Multiscale finite-element modelling of river-sea continua

Coastal zones and rivers are most of the time modelled using different tools and approaches. Therefore, coupling two such models is a task that is far from trivial. With the finite-element method, unstructured meshes can be used and the spatial resolution can vary widely over the domain, making it possible to simulate river networks and the adjacent coastal zone in the same model. Investigating the feasibility thereof is one of the objectives of this thesis, in which the model utilized is SLIM, i.e. the Second-generation Louvain-la-Neuve Ice-ocean Model (www.climate.be/slim). Two applications have been developed. The first one is the Scheldt continuum (Belgium/The Netherlands) for which the grid covers the freshwater tidal river network around Ghent, the Scheldt Estuary and the whole continental shelf. The second is the Mahakam continuum (Indonesia). In this application, the domain is composed of three lakes connected to a river network that leads to a complex delta before reaching the sea. The hydrodynamics was calibrated in the two domains and the model was used to compute the renewing timescales of the Scheldt Estuary and the Mahakam Delta. The renewing timescales such as the residence time, the exposure time and the age are measures of the rate at which the water initially in the estuary or the delta is renewed. Such diagnoses have direct links with many environmental variables and can be used to improve the understanding of the ecological dynamics inside the continuum.(PHYS 3) -- UCL, 201

Water renewal timescales in the Scheldt Estuary

TIMOTH

Finite element modelling of the Scheldt estuary and the adjacent Belgian/Dutch coastal zone

A fundamental problem in coastal modelling is the need to simultaneously consider large- and small-scale processes, especially when local dynamics or local environmen- tal issues are of interest. The approach widely resorted to is based on a nesting strategy by which coarse grid large scale model provide boundary conditions to force fine res- olution local models. This is probably the best solution for finite difference methods, needing structured grids. However, the use of structured grids leads to a marked lack of flexibility in the spatial resolution. Another solution is to take advantage of the po- tential of the more modern finite element methods, which allow the use of unstructured grids in which the mesh size may vary over a wide spectrum. With these methods only one model is required to describe both the larger and the smaller scales. Such a model is use herein, namely the Second-generation Louvain-la-Neuve Ice- ocean Model (SLIM, http://www.climate.be.SLIM). For one of its first realistic appli- cations, the Scheldt estuary area is studied. The hydrodynamics is primarily forced by the tide and the neatest way to take it into account is to fix it at the shelf break. This results in a multi-scale problem since the domain boundary lies at the shelf break, and covers about 1000 km of the North Sea and 60 km of the actual estuary, and ends with a 100 km long section of the Scheldt river until Ghent where the river is not more than 50 m wide. Such a broad spectrum of characteristic length scales is an ideal test case for a multi-scale finite element model. Two-dimensional elements are used to simulate the hydrodynamics from the shelf break to Antwerp (80 km upstream of the mouth) and one-dimensional elements for the riverine part between Antwerp and Ghent. The model will be described in detail and the simulation results will be discussed. This modelling exercise actually falls within the framework of the interdisciplinary project TIMOTHY (http://www.climate.be/TIMOTHY) dedicated to the modelling of ecological indica- tors in the Scheldt area

Towards a complete study of water renewal timescales of the Scheldt Estuary

Making sense of such a huge amount of information contained in present-day model outputs requires specific post-processing approaches presenting the model results in a format that is amenable to analysis. One of the strategies is to compute the timescales associated with the main processes occuring. These timescales synthesize the information hidden in the produced model results, and at the same time they give a quantitative insight into the dynamics and rate of functioning of the system. In this study we choose to follow this strategy to perform an in-depth analysis of the water renewal processes in the Scheldt Estuary. Applying the Constituent-oriented Age and Residence time Theory (CART, www.climate.be/CART) we compute the following timescales: (i) the age of the different renewing water types, (ii) the residence time, (iii) the exposure time, and (iv) the transit time. The numerical simulations are performed by the finite element model SLIM (www.climate.be/SLIM), which allows the use of a multiscale mesh going from the river scale (10 m) to the continental shelf break (100 km). We investigate the timescales interrelations and investigate how they vary in time and space. In order to further understand this spatio-temporal variability, we try to identify the major drivers of this variability

