Adaptive wavelet modelling of geophysical flows on the sphere

Abstract

In this thesis the development of a dynamically adaptive wavelet method for geophysical applications is described. Being targeted at geophysical applications, a discrete shallow water model is derived in a way to retain mimetic properties of the continuous setting. Based on an investigation of properties of second generation wavelets, wavelet transforms for the sphere are designed for height and non-separable velocity that provide conservation of mass and consistent advection of vorticity. The model has been implemented in Fortran-95 with careful choice of data-structure and algorithms with the result that the computational cost per grid point of the adaptive method is only three times as large as for an optimized non-adaptive method. The Message Passing Interface (MPI) has been used to enable the model to run on 100 to 1000 of computer cores with generally high parallel efficiency (above 80%), but depending on the test-case. Standard tests by Williamson (1992) and a more recent test-case by Galewsky (2004) have verified numerical accuracy and convergence of the adaptive method. A simulation of homogeneous shallow water turbulence demonstrates that the model is capable of compression ratios of 20-50 even in a challenging setting. Finally the 2004 tsunami in the Indian ocean is computed as a real application to ocean simulation.