Morphological Time Scale Research Articles

Mechanisms and Morphological Time Scales of Avulsed Channel Process on the Modern Yellow River Delta

AbstractThe modern Yellow River Delta (YRD) has witnessed frequent channel avulsions followed by the morphological processes of “wandering‐ short‐lived braiding ‐merging” in history. However, process‐based investigation and relevant physics behind these processes remain poorly constrained. The present study complements the understanding for this evolution through numerical experiments. This is achieved by applying a two‐dimensional (2‐D) depth‐averaged fully coupled morphodynamic model that considers the feedbacks of sediment‐laden flow and bed deformation to a schematized fan‐shaped YRD. Under an uneven bed of uniform sediment, the avulsed processes of “wandering‐ short‐lived braiding ‐merging” during new channel routing on the YRD are satisfactorily reproduced by the present modelling in terms of the time evolution of planar channel pattern and channel length. Moreover, the mechanisms of the avulsed evolution have been elucidated through factor analysis on delta slope, incoming flow‐sediment conditions and artificial trenching, etc. It is suggested that morphological stability could be reached when a single meandering channel is finally sustained, of which the time scale is 4–8 years echoing the documented data of abandoned channels on the YRD. In addition, quantitative criteria have been advocated to help distinguishing the sub‐stages of the avulsed evolution together with the characteristic pattern judgement. Based on the above, implications for the YRD management are discussed.

Future Response of the Wadden Sea Tidal Basins to Relative Sea-Level rise—An Aggregated Modelling Approach

Climate change, and especially the associated acceleration of sea-level rise, forms a serious threat to the Wadden Sea. The Wadden Sea contains the world’s largest coherent intertidal flat area and it is known that these flats can drown when the rate of sea-level rise exceeds a critical limit. As a result, the intertidal flats would then be permanently inundated, seriously affecting the ecological functioning of the system. The determination of this critical limit and the modelling of the transient process of how a tidal basin responds to accelerated sea-level rise is of critical importance. In this contribution we revisit the modelling of the response of the Wadden Sea tidal basins to sea-level rise using a basin scale morphological model (aggregated scale morphological interaction between tidal basin and adjacent coast, ASMITA). Analysis using this aggregated scale model shows that the critical rate of sea-level rise is not merely influenced by the morphological equilibrium and the morphological time scale, but also depends on the grain size distribution of sediment in the tidal inlet system. As sea-level rises, there is a lag in the morphological response, which means that the basin will be deeper than the systems morphological equilibrium. However, so long as the rate of sea-level rise is constant and below a critical limit, this offset becomes constant and a dynamic equilibrium is established. This equilibrium deviation as well as the time needed to achieve the dynamic equilibrium increase non-linearly with increasing rates of sea-level rise. As a result, the response of a tidal basin to relatively fast sea-level rise is similar, no matter if the sea-level rise rate is just below, equal or above the critical limit. A tidal basin will experience a long process of ‘drowning’ when sea-level rise rate exceeds about 80% of the critical limit. The insights from the present study can be used to improve morphodynamic modelling of tidal basin response to accelerating sea-level rise and are useful for sustainable management of tidal inlet systems.

Assessment of a numerical model to reproduce event-scale erosion and deposition distributions in a braided river.

Numerical morphological modeling of braided rivers, using a physics‐based approach, is increasingly used as a technique to explore controls on river pattern and, from an applied perspective, to simulate the impact of channel modifications. This paper assesses a depth‐averaged nonuniform sediment model (Delft3D) to predict the morphodynamics of a 2.5 km long reach of the braided Rees River, New Zealand, during a single high‐flow event. Evaluation of model performance primarily focused upon using high‐resolution Digital Elevation Models (DEMs) of Difference, derived from a fusion of terrestrial laser scanning and optical empirical bathymetric mapping, to compare observed and predicted patterns of erosion and deposition and reach‐scale sediment budgets. For the calibrated model, this was supplemented with planform metrics (e.g., braiding intensity). Extensive sensitivity analysis of model functions and parameters was executed, including consideration of numerical scheme for bed load component calculations, hydraulics, bed composition, bed load transport and bed slope effects, bank erosion, and frequency of calculations. Total predicted volumes of erosion and deposition corresponded well to those observed. The difference between predicted and observed volumes of erosion was less than the factor of two that characterizes the accuracy of the Gaeuman et al. bed load transport formula. Grain size distributions were best represented using two φ intervals. For unsteady flows, results were sensitive to the morphological time scale factor. The approach of comparing observed and predicted morphological sediment budgets shows the value of using natural experiment data sets for model testing. Sensitivity results are transferable to guide Delft3D applications to other rivers.