Numerical Simulation of Water Renewal Timescales in the Mahakam Delta, Indonesia

Water renewal timescales, namely age, residence time, and exposure time, which are defined in accordance with the Constituent-oriented Age and Residence time Theory (CART), are computed by means of the unstructured-mesh, finite element model Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM) in the Mahakam Delta (Borneo Island, Indonesia). Two renewing water types, i.e., water from the upstream boundary of the delta and water from both the upstream and the downstream boundaries, are considered, and their age is calculated as the time elapsed since entering the delta. The residence time of the water originally in the domain (i.e., the time needed to hit an open boundary for the first time) and the exposure time (i.e., the total time spent in the domain of interest) are then computed. Simulations are performed for both low and high flow conditions, revealing that (i) age, residence time, and exposure time are clearly related to the river volumetric flow rate, and (ii) those timescales are of the order of one spring-neap tidal cycle. In the main deltaic channels, the variation of the diagnostic timescales caused by the tide is about 35% of their averaged value. The age of renewing water from the upstream boundary of the delta monotonically increases from the river mouth to the delta front, while the age of renewing water from both the upstream and the downstream boundaries monotonically increases from the river mouth and the delta front to the middle delta. Variations of the residence and the exposure times coincide with the changes of the flow velocity, and these timescales are more sensitive to the change of flow dynamics than the age. The return coefficient, which measures the propensity of water to re-enter the domain of interest after leaving it for the first time, is of about 0.3 in the middle region of the delta

A fully implicit wetting-drying method for DG-FEM shallow water models, with an application to the Scheldt Estuary

Resolving the shoreline undulation due to tidal excursion is a crucial part of modelling water flow in estuaries and coastal areas. Nevertheless, maintaining positive water column depth and numerical stability has proved out to be a very difficult task that requires special attention. In this paper we propose a novel wetting–drying method in which the position of the sea bed is allowed to fluctuate in drying areas. The method is implemented in a Discontinuous Galerkin Finite Element Model (DG-FEM). Unlike most methods in the literature our method is compatible with fully implicit time-marching schemes, thus reducing the overall computational cost significantly. Moreover, global and local mass conservation is guaranteed which is crucial for long-term environmental applications. In addition consistency with tracer equation is also ensured. The performance of the proposed method is demonstrated with a set of test cases as well as a real-world application to the Scheldt Estuary. Due to the implicit time integration, the computational cost in the Scheldt application is reduced by two orders of magnitude. Although a DG-FEM implementation is presented here, the wetting–drying method is applicable to a wide variety of shallow water models

A finite-element, multi-scale model of the Scheldt tributaries, river, estuary and ROFI

We report on the development and validation of a coupled two- and one-dimensional finite-element model for the Scheldt tributaries, river, estuary and region of fresh water influence (ROFI). The hydrodynamic equations are solved on a single, unstructured, multi-scale mesh stretching from the shelf break to the Scheldt tributaries. The tide is forced on the shelf break and propagates upstream in the riverine network. Upstream boundaries lie on sluices or outside of the region of tidal dominance where daily averaged discharges are imposed. Two-dimensional, depth-averaged shallow water equations are solved by means of the discontinuous Galerkin (DG) method over the marine and estuarine parts of the computational domain. In the rivers, however, one-dimensional equations are dealt with using the DG method with the addition of a technique to cope with confluence points. Model parameters are carefully calibrated, leading to the simulation of wind- and tide-forced flows that are in excellent agreement with available data. The diffusivity in the transport equation is calibrated using time series of salinity at various locations in the estuary. Finally, the Lagrangian residual transport in the estuary and the adjacent coastal zone is investigated. This work is a major step towards an integrated model for studying the dynamics of waterborne contaminants and the water renewal timescales in the Scheldt land-sea continuum. (C) 2010 Elsevier B.V. All rights reserved