Partitioned time discretization for atmosphere-ocean interaction

Numerical algorithms are proposed, analyzed and tested for improved efficiency and reliability of the dynamic core of climate codes. The commonly used rigid lid hypothesis is assumed, which allows instantaneous response of the interface to changes in mass. Additionally, moisture transport is ignored, resulting in a static interface. A central algorithmic feature is the numerical decoupling of the atmosphere and ocean calculations by a semi-implicit treatment of the interface data, i.e. partitioned time stepping. Algorithms are developed for simplified continuum models retaining the key mathematical structure of the atmosphere-ocean equations.;The work begins by studying linear parameterization of momentum ux in terms of wind shear, coupling the equations. Partitioned variants of backward-Euler are developed allowing large time steps. Higher order accuracy is achieved by deferred correction. Adaptations are developed for nonlinear coupling. Most notably an application of geometric averaging is used to retain unconditional stability. This algorithm is extended to allow different size time steps for the subcalculations. Full numerical analyses are performed and computational experiments are provided.;Next, heat convection is added including a nonlinear parameterization of heat flux in terms of wind shear and temperature. A partitioned algorithm is developed for the atmosphere and ocean coupled velocity-temperature system that retains unconditional stability. Furthermore, uncertainty quantification is performed in this case due to the importance of reliably calculating heat transport phenomena in climate modeling. Noise is introduced in two coupling parameters with an important role in stability. Numerical tests investigate the variance in temperature, velocity and average surface temperature.;Partitioned methods are highly efficient for linearly coupled 2 fluid problems. Extensions of these methods for nonlinear coupling where the interface data is processed properly before passing yield highly efficient algorithms. One reason is due to their strong stability properties. Convergence also holds under time step restrictions not dependent on mesh size. It is observed that two-way coupling (requiring knowledge of both atmosphere and ocean velocities on the interface) generates less uncertainty in the calculation of average surface temperature compared to one-way models (only requiring knowledge of the wind velocity).