Bar response to tides under regular waves

The morphological time scale for the response of outer bar crest level to tidal water-level changes is found to be remarkably short, namely around 15min for near-prototype wave heights and depths and regular waves. This corresponds to the bar crest level range being 0.77 times the tidal range with a time-lag of only 15min. Only one near-prototype scale experiment with tide and sufficient time resolution is known to the writers, namely Kraus & Larson (1988) Case 911, which had hmax=4.4m, d50=0.4mm, a semidiurnal tide range of ca 1m and regular waves with H=1.34m, T=7.9s. However, the fast crest-level response is also seen in profile development studies without tide, i.e., the bar crest level generally gets close to its final value in an hour or so while the overall profile adjustment (e.g. seaward bar migration) continues for tens of hours.

MORPHOLOGY OF COASTAL LAGOON ENTRANCES: WAVES VERSUS TIDES

Tidal inlets are important parts of coastal ecosystems and have been the topic of active coastal engineering research for close to a century. The earliest researchers probably realised that the equilibrium cross-section shape, around which a given inlet oscillates due to changing tides and waves and due to occasional storm surges and/or freshwater floods, can be described in terms of the potential bay or lagoon area and the typical wave and tide parameters for the location. However, till now, the effects of waves and tides have not been combined into an effective parameter for inlet classification or formulae for inlet cross-section area, delta volumes, or morphological time scales. This paper gives such a parameter, which necessarily accounts for tidal period as well as tidal prism and wave height. The effectiveness of this new parameter for quantitative classification of inlets is subsequently demonstrated.

Long-Term Effects of Water Diversions on the Longitudinal Flow and Bed Profiles

Water diversions along alluvial rivers cause water and sediment loss, and thereby affect morphological development. Assuming spatially continuous diversions along a constant-width channel, previous studies suggest a longitudinally convex bed at the equilibrium state. However, the validity of a convex bed profile for practically discrete diversions in natural channels of longitudinally varying width remains to be justified. Moreover, such equilibrium analysis does not reveal the morphological time scale (MTS) associated with water diversions. To solve these issues, a general theoretical framework is proposed for predicting the equilibrium state of the fluvial system, which is applicable to both continuous and discrete water diversions in a longitudinally width-varying channel. Numerical experiments complement the MTS studies for water diversions. The effects of diversion intensity, diversion placement (discrete and continuous), and diversion scheme (pure water and water-sediment mixture) are also systematically studied. The present work confirms the previous findings that water diversions lead to a decrease of the equilibrium depth with respect to natural conditions and a convex bed in a constant-width channel. Moreover, it reveals that in a widening channel a convex bed also develops under water diversions, whereas convex, concave, or quasi-linear beds may occur in a narrowing channel. Nonmonotonic beds may develop in a strongly narrowing channel, depending on the diversion schemes. On large spatial scales, diversion placement is less important for the equilibrium development. The MTS for water diversions and natural development are very similar and large, indicating considerable influences of water diversions on river morphology. The present work advances the understanding of the long-term effect of water diversions on river evolution.

QUANTIFYING NEARSHORE MORPHOLOGICAL RECOVERY TIME SCALES USING ARGUS VIDEO IMAGING: PALM BEACH, SYDNEY AND DUCK, NORTH CAROLINA

Time scales of post-storm nearshore morphological recovery and physical processes governing these time scales are poorly understood at present. The ability to predict nearshore morphological recovery time scales based on pre-, during- or post-resetting storm conditions is an essential requirement for building and validating scale aggregated models that operate at macro- and higher spatio-temporal scales. In this study, quality controlled ARGUS video derived beach states at Palm Beach, Sydney (4 years) and Duck, NC (2 years) and concurrent wave data are analysed to quantify the nearshore morphological recovery time scales (Tmr) and to determine the physical processes that may govern Tmr. The results show that Tmr is of the order of 5-10 days at these two beaches. Tmr is moderately positively correlated with the averaged longshore current over the 3 days immediately after the resetting storm, indicating that it might be possible to develop a predictor for Tmr based on wave conditions immediately after the resetting storm. Weak correlations are present between Tmr and several pre-storm, during-storm and post-storm parameters at the two sites. However, these correlations are inconsistent between the two sites. A thorough analysis employing long-term beach state and wave data at several different study sites is required to fully understand this phenomenon.

Influence of the nodal tide on the morphological response of estuaries

The nodal tide causes a periodic variation in the mean tidal range, with a period of 18.6years and amplitude of about 4% of the mean range. As the cross-sectional area of the channel in an estuary has been observed to be related to the tidal prism, such a variation of the tidal range can significantly influence the morphological development of tide-dominated estuaries. Field observations from the Humber Estuary in England confirm that there is indeed an 18.6year cycle in the total water volume of the estuary. In this estuary, with a relatively small morphological time scale, the response to the nodal tide variation appears to dominate the long-term large-scale sediment budget changes of the estuary. The semi-empirical model ESTMORF was able to reproduce these observations, in terms of the observed amplitude and phase lag (relative to the variation of the tidal amplitude) of the morphological response. It also showed good agreement with the along estuary variation in both the magnitude and phase of the response. To examine the character of the response in more detail, a simplified analytical solution has been derived from the governing non-linear equations. This has been investigated in terms of the sensitivity of the model to the various model parameters and by comparison with the historic data. The results demonstrate how the system response is strongly dependent on the morphological time scale of the estuary. Furthermore, the response is not uniform but varies along the length of the estuary, being most marked at the mouth and decaying up estuary. When examining changes in geomorphological features, such as the intertidal area, an appreciation of the role of the nodal tide is shown to be essential if historic data are to be properly interpreted.

Scaling laws for beach and dune erosion processes

This paper is focussed on the derivation of a set of general scaling laws valid for both beach and dune erosion volumes based on scaling law analysis, existing and new experimental results. This latter experiments concern beach profile changes in three different laboratory flumes using identical wave conditions based on Froude scaling. The experiments with planar sloping beaches have been done at three scales: large-scale Hannover wave flume experiment (beach slope of 1 to 15), medium scale Barcelona wave flume experiment (beach slope of 1 to 15) and small-scale Delft wave flume experiments (beach slopes of 1 to 10, 15 and 20) using an identical wave train of irregular waves (single topped spectrum). The available data sets have been used to derive a general set of scaling laws which is valid for both beach and dune erosion under storm conditions. The morphological time scale depends on the depth scale and the length scale, and only indirectly on the sediment size scale. The analysis of the scaling laws shows that laboratory scale models can be operated at distorted scales, if necessary. Finally, two applications of the scaling laws are presented.

Impact of water diversion on the morphological development of the Lower Yellow River

In this paper we carry out a theoretical analysis based on the general one-dimensional morphodynamic model for rivers in order to show how the morphological equilibrium of a river is influenced by water and sediment diversion/supply along the river. The results of the analysis show that large scale water diversions, like those along the Lower Yellow River, can cause the development of a convex riverbed profile in the long-term. Deposition will take place along the whole reach of the river, with an increasing deposition depth from downstream to upstream. The slope of the river bed increases from upstream to downstream. Furthermore, an analysis on the morphological time scale shows that this development in the Lower Yellow River will take a time period on the order of decades to centuries. The results of the analysis have been compared with observations in the Lower Yellow River. Since the second half of the 1980's large scale water diversions from the Yellow River have been taking place. The observations show that this has indeed led to significant sedimentation along the river.

Nearshore subtidal bathymetry from time‐exposure video images

Time‐averaged (over many wave periods) nearshore video observations show the process of wave breaking as one or more white alongshore bands of high intensity. Across a known depth profile, similar bands of dissipation can be predicted with a model describing the time‐averaged cross‐shore evolution of organized wave and roller energy. This close correspondence between observed and modeled dissipation proxies is used to develop a new remote sensing technique, termed Subtidal Beach Mapper (SBM), to estimate nearshore bathymetry. SBM operates on a time series of cross‐shore intensity profiles to resolve the pattern in depth change on a morphological timescale (including overall gain or loss of sediment) rather than to focus on the particular change induced by a single intensity profile. From each intensity profile, the breaking‐induced component is isolated by removing the contribution of background illumination and persistent foam. The depth profile is updated based on a comparison between this video‐derived dissipation proxy and a cross‐shore profile of the dissipation of the roller energy. This updating is implemented through time‐dependent mass balance equations for the seabed and a buffer layer above the bed. SBM was tested using 1 year of hourly video data collected at Egmond aan Zee, Netherlands. The dominant morphological changes observed from ground truth data were reproduced reasonably well, including the shoreward migration of the outer bar and the net sediment gain in the profile. Root‐mean square differences between surveyed and SBM derived depth after 1 year of video‐based depth updating with an average of about 70 intensity profiles per month were smallest (∼0.2 m) on the inner bar and largest (∼0.6 m) in the outer bar trough, with a profile average value of about 0.4 m. Despite the many processes included in SBM, the implementation of a heuristic scaling function in the mass balance equations to spatially adjust morphological growth rates was essential to these results, in particular near the shoreline, where otherwise the profile is prone to an unrealistic deepening.

Sand?mud morphodynamics in a short tidal basin

The influence of sand and mud transport on the morphological behaviour of a short tidal basin is investigated in this paper. For this purpose, a morphological model is applied in which sand and mud transport are included and the temporal and spatial bed composition variations are taken into account. Initially, the morphological development shows a sand wave near the entrance of the basin and a mud deposition wave more landward. A quasi equilibrium bed level profile is found after a long period (order century) with a sandy bed surface over almost the entire basin and only a small muddy area near the landward end. The dimensionless ratio between the deposition and erosion flux turns out to be a crucial parameter for the understanding of the observed behaviour. Comparison with previous studies on short tidal basins for sand indicates only that the presence of mud in a combined sand mud model does not change the equilibrium bed level profile considerably for the applied parameter settings herein, but drastically decreases the morphological time scale. Comparison between model results and field data of the Wadden Sea suggests that the obtained bed level and bed composition profile are realistic, indicating that the process-based sand mud model is a first step towards a better understanding of sand mud distributions in tidal basins.

An analytical model for the morphodynamics of a trench in the presence of tidal currents

Equations are derived for the displacement and deformation of the cross-section of a trench in a sandy bottom. The trench is subject to tidal currents and waves. Tidal currents are rectilinear and perpendicular to the longitudinal axis of the trench. The tidal velocity comprises the residual velocity M0 and the harmonic constituents M2 and M4. The effect of waves on the sediment transport is incorporated as stirring. Separate equations are derived for bed-load and suspended-load transport. The equations are averaged over the tidal time scale assuming that the morphological time scale is large compared to the tidal period. To determine the leading order terms, variables are scaled and the equations are written in dimensionless form. The relative magnitude of the terms is determined by a small parameter ε. ε is the ratio of trench depth and undisturbed water depth. Retaining only leading order terms, the equations reduce to advection–diffusion equations with constant coefficients. The cross-section migrates, widens and shallows. The velocity of migration is a function of the residual velocity and the amplitudes and phases of the M2 and M4 constituents. Widening and shallowing is a result of diffusion. For bed-load transport, diffusion derives from the effect of the bed slope on the sediment transport. For suspended-load transport, diffusion is assumed to be the result of velocity shear and vertical turbulent mass exchange (shear dispersion). When accounting for higher order nonlinear terms an initially symmetric cross-section becomes asymmetric. Application to the access channel to the Port of Amsterdam yields displacement velocities of 1.3myr−1 for bed-load transport and 1.8myr−1 for suspended-load transport. The initial rates of increase of the half-width of the channel are, respectively, 0.33 and 1.02myr−1.

Morphological response to a North Sea bed depression induced by gas mining

Gas mining leads to saucer‐like surface depressions. In the North Sea, gas is currently mined at several offshore locations. The associated bed depression has a similar spatial extent as offshore tidal sandbanks, which are large‐scale bed patterns covering a significant part of the North Sea bottom. The morphological time scales of bed depressions and tidal sandbanks are similar, so that significant interaction between these features is expected. In this paper we allow the bed depression to become morphologically active. A simple depression model based on a homogeneous soil is tuned with data of a bed depression near the Dutch barrier island of Ameland. Next, this subsidence model is included in a morphodynamic model. We show that this model is able to explain tidal sandbanks, which represent natural bed behavior. Here we approximate the solution by an expansion up to first order. The zeroth‐order solution of the model is a flat bed with a spatially uniform, time‐independent current. The first‐order solution is investigated using a Fourier transformation. In general, we observe significant interaction between the bed depression and the natural sandbank formation process. The process of induced bed depression triggers and intensifies the natural morphological behavior of the offshore seabed. The model also shows essential differences between modeling a morphodynamically active marine bottom depression and a bottom depression below the threshold for sediment motion. The maximum bed level depression in the active case is significantly larger, and the circular shape of depression contours is affected by stretching toward the preferred orientation of the tidal sandbank formation process.

