confluences. At present a method to describe a channel network pattern and changes in the network beyond the simplistic braiding index is unavailable. Our objectives are to test a network approach to understand the character, stability and evolution of a multi‐channel river pattern under natural discharge conditions. We developed a semi‐automatic method to derive a chain‐like directional network from images that represent the multi‐channel river and to connect individual network elements through time. The Jamuna River was taken as an example with a series of Landsat TM and ETM+ images taken at irregular intervals between 1999 and 2004. We quantified the overall importance of individual channels in the entire network using a centrality property. Centrality showed that three reaches can be distinguished along the Jamuna with a different network character: the middle reach has dominantly one important channel, while upstream and downstream there are about two important channels. Temporally, relatively few channels changed dramatically in both low‐flow and high‐flow periods despite the increase of braiding index during a flood. Based on the centrality we calculated a weighted braiding index that represents the number of important channels in the network, which is about two in the Jamuna River and which is larger immediately after floods. We conclude that the network measure centrality provides a novel characterization of river channel networks, highlighting properties and tendencies that have morphological significance. Copyright © 2013 John Wiley & Sons, Ltd.     

A study of tides and currents in Cook Strait, New Zealand

Greater Cook Strait (GCS) lies between the North and the South Islands of New Zealand. Its location at the convergence of the Pacific and Indo-Australian tectonic plates leads to interesting bathymetry with an adjacent shallow shelf and deep ocean trench as well as numerous crossing faults and complex shoreline geometry. Our purpose in this study is to examine tides and currents in GCS and, in particular, identify the major forcing mechanisms for the residual currents. Toward this end, we use an unstructured-grid numerical model to reproduce the tides and currents, verify these results with observations and then use the model to separate the various forcing mechanisms. The physical forcing includes nonlinear generation from tides and tidal currents, differences in sea level between the Pacific Ocean and Tasman Sea boundaries, density variations, wind stress and river discharge into GCS. Each of these mechanisms is important in different areas.     

Modeling the morphodynamic response of tidal embayments to sea-level rise

Sea-level rise has a strong influence on tidal systems, and a major focus of climate change effect studies is to predict the future state of these environmental systems. Here, we used a model to simulate the morphological evolution of tidal embayments and to explore their response to a rising sea level. The model was first used to reproduce the formation of channels and intertidal flats under a stable mean water level in an idealised and initially unchannelled tidal basin. A gradual rise in sea level was imposed once a well-developed channel network had formed. Simulations were conducted with different sea-level rise rates and tidal ranges. Sea-level rise forced headward erosion of the tidal channels, driving a landward expansion of the channel network and channel development in the previously non-inundated part of the basin. Simultaneously, an increase in channel drainage width in the lower part of the basin occurred and a decrease in the overall fraction of the basin occupied by channels could be observed. Sea-level rise thus altered important characteristics of the tidal channel network. Some intertidal areas were maintained despite a rising sea level. However, the size, shape, and location of the intertidal areas changed. In addition, sea-level rise affected the exchange of sediment between the different morphological elements. A shift from exporting to importing sediment as well as a reinforcement of the existing sediment export was observed for the simulations performed here. Sediment erosion in the inlet and the offshore transport of sediment was enhanced, resulting in the expansion of the ebb-tidal delta. Our model results further emphasise that tidal embayments can exhibit contrasting responses to sea-level rise.

