Adaptive Multi-Scale Methods

Adaptive Tsunami Simulation

In principle, multi-scale interactions need to be accurately represented in climate models; yet many climate processes expose their true character only if small scale processes interacting with large-scale processes are accurately resolved, i.e., if sufficient spatial resolution is available, Normally this is not affordable in long climate simulations. In CliSAP-2, the previously developed multi-scale methods will be applied to various multi-scale interaction applications. A typical example is that of the dynamics of ice sheets at their interface between land and the ocean. In collaboration with the CRG Humbert, the processes acting at the ice sheet boundary between land and sea will be studied using a numerical implementation with sufficient spatial resolution to simulate the dynamical interaction of melting ice, seawater and solid ice. It is planned to improve ice sheet models through the implementation of new numerical methods, including new discretization methods for the full Stokes governing equations, time integrators suitable for stable numerical computation of the stiff and non-stiff components involved, as well as optimization on high performance computing platforms. A second example is the numerical simulation of tropical cyclones. High spatial resolution is required to resolve physical processes within the cyclone, but a large spatial extent with a moving cyclone requires dynamically changing refinement areas. To cope with these problems a simplified cyclone model will be developed jointly with the CRG Frisius. By this means, even with simplified physical approximations it is anticipated to be able to simulate cyclonic dynamics realistically. Insight gained from these efforts will be utilized during new climate model developments. This relates to the representation of multi-scale processes in coarse-resolution climate models. It also relates to uncertainty propagation and quantification methods, developed in the context of tsunami early warning (Behrens et al., 2010), which in collaboration with CRG Baehr will be applied to problems in climate sciences.