The shoreface-connected ridges along the central Dutch coast — part 2: morphological modelling

The long-term (decades, centuries) morphological behaviour of the shoreface-connected ridges along the central Dutch coast was studied with a simplified modelling approach, consisting of a 1D current model ( Trenchflow), combined with a 2DV morphodynamic model ( Sutrench). The analysis focused on a cross-section of a single sand bank, assuming that the interaction of the water motion and morphology could be considered a local phenomenon. The modelling was used for a sensitivity analysis of the relevant processes. The present model reveals a positive feedback: the schematized sand bank is predicted to grow, while there is no damping, even not during high waves. However, using the observed flow response, which differs from the theoretical flow response as described in Part 1 of this paper, actual growth rates are close to zero. The modelling shows that the ridges are stable on a time scale of years to decades, while they may be considered active on the time scale of thousands of years. Calculated migration rates of the ridges are in the order of 1 m/yr. Morphological time scale and migration rate correspond to the results from a geological reconstruction.

Physical impact on the reclamation area resulting from offshore dredging at the Changhwa coast, Taiwan

The physical impact of offshore dredging on the reclamation area at the Changhwa coast, Taiwan, is investigated using a three-dimensional movable-bed model test. A distorted modeling law consisting of maintaining similarity of the equilibrium beach profile between the model and prototype is proposed. The geometric distortion was verified through a series of preliminary experiments conducted in a wave flume. Experimental results show that the distorted modeling is able to reproduce the beach-face slope in nature. An appropriate long-term morphological time-scale was determined based on a comparison of model longshore littoral transport rates and equivalent prototype values. Seabed topographical changes before and after offshore dredging are evaluated in model tests. A suitable countermeasure to prevent beach erosion from wave attack along the reclamation area is suggested from the experimental results.

Stability of river bifurcations in ID morphodynamic models

Based on model-technical as well as physical considerations a nodal-point relation at bifurcations is proposed for one-dimensional (ID) network morphodynamic models: the ratio between the sediment transports into the downstream branches is proportional to a power of the discharge ratio. The influence of the nodal-point relation on the behaviour of the morphodynamic model is analyzed theoretically. The exponent in the nodal-point relation appears to be crucial for the stability of the bifurcation in the model. For large values of the exponent, the bifurcation is stable, i.e. the downstream branches remain open. For small values of the exponent, the bifurcation is unstable: only one of the branches tends to remain open. The exponent also has a strong influence on the morphological time scales of the network. The conclusions from the analysis have been verified by numerical simulations using a package for one-dimensional network modelling.

Genetic variation in aspects of leaf growth of Populusclones, using the leaf plastochron index

Leaf growth characteristics of seven clones of Populustrichocarpa, P. nigra, and interspecific hybrids with P. deltoides were examined on 1-year-old cuttings grown in a controlled-environment growth chamber. The plastochron index, a morphological time scale that is a linear function of time and correlated with other morphogenetic and physiological developmental processes, was applied to this development and growth study. Uniformity of leaf initiation was studied; new leaves were initiated at regular time intervals, at least under the controlled conditions of this study. Clones with a high leaf production rate (e.g., P. nigra clone Italica) had a low leaf growth rate and leaves reached maturity at a high leaf plastochron index (LPI 11). Fast-growing and high-yielding P. trichocarpa × P. deltoides hybrids showed the highest leaf growth rates and had a similar leaf production rate to P. trichocarpa. Despite considerable differences in leaf production rates, leaf maturity, and absolute leaf growth rates, only small differences in relative leaf growth rate were observed among the clones.

SPECIAL PAPER: THE PLASTOCHRON INDEX: A REVIEW AFTER TWO DECADES OF USE

The plastochron index provides a morphological time scale which has proved more reliable than chronological age in studies relating morphological and physiological development of a whole plant or plant organ. Since its inception in 1957, the index has been utilized in a variety of investigations from leaf ontogeny in cottonwood trees to rhizoid cluster initiation in algae. The plastochron index has been extensively used in studies involving source and sink relationships, leaf anatomy, cell differentiation, and primary vascularization. It has been used in investigations of hormonal regulation of plant growth and in studies of the effects of various environmental factors on developmental processes in crops. This paper reviews some of the literature from 1957 to present concerning the development and use of the plastochron index.

The Plastochron Index: A Review After Two Decades of Use

The plastochron index provides a morphological time scale which has proved more reliable than chronological age in studies relating morphological and physiological development of a whole plant or plant organ. Since its inception in 1957, the index has been utilized in a variety of investigations from leaf ontogeny in cottonwood trees to rhizoid cluster initiation in algae. The plastochron index has been extensively used in studies involving source and sink relationships, leaf anatomy, cell differentiation, and primary vascularization. It has been used in investigations of hormonal regulation of plant growth and in studies of the effects of various environmental factors on developmental processes in crops. This paper reviews some of the literature from 1957 to present concerning the development and use of the plastochron index.