     

Modeling the morphodynamic response of tidal embayments to sea-level rise

Sea-level rise has a strong influence on tidal systems, and a major focus of climate change effect studies is to predict the future state of these environmental systems. Here, we used a model to simulate the morphological evolution of tidal embayments and to explore their response to a rising sea level. The model was first used to reproduce the formation of channels and intertidal flats under a stable mean water level in an idealised and initially unchannelled tidal basin. A gradual rise in sea level was imposed once a well-developed channel network had formed. Simulations were conducted with different sea-level rise rates and tidal ranges. Sea-level rise forced headward erosion of the tidal channels, driving a landward expansion of the channel network and channel development in the previously non-inundated part of the basin. Simultaneously, an increase in channel drainage width in the lower part of the basin occurred and a decrease in the overall fraction of the basin occupied by channels could be observed. Sea-level rise thus altered important characteristics of the tidal channel network. Some intertidal areas were maintained despite a rising sea level. However, the size, shape, and location of the intertidal areas changed. In addition, sea-level rise affected the exchange of sediment between the different morphological elements. A shift from exporting to importing sediment as well as a reinforcement of the existing sediment export was observed for the simulations performed here. Sediment erosion in the inlet and the offshore transport of sediment was enhanced, resulting in the expansion of the ebb-tidal delta. Our model results further emphasise that tidal embayments can exhibit contrasting responses to sea-level rise.     

Tidal and meteorological forcing of sediment transport in tributary mudflat channels

Field observations of flow and sediment transport in a tributary channel through intertidal mudflats indicate that suspended sediment was closely linked to advection and dispersion of a tidal salinity front. During calm weather when tidal forcing was dominant, high concentrations of suspended sediment advected up the mudflat channel in the narrow region between salty water from San Francisco Bay and much fresher runoff from the small local watershed. Salinity and suspended sediment dispersed at similar rates through each tidal inundation, such that during receding ebbs the sediment pulse had spread spatially and maximum concentrations had decreased. Net sediment transport was moderately onshore during the calm weather, as asymmetries in stratification due to tidal straining of the salinity front enhanced deposition, particularly during weaker neap tidal forcing. Sediment transport by tidal forcing was periodically altered by winter storms. During storms, strong winds from the south generated wind waves and temporarily increased suspended sediment concentrations. Increased discharge down the tributary channels due to precipitation had more lasting impact on sediment transport, supplying both buoyancy and fine sediment to the system. Net sediment transport depended on the balance between calm weather tidal forcing and perturbations by episodic storms. Net transport in the tributary channel was generally off-shore during storms and during calm weather spring tides, and on-shore during calm weather neap tides.     

Evaluating competing hypotheses for the origin and dynamics of river anastomosis

Anastomosing rivers have multiple interconnected channels that enclose flood basins. Various theories potentially explain this pattern, including an increased discharge conveyance and sediment transport capacity of multiple channels, deltaic branching, avulsion forced by base‐level rise, or a tendency to avulse due to upstream sediment overloading. The former two imply a stable anabranching channel pattern, whereas the latter two imply disequilibrium and evolution towards a single‐channel pattern in the absence of avulsion. Our objective is to test these hypotheses on morphodynamic scenario modelling and data of a well‐documented case study: the upper Columbia River. Proportions of channel and floodplain sediments along the river valley were derived from surface mapping. Initial and boundary conditions for the modelling were derived from field data. A 1D network model was built based on gradually varied flow equations, sediment transport prediction, mass conservation, transverse slope and spiral meander flow effects at the bifurcations. The number of channels and crevasse splays decreases in a downstream direction. Also, measured sediment transport is higher at the upstream boundary than downstream. These observations concur with bed sediment overloading from upstream, which can have caused channel aggradation above the surrounding floodplain and subsequent avulsion. The modelling also indicates that avulsion was likely caused by upstream overloading. In the model, multi‐channel systems inevitably evolve towards single‐channel systems within centuries. The reasons are that symmetric channel bifurcations are inherently unstable, while confluenced channels have relatively less friction than two parallel channels, so that more discharge is conveyed through the path with more confluences and less friction. Furthermore, the present longitudinal profile curvature of the valley could only be reproduced in the model by temporary overfeeding. We conclude that this anastomosing pattern is the result of time‐varying sediment overloading and is not an equilibrium pattern feature, and suggest this is valid for many anastomosing rivers. Copyright © 2012 John Wiley & Sons, Ltd.