Trans-scale modelling of river morphodynamics

Abstract

In a river, the local hydraulics, channel form and in-stream vegetation are interdependent. Although water, sediment and vegetation processes interact, they respond individually to flow characteristics at different spatial and temporal scales. This study employs a modelling approach that is based on the tendency of river systems to self-organise and produce emergence (emergent structures) in scale hierarchies. A hierarchical modelling strategy is proposed that arranges separate models describing vegetation and sediment dynamics at their appropriate scales, with their interaction described through feedback between the models. Prediction of the river state at time scales of decades, over a range of spatial scales, is required for ecological river management to be more effective. However, river systems are complex, with complexity rooted deep in the river processes of water, sediment and vegetation holding implications for their modelling. Dealing with complexity in river geomorphological modelling is vital for achieving reliable predictions over decades, especially when considering that small-scale processes must be described to achieve this. Description of small-scale river form is not only required for river habitat management, but also affects the rates at which river form at larger scales changes. Hierarchy and non-linear theory provide a way to deal with the complexity of rivers by separating the river system into parts, and enabling these parts to interact. Appropriate models and modelling methodologies were chosen or developed to represent the effect of interacting river processes of water, sediment and reeds at the progressively nested (largest) reach scale, the channel-type scale and (smallest) geomorphological-unit scale. Existing water flow models at the reach scale and the next largest channel-type scale are used. The reach scale water flow model solves one-dimensional (1-D) Saint-Venant equations whereas the channel-type scale water flow model is governed by twodimensional (2-D) Saint-Venant equations. The water flow model at the smallest organisational level chosen for modelling is the geomorphological-unit scale. Water flow at the geomorphological-unit scale is not based on the actual physics of water flow, but it does account for the smaller scale variability of the water distribution. ix The sediment model at the reach scale employs the Exner equation of sediment continuity in combination with gravel-bed-load transport equations to determine changes in bed elevation. At the channel-type scale, a Cellular Automaton (CA) model describes sediment transport through a river. The CA represents the river as a lattice of cells and predicts the volume of sediment stored in the cells. The sediment distribution obtained from the CA model describes the habitat for reeds. At the geomorphologicalunit scale, a combination of existing formulations is used to predict the dimensions and growth of bed-forms representing sediment dynamics. The vegetation models at the reach scale and the channel-type scale were developed specifically to describe dynamics of common reeds or Phragmites Australis. Reeds were chosen for modelling because of the large role they play as geomorphological modifiers. The reach scale model predicts the distribution of reed populations along the lateral river bank gradient whereas the channel-type scale reed model is a CA model that predicts the expansion of reed patches. The vegetation model at the geomorphological-unit scale is an existing model describing the growth of reeds by integrating finite differential equations of reed biomass growth. River process interactions affect river geomorphology across these organisational levels. The models are integrated to provide feedback within a hierarchical modelling structure. Process models simulating sediment, water and vegetation dynamics within a specific organisational level are coupled through sharing the same spatial scale. Models of the same process producing patterns at various organisational levels are linked to share model information across organisational levels. Trans-organisational modelling linkage allows models to share outputs which provide boundary conditions and values for model parameters at specific locations within the modelling domain. A hierarchical framework allows prediction of small-scale geomorphology and accounts for its variability at the large scale. The modelling strategy is demonstrated by simulations based on hypothetical scenarios of a gravel-bed river. The effect of sediment size and frequency of the flood event moving sediment, together with typical channel geometry, is shown for these. The modelling was computationally very intensive. x Results show that models focusing on only one organisational level can have very different outputs form those produced by trans-organisational modelling. the difference is due to emergence produced by dynamic small-scale processes that manifest at large scales.Emergence was found in changing flow resistance coefficients obtained from smaller scale modelling. The flow resistance affected the river bed elevation at the reach scale. Emergence was indicated by the channel aggrading more for modelling with the inclusion of the effect of smaller scale river process interactions than without it. Thes snall-scale process interactions include water flow affected by bed-forms and reeds. bed-forms and reed affected energy loss significantly and provided a strong coupling between the flow and the river bed elevation. Hierarchical modelling therefore allows for reliable river geomorphology modelling over a decadal time scale by describing river complexity more realistically