Multi-scale hydro-morphodynamic modelling using mesh movement methods

Hydro-morphodynamic modelling is an important tool that can be used in the protection of coastal zones. The models can be required to resolve spatial scales ranging from sub-metre to hundreds of kilometres and are computationally expensive. In this work, we apply mesh movement methods to a depth-averaged hydro-morphodynamic model for the first time, in order to tackle both these issues. Mesh movement methods are particularly well-suited to coastal problems as they allow the mesh to move in response to evolving flow and morphology structures. This new capability is demonstrated using test cases that exhibit complex evolving bathymetries and have moving wet-dry interfaces. In order to be able to simulate sediment transport in wet-dry domains, a new conservative discretisation approach has been developed as part of this work, as well as a sediment slide mechanism. For all test cases, we demonstrate how mesh movement methods can be used to reduce discretisation error and computational cost. We also show that the optimum parameter choices in the mesh movement monitor functions are fairly predictable based upon the physical characteristics of the test case, facilitating the use of mesh movement methods on further problems.

The use of B-splines to represent the topography of river networks

This work presents a new extension to B-Splines that enables them to model functions on directed tree graphs such as non-braided river networks. The main challenge of the application of B-splines to graphs is their definition in the neighbourhood of nodes with more than two incident edges. Achieving that the B-splines are continuous at these points is non-trivial. For both, simplification reasons and in view of our application, we limit the graphs to directed tree graphs. To fulfil the requirement of continuity, the knots defining the B-Splines need to be located symmetrically along the edges with the same direction. With such defined B-Splines, we approximate the topography of the Mekong River system from scattered height data along the river. To this end, we first test and validate successfully the method with synthetic water level data, with and without added annual signal. The quality of the resulting heights is assessed besides others by means of root mean square errors (RMSE) and mean absolute differences (MAD). The RMSE values are 0.26 m and 1.05 m without and with added annual variation respectively and the MAD values are even lower with 0.11 m and 0.60 m. For the second test, we use real water level observations measured by satellite altimetry. Again, we successfully estimate the river topography, but also discuss the short comings and problems with unevenly distributed data. The unevenly distributed data leads to some very large outliers close to the upstream ends of the rivers tributaries and in regions with rapidly changing topography such as the Mekong Falls. Without the outlier removal the standard deviation of the resulting heights can be as large as 50 m with a mean value of 15.73 m. After the outlier removal the mean standard deviation drops to 8.34 m.

A survey on multiscale mollifier decorrelation of seismic data

In this survey paper, we present a multiscale post-processing method in exploration. Based on a physically relevant mollifier technique involving the elasto-oscillatory Cauchy–Navier equation, we mathematically describe the extractable information within 3D geological models obtained by migration as is commonly used for geophysical exploration purposes. More explicitly, the developed multiscale approach extracts and visualizes structural features inherently available in signature bands of certain geological formations such as aquifers, salt domes etc. by specifying suitable wavelet